Enharmonic Scale
Get Enharmonic Scale essential facts below. View Videos or join the Enharmonic Scale discussion. Add Enharmonic Scale to your PopFlock.com topic list for future reference or share this resource on social media.
Enharmonic Scale
Enharmonic scale [segment] on C.[1][2] [2] Note that in this depiction C and D are distinct rather than equivalent as in modern notation.
Enharmonic scale on C.[3]

In music theory, an enharmonic scale is "an [imaginary] gradual progression by quarter tones" or any "[musical] scale proceeding by quarter tones".[3] The enharmonic scale uses dieses (divisions) nonexistent on most keyboards,[2] since modern standard keyboards have only half-tone dieses.

More broadly, an enharmonic scale is a scale in which (using standard notation) there is no exact equivalence between a sharpened note and the flattened note it is enharmonically related to, such as in the quarter tone scale. As an example, F and G are equivalent in a chromatic scale (the same sound is spelled differently), but they are different sounds in an enharmonic scale. See: musical tuning.

Musical keyboards which distinguish between enharmonic notes are called by some modern scholars enharmonic keyboards. (The enharmonic genus, a tetrachord with roots in early Greek music, is only loosely related to enharmonic scales.)

Diesis defined in quarter-comma meantone as a diminished second (m2 - A1 ? 117.1 - 76.0 ? 41.1 cents), or an interval between two enharmonically equivalent notes (from C to D).

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 Pythagorean scale is enharmonic:

Note Ratio Decimal Cents Difference
(cents)
C 00001:1 1 0000
D 00256:243 1.05350 0090.225 23.460
C 02187:2048 1.06787 0113.685
D 00009:8 1.125 0203.910
E 00032:27 1.18519 0294.135 23.460
D 19683:16384 1.20135 0317.595
E 00081:64 1.26563 0407.820
F 00004:3 1.33333 0498.045
G 01024:729 1.40466 0588.270 23.460
F 00729:512 1.42383 0611.730
G 00003:2 1.5 0701.955
A 00128:81 1.58025 0792.180 23.460
G 06561:4096 1.60181 0815.640
A 00027:16 1.6875 0905.865
B 00016:9 1.77778 0996.090 23.460
A 59049:32768 1.80203 1019.550
B 00243:128 1.89844 1109.775
C? 00002:1 2 1200

In the above scale the following pairs of notes are said to be enharmonic:

• C and D
• D and E
• F and G
• G and A
• A and B

In this example, natural notes are 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 (about 23.46 cents).

## Sources

1. ^  Moore, John Weeks (1875) [1854]. "Enharmonic scale". Complete Encyclopaedia of Music. New York: C. H. Ditson & Company. p. 281.. Moore cites Greek use of quarter tones until the time of Alexander the Great.
2. ^ a b c John Wall Callcott (1833). A Musical Grammar in Four Parts, p.109. James Loring.
3. ^ a b Louis Charles Elson (1905). Elson's Music Dictionary, p.100. O. Ditson Company.

This article uses material from the Wikipedia page available here. It is released under the Creative Commons Attribution-Share-Alike License 3.0.