Lexicon cont.

Thesis almost final title:

Agile: The Study of Human interactions and mechanics involving movement


------ Agile as a Lexicon terminology / clarity

Agile is a term used on lots of different levels, currently in the tech state we are in, we use the term agile to refer to software, and project management methodologies. I am not referring to agile in either of those ways. I am going back and bring my past soccer experience to use agile as a way to be quick on your toes, nimble, or to move quickly. In this thesis, agile refers directly to movement. This thesis is talking about design; it is not referring to start-ups or methodologies. This thesis is trying to understand the direct relationship between things and people that move and design such as graphics, interactions and objects.

Orientation: the determination of the relative position of something or someone (especially oneself) or one's position in relation to true north, to points on the compass, or to a specific place or object.Spatial cognition

Active: etc. actions, micro-motion: etc. micro-actions, noun a motion, especially a periodic one, of very short duration or length. 2.(in time and motion study) the analysis of the time of a work performance in its basic subdivisions with the aid of a timing apparatus, motion-picture equipment, etc.tiny opportunities for small actions to substantiate a full interaction, action or moment.

Contagious: an action or moment likely to spread to and affect others.

Wayfinding and Navigation: are related concepts, but they aren’t exactly the same. So, what’s the difference? Wayfinding, the broader term, refers to how people find their way around environments. Navigation refers to the specific means by which people find their way, including route navigation, landmark navigation, and map navigation.

Orientation: the determination of the relative position of something or someone (especially oneself) or one's position in relation to true north, to points on the compass, or to a specific place or object.Spatial cognition

Agile: adjective / ˈajəl/ able to move quickly and easily. able to move quickly and easily. "Ruth was as agile as a monkey."
synonyms: nimble, lithe, supple, limber, acrobatic, fleet-footed, light-footed, light on one's feet; Morel iterary feet, lightsome. "she was as agile as a monkey. alert, sharp, acute, shrewd, astute, perceptive, quick-witted "an agile mind." antonyms: clumsy, stiff, slow, dull able to think and understand quickly. "his vague manner concealed an agile mind.”

The Study of Human interactions and mechanics involving movement.

Moment: a very brief period. "she was silent for a moment before replying.” synonyms:little while, short time, bit, minute, instant, second, split second; informal sec "he thought for a moment."
a particular set of micro moments to create a brief moment. formal importance. "the issues were of little moment to the electorate.” synonyms: importance, import, significance, consequence, note, weight, concern, interest "issues of little moment."

Movement: ˈmo͞ovmənt/ noun: movement; plural noun: movements. etc. motion 1. an act of changing physical location or position or of having this changed. "a slight movement to the right."synonyms:    motion, move; gesture, gesticulation, sign, signal: action, activity "Therese a lot of movement in the gallery ."

Co-create: verb (transitive) to create jointly. etc. Collaborate

Sports: Physical games, especially preferring to European football (soccer) active: , etc. actions

Microcosms:community, place, or situation regarded as encapsulating in miniature the characteristic qualities or features of something much larger.
"Berlin is a microcosm of Germany, in unity as in division."

Micro-Motion: etc. micro-actions. noun: motion, especially a periodic one, of very short duration or length. 2. (in time and motion study) the analysis of the time of a work performance in its basic subdivisions with the aid of a timing apparatus, motion-picture equipment, etc. Tiny opportunities for small actions to substantiate a full interaction, action or moment.

Contagious: an action or moment likely to spread to and affect others.

location: Geolocation. Information / data: digital media: images, data movement

Innate: existing naturally or by heredity rather than being learned

Sequence:ˈsēkwəns/ noun/ sequence; plural noun: sequences. a particular order in which related events, movements, or things follow each other. Or a set of related events, movements, or things that follow each other in a particular order. Or arrange in a particular order.

Other Terms Used:

senses, experience, layers of movement, migration, distance: small or large, direction,velocity, olfactory,orientation,in motion, circumambient ,digitigrade, activity, alacrity, alertness, animation, commotion, dash,deal,energy,force,functioning,going, haste, liveliness, motion, movement, operation, plan, power, process, proposition, racket, reaction, response, rush, scene, spirit, stir, stunt, trip, turmoil, vigor, vim, vitality, vivacity, etc.






 I. Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.

I. Every typeface is a state of uniform trends that keep those assest in circulation, unless external forces intervine.

 II. The relationship between an object's mass m, its acceleration a, and the applied force F is F = ma. Acceleration and force are vectors (as indicated by their symbols being displayed in slant bold font); in this law the direction of the force vector is the same as the direction of the acceleration vector.

II. The relationship between a composition c, it's graphics g and the applied typography t is T = ca. Graphics and Typography are vectors in the law of art direction.

 III. For every action there is an equal and opposite reaction.

III. For every creation there is an equal and opposite reaction.

What is Tempo

A major structural feature of Conlon Nancarrow’s tempo canons, where canonic material moves at different speeds in different voices, is the places where the musical lines converge. These convergence points can vary in importance and function, and, depending on the type of canon being used in the piece, there may be only one or two convergence points per piece, or many. This paper will examine the features of convergence points in Nancarrow’s tempo canons and illustrate the many ways they are used in his Studies for Player Piano.

[1] The most characteristic structural feature of Conlon Nancarrow’s tempo canons is the convergence point, or “the infinitesimal moment at which all lines have reached identical points in the material they are playing” (Gann 1995, 21). Convergence points (CPs) serve varying purposes in Nancarrow’s Studies: sometimes they seem to be the raison d’être for an entire piece (particularly in his earlier brief tempo canons with just one CP, such as Nos. 14, 18, and 19), sometimes they vary considerably in significance within the same piece (such as the thirteen CPs in No. 24), or they may serve to mark the most structurally significant points in a piece (such as the three CPs in No. 27). 

[2] Unlike conventional canons in which the voices proceed at the same tempo, tempo canons present the possibility for one or more CPs between the canonic voices because the voices are moving at different speeds and either converging or diverging. Margaret Thomas classified tempo canons into four basic types: (1) the converging canon, with one CP at the end; (2) the diverging canon, which begins with a CP; (3) the converging-diverging (arch) canon, in which a single CP is somewhere in the middle; and (4) the diverging-converging canon, which begins and ends with a CP. Nancarrow wrote examples of each type (although he did not write any complete diverging canons—there is, after all, not much aural interest in a piece that diverges immediately away from a beginning point of convergence, never to return).  (1)

[3] This paper will examine the presence and placement of CPs in Nancarrow’s tempo canons and their significance to the overall structure. CPs will be examined in their more conventional uses in the canons, and other devices examined will include tempo switches and overlaps (which can be used to create additional CPs) and techniques for emphasizing and de-emphasizing CPs. Several of Nancarrow’s more complex works feature many CPs, and further complexity is possible through the addition of more voices to a canon, providing opportunities for interior CPs among smaller groups of voices. A special sub-type of Nancarrow’s tempo canons is the “acceleration canon,” in which voices are accelerating or decelerating. 

[4] The effect of convergence in Nancarrow’s tempo canons is perceptually heightened because it involves not only temporal convergence, but convergence of canonic material. The choice of canon as a means of portraying temporal proportions is quite natural. Thomas notes the aptness of this technique when she says “One of the clearest compositional strategies in which to hear proportions is canon” (Thomas 1996, 97). She adds further that in Nancarrow’s tempo canons “there is a palpable sense of the voices being in different places at the same time, of gradually moving closer together, of a brief moment of coordination, and then a departure” (p. 66). This “brief moment of coordination” is the CP, or Gann’s “infinitesimal moment” at which temporally divergent voices converge. 

[5] A CP is an excellent example of what Jonathan Kramer refers to as a “timepoint,” or “an instant, analogous to a geometrical point in space” (Kramer 1988, 454). A time-point has no dimension, as explained by Kramer: 

But what is a timepoint? Whereas a timespan is a specific duration (whether of a note, chord, silence, motive, or whatever), a timepoint really has no duration. We hear events that start or stop at timepoints, but we cannot hear the timepoints themselves [emphasis mine]. A timepoint is thus analogous to a point in geometric space. By definition, a point has no size: It is not a dot on the page, although a dot may be used to represent a point. Similarly, a staccato note or the attack of a longer note necessarily falls on and thus may represent a timepoint, but a timepoint in music is as inaudible as a geometric point is invisible. (Kramer 1988, 82–83) 



[6] Like one-dimensional geometric lines in space, Nancarrow’s canonic lines converge at this dimensionless point in time, the timepoint, and the CP is an audible event that takes place at this point. Eytan Agmon, in his discussion of musical durations as mathematical intervals, noted that “every common musical duration is uniquely associated with a single moment in time, namely its attack” (Agmon 1997, 48). Indeed, most of Nancarrow’s CPs do occur on a coincident beat attack; in a number of cases, however, CPs occur on rests; and, in several cases (the end of Studies No. 32 and 37), a CP is at the end of a long held note. But, whether articulated or not, a CP always represents a timepoint. 


Tempo Canon Terminology and Features

[7] In addition to convergence point, Gann defined several terms relevant to tempo canons. An illustration directly from Nancarrow’s scores will be given here to show these features and introduce some additional concepts. Figure 1 shows a portion of Study No. 14 (“Canon 4/5”) at the point where the CP occurs, and this example will illustrate the relationships among the terms convergence point, convergence period, echo distance, and potential points of simultaneity. Study No. 14 is a two-voice arch (converging-diverging) canon in which the CP occurs exactly in the middle of the piece. Echo distances (“the temporal gap between an event in one voice and its corresponding recurrence in another”; Gann 1995, 21) are shown in Figure 1 by arrows. Gann pointed out that the echo distance “will grow shorter and shorter as the convergence point is approached, reach zero at the convergence point, then grow progressively longer as it moves away” (ibid., 21), and this is clearly seen in this example. Thomas alludes to the aural effect of the echo distance when she discusses the relative degree of temporal dissonance near what she calls the “point of synchrony”: 

The notable and increasingly proportionately significant changes in the gaps, and the attendant modifications in temporal dissonance, are responsible for the intense perceptual focus a point of synchrony achieves in a tempo canon, whether that synchrony occupies the beginning of a diverging canon, the ending of a converging canon, or the middle of a converging-diverging canon. Although it is clear that voices at different tempos are gradually and continuously drawing near to or away from one another, their degree of dissonance can seem nearly uniform for a good portion of a canon. Only near the point of synchrony does the fast approaching/departing [temporal] consonance claim perceptual prominence. (Thomas 1996, 138) 

[8] Gann generalizes that as a CP approaches in a piece and the echo distance decreases, motives tend to splinter and become briefer, and that the opposite occurs as a CP recedes and the echo distance increases: 

Typically, in the late canons, the following motion occurs: immediately following any convergence point, a quick echoing of brief figures creates excitement signalling the entrance to a new section of the piece. Usually voices lose their distinguishability in a bristling texture, then slowly separate. Short figures are gradually displaced by longer and longer motives which sound calmer (by virtue of their temporal stability) but also more complex, even developmental. As a new convergence point is approached, the echo-tempo picks up again, and figures splinter into ever briefer motives, creating a deliciously gradual feeling of cumulative climax. (Gann 1995, 173–74) 

[9] Gann defines the convergence period as the distance between potential simultaneities, and points out that in canons involving superparticular ratios the echo distance “will approximate n beats at a point n convergence periods from a convergence point” (Gann 1995, 21). In Fig. 1, this is obscured somewhat by rests but can be most clearly seen at the points marked ⊗, where the echo distance is equal to the convergence period of five beats in the top voice and four beats in the bottom. At these points it is easiest to see that the respective lengths of the echo distance (in beats) in each voice are proportional to the operational tempo ratio at that point; for example, at a point in this 4:5 canon where the echo distance is 2 beats in the top voice, it will be 1.6 beats in the bottom voice. 

[10] In some of Nancarrow’s canons where the meter does not change, the location of some convergence periods is clearly marked by shared barlines. Also, for as long as the metric pulse does not change, the length of the convergence period remains the same. Shared barlines in Nancarrow’s scores are important markers of convergence and sometimes the only way one can accurately measure the location of events elsewhere in the score (such as the number of beats elapsed to the entrance of a later voice).

[11] Two additional terms, timespan and point of simultaneity, are important in making determinations about the placement of CPs and the amount of delay that is needed in later-entering voices to make a CP occur at a certain point. Kramer defines the timespan as the “interval between two timepoints” (Kramer 1988, 454). For determining the timespan of Nancarrow’s canonic subjects, the critical question becomes the location of the first and last timepoints. The first timepoint is clearly the first beat attack. There are generally two possibilities, however, for the location of the final timepoint: coinciding with either the attack of the final note, or the release of the final note (which can be said to coincide with the attack of the hypothetical beat that would follow the end of the final note). The most important criteria for making the determination of which should be the final timepoint are usually how the canon ends metrically and its prevailing metric pulse.

[12] Study No. 14 will serve as an example of a canonic subject in which the final timepoint coincides with the final attack. Gann notes that there are 337 total eighth-note beats in the subject of Study No. 14 (Gann 1995, 117). I concur with this assessment because of the concluding nature of the final attack (with the remainder of the final measure filled with rests) and because the final note matches the prevailing eighth-note metric pulse (see Fig. 2). By measuring from the attack of beat 1 to the attack of beat 337, the distance between these two timepoints, or the timespan, is 337 – 1 = 336 beats. From that measurement we can determine that the midpoint of the canon, where the CP occurs, is the attack of beat 169, with 168 beats occurring prior to this point and 168 beats after. Beat 169 is, indeed, the location of the CP (see Fig. 3).

[13] Measuring the timespan is straightforward when the CP occurs at the end of the canon (i.e., converging and diverging-converging canons) because, in these pieces, the final CP defines the concluding timepoint. Most of the time (e.g., Studies No. 18, 19, and 24) the CP occurs on the final attack and the timespan would be measured from the first attack to the final attack. Occasionally, however, the CP occurs after the final attack (e.g., Study No. 32) and the timespan must be measured to a timepoint that follows the CP (usually a mentally-supplied terminal beat). In other cases (e.g., Study No. 36), the final timepoint is the release of the final note.

[14] Potential points of simultaneity (i.e., the beginning of a convergence period) have tremendous importance in the structure of tempo canons. Obviously, a CP can occur only at a point of simultaneity in all sounding voices. A piece may have a large number of potential points of simultaneity, if the tempo ratio involves fairly small numbers, or it may theoretically have only one point of simultaneity (especially in those tempo canons whose proportions involve irrational numbers). At the same time, many potential points of simultaneity are de-emphasized through the use of rests or held notes. The importance of the location of potential points of simultaneity to the structure of tempo canons can be illustrated as shown in Fig. 4. This example compares two Studies already mentioned, Nos. 14 and 36, both arch canons with a single CP in the middle. Nancarrow composed Study No. 14 so that its CP would fall exactly in the middle of its 337-beat theme—that is, on beat 169. In Study No. 36, the midpoint of the canon’s 843-beat timespan falls between beats 421 and 422, and is obviously not an appropriate spot for an audible CP. Nancarrow thus moves the CP slightly later to beat 427; this slight shift means that 426 half-note beats occur before the CP, and 417 occur after (see Fig. 8).

[15] If it does not matter to the composer whether or not the entrances of later-entering voices coincide with beat attacks in voices that are already sounding (i.e., with the beginning of a convergence period)—and for Nancarrow it often did not—then the CP can essentially be placed wherever the composer chooses. Convergence periods will then proceed both backward and forward from the CP, depending on its location. In the two Studies shown in Fig. 4, the entrance of the second voice in No. 14 is between beats 33 and 34 of the first voice, and none of the later voices in No. 36 enters on a beat attack in an earlier voice. In fact, in most of Nancarrow’s canons’ later entrances do not coincide with beat attacks.(2)

[16] Finally, two tempo change devices are used with some frequency in Nancarrow’s tempo canons: the tempo switch and the tempo overlap. The tempo switch is defined by Gann:

Another major, but less audible, event is the tempo switch, a device in which Nancarrow switches the fastest line to the slowest tempo and vice versa, so that the line that has been lagging catches up with the one that has been pulling ahead. By mathematical necessity, the tempo switch always occurs halfway between two convergence points. (Gann 1995, 21) 

Tempo switches are useful in creating additional CPs. They are a significant part of Study No. 24 (“Canon 14/15/16”), where they are used to create thirteen CPs which delineate twelve sections.

[17] Occasionally a tempo changes in only one voice to create a tempo overlap, where the same tempo is occurring in more than one voice. Fig. 5shows how two tempos can form a tempo overlap in a diverging-converging canon. This is, in fact, exactly how Study No. 15 (“Canon 3/4”) is configured. The tempo overlap section in a two-voice canon will consist of a portion of the entire canon that is equal to  , where m and n are the two elements of the tempo ratio. For instance, in Fig. 5 the two tempos (and the sectional durations) are related by the ratio 3:2, so the tempo overlap section occupies one-fifth of the entire canon.

[18] Another Study with tempo overlaps is No. 17 (“Canon 12/15/20”). Tempo overlaps occur between section A in the top and bottom voices, and between section B in the top and bottom voices (see Fig. 6). Because of the inverse relationship between time and duration, the “duration ratio” of this 12:15:20 tempo canon is 3:4:5, which is how the durations of sections C, A, and B, respectively, relate to each other. In general, in a three-voice tempo canon where the elements of the duration ratio (not the tempo ratio) are x:y:z (with x being the smallest element and z the largest), the difference between the durations of x and y related to the length of the entire piece is, between y and z it is, and between x and z it is. Thus, in No. 17 the sum of the duration ratio’s elements, x:y:z, is 12, and the durational relationship between contiguous elements in the ratio (3:4 and 4:5) is one-twelfth of the whole piece while between the outer elements (3:5) it is one-sixth. As shown in Fig. 6, the tempo overlap involving section A occupies one-twelfth of the piece, and that involving section B occupies one-sixth of the piece. The section B overlap is long enough to be bisected by a tempo change in the middle voice between sections C and A.
Convergence Points in Nancarrow’s Tempo Canons
Tempo Canons With One (or Almost One) CP

[19] Two of the basic types of tempo canon classified by Thomas have just one CP: the converging-diverging (arch) canon, and the converging canon.  In the arch canon the CP falls somewhere in the middle, and in the converging canon it falls at the end. Fig. 7 shows line diagrams of Nancarrow’s tempo canons with just one CP.


Convergence Points in Nancarrow’s Tempo Canons

Tempo Canons With One (or Almost One) CP

[19] Two of the basic types of tempo canon classified by Thomas have just one CP: the converging-diverging (arch) canon, and the converging canon.(3)
In the arch canon the CP falls somewhere in the middle, and in the converging canon it falls at the end. Fig. 7 shows line diagrams of Nancarrow’s tempo canons with just one CP.



Arch Canons

[20] Nancarrow’s arch canons vary widely in ambition and scope. Study No. 14 has its CP exactly at its canonic midpoint, and the realization of this structure seems to be the primary goal for the piece. Study No. 36 has one of the most spectacular CPs in all of Nancarrow’s oeuvre in terms of its preparation and realization. Study No. 21 has one true canonic CP in addition to an area of “crossing tempos” and a loosely canonic CP on the last note. Study No. 49B returns to a simpler texture but also has a rather arresting CP.

[21] Study No. 14 (the first that Nancarrow subtitled “Canon”) exhibits the basic arch canon form with the CP exactly in the middle of its 337-beat theme (see Fig. 3). With a tempo ratio of 4:5, the faster voice occupies 80% of the duration of the slower voice, with the remaining 20% of the timespan split so that 33.6 beats elapse prior to that voice’s entrance, and 33.6 beats after it concludes; thus, the second voice does not begin at the beginning of a convergence period with the lower voice, but rather three-fifths of the way between the lower voice’s beats 33 and 34.

[22] Another important feature of arch canons, and any tempo canons with interior CPs, is the changing leader-follower relationship between the voices that takes place at interior CPs (see the CP in Fig. 1). In fact, in Study No. 14 there is so little else calling attention to the CP that the changing leader-follower relationship is thrust into relief and is what most immediately captures the listener’s attention. Gann points out (p. 118) that Nancarrow exerted so much rhythmic control in the creation of his canonic subject in No. 14 that melodic and harmonic coordination between the voices is virtually absent, and this lack of coordination does little to prepare and support the CP. There is also a fairly low incidence, in general, of rhythmic coordination between the voices due to the numerous rests; both Gann and Thomas note that the fairly small 4:5 ratio between the voices would potentially allow for convergence every four to five beats, but actual simultaneous attacks are avoided more often than realized. Thus, in Study No. 14 the CP’s placement at the exact midpoint defines the structure, but Nancarrow’s highly contrived rhythmic scheme precludes a high incidence of convergence at the metric level.

[23] The formal sophistication of Study No. 36 (“Canon 17/18/19/20”) makes it a stark contrast to the somewhat humble beginnings of Study No. 14. It is an arch canon in which the canonic midpoint falls between beats because the timespan is an odd number: 843 half-note beats, placing the canonic midpoint between beats 421 and 422. In this canon, then, it is not possible for the CP and midpoint to coincide on a beat attack as they did in Study No. 14 (Fig. 4). Nancarrow instead delays the CP to beat 427, thus creating two sections consisting of 426 and 417 beats (see Fig. 8). The final timepoint in this canon falls silently on the final release.

[24] Philip Carlsen notes that the placement of the CP on beat 427 creates a particular relationship of the elapsed time between statements of a recurring theme (which he calls a rondo theme) within the canon and the CP (see Fig. 8, bottom diagram):


The rondo theme’s second appearance [at m. 107] is twice as fast as the first; it occurs at a point (system 36 in the bass voice)(4)
exactly halfway between the beginning and the canonic midpoint, providing an obvious parallel with the well-known acoustical fact that the halves of a string vibrate twice as fast as the whole. (Carlsen 1988, 30)

The halfway point that Carlsen refers to is actually with the CP and not the canonic midpoint, as shown in Fig. 8. Carlsen’s observation concerning the acoustical parallel can be carried further by noting that the first three statements of the theme occur on C2, F#2, and C3 so that the second statement “bisects” not only the elapsed time to the CP but the octave between the first and third statements. Such connections are quite common in Nancarrow’s Studies.

[25] The table of elapsed beats in Fig. 8 describes the number of beats elapsed to the entrance and from the drop-out point of the top three voices, in relation to the first (or lowest) voice. The first column shows the beat elapse needed to place the CP exactly at the canonic midpoint; the second and third columns show the beat elapses that actually occur prior to and after, respectively, the statements in the top three voices.

[26] None of the voices enters at the beginning of a convergence period, as shown in Fig. 9. In fact, even the first voice begins on the last beat of a convergence period, as half-note beat 2 marks the beginning of the first complete convergence period. The second voice’s 23.7-beat elapse places its entrance within the second convergence period. Fig. 9 also shows how the echo distance decreases by one beat with the passing of each convergence period; at the beginning of each period, the number of beats between the voices is equal to the number of convergence periods remaining to the CP.

[27] The stunning CP in Study No. 36 (Fig. 10) is one of Nancarrow’s finest moments. Even the composer was surprised to hear the effect of what Reynolds refers to as “low-register difference tones” (Reynolds 1984, 16) generated by the extremely rapid iteration of notes in all the voices. Carlsen describes the passage this way:


In this passage, the four voices sweep up to their point of convergence with rapid chromatic glissandos, arriving simultaneously on their highest notes—B3, D5, F6, and A7.(5)
Each high note is then rapidly repeated at the speed of a quarter-note in its own voice’s particular tempo. . . . Even in the slowest voice, the reiterated high notes fly by at a rate of more than 340 per minute (5 per second). But that is not all: the spaces between high notes are filled in with ascending thirty-second-note glissandos. At such speeds, the perception of individual pitches is impossible. The thirty-second-notes (which, in the bass voice, move at over 3000 per minute or 50 per second) are fast enough to theoretically start generating additional low pitches with frequencies in the range of approximately 50–60 Hz. (Carlsen 1988, 25)

[28] The convergence point is preceded by what Gann identifies as a “mega-glissando” that begins 80 measures before the CP, creating a fine example of a “collective effect” that is an extraordinarily long preparation to the CP. Fig. 11 shows a section in the middle of this passage. Exactly halfway between the beginning of the mega-glissando and the CP, the C1 half note in the lowest voice begins a restatement of the opening transposition levels, which spell out a widely spaced major seventh chord. The last voice reaches its restatement at the beginning of the next convergence period; two measures prior to this, the lowest voice starts another restatement, this time an octave higher.

[29] This section of rising glissandos creates a tremendous build-up to the CP. The glissandos emphasize to the listener the leader-follower relationship of the four voices, and Nancarrow very cleverly manipulates the decreasing echo distance, by using steadily decreasing gaps between the glissandos, to eventually create long, continuous glissandos through the four voices. After the CP, the glissandos descend through the voices and the listener is once again acutely aware of how the leader-follower relationship has changed at the CP.

[30] An unusual and unique canon is Study No. 21 (“Canon X”), an acceleration canon whose subtitle is derived from the manner in which the tempos of the two voices “cross” in the course of the piece. Study No. 21 is unlike any of the other tempo canons, with its gradually changing tempos (accelerating in one voice while the other voice decelerates) that almost imperceptibly “cross” somewhere in the middle of the piece. In No. 21’s proportionally-notated score,(6)
there is no meter and no shared downbeats are notated, but it appears that there are three significant convergences. This Study thus fits somewhat uneasily into this section on arch canons with one interior CP; however, only one of the convergences is a true canonic CP, and it does appear in the interior of the piece. The first convergence, just over one-third of the way through the piece where the two voices cross tempos, is not a canonic convergence point but more of a convergence area (see Fig. 12). Thomas (1996, pp. 126, 281) identifies the bracketed area in the figure as a passage of “nearly simultaneous motion,” which occurs just before the tempos of the two lines actually coincide somewhere near the beginning of the next system (at a point where the note articulations are nearly evenly staggered between the voices). The crossing of the tempos is thus not marked by a convergence point.

[31] At just over two-thirds of the way through the piece, an actual canonic CP does occur (see Fig. 13). Its significance is enhanced by several factors: the 54-note row (B–C–Aβ. . .) that comprises the canon begins again in each voice; there is a registral shift upward in the lower voice; and the texture of the upper voice changes from triple octaves to quadruple octaves. Thus, this CP is both the conclusion of a converging canon and the beginning of a diverging canon. At this point in the piece there are about 16 notes in the bottom voice between successive articulations in the upper voice. Study No. 21 concludes with a non-canonic CP on the final note; at this point there are about 48 notes in the lower voice between articulations in the upper voice. The canon is altered at the end so the piece ends on a V–I cadence with a quintuple C octave.

Converging Canons

[32] The next group of canons to be examined is the converging canons shown in Figure 7, which include Nos. 18, 19, 31, 32, 34, 48, 49A, and 49C. One of the distinguishing characteristics of converging canons is that the leader-follower relationship of voices is maintained to the final CP. This is easily seen in a structural diagram for Study No. 18 (“Canon 3/4”), which was mentioned earlier as an example of a canon where the entrance of a later voice coincides with the beginning of a convergence period (see Fig. 14). This is made possible because the canon’s timespan (1,680 eighth-note beats) is divisible by both 3 and 4 and the first voice begins at the beginning of a convergence period.

[33] In Study No. 19 (“Canon 12/15/20”), like most of Nancarrow’s tempo canons, later-entering voices do not enter at the beginning of a convergence period (Fig. 15). The voices are related to each other by a duration ratio of 3:4:5,(7)
and the bottom voice relates to the middle voice by the ratio 4:5 and to the top voice by the ratio 3:5. The timespan of 336 eighth-note beats is divisible by 3 and 4, but not by 5; thus, since both the middle and top voices relate to the bottom voice in ratios containing the factor 5, neither of these voices enters at the beginning of a convergence period with the bottom voice. The CP at the end of Study No. 19 is noteworthy because Nancarrow somewhat uncharacteristically alters the interval of imitation between the voices (from elevenths to double octaves) to create a unison V–I cadence (see Fig. 16). I surmise that he likely did this to convey an additional sense of finality because this canon concludes the six-canon set of Nos. 13–19, all of which are based on the rhythmic series {n – 1, n, n + 1, n}.

[34] Study No. 32 (“Canon 5/6/7/8”) is a straightforward four-voice converging canon whose structure is shown in Fig. 17. No. 32’s final convergence point (see Fig. 18) is unusual in that it occurs at the final cut-off—that is, at the hypothetical downbeat that follows the final beat. There are 431θ. beats in the canon, and the timespan is the same number because the CP actually occurs on hypothetical beat 432.
[35] In Study No. 34 (“Canon  ”), measuring entrances to later-entering voices is complicated by the almost complete lack of noted shared downbeats in the score, the multiple sections of the canon, and the unmetered rests that occur between many of the sections (making it impossible to establish a length for the canon’s timespan). The CP (Fig. 19) occurs on the attack of the final beat (this is, in fact, the only downbeat in the entire score shared by all three voices).

[36] Study No. 48 (“Canon 60/61”) is a remarkable achievement in convergence. It consists of three movements: movements A and B are each 60:61 canons, which are then played together to create movement C (with approximately a 60:61 ratio between A and B). The performance of C involves two carefully coordinated player pianos. Movement A has a major tenth level of imitation, with an echo distance that begins at about eight seconds (the score is proportionally notated and includes additive acceleration in all four voices, thus measurements are inexact), dwindling to zero over the course of some 127 pages. There is a minimal level of convergence between the two voices built into the canon; the most pervasive is regularly-recurring pairs of arpeggios in which the second of the pair in the bottom voice aligns with the first in the top voice (see Fig. 20a).

[37] Movement B is slightly shorter than movement A, as, during the performance of C, it should enter after movement A’s 61-voice (see Fig. 20b). Movement B’s interval of imitation is the perfect fifth; this allows the final chord of movement C to spell out a Bβ major seventh chord at the extraordinary moment of coordination where all four voices converge. Dynamics play a critical role in the preparation for this convergence; Nancarrow brilliantly creates an almost complete coordination of rapidly changing and highly contrasting dynamics (mostly between ΦΦ and ) for the final 28 pages of the piece, creating a convergence of dynamics long before the temporal convergence.

[38] Study No. 31 (“Canon 21/24/25”) is an unusual case. It is a converging canon with no CP, as the canon is truncated before the CP is reached. As shown in Fig. 21, the canon’s actual length is 669 eighth-note beats, which is 36 beats shy of the 705 needed to reach convergence (the timespan is 704 beats) at a ratio of 21:24:25. The lack of a temporal convergence is seemingly underscored by the three key areas a fifth apart to create what Thomas (1996, p. 67) refers to as an “unresolved asynchronicity” (see the canon’s conclusion in Fig. 22). The canon is in three distinct sections, each separated by an eight-measure rest, and the third section is both registrally enlarged (the level of imitation increases from a fifth between voices to an octave plus a fifth) and the canonic line reinforced by octaves and full of melodic leaps. Based on these features, Thomas offers a very perceptive and plausible reason for the lack of convergence at the end:



It is in the final section of the study that the canon becomes most difficult to perceive, and in this lies what may have been a potential reason for ending the study before it can converge on a point of synchrony. Each single voice is difficult to follow in and of itself in this section because of its extreme registral leaps and because the articulation types are limited exclusively to staccato. . . . Since it is difficult to follow a single voice, it is nearly impossible to follow the canonic relationship among voices. The staggered ending thus reorients us to the canonic nature of the passage: as each voice drops from the texture in quick succession we are reminded retrospectively of them as linear entities, and we hear in their concluding gestures their shared material and imitative relationship. (Thomas 1996, 69–70)



Tempo Canons With More Than One CP

[39] Canons with more than one CP are of the following types: diverging-converging canons (which begin and end with a CP), canons with interior tempo switches, and special cases such as acceleration canons. Fig. 23 shows the simpler canonic structures that contain more than one CP. One of the basic types of tempo canon, the diverging-converging canon, has two CPs (one at the beginning and one at the end). Nancarrow wrote two examples of this type of canon: Studies No. 15 and 17. Canons of the diverging-converging type have at least one tempo overlap (the number depends on the number of voices and tempos in the canon). Study No. 15 contains a simple example of a tempo overlap. This two-voice Study has a tempo and duration ratio of 3:4 and a canonic subject of 336 eighth-note beats; the canon is stated twice in each voice, once at the slower tempo and once at the faster tempo. When the faster voice repeats the canon at the slower tempo, both voices are stating the slower tempo for a period of 84 eighth notes (one-fourth of the canon’s length), and this section comprises the middle one-seventh of the entire length of the piece (see Fig. 24). An interesting by-product of this structure is that the top voice, which initially states the faster tempo, remains the leader in stating the canon throughout the piece. 

[40] Another important structural feature of diverging-converging canons is that each voice successively states every tempo, with each voice stating the tempos in a different order and each tempo uniquely associated with a canonic section that is the same length in each voice. This can be clearly seen in the structure of Study No. 17 (“Canon 12/15/20”), which was shown in Fig. 6. The three sections are stated once in each voice, with the A section associated with the tempo η = 172.5 and a duration of 4, the B section associated with the tempo η= 138 and a duration of 5, and the C section associated with the tempo η= 230 and a duration of 3. As shown in Fig. 6, there are no tempo overlaps involving C, the shortest section. The longest section, B, has the longest overlap, with the A section having an overlap half that length.

[41] Study No. 17 does not exhibit as much harmonic convergence at section changes as No. 15 does, and, with almost continuous eighth-note motion in three different (and quite fast) tempos, it would be difficult to hear such coordination anyway. The CP at the beginning of No. 17 coordinates on a F major triad while the final CP features a cadence on A (see Fig. 25). Throughout the piece, the A section always begins on the note C, the B section on A, and the C section on F. Nancarrow keeps to a limited number of frequently changing key areas (mostly F, A minor, C, G, and D, with their affiliated accidentals Bβ, F#, C#, and G#), which allows some brief and random areas of harmonic convergence to occur. 

[42] Several Studies (Nos. 24, 33, and 43) use internal tempo switches to create additional CPs. The structures of Nos. 33 and 43 are shown in Fig. 23; No. 24’s structure is shown in Fig. 28. Study No. 43 (“Canon 24/25”), with its single tempo switch and two CPs, provides a simple structural framework for looking at the tempo switch; its two CPs and the tempo switch are shown in Fig. 26. The two voices of Study No. 43 are not only very close in tempo ratio (24:25) but also in their interval of imitation, a major third. Gann describes the proportions of the Study in relation to the CPs as follows (p. 219):




Thus, the tempo switch occurs exactly halfway between the two CPs, after twelve convergence periods at a point where the echo distance is twelve quarter-note beats (this is shown by the arrow connecting the bars in the middle example of Fig. 26). 

[43] As he did in Study No. 36, Nancarrow precedes the first CP in No. 43 with ascending movement. The second CP, which is actually a rest, is followed by descending movement in sixteenth notes (the most rhythmically active section of the piece). The CPs are used to set off a middle section in the palindromic structure of the piece; Gann describes that structure in this way:



This 24/25 canon is more nearly palindromic than No. 36; no extravagant post-CP event appears to throw the symmetry off balance. Instead, the textures and motives of the first half of the piece return in almost exact reverse order in the second half, though varied, some of them more elaborately developed, others shortened.
    . . . No. 43 is palindromic in spirit, although there are no actual retrograde passages. (Gann 1995, 218)

The “palindromic spirit” and arch shape of the piece are also reinforced by increases and then decreases in note density and dynamics before and after the CP section. Gann’s generalization about the splintering of motives that become briefer as a CP approaches somewhat holds true here, as some of the motives prior to the first CP are subjected to rhythmic compression, and in the section leading up to the CP there is a countdown extending from 12 quarter notes down to 1.

[44] Study No. 33, with its irrational tempo ratio of √2:2, presents special challenges in measuring and calculating distances and durations. The structure of the Study is shown in Fig. 23. There are four distinct canons (which Gann labels A through D in the diagram, but refers to as Canons 1 through 4 in his narrative): Canon 1 is a diverging-converging canon with a tempo switch in the middle; Canon 2 is an arch canon with a CP in the middle; Canon 3 is another diverging-converging canon; and Canon 4 is also a diverging-converging canon, but it begins with a short interlude prior to the canon’s first CP. All told, there are seven CPs. Only the first one takes place on a note attack in both voices; most of the remainder occur either on held notes or rests. Even the final CP does not take place on a coincident beat attack. See Table 1 for a description of the canons and convergence points in Study No. 33.



Table 1
Description of Canons and Convergence Points in Study No. 33

[45] Fig. 27 shows three of the unarticulated CPs in Study No. 33. CP 4 marks the beginning of Canon 3, and begins on a rest. CP 6 is technically the beginning of the diverging-converging canon in Canon 4, but it also occurs at a rest. CP 7 is an enigma—the final beat attacks in both voices are almost coincident, but not quite, as indicated by the lack of a shared barline at the final measure. The effect, then, is that the top voice finishes slightly ahead of the bottom voice to create a sort of V–I cadence in Dβ. Unfortunately, it is impossible to calculate exactly where the final CP falls in the last measure. Due to a shared barline, the exact location of CP 6 is discernible, but because the exact measurement from CP 6 to the tempo switch between CP 6 and CP 7 is not known or calculable, it is not possible to use the measurement of that half of Canon 4 to determine the full canon’s length and project the exact ending point of the canon. If it were possible to calculate the exact measurement of the first half of the canon to the tempo switch, the exact location of CP 7 would be calculable. Thus its location can only be approximated.

[46] Study No. 24 (“Canon 14/15/16”) has twelve canonic sections demarcated by thirteen CPs (see Fig. 28). Each of the twelve canons is of the diverging-converging type, with a tempo switch between the outer voices (i.e., the fastest and slowest voices) in the middle of each canon; the middle voice stays at the middle tempo throughout the piece. Canon 10, however, has a tempo overlap section in the middle before the tempos switch. Also, in addition to the tempo switches in each of the other eleven canons, an additional tempo switch is inserted at the beginning of Canon 9. Thus, there are twelve tempo switches and one tempo overlap in this Study.

[47] Table 2 lists and describes the canons and CPs that occur in Study No. 24. As the table shows, the majority of the CPs elide the end of one canon with the beginning of another; the exceptions are CPs 4, 7, and 10. The table also shows that CPs 1, 4, 5, 7, 8, 11, and 13 are articulated in all voices while the others are unarticulated (i.e., take place on rests or held notes).

[48] CPs and tempo switches sometimes occur with startling rapidity in this Study, particularly in the area of Canons 6–9 where (as shown in Fig. 28) CPs occur every 3, 4, 1, and 2 convergence periods, respectively. Fig. 29 shows Canon 8 (the briefest canon, consisting of only one convergence period of 15 sixteenth notes) and the beginning of Canon 9. As mentioned earlier, an additional tempo switch is inserted at the beginning of Canon 9. Normally the leader-follower relationship between the top and bottom voices reverses at each CP; at Canon 9, however, the additional tempo switch allows the bottom voice to remain the leader for both canons.

[49] At Canon 10 (by far the longest canon, comprising 74 convergence periods), Nancarrow inserts a tempo overlap on the middle tempo (θ. = 240) that lasts for 60 sixteenth notes (four convergence periods). The tempo overlap allows for a rare rhythmic convergence to be created in all three parts by repeating the same rhythmic pattern three times, as shown in Fig. 30. After this rhythmic convergence, the top and bottom voices switch to the tempo opposite the one they had before the convergence.




[50] Study No. 37, whose structure is shown in Fig. 31, is another canon with multiple CPs. Its twelve voices state the tempo ratio of the justly-tuned scale, which seems imposing but allows Nancarrow the ability to create widely-ranging textures and to combine the tempos in different groupings (comparable to chordal structures) that are no longer rigidly bound by his practice of assigning the slowest tempo to the lowest voice, etc. Gann identifies twelve canons and five CPs in this Study, and although the structure in Fig. 31 does not show this, different tempos are consistently applied to different voices. In Canon 1, the tempos are in Nancarrow’s usual order of fastest tempo in the top voice to slowest in the bottom voice and expressing a rhythmic analogue of just intonation. In Canon 2, the order of tempos is reversed. In later sections of the Study, Nancarrow creates “chordal” groupings of tempos, such as in Canon 6 where the tempo order from bottom to top is 150187   240160   200250168   210262    180225281   (see Fig. 32, left edge of score); as shown by the bold and italic type, the tempos are arranged into three interlocking “diminished seventh chord” groupings.

[51] Convergences between voices are clearly important here as in many places Nancarrow has marked with vertical broken lines where entrances of new voices coincide with beats in other voices (something he could have marked in many other scores, but did not), even when the voices are widely separated in the score and the convergence is with an interior beat rather than a downbeat. These convergences between voices are more common than might be supposed from the unwieldy tempo ratios. In several of the later canon sections (e.g., canons 8, 9, and 10) where tempos are in “minor third” groupings, simpler tempo ratios such as 6:5 and 7:6 are common between voices. These middle and later canonic sections, then, are more temporally consonant, which is a virtual necessity for perceptual purposes because the melodic material here is much more active than in the earlier sections.

[52] Gann says about the convergence points in No. 37, “Convergence points are brilliantly de-emphasized in this study, for this is the work in which Nancarrow learned how to create beautiful effects with convergence points by omitting them” (p. 195). The CPs are not really omitted, of course, but unarticulated, as not one of the five CPs occurs at a note attack. CPs 1 and 2 occur on a rest, with the voices entering in a staggered fashion just after the CP. CP3 also takes place at a rest, just after the conclusion of canon 3. The most climactic CP is unquestionably CP4 at the beginning of canon 7 (Fig. 32). This CP marks the most rhythmically active section of the piece and comes at a place where the texture thickens to all twelve voices after an extended section in canons 4, 5, and 6 where the voice saturation is considerably thinner. In comparison, the concluding CP5 is notably anti-climactic, occurring at a whole note in all twelve voices that is held over from twelve tied half notes and marked with a fermata.

[53] The processes of acceleration and deceleration create special challenges (and opportunities) for planning and placement of convergence points, and for this we look at Studies No. 8 and 22.(8)
Nancarrow used two varieties of acceleration: arithmetical and geometric, where arithmetical tempo changes involve adding or subtracting the same invariable rhythmic unit to the previous value, and geometric changes involve changing note values by an invariable percentage. Arithmetical acceleration creates a constantly increasing or decreasing rate of change, but can be notated in conventional notation; geometric acceleration creates a smooth continuum of changing speed that must be notated in proportional notation.

[54] Although it predates the first tempo canons, Study No. 8, an early example of Nancarrow’s acceleration technique, makes considerable use of convergence points. Its first section, called by Carlsen the “trio” because it is in three voices, consists of canonic lines that alternately accelerate and decelerate within a series of nineteen durations, each of which consists of a pair of notes in a 2:1 rhythmic relationship (notated as an eighth note followed by a quarter note with a sustain line); the 2:1 rhythmic pattern creates a loping effect that particularly elucidates the processes of acceleration and deceleration. Although the notation is proportional, the process of tempo change is arithmetical as an invariable background unit is continually added or subtracted to determine the next note values.

[55] Nancarrow imposes strict order on the form of this section by bringing in each new voice at a convergence point as shown in Fig. 33. As Carlsen notes, the main pitch in this section is G, and all CPs take place on G octaves or triadic intervals involving G. No two voices are ever stating the same rate of change at the same time, even if they are using the same tempo process. For instance, in the fourth phrase of this section, where both the first and second voices are in accelerating-decelerating patterns, the patterns begin and end at different places in the nineteen-duration series and also change speed direction at different places. One of the interesting effects of this procedure is that the echo distance between voices is constantly different, and not steadily increasing or decreasing as would normally be the case. Despite this variety in rate of change within the voices, Nancarrow is able to ensure convergences at regular time intervals by keeping the total number of background units the same in each voice within each phrase. There are also occasional near-convergences that pop out of the texture due to the use of the same limited number of durations within each voice; also, the short note in each durational pair casts such nearly-aligned attacks, when they do occur, in stark relief.

[56] In contrast, Study No. 22 (“Canon 1%/1½%/2¼%”(9)
), with its geometric acceleration, has only three widely-spaced convergence points (see Fig. 23): the first concludes Canon A, a converging canon; the second is in the middle of canon B, an arch canon; and the third begins Canon A’, a diverging canon. Study No. 22 is a strict palindrome in both rhythm and pitch; CP2, which takes place at a rest, is thus the rhythmic line of symmetry in the piece. In Canon A, the first note of each voice is the same length (75 millimeters in the score’s proportional notation), but by the CP the different rates of acceleration (with the 2¼% line accelerating 125% as fast as the 1% line) have resulted in very different lengths for the last note before the CP: 7.5 mm. in the fastest voice, or a duration 10% as long as at the beginning; 17 mm. in the middle voice, or about 23% as long as at the beginning; and 30 mm. in the slowest voice, or about 40% as long as at the beginning. Thus, at the CP the fastest voice has sped up to four times the speed of the slowest voice. As a result, as the CP approaches one hears the exponential change in the echo distance between the voices.



[57] By exploring so many techniques through which he varied the tempo relationships between voices in his tempo canons, Nancarrow developed a variety of musical structures in which convergence points between voices play a primary role. Besides their structural importance, they are often the most arresting aural features of each piece. One knows they are there, even if they are not articulated or otherwise de-emphasized, and Nancarrow became a master at using CPs to create a palpable sense of anticipation for the listener. The great variety of effects he was able to achieve with CPs is a fascinating and fruitful area of study for music analysts.


Agmon, Eytan. “Musical Durations as Mathematical Intervals: Some Implications for the Theory and Analysis of Rhythm.” Music Analysis 16/i (1997): 45–75.

Carlsen, Philip. The Player Piano Music of Conlon Nancarrow: An Analysis of Selected Studies. I.S.A.M. Monographs, no. 26. Brooklyn, N.Y.: Institute for Studies in American Music, 1988.

Gann, Kyle. The Music of Conlon Nancarrow. Cambridge: Cambridge University Press, 1995.

Kramer, Jonathan D. The Time of Music: New Meanings, New Temporalities, New Listening Strategies. New York: Schirmer Books, 1988.

Reynolds, Roger. “Conlon Nancarrow: Interviews in Mexico City and San Francisco.” American Music 2/1 (1984): 1–24.

Scrivener, Julie A. [Julie A. Nemire]. Representations of Time and Space in the Player Piano Studies of Conlon Nancarrow [Ph.D. dissertation, Michigan State University, 2002].

Thomas, Margaret Elida. Conlon Nancarrow’s ‘Temporal Dissonance’: Rhythmic and Textural Stratification in the Studies for Player Piano [Ph.D. dissertation, Yale University]. Ann Arbor, Mich.: University Microfilms, 1996.


(1) Perhaps a good real-life analogy to the perception of the diverging-converging process is airplane travel. A passenger on an airplane has a far more accurate perception of when the plane is going to meet the ground during the landing process (i.e., convergence) than of when the plane is going to reach cruising altitude after takeoff (i.e., divergence). Also, the passenger’s perception of exactly when plane and ground will meet becomes more acute as the plane approaches the point of “convergence” with the ground and is much more acute than the perception of when cruising altitude will be reached
(2)  One clear exception is Study No. 18 (“Canon 3/4”), a two-voice converging canon with the CP on the final attack. Since the 1,680 half-note-beat timespan of this canon is divisible evenly by both factors in the canon’s ratio (3 and 4), the faster voice in this canon enters after 420 half-note beats have elapsed, coincident with the 421st beat attack of the slower voice. Thus, in this Study the second voice enters at the beginning of a convergence period, and this is confirmed in the score by a shared barline at the entrance of the second voice.
(3) The diverging canon type also has a single CP, but Nancarrow did not write any complete examples of these.
(4)  Since there are no measure numbers in Nancarrow’s scores, analysts often number the systems and refer to these.
(5) The levels of imitation in Study No. 36 spell out a major seventh chord.
(6) Note values in Nancarrow’s scores do not always have a relative time value but instead, in his proportional notation, the length of the note is approximated by the distance between notes on the page.
(7)  The inverse relationship between tempo ratios and duration ratios is discussed in Ch. 2 of my 2002 dissertation, Representations of Time and Space in the Player Piano Studies of Conlon Nancarrow.
(8)   Study No. 27, “Canon 5%/6%/8%/11,” is Nancarrow’s tour-de-force in the use of geometric acceleration. This piece is analyzed separately in a companion paper to this symposium.
(9) Each contiguous pair of percentages relates to the same ratio—3:2.

Layers of movement

I had a few thoughts centering around Layers. I began to think about what it takes to develop a brand, an experience, an object, things that we use everyday. In so many obvious ways, we are layers and for it design is a function of finding the right layers to develop product or design interventions. Many times we find design to be a strong hold for benefiting a certain audience, but when does those layers or pieces of history create a new product. I am sure you have heard the rule of 3. Like Google, Apple and other companies. It takes the 3rd round of something to develop it for the right people or reasons. Layers are the reason we are able to find an audience or a voice. Layering is a way to create experiences or learn from our past. It takes significant moments in your life to create a single layer. They are the point of memories or structures in our cities systems. We are scared by layered experiences and at the same time, we are pushed to move forward by these layers. 


There is something intriguing about how Layers take hold or capitalize on life. They are the reason we stay in the same town for our entire lives or why we don't. There are apart of our decisions and values. They permeateseconds, moments or decades of our lives. 


What is the compelling value design offers or exposes about these layers. 

Finding your coordinates though analog means

Equatorial Coordinate System :

Because the altitude and azimuth of a star are constantly changing, it is not possible to use the horizontal coordinate system in a catalog of positions. A more convenient coordinate system for cataloging purposes is one based on the celestial equator and the celestial poles and defined in a similar manner to latitude and longitude on the surface of the Earth. In this system, known as the equatorial coordinate system, the analog of latitude is the declination, δ. The declination of a star is its angular distance in degrees measured from the celestial equator along the meridian through the star. It is measured north and south of the celestial equator and ranges from 0° at the celestial equator to 90° at the celestial poles, being taken to be positive when north of the celestial equator and negative when south. In the figure below, the declination of the star X is given by the angle between Y and X.


The analog of longitude in the equatorial system is the hour angle, H (you may also see the symbol HA used). Defining the observer's meridian as the arc of the great circle which passes from the north celestial pole through the zenith to the south celestial pole, the hour angle of a star is measured from the observer's meridian westwards (for both northern and southern hemisphere observers) to the meridian through the star (from 0° to 360°). Because of the rotation of the Earth, hour angle increases uniformly with time, going from 0° to 360° in 24 hours. The hour angle of a particular object is therefore a measure of the time since it crossed the observer's meridian - hence the name. For this reason it is often measured in hours, minutes and seconds of time rather than in angular measure (just like longitude). In figure above, the hour angle of the star X is given by the angle Z-NCP-X. Note that all stars attain their maximum altitude above the horizon when they transit (or attain upper culmination on, in the case of circumpolar stars) the observers meridian.

The declination of a star does not change with time. The hour angle does, and hence it is not a suitable coordinate for a catalogue. This problem is overcome in a manner analogous to the way in which the Greenwich meridian has been (arbitrarily) selected as the zero point for the measurement of longitude. The zero point chosen on the celestial sphere is the first point of Aries, γ, and the angle between it and the intersection of the meridian through a celestial object and the celestial equator is called the right ascension (RA) of the object. Right ascension is sometimes denoted by the Greek letter α and is measured from 0h to 24h along the celestial equator eastwards (in the direction of a right-handed screw motion about the direction to the north celestial pole) from the first point of Aries, that is, in the opposite direction to that in which hour angle is measured. Like the definition of hour angle, this convention holds for observers in both northern and southern hemispheres. In above figure, the right ascension of the star X is given by the angle -NCP-Y. ( )

Long distance migration

Among the many animals that perform long distance migration, such as butterflies, fish, marine-turtles and marine mammals, birds represent the most impressive performers. They are also the best-studied group, with many more details known of their migratory accomplishments and the factors involved in their orientation, than in other groups. The main question of how birds actually do navigate, however, remains unanswered. In this article Professor Schmidt-Koenig reviews the available evidence and suggests that a multiplicity of cues and strategies may be involved.

Thesis Progress

I have four things I am focusing on.

\ 1. an event or experience (design for delight)
\ 2. a product (Future product Design)
\ 3. a screen dedicated project (designing for screens)
\ 4. a service (service entrepreneurship)

I settled for my goal of the thesis to be divulging how people move through Navigation and Wayfinding. I found the "design" moment to be the relationship between movement and direction. So it sparked a few ideas and interests.

Movement > Design < Direction & Movement = Time + Location

The opportunities became greater as I narrowed the field of movement. (obvious realization) But more so I am constantly intrigued how we use movement to locate or find “place.” I see a few really great opportunities to push the concept of wayfinding and navigation further.

My goal is to unify these four things to become compliments from one another. It's tricky, to say the least, but let me walk you through my ideas.

\ 1

- an event or experience (design for delight). I found a few articles on navigation though senses which helped me craft a few ideas around an event I can create for my thesis.

These articles talk about different ways birds, esp. Pigeons navigation though their olfactory sense.

Which made me think of all the streets I avoid because they stink or all the streets I am eager to walk down. I even remembered the times of day Edmond smelled like dog food because of the Purina plant in the city and all the times Abq smelled like cereal because General Mills had a plant there as well. All of these experiences bring back very specific thought surrounds place / my location, what I was doing, what I would do again and what I would rather never experience again. I think about smell a lot, especially when I walk to school. I have different breathing patterns for different parts of the city. There is a sushi place that I always hold my breath while I pass. It always has a smell of gutted fish and Clorox, which is just yuck! I will go the length of crossing the street to get away from it. But there are other smells that I am eager to pass. The flower district, there is an incense guy I enjoy walking past and a few coffee shops. There is lots of little smells; elevators, hallways, store fronts, humans passing, subway cars, subway people, exhaust from buses is especially sour to me — I am sure you get what I am throwing down. They all marks of a particular place and time. We navigate though understanding please and time plus the added outcome of the objective.

After telling a bit of this to Allan, he wanted me to look up orientation.

noun: orientation — the determination of the relative position of something or someone (especially oneself) or one's position in relation to true north, to points on the compass, or to a specific place or object.Spatial cognition

\ 2

- a product (Future product Design). Over the last three weeks, we were asked to craft two stories. One for a utopian future and one for a dystopian future. I chose to the dystopian, future where the world is in an apocalyptic state is 2070, and the world lacks resources to stay in one place, like we do now. Our societies begin to migrate for different aspects of food, water, shelter, etc. thus creating land migration paths, which need to be marked by various groups or tribes which are developed over time. So I created a series of markers / stakes which could be placed along paths to indicate / help navigate people to specific areas. I would consider them primitive wayfinding tools adjustable to different circumstances. This first pass at navigation tools led me to think about creating a series of different navigation tools for navigation. These tools could be traditional or non-traditional products. Currently, I am coming up with different ideas that I will be pitching next week.

Since I wanted the product to be a series I found a few projects I really admire. A series of products in the same family has really interested me for some time now. I have yet to do a product series of any sort.

\ 3

- a screen dedicated project (designing for screens). I had a one on one with Allan yesterday to have him catch up on my thesis and help brainstorm ideas for my thesis. He seems to really like where I am headed with navigation and wayfinding, but he has asked me to continue to develop my apps from last semester. He is interested in both Floc and Blip, esp. Blip, although I think he sees the idea differently than I do, so it’s a bit hard to get a true feel for what his idea of the app might be. He was intrigued by the dissection of daily information though the powers of ten. But where I think we diverge is what information is extrapolated. I believe he thinks that the app pulls apart circumstances. Like “grad school” or air travel. He thinks it is more of a look at the powers of ten in an event or decision. Where I initially looked at fed data. For example, take Facebook, where you can find every range of information that might be of interest. So you have international: news, stories, and friends, national: news, stories, friends, a section of the nation (Midwest): “” state: “”  city: “” community: “”, work: “”, friends: “”, and family “”. But Facebook does not breakdown the relationships you might have to those pieces of information. Recently they have allowed you to star favorite profiles to see at the begging of your feed, but it has yet to illustrate the relevance between friends, national news, and global data, but Blip is a way to harness the connection and segregation of those elements of information. Blip lets see the scale of how information is relevant to us and others we know. So, I am unsure if this app should be more about circumstance being re-contextualized or information being broken down and grouped together.

I don’t know yet.

\ 4

- a service (service entrepreneurship) So I pitched Floc as my service last week (projects can overlap), and it bombed. It was just not awesome and wasn’t a simple service. Floc is the geolocation app that pulls data from that particular location to inform the user of what is around them at that moment or past moments in that specific location. I used an example of the a photographer searching for inspirational place around that specific area. The instructor wants something simple, maybe even less technological. I need to develop a new idea, ideally focused on navigation. Maybe these senses could come into play. Maybe an app or device to record all the sounds and smells an individual commute. A map of sorts.

Working Diagrams of Movement


5. Design Principles for Wayfinding

This set of design principles is concerned making information spaces effectively navigable. Navigability means that the navigator can successfully move in the information space from his present location to a destination, even if the location of the destination is imprecisely known. Three criteria determine the navigability of a space: first, whether the navigator can discover or infer his present location; second, whether a route to the destination can be found; and third, how well the navigator can accumulate wayfinding experience in the space.

The first criterion, successful recovery of location and orientation, asks the navigator if he can definitively answer the questions, ``Where am I?'' and ``Which way am I facing?'' A response to these questions could be verbal, such as ``I am in Lobby 7, facing Massachusetts Avenue3,'' or written, by drawing an arrow on a map of the environs.

The second criterion for navigability is the ability to successfully perform wayfinding tasks. Successful wayfinding occurs when the navigator can make correct navigation decisions that take him from his present location to a destination that fulfills his larger purpose. Examples of such decisions are whether to continue along the present route or to backtrack, what turn to take at an intersection of paths, or whether to stop and aquire information from the environment to confirm the present route. Arthur and Passini call wayfinding spatial problem solving [Arthur and Passini, 1992], in which the navigator finds a satisfactory solution to a larger task through navigation.

The third criterion for navigability is how well the navigator can accumulate wayfinding experience in the space. The imageability of a large-scale space is the ability of a navigator to form a coherent mental image or map of it. Kevin Lynch, an urban planner, first investigated how the characteristics of an urban space affected how well people remembered features in it [Lynch, 1960]. Lynch interviewed residents of Boston, Los Angeles, and Jersey City, New Jersey, and asked them to draw sketch maps of their city from memory. From these sketch maps and verbal interviews Lynch compared the imageability of the the cities: how well the sketch maps and interviews reflected the actual layout of each city. Lynch found that the respondents organized their city images using a set of common features: paths, landmarks, regions, edges (barriers), and nodes (intersections).

What makes Lynch's findings especially interesting is that the imageable or memorable features of a space are used by people to assist wayfinding. Landmarks are memorable locations that help to orient the navigator; regions are distinct areas that place him in one part of the environment; and nodes mark points where wayfinding decisions are made. Since a navigator's uses these features to record his past route-following experiences, a designed space that employs them should be more effectively navigable.

These last two criteria, wayfinding ability and imageability, have special relevance for information spaces. Wayfinding in an information space, we have argued, should correspond with information-seeking behavior in an information access environment. Successful wayfinding then implies that the user can use the information access environment to fulfill his information need. In a navigable information space, the problem of being ``lost in hyperspace'' [Edwards and Hardman, 1993] could then be solved.

In an imageable space, each episode of successful navigation can contribute in building a coherent mental picture of the information environment and of the content therein. Ideally, the user becomes more and more effective in fulfilling information needs every time he navigates through the environment. And in an information space organized on a principle relevant to the user's task, the mental map corresponds to a conceptual map of the content, reflecting important relationships in the information and the principles used to organize it.

The principles here come from both the study of museum exhibits and the research of environmental psychologists, cognitive scientists, and others who study how humans represent and navigate in the physical environment.

Principles for effective wayfinding include:



  • Create an identity at each location, different from all others.


  • Use landmarks to provide orientation cues and memorable locations.


  • Create well-structured paths.


  • Create regions of differing visual character.


  • Don't give the user too many choices in navigation.


  • Use survey views (give navigators a vista or map).


  • Provide signs at decision points to help wayfinding decisions.


  • Use sight lines to show what's ahead.



1. The Principles


1. Create an identity at each location, different from all others.

The principle. Give every location in a navigable space a unique perceptual identity, so that the navigator can associate his immediate surroundings with a location in the larger-scale space. It speaks most directly to the first criterion for navigability, the ability to recover position and orientation. This principle indicates that every place should function, to some extent, as a landmark - a recognizable point of reference in the larger space.

Source. The idea of places needing an identity for wayfinding is discussed in Arthur and Passini [Arthur and Passini, 1992]. They introduce the notions of identity and equivalence for speaking of the perceptions of places. Identity is what makes one part of a space distinguishable from another, and equivalence is what allows spaces to be grouped by their common attributes. They argue that identifiable places form the building blocks of our cognitive maps and the spatial anchors for the decisions made during wayfinding.

Applicability and design consequences. Ideally, a space should have just enough differentiability for this principle to hold, but no more. Neon lights should not be necessary. And, if the information space is built around an organizational principle, differentiability may be reflected by that organization naturally. For example, suppose the navigator is traversing a spatial timeline. Then each location corresponds to a point in time, giving a ready-made identity to it.

An example. Perhaps the best way to illustrate this principle is to see what happens when it fails. Those familiar with the original text-adventure game ADVENT will know that the adventurer will eventually find his way into a part of the cave which the game describes as:


You are in a maze of twisty little passages, all alike.

No matter which direction the player moves, the system will again respond


You are in a maze of twisty little passages, all alike.

(unless the player is fortunate enough to emerge from the maze strictly by chance.) What to do?

An effective strategy is for the player to drop one of the items he is carrying in the room, then make a move and see what happens. When the player re-encounters a room with an item, the system responds


You are in a maze of twisty little passages, all alike.
There is a bag of coins here.

Now the room has an identity. The player can repeat this process to map out the entire maze as a directed graph, and emerge on the other side.


2. Use landmarks to provide orientation cues and memorable locations.

The principle. Landmarks serve two useful purposes. The first is as an orientation cue. If the navigator knows where a landmark is in relation to his present position, he can say something about where he is, and which way he is facing, in the space he shares with the landmark. A desirable property of a landmark for this use is visibility, the ability to be seen from a large surrounding area. Such global landmarks can help the navigator judge his orientation within a wide area, as opposed to local landmarks, which can be seen only in the immediate vicinity. A system of local landmarks which exhaustively cover the space can also provide the same cues as a single, towering landmark. The second use of a landmark is as an especially memorable location. In his sketch-map interviews, Lynch noted that different respondents marked or mentioned many of the same places. It is these memorable places that can provide instant recognition of one's location. A shared vocabulary of landmarks provides the basis for verbal or written descriptions of locations or routes. Landmarks associated with decision points, where the navigator must choose which path of many to follow, are especially useful as they make the location and the associated decision more memorable.

Source. Lynch [Lynch, 1960] dicusses landmarks in an urban context at length, and describes their defining physical characteristic as ``singularity, some aspect that is unique or memorable in context.''

Landmarks were also evident in an exhibit setting. Landmarks such as the large water pump model in Leonardo (catalog number 112) and the octagonal case holding Jacqueline Kennedy's dinner gown (catalog number O26) were both physically large and visually distinct from their context, meeting Lynch's requirements as landmarks. Landmarks can be distinguished spaces as well as memorable objects; for example, the Oval Office exhibit marked the midpoint of the Kennedy museum.

Applicability and design consequences. A system of landmarks helps to organize and define an information space. However, they should be used sparingly; placing too many landmarks in the space belies their usefulness as memorable and unique locations. Landmarks, then, are a scarce resource that can be used not only to assist wayfinding but also to serve the space's larger purpose. Since a landmark defines a surrounding region to which it is adjacent, it could stand as a exemplar or representative for that region's content. Landmarks can also head paths emanating from junctions, and indicate what's down the road. Landmarks are the anchors along which paths are defined and our mental maps are built; they should reflect the top level of the organizing principle of the space.

An example. An interesting use of a landmark is found in the National Museum of Natural History's fossils exhibit. Near the entrance, a tall (approximately 20 meters high) ``time tower'' is visible from most of the central area of the exhibit (Figure 5-1). In a multi-level exhibit with a complex circulation pattern, it is a valuable physical landmark and point of reference with wide visibility. It also displays the time periods represented by the fossils in the exhibit and the corresponding terms associated with them. So, it serves as both a wayfinding aid and a way of communicating information important to understanding the exhibit.



Figure 5-1: The time tower in the Fossils exhibit.



3. Create well-structured paths.

The principle. Paths should possess a set of characteristics to be ``well-structured.'' Well-structured paths are continuous and have a clear beginning, middle, and end when viewed in each direction. They should confirm progress and distance to their destination along their length. And a navigator should easily infer which direction he is moving along the path by its directionality or ``sidedness.'' These concepts are summarized in Figure 5-2. A well-structured path maintains a navigator's orientation with respect to both the next landmark along the path and the distance to the eventual destination.



Figure 5-2: Well-structured paths. Top: In the abstract. Below: The Kennedy museum as a well-structured path.


Source. The exhibits studied can each be thought of as a well-structured path. For those that were spatial timelines, the start of the timeline, its extent, and its end create the path. For those that communicated messages, movement from one message to the next marked progress. Exhibits with memorable introductions and conclusions have well-defined beginning and end-points for their paths.

Applicability and design consequences. This principle informs how the traversal of a pre-defined route will appear to the navigator. The features of a well-structured path should again correspond to concepts relevant to the content of the space. The beginning and end of the path form an introduction and conclusion, and progress is marked by moving from one concept or message to the next. A continuous path should have both shared attributes that define it as distinct from its context, and evolving or changing features that mark its length and connect one part to a subsequent part.

An example. The Kennedy museum, as a spatial timeline, was a well-structured path (again, refer to Figure 5-2). The beginning of the path is the 18-minute introductory film; progress is marked by proceeding through his campaign, administration, family life, assassination, and legacy; and the pavilion provides an end-point. Directional ambiguity is resolved by whether motion is forward or backward in time through the events in Kennedy's life.

Another example outside of the domain of exhibits are interstate highways. The entrances and exits along the highway are clearly marked by signs, and mile markers indicate progress and relative distance to destinations. In this case, the path is structured not so much by diversity of appearance or meaning, but by a system of signs arranged along its length.


4. Create regions of differing visual character.

The principle. Subdivide the space into regions with a distinct set of visual attributes to assist in wayfinding. The character that sets a region apart can be some aspect of its visual appearance, a distinction in function or use, or some attribute of its content that is consistently maintained within the region but not without. Regions may not have sharply defined boundaries, or their extent may be in some part subjective; but a minimal requirement is that there is a generally agreed space said to be within the region, and a surrounding area said to be outside it.

Regions assist wayfinding by providing another set of cues for recovering location. They associate a set of defining features with an area in space, and give a way of identifying a place as being in a certain region. When the navigator moves from one region to another, the shift in the character of the space is another fact that informs him of his location along the boundary of the two regions.

Source. Regions are used in exhibits in two ways. The first is as another aspect of the environmental look principle, from a wayfinding perspective. The consistent environmental elements that make for the visual identity of the exhibit as a whole define it as a region, apart from the rest of the museum. In addition, the distinct appearance of individual parts of the exhibit define sub-regions within that larger region.

The second is the use of enclosures to create regions in an exhibit. Moving from one room or gallery to another through a threshold makes explicit the motion from one region of the exhibit to another.

Applicability and design consequences. Regions allow the navigator to distinguish one part of the space from another and to know when he has moved across the boundary between two regions. These boundaries can serve as demarcations along a well-structured path through several regions. For communication, a region can correspond to some attribute shared by the content within, such as supporting the same message, teaching the same concept, or relating the same event.

An example. In Leonardo, Ed Rodley [Rodley, 1997] cited how visual elements marked the boundaries of the main areas of the exhibit; variations in color treatments of walls and moldings, archways of differing shapes, and differing light levels all reinforced the transitions through archways from one region to another. And, referring back to the message hierarchy for Leonardo, we see that each message corresponds to a particular, enclosed region of the exhibit (Figure 4-1).


5. Don't give the user too many choices in navigation.

The principle. If there is a story to tell, design the space so that it is coherent for every route the navigator might take.

Source. This principle was explicitly used to inform the design of the Leonardo exhibit. In particular, the visitor was given a choice at the ``Florence in 1470'' room to proceed straight ahead into the ``Art Gallery'' to or to veer right into the ``Art Studio'' rooms. According to Ed Rodley [Rodley, 1997], the exhibit was designed to repeat the messages conveyed in the Art Studio in a display in the Art Gallery, so that even if a visitor missed the ``Art Studio'' they would be exposed to these messages. This principle was applied throughout the exhibit, with the layout designed to ensure that people encountered the main points no matter what route they took.

Applicability and design consequences. This principle is best used when there is a story you want every navigator to see. This basic story should be communicated by every path the navigator can take through the space. Opportunities for detours, side-tours, and exploration can branch off of this main path, eventually returning to resume the main story.

This principle, and the underlying assumption of a narrative for the space, indicate that the organization should have a primary path for visitors to follow (for example, as in Figure 4-3). The underlying question that this principle tries to address is, how many choices should be made for the navigator? An answer is, enough for the navigator to learn what the communicators intend.

An example. We can also look at what happens when this principle is not applied. The original Kennedy museum had a plan in which the visitor entered a central area with his desk and had to then choose where to explore from this area (see Figure 5-3). By making a right turn, the visitor could skip the majority of the central area of the exhibit, possibly without being aware of it, and proceed to exit onto the pavilion. Frank Rigg noted this problem in an interview [Rigg, 1998].



Figure 5-3: Schematic plan of the original Kennedy museum. Some visitors would enter from below (1) to the central area with his desk (2) and proceed directly to the exit (3).



6. Use survey views (give navigators a vista or map).

The principle. When navigating in any type of space, a map is a valuable navigation aid. It places the entire space within the navigator's view, and several kinds of judgements can be made readily:


  • the location of the navigator, and what is in the immediate vicinity;
  • what destinations are available, and what routes will take the navigator there; and


  • the size of the space, and how far the navigator is along his chosen path.


In addition, the survey view provides a ready image of the space, which can provide the basis for the navigator's mental map. Several researchers have found that giving subjects access to only survey knowledge of an environment can give comparable or superior performance to knowledge gained from route-following experience on landmark estimation and sketch-mapping tasks [Thorndyke and Hayes-Roth, 1982] [Golledge et al., 1995]. The navigator's mental map, primed with the image of his environment, can be augmented readily with experience gained from actual navigation in the space.

For an information space, a survey view has another role. It not only assists navigation in the space, but because the space corresponds to a conceptual organization of the information it contains, it serves as a succinct expression of meaningful relationships in that information. In more concrete terms, it assocaties the location of every document, image, or object with a message, a point on a timeline, or a concept to be learned. A map of the physical (or virtual) space can thus serve as an external representation of the conceptual map of the content. This conceptual map uses the navigator's ability to form mental representations of a physical space to store knowledge about conceptual relationships in the information space.

Source. Nearly every exhibit studied had a plan map either on a brochure distributed to visitors as they went in or mounted as wall plaques inside the exhibit itself.

Applicability and design consequences. Although it would seem to always be beneficial to provide a map, there may be sufficient wayfinding aids (such as signs and landmarks) already embedded in the space already to make a map unnecessary. Small spaces with which the navigator is already familiar may not need a map. A map can serve as reference material: available when needed, and able to be tucked away when not.

Maps are more useful when views in the space are insufficient to give information about unfamiliar regions, which is true in enclosed spaces with limited views in each direction.

An example. Leonardo had two maps situated at the entrances to the two latter sections of the exhibit (catalog numbers 74 and 148), identical to the map on visitor brochures (Figure 3-1). The Holocaust exhibit had wall-mounted maps at the beginning of each floor, labeled with each major section of that floor. Maps of the entire Holocaust Memorial Museum were also provided in visitor brochures (Figure 3-13).


7. Provide signs at decision points to help wayfinding decisions.

The principle. Place signs, when necessary, at decision points. Decision points are where the navigator must make a wayfinding decision (for example, whether to continue along the current route or to change direction.) A sign embeds additional information into the space to direct the navigator's next navigational choice. This information should be relevant to both the choices offered to the navigator at that point, and the larger goal of the navigational task. Simply put, a sign should tell the navigator what's in the direction it points, and the destinations so indicated should help the navigator reach his eventual goal.

Source. Passini describes this principle as part of his theory for wayfinding as spatial decision-making [Arthur and Passini, 1992] [Passini, 1984]. According to this theory, a navigator begins with a high-level goal, and acquires information from his environment (or uses what he already knows about the space) to make his first move towards a top-level destination. At decision points along the route, the navigator combines observation of local features with previous knowledge of the space to make the proper navigational move.

When the navigator does not have previous knowledge of the space, or a map to refer to, only the local features at the decision point can inform his navigational choice. A sign placed at a decision point in this framework, needs to inform the navigator of the correct route.

Applicability and design consequences. When placing signs, we can ask two questions at the decision points in the space:


  • Should a sign be placed here? Signs have navigational information that is authoritative and unambiguous. If the cost of making a wrong choice is high for the navigator or insufficient information is available from the view at the decision point for the navigator to make the correct choice, a sign is necessary.
  • What destinations should be included on the sign? Considerations that come into play are the destination's frequency (how often is it a navigator's goal?), its importance or memorability (is it a landmark, a place that could be used as a point of reference for other destinations?), its immediacy ( how close is it?), and its utility (Does the destination help navigator complete a task?). Each of these argue for adding a sign for that destination.


By design, signs must be in a location to acquire the navigator's attention, yet space for signage is a scarce resource. The benefits of signage must be weighed against the other potential uses for the space it occupies.

An example. One example of effective signage in action is at an airport. The environment may be completely unfamiliar to first-time visitors, and signs are the main means of directing them to their destination. Departing travelers have a typical routine of leaving from ground transportation or parking, checking in with their baggage, passing through security, and going to the departure gate. Arriving passengers must claim their baggage and proceed to ground transportation or parking. Effective signs in an airport both direct visitors at decision points to useful destinations and confirm their route along the way.


8. Use sight lines to show what's ahead.

The principle. Give the navigator a more extensive view in a particular direction and a goal to draw him in that direction. In an exhibit space, in which the first-time visitor has uncertain expectations as to its extent and purpose, sight lines are valuable means of giving enough information about what's ahead to encourage the visitor to move farther. Sight lines give long but narrow samples of unfamiliar space. Based on that sample, the viewer can determine if that direction is of interest or not.

To make a sight line interesting, the designer can provide a ``wienie'' - a goal to navigate toward. It might be some feature or object that is striking or unusual, something to spark the navigator's interest. It is the reward for choosing the path that it lies at the end of.

Source. This principle comes from Martin Sklar, president of Disney Imagineering, relating ``Mickey's Ten Commandments'' for museum exhibitions at the 1987 American Association of Museums Annual Meeting [McLean, 1993]: ``Create a `wienie' [ sic]... That's what Walt Disney called it...You lead visitors from one area...or one exhibit to the next by creating visual magnets. Reward people for walking from point A to point B.''

Applicability and design consequences. Providing selective views into a larger space is a way of letting the viewer take a representative sample of what's available and letting him make wayfinding decisions on that basis. It could be thought of as an alternative to a sign; instead of telling him that the destination is down this path, you can show him where it is (although it might be far away). The information available at a decision point should also depend on what sight lines are offered by each of the choices. Sight lines and wienies are tools the designer has to lead the visitor from one part of the space to the next.

An example. Sight lines were important in the Kennedy museum. At the end of the main corridor, an octagonal case with Jacqueline Kennedy's dinner gown was visible from the beginning, and served to draw people forward through the corridor. The case was situated in a temporary exhibit space that formerly housed an exhibit on the Nuclear Test Ban Treaty, which apparently was less interesting; once the case was installed, it actually improved visitor traffic into the adjacent exhibit on Robert F. Kennedy [Rigg and Wagner, 1997].

Another example is from the original Kennedy museum, before redevelopment. In exhibit 17, a film clip of a press conference was activated by a floor sensor: the monitor in the exhibit was blank until the visitor stepped in. Visitors would glance into the exhibit, see a blank screen, and move on. Once the clip was made into a continuous loop, traffic flow improved into the exhibit.


2. Reflections

These principles can be roughly divided into two classes. The first class of principles, one through four, develop a basic vocabulary of spatial features that assist wayfinding and imageability: identifiable places, landmarks, paths, and regions. In an information space, these features should be used to communicate the conceptual organization of its content. It is this correspondence that makes meaningful navigation possible in the space.

Principles in the second class, six through eight, are about the views that the navigator has into the space, and how designers can provide the information necessary for wayfinding and decision-making. Survey views are maximal; they give the navigator the most information about the space at once. Sight lines are local views deep into the space in an interesting direction. And signs are the authorities in information spaces, providing locally relevant wayfinding cues.

The remaining principle, the fifth, ties the structure of the space to the task of interest - communication of some body of knowledge - by ensuring that the route the navigator takes will expose him to the ideas the communicator wishes to express.

Wayfinding Definitions, Terms and Terminology

Cardinal Directions – are directions which involve the main compass routes i.e. North, East, South and West. Giving or receiving directions which for example tell you to head south and to turn north at the main intersection, would be using cardinal directions.

Changeable Message Sign (CMS) – is a sign which is normally electronic and which can change to show different messages. A good example is an electronic parking sign which shows the number of available parking spaces to motorist. These signs can also be referred to as Dynamic Message Signs (DMS).

Cognitive Map – is a mental mind map or we could say visual representation of which we use to store information on spatial connections and distances and geographical relationships between locations.
Example: When we visit a new holiday resort, the visual representation in our minds of the place gets clearer each day and more developed.

Context Awareness Service – A mobile service which helps in understanding the context i.e. the environment of your location and situation and which can aid navigation and the overall experience (more on context awareness).

Dwell Time – refers to the amount of time we spend in the same place. In terms of wayfinding, increasing the amount of possible dwell time for a passenger, such as in an airport, means that airport managers can make the airport more commercially viable through increased retail spending. Move passengers efficiently such that they have time to spend in the parts of the airport you want them to.

Dead Reckoning – involves understanding your present position by analysing the distance you are from your original point and amount of time spent and your original position.

Einstellung Effect – Although not a term specific to wayfinding, this term I have included because I think it can be very interesting within this subject area. The Einstellung Effect refers to how we sometimes use tried and tested methods for doing something, even when a simplier technique can be used.

Environmental Differentiation – The use of colours and other stimuli to create differentiation between environmental factors.
Example: The cruise ship painted each floor a different colour to make it possible for travellers to recognize their floor via colour coding.

Environmental Visibility – The ability to see the environment and the wayfinding signage. Is the background lighting effective, the space used efficiently for example.

Field of View (FOV) – This refers to having a clear and visible view of the line or field of sight, i..e you can see the path ahead to be travelled or navigated.

Flight Information Displays (FIDs) – Display boards you see in airports which detail the arrivals and departures information.

Geo-spatial Information Systems (GIS) – rather than a positioning system is software which manipulates data as part of a framework.

Global Positioning System (GPS) – is quite well known and can locate specific locations and positions on earth, using satellites. Car SatNavs for example use this system.

Gyroscope – A navigational device which words on an angular basis, which can rotate and detect motion through a three angled axis spinning device.

Heuristic wayfinding – is an expression we use here on in our audits and evaluations to explain a key concept in the way in which many of us wayfind and navigate in the real world. ‘Heuristic wayfinding’ refers to a practical and common-sense real-world way of finding solutions to routes, deciding on directions and paths we will take. We do not in reality have time to evaluate every possible route, every option and every outcome, so we wayfind by using an educated guess and make decisions based on these guesstimates.

Kinesthetic Learning (aka Tactile Learning – this involves learning by experiencing the practical experience and by learning by experience.

Kinetics – is the study of movement and motion. Although not specific to wayfinding, this term does sometimes get used in relation to the corporeal aspects of the field.

Landmark based learning – learning a route through following man-made and/or natural landmarks including hilltops, tall buildings, monuments and other sites visible such as from a survey point of view.

Location Awareness – is when a product such as a SatNav can work out its own location. In the case of a SatNav, this geographical location is then used to guide you to your desired end location.

Location Based Services (LBS) – is a computerised system for using the location of a user to affect a certain program. If you imagine Facebook, they can send you targeted ads according to your location. LBS though is also becoming increasingly useful in wayfinding and navigation.

Level of Service (LOS) – Not specific to wayfinding but pertinent to this field of study. It can be a very valuable exercise to undertake LOS surveys frequently in tourism spaces such as an airport, to evaluate and to get a good understanding of the efficiency of your wayfinding system.

MUFIDS – This terms refers to Multiple User Flight Information Display Systems, an example being the electronic departures or arrivals broad at an airport.

Markov Decision Process (MDP) – Although not a term specific to wayfinding or navigation, this process is sometimes used in analysing route decisions. The main concept behind the Markov process is that decisions are often a combination of the traveller’s decision making and partly based on other, random factors. MDP provides a mathematical equation and paradigm for analysing routes which involve the random and personal decisions.

Personal Navigation System (PNS) – This type of system is the natural progression from GPS technology, with a personalised service using wireless and mobile technologies.

Point of Interest (POI) – Another similar term and alternative to the word landmark. The term differs from landmarks though in its use in sectors such as the medical industry where it can refer to a particular area of interest set against a background, one example being when an optometrist tests your eyes.

Reverse Perspective – In terms of wayfinding, this expression was used by Erik Cohen to express the way in which we can draw cognitive maps of a place, and we inadvertently  draw the places and pieces we know in an exaggerated size, whilst drawing the others places in reduced size.

Route angularity effect – Research has found that routes with many angles are perceived to be longer than they actually are because of the angles i.e. the turn around a number of corners.

Route based learning – See definition below.

Route Knowledge and Strategy – Navigating somewhere based on quite precise directions such as turn left and take a 2nd right and so on, as opposed to following landmarks and taking a more general path.

Shoreline – Refers to a clear outline along or through a part or all of a building.

Slow Tourism – This relatively new term and concept, and which originates from the idea of slow food, is general about not rushing to travel somewhere and taking the time to enjoy the journey. Engaging with local communities is also included in some definitions of slow tourism. For many, cruise holidays typify the meaning of slow tourism in that the journey and slowly getting somewhere and appreciating the journey itself and taking time to enjoy the open seas, rather than rushing to fly somewhere, is a great example. Cruise travel on the other hand completely contradicts what some people see as slow tourism, because some advocates of slow tourism emphasise the avoidance of mass tourism. As you can see, the term is somewhat complex in meaning and is a term which is debatable according to one’s ontological views.

Steering Behavior – This is a form of wayfinding and navigation which is based on the intentional attempt to draw people into or towards a location. An example being a vendor in an airport finding ways to draw people into their shop, by finding ways to affect the routes.

Survey Directions – Using an overall view of the area and often using what can be seen using an aerial view.

Tactile Ground Surface Indicators (TGSI) – TGSI’s are invaluable for helping those with disabilities such as those with visual sight problems to navigate. Through the design of features such as paving stones which have a tactile surface such as rough edges as you are about to each a step or a kerb give the user a sign with to read the environment. TGSIs are on other words a way we can give those with sight problems, environmental clues as they wayfind. You may yourself have experienced tactile surfaces on motorways whereby the road becomes harder on your wheels and makes a noticeable noise, if you stray onto the edge inside the inside lane.

Trajectory – The path or route than an object takes.

Visibility Index – Is a way of measuring the lines of sight in a quantitative way, for the planning and evaluating wayfinding design.

Way-Signing – Is NOT a commonly used term but it is one I have heard used now and again so it worth perhaps mentioning. Some people who are not familiar with wayfinding see this subject area as being about directional signage. Wayfinding of course is a much more complex subject area and includes for example, the use of space and design. If a town for example uses space well and has a landmark which can be seen from most points, then the need for signage is decreased and natural paths are much easier to follow. It is important to get away from thinking of wayfinding as just about directional signage in order to fully understand this subject areas.


Design a post card for an event

Dear Evelyn, 

I think I found a perfect event for you! Bzzz is a workshop that allows you  to further connect to others moving around you, but lots of short movements. This workshop helps you interpret and digest how you feel and how you relate to other's moving around you. It's great to feel in personal flow and flow with others. This workshop will allow you to reflect and grow individually. I hope you can make it next month. 





Create and connect, not through a workshop, but by another means. Like making food or other outlets. Great it back to sport or community. Have them come together or move apart to represent the individual interpretation of the movements but, also creating instances of togetherness and unification. How can they practice apart and then come together? Viral video or choreography? Learning more about movement and instinct? to create a beautiful experience? 

Ideally this movement creates moments that celebrate or make apparent the differences or similarities of individuals move movements. This moment is crucial. 


Look up choreography? or etc. 

Wayfinding as a medium to understand movement



signs, maps, and other graphic or audible methods used to convey location and directions to travelers; also written way-finding


Wayfinding and Navigation: What’s the Difference?

architectural signage, wayfinding

December 5, 2011

by asi | signage innovations

Wayfinding and navigation are related concepts, but they aren’t exactly the same. So, what’s the difference? Wayfinding, the broader term, refers to how people find their way around environments. Navigation refers to the specific means by which people find their way, including route navigation, landmark navigation, and map navigation.

Landmark Navigation

Landmark navigation occurs when a person selects a particular landmark to use as a navigational anchor. This type of navigation can be seen when people are in unfamiliar buildings. They often select, say, the Information Desk as their landmark, from which they can venture farther out by degrees and to which they can easily return if they start feeling unsure of themselves. As people become more familiar with an environment, they select additional landmarks to serve as anchors, which then help them navigate the environment as a whole. Landmark navigation is a simple, basic means by which people accomplish wayfinding. To help landmark navigators, built environments can provide many kinds of visual cues to serve as landmarks, whether through their structure, through architectural signage, or both.

Route Navigation

When people become comfortable with landmark navigation as a means of wayfinding, many of them progress to route navigation. People who use route navigation learn the routes that connect one place to another in the context of the environment. The process tends to build on itself as people become more comfortable with multiple routes and connect them all together. Once people have created a comprehensive route navigation system in their minds, it can encompass a complete environment, whether one built facility, a campus with multiple buildings, or an entire city. Route navigation is more abstract in its methodology than landmark navigation. Both architectural design elements and signage that employs directional navigation can be utilized to help route navigators easily learn and connect new routes to aid their wayfinding.

Map Navigation

Some people progress from route navigation to map navigation, the most sophisticated of the three types of navigation. Map navigation isn’t just about physical maps. Rather, it adds the spatial element to the point (that is, the landmark) and the line (that is, the route). Map navigators build up a map of their environments in their minds that includes landmarks, routes, and the spaces between them. Digital signage kiosks can aid map navigators in building their mental maps, even in brand new environments.

With all these elements in place, map navigators can move around their environments with confidence. When new structures – or buildings – arrive on the scene, map navigators can seamlessly incorporate them into their mental models. And here we come to what is perhaps the most obvious distinction between the concepts of wayfinding and navigation. People’s navigational skills can progress in sophistication over time, resulting in greater and greater efficiency with wayfinding.

Wayfinding is an umbrella term which includes the various means by which people not only navigate but also orient themselves in their environments. The terms wayfinding and navigation differ in their scope: wayfinding is the overall concept, and navigation is one of the means by which people can find their way. Good wayfinding systems contain diverse elements that aid each type of navigator, whether landmark, route, or map.