Pitch class: Difference between revisions
→See also: octave equivalence |
m Cleanup |
||
| Line 2: | Line 2: | ||
A '''pitch class''' is a set (equivalence class) of all pitches that are a whole number of [[octave]]s (2/1) apart, e.g., the pitch class C consists of the Cs in all octaves. Thus the pitch class "C" is the set | A '''pitch class''' is a set (equivalence class) of all pitches that are a whole number of [[octave]]s (2/1) apart, e.g., the pitch class C consists of the Cs in all octaves. Thus the pitch class "C" is the set | ||
<math> | <math>\left\lbrace \ldots, C_{-2}, C_{-1}, C_0, C_1, C_2, \ldots \right\rbrace</math> | ||
In terms of frequencies expressed in [[Hertz]], assuming a base frequency for middle C of 262 Hz, this would be { | In terms of frequencies expressed in [[Hertz]], assuming a base frequency for middle C of 262 Hz, this would be {…, 65.5, 131, 262, 524, 1028, …}. In terms of [[MIDI]] note numbers, we can write it as {…, 36, 48, 60, 72, 84, …}. | ||
In a [[nonoctave]] xenharmonic system, an interval other than the octave might be used to define [[equivalence]]. For example, in [[Bohlen–Pierce]] tuning and other [[edt|equal divisions per tritave]], all pitches separated by a whole number of tritaves (3/1) may be considered equivalent. | In a [[nonoctave]] xenharmonic system, an interval other than the octave might be used to define [[equivalence]]. For example, in [[Bohlen–Pierce]] tuning and other [[edt|equal divisions per tritave]], all pitches separated by a whole number of tritaves (3/1) may be considered equivalent. | ||
Revision as of 09:45, 21 July 2025
A pitch class is a set (equivalence class) of all pitches that are a whole number of octaves (2/1) apart, e.g., the pitch class C consists of the Cs in all octaves. Thus the pitch class "C" is the set
[math]\displaystyle{ \left\lbrace \ldots, C_{-2}, C_{-1}, C_0, C_1, C_2, \ldots \right\rbrace }[/math]
In terms of frequencies expressed in Hertz, assuming a base frequency for middle C of 262 Hz, this would be {…, 65.5, 131, 262, 524, 1028, …}. In terms of MIDI note numbers, we can write it as {…, 36, 48, 60, 72, 84, …}.
In a nonoctave xenharmonic system, an interval other than the octave might be used to define equivalence. For example, in Bohlen–Pierce tuning and other equal divisions per tritave, all pitches separated by a whole number of tritaves (3/1) may be considered equivalent.