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| modulatory space ： ウィキペディア英語版 |
modulatory space
The spaces described in this article are pitch class spaces which model the relationships between pitch classes in some musical system. These models are often graphs, groups or lattices. Closely related to pitch class space is pitch space, which represents pitches rather than pitch classes, and chordal space, which models relationships between chords.
==Circular pitch class space==
The simplest pitch space model is the real line. In the MIDI Tuning Standard, for example, fundamental frequencies ''f'' are mapped to numbers ''p'' according to the equation
:
This creates a linear space in which octaves have size 12, semitones (the distance between adjacent keys on the piano keyboard) have size 1, and A440 is assigned the number 69 (meaning middle C is assigned the number 60). To create circular pitch class space we identify or "glue together" pitches ''p'' and ''p'' + 12. The result is a continuous, circular pitch class space that mathematicians call Z/12Z.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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