An enharmonic scale is a musical scale in which there is no exact equivalence between a sharpened note and the flattened note it is enharmonically related to. As an example, F# and Gb are generally equivalent in a chromatic scale, but they would be distinguished in an enharmonic scale.
Consider a scale constructed through Pythagorean tuning. A Pythagorean scale can be constructed "upwards" by wrapping a chain of perfect fifths around an octave, but it can also be constructed "downwards" by wrapping a chain of perfect fourths around the same octave. By juxtaposing these two slightly different scales, it is possible to create an enharmonic scale.
The following scale is enharmonic:
Note
Ratio
Decimal
C
1:1
1
C#
256:243
1.053497
Db
2187:2048
1.067871
D
9:8
1.125
D#
32:27
1.185185
Eb
19683:16384
1.201354
E
81:64
1.265625
F
4:3
1.333333
F#
1024:729
1.404663
Gb
729:512
1.423828
G
3:2
1.5
G#
128:81
1.580246
Ab
6561:4096
1.601806
A
27:16
1.6875
A#
16:9
1.777777
Bb
59049:32768
1.802032
B
243:128
1.898437
C'
2:1
2
In the above scale the following pairs of notes are said to be enharmonic:
C# and Db
D# and Eb
F# and Gb
G# and Ab
A# and Bb.
A natural note is sharpened by multiplying its frequency ratio by 256:243 (called a limma), and a natural note is flattened by multiplying its ratio by 243:256. A pair of enharmonic notes are separated by a Pythagorean comma, which is equal to 531441:524288.
Enharmonic scales are the third genus of musical scales.
The one-octave major scale (C to C) is sometimes called "the diatonic scale"; in all, there are seven diatonic modes that may be derived from the diatonic scale.
(scale or mode): In the sense we use it here, based on a series of intervals which may be smaller or larger than the steps, half steps, etc., found in diatonic and diatonic-chromatic scales and modes.
Enharmonicscales and modes are commonly derived from diatonic and diatonic-chromatic scales and modes.
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