Subset notation
Subset notation is the practice of applying a musical notation system designed for a tuning system to a subset tuning system. It is mostly used with dual-fifth tunings, for which the native fifth notation may be ambiguous or counterintuitive.
Subset notation allows multiple tuning systems that have common intervals to share the same notation for these intervals. It also helps avoiding issues that may arise when trying to apply the native fifth notation to certain tuning systems, such as negatively mapped accidentals.
The trivial case of subset notation is 12edo subset notation for 1edo, 2edo, 3edo, 4edo and 6edo. Since these edos only include intervals which are also in 12edo, it is easy to apply standard notation to these tuning systems.
Most commonly used subset notations include every other element of the original notation, or one element every three, etc., in a regular fashion. This method allows notating edos which don't have a good approximation of the perfect fifth (3/2) by using the standard notation of a superset edo which has a good approximation of the perfect fifth. For example, 13edo can be notated using 26edo subset notation.
| Tuning system | Notated as a subset of... |
|---|---|
| 1edo | 12edo |
| 2edo | 12edo |
| 3edo | 12edo |
| 4edo | 12edo |
| 6edo | 12edo |
| 8edo | 24edo |
| 9edo | 36edo (or 27edo) |
| 11edo | 22edo |
| 13edo | 26edo |
| 16edo | 48edo |
| 18edo | 36edo |
| 23edo | 46edo |
| 25edo | 50edo |
| ... | ... |
|
Todo: complete table |