Enharmonic scale.html



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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:

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.