In music theory, an enharmonic scale is "an gradual progression by quarter tones" or any " scale proceeding by quarter tones".. The enharmonic scale uses dieses (divisions) nonexistent on most keyboards, 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 sharp and G flat are equivalent in a chromatic scale (the same sound is spelled differently), but they would be different sounds in an enharmonic scale. See: musical tuning.
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 by some modern scholars enharmonic keyboards.
Famous quotes containing the word scale:
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