Английская Википедия:Enharmonic scale
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, FШаблон:Music and GШаблон:Music 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.)
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 | Шаблон:01:1 | 1 | Шаблон:00 | |
| DШаблон:Music | Шаблон:0256:243 | 1.05350 | Шаблон:090.225 | 23.460 |
| CШаблон:Music | Шаблон:02187:2048 | 1.06787 | Шаблон:0113.685 | |
| D | Шаблон:09:8 | 1.125 | Шаблон:0203.910 | |
| EШаблон:Music | Шаблон:032:27 | 1.18519 | Шаблон:0294.135 | 23.460 |
| DШаблон:Music | 19683:16384 | 1.20135 | Шаблон:0317.595 | |
| E | Шаблон:081:64 | 1.26563 | Шаблон:0407.820 | |
| F | Шаблон:04:3 | 1.33333 | Шаблон:0498.045 | |
| GШаблон:Music | Шаблон:01024:729 | 1.40466 | Шаблон:0588.270 | 23.460 |
| FШаблон:Music | Шаблон:0729:512 | 1.42383 | Шаблон:0611.730 | |
| G | Шаблон:03:2 | 1.5 | Шаблон:0701.955 | |
| AШаблон:Music | Шаблон:0128:81 | 1.58025 | Шаблон:0792.180 | 23.460 |
| GШаблон:Music | Шаблон:06561:4096 | 1.60181 | Шаблон:0815.640 | |
| A | Шаблон:027:16 | 1.6875 | Шаблон:0905.865 | |
| BШаблон:Music | Шаблон:016:9 | 1.77778 | Шаблон:0996.090 | 23.460 |
| AШаблон:Music | 59049:32768 | 1.80203 | 1019.550 | |
| B | Шаблон:0243:128 | 1.89844 | 1109.775 | |
| C′ | Шаблон:02:1 | 2 | 1200 |
In the above scale the following pairs of notes are said to be enharmonic:
- CШаблон:Music and DШаблон:Music
- DШаблон:Music and EШаблон:Music
- FШаблон:Music and GШаблон:Music
- GШаблон:Music and AШаблон:Music
- AШаблон:Music and BШаблон:Music
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).
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