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Encyclopedia of Microtonal Music Theory

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heptatonic

[John Chalmers, Divisions of the Tetrachord]

A scale with seven tones per octave is called a heptatonic scale.

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[Joe Monzo]

The most typical examples of heptatonic scales are the usual diatonic major and minor scales, composed of 5 Large (L) steps and 2 small (s) steps (which in this case are synonymous with tone and semitone, respectively. The minor scales are given below in their "natural minor" form:

            L  s  L  L  s  L  L                 L  L  s  L  L  L  s

A#-minor   A# B# C# D# E# F# G#     C#-major   C# D# E# F# G# A# B#     7 sharps

D#-minor   D# E# F# G# A# B  C#     F#-major   F# G# A# B  C# D# E#     6 sharps

G#-minor   G# A# B  C# D# E  F#      B-major   B  C# D# E  F# G# A#     5 sharps

C#-minor   C# D# E  F# G# A  B       E-major   E  F# G# A  B  C# D#     4 sharps

F#-minor   F# G# A  B  C# D  E       A-major   A  B  C# D  E  F# G#     3 sharps

 B-minor   B  C# D  E  F# G  A       D-major   D  E  F# G  A  B  C#     2 sharps

 E-minor   E  F# G  A  B  C  D       G-major   G  A  B  C  D  E  F#     1 sharp

 A-minor   A  B  C  D  E  F  G       C-major   C  D  E  F  G  A  B      no sharps or flats

 D-minor   D  E  F  G  A  Bb C       F-major   F  G  A  Bb C  D  E      1 flat

 G-minor   G  A  Bb C  D  Eb F      Bb-major   Bb C  D  Eb F  G  A      2 flats

 C-minor   C  D  Eb F  G  Ab Bb     Eb-major   Eb F  G  Ab Bb C  D      3 flats

 F-minor   F  G  Ab Bb C  Db Eb     Ab-major   Ab Bb C  Db Eb F  G      4 flats

Bb-minor   Bb C  Db Eb F  Gb Ab     Db-major   Db Eb F  Gb Ab Bb C      5 flats

Eb-minor   Eb F  Gb Ab Bb Cb Db     Gb-major   Gb Ab Bb Cb Db Eb F      6 flats

Ab-minor   Ab Bb Cb Db Eb Fb Gb     Cb-major   Cb Db Eb Fb Gb Ab Bb     7 flats
	

These scales may be tuned in a wide variety of different tunings, which is one fact which helps to account for their great popularity.

These diatonic scales are recorded unambiguously in ancient Greek music-theory texts, almost always in pythagorean tuning.

As the diatonic scales developed in medieval Europe they were expected to be tuned according to one of the various members of the meantone family of temperaments.

Today the diatonic scales are most commonly presented in 12-edo. Note that in 12-edo, 3 pairs of keys in each mode (major and minor) are enharmonically equivalent: Bb/A#, Eb/D#, and Ab/G# minor, and Db/C#, Gb/F#, and Cb/B major.

There are probably thousands of other heptatonic scales, 7 being one of the most important numbers of the Miller Limit.

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