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The chromatic circle is useful because it represents melodic distance, which is often correlated with physical distance on musical instruments. For instance, assuming 12-tone equal temperament, to move from any C on a keyboard to the nearest E, one must move up four semitones, corresponding to four
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The semitonal generator gives rise to the chromatic circle, while the perfect fourth and perfect fifth give rise to the
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chromatic pitch classes in between. Since the space is circular, it is also possible to descend by semitone.
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is that the former is truly a continuous space: every point on the circle corresponds to a conceivable
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by eight semitones, corresponding to eight counterclockwise steps on the pitch class circle.
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structure, and there is no obvious way to assign pitch classes to each of its points.
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modulo twelve, Z/NZ. For example, in twelve-tone equal temperament, the group
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If one starts on any equal-tempered pitch and repeatedly ascends by the
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Brower, Candace (2000), "A Cognitive Theory of
Musical Meaning",
268:"Symmetry in creative work of Mikalojus Konstantinas Čiurlionis"
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Clock diagram for displaying relationships among pitch classes
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clockwise steps on the chromatic circle. One can also move
211:"Prelude to Musical Geometry", p.364, Brian J. McCartin,
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A key difference between the chromatic circle and the
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327:- IPhone app which utilizes pitch constellations.
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38:diagram for displaying relationships among the
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320:On-line app illustrating pitch constellations
45:making up a given equal temperament tuning's
215:, Vol. 29, No. 5 (Nov., 1998), pp. 354-370.
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103:drawn within the chromatic circle as a
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243:(2), Duke University Press: 323–379,
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179:Comparison with circle of fifths
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213:The College Mathematics Journal
121:-tone equal temperament by the
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24:Twelve-tone equal temperament
314:Notenscheibe web application
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266:Kučinskas, Darius (2005),
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393:Fokker periodicity blocks
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113:For any positive integer
101:12-tone equal temperament
289:Olson, Harry F. (1967),
458:Post-tonal music theory
237:Journal of Music Theory
129:, or equivalently, the
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153:{\displaystyle Z_{12}}
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84:Larger motions (or in
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331:PDF of musical scales
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166:31 equal temperament
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408:Pitch constellation
26:'s chromatic circle
413:Spiral array model
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57:Explanation
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281:(1): 42–46
217:(abstract)
199:References
162:generators
160:has four
125:of order
108:dodecagon
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193:discrete
67:semitone
423:Tonnetz
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220:(JSTOR)
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271:(PDF)
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