Enharmonic scale

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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 sharp and G flat 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 Pythagorean scale is enharmonic:

Note Ratio Decimal Cents Difference (Cents)
C 1:1 1.00000 0.00000
D♭ 256:243 1.05350 90.2250 23.4600
C♯ 2187:2048 1.06787 113.685
D 9:8 1.12500 203.910
E♭ 32:27 1.18519 294.135 23.4600
D♯ 19683:16384 1.20135 317.595
E 81:64 1.26563 407.820
F 4:3 1.33333 498.045
G♭ 1024:729 1.40466 588.270 23.4600
F♯ 729:512 1.42383 611.730
G 3:2 1.50000 701.955
A♭ 128:81 1.58025 792.180 23.4600
G♯ 6561:4096 1.60181 815.640
A 27:16 1.68750 905.865
B♭ 16:9 1.77778 996.090 23.4600
A♯ 59049:32768 1.80203 1019.55
B 243:128 1.89844 1109.78
C' 2:1 2.00000 1200.00

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).

The enharmonic genus is only loosely related to enharmonic scales, being a scale that has a pitch distinction too fine to accommodate with flat and sharp notation.Musical keyboards which distinguish between enharmonic notes are called enharmonic keyboards.

Musical scales by edit
# | pentatonic | hexatonic | heptatonic | octatonic | chromatic
Types | Altered | Bebop | Diatonic scale | Enharmonic | Jazz scale | Minor scale
Name | Acoustic | Blues | Bohlen-Pierce | Diatonic | Double harmonic | Half diminished | Harmonic major | Lydian dominant | Major | Major locrian | Pelog | Phrygian dominant scale | Slendro
"Ethnic" name | Arabic | Gypsy | Jewish
Modes of the diatonic scale edit
Ionian (I) | Dorian (II) | Phrygian (III)
Lydian (IV) | Mixolydian (V) | Aeolian (VI) | Locrian (VII)
Modes of the melodic minor scale edit
Melodic minor (I) | Dorian b2 (II) | Lydian Augmented (III)
Lydian Dominant (IV) | Mixolydian b13(V) | Locrian #2 (VI) | | Altered (VII)