Subset notation: Difference between revisions
Created page with "A '''subset notation''' is a musical notation system that reuses certain elements of an existing notation system, but excludes other elements which are not necessary for a..." |
ArrowHead294 (talk | contribs) mNo edit summary |
||
| (11 intermediate revisions by 5 users not shown) | |||
| Line 1: | Line 1: | ||
'''Subset notation''' is the practice of applying a [[musical notation]] system designed for a [[tuning system]] to a {{w|subset}} tuning system. It is mostly used with [[dual-fifth]] tunings, for which the [[native fifth notation]] may be ambiguous or counterintuitive. | |||
The trivial case of subset notation is 12edo subset notation for {{EDOs|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. | The trivial case of subset notation is 12edo subset notation for {{EDOs|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. | ||
The 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 {{w|superset}} edo which has a good approximation of the perfect fifth. For example, [[13edo]] can be notated using [[26edo]] subset notation. | |||
== Properties == | |||
Subset notation allows multiple tuning systems that have common intervals to share the same notation for these intervals. For example, a piece in [[11edo]] will be more easily read in [[22edo]] for anyone already familiar with 22edo notation. | |||
Subset notation also helps avoiding issues that may arise when trying to apply the [[native fifth notation]] to certain tuning systems, such as negatively mapped accidentals. In particular, there is no consensus on the signification of sharps and flats in tunings with a fifth narrower than 4\7, between the regular or harmonic mapping (sharps down, flats up) and the melodic mapping (sharps up, flats down), with both options featuring important drawbacks about which one must be careful. | |||
On the other hand, subset notation allows multiple ways to name notes, depending on the choice of the root note. For example, in 11edo as a subset of 22edo, one option excludes C, D and E natural, while the other excludes F, G, A and B natural. Without a consensus on which of the two subsets to use, one has to become fluent in both subsets. | |||
== Edos suitable for subset notation == | |||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|+ Table of edos with subset notation | |+ style="font-size: 105%;" | Table of edos with subset notation | ||
|- | |||
! Tuning system | ! Tuning system | ||
! Notated as a subset of... | ! Notated as a subset of... | ||
|- | |- | ||
| [[1edo]] | | [[1edo]] | ||
| [[12edo]] | | [[12edo]] (actually equivalent to any EDO) | ||
|- | |- | ||
| [[2edo]] | | [[2edo]] | ||
| Line 26: | Line 35: | ||
|- | |- | ||
| [[8edo]] | | [[8edo]] | ||
| [[24edo]] | | [[24edo]] (or [[32edo]], [[40edo]], [[48edo]], [[56edo]]) | ||
|- | |- | ||
| [[9edo]] | | [[9edo]] | ||
| Line 32: | Line 41: | ||
|- | |- | ||
| [[11edo]] | | [[11edo]] | ||
| [[22edo]] | | [[22edo]] (or [[33edo]], [[55edo]]) | ||
|- | |- | ||
| [[13edo]] | | [[13edo]] | ||
| [[26edo]] | | [[26edo]] (or [[39edo]]) | ||
|- | |- | ||
| [[16edo]] | | [[16edo]] | ||
| [[48edo]] | | [[48edo]] (or [[32edo]]) | ||
|- | |- | ||
| [[18edo]] | | [[18edo]] | ||
| Line 46: | Line 55: | ||
| [[46edo]] | | [[46edo]] | ||
|- | |- | ||
| | | [[25edo]] | ||
| | | [[50edo]] | ||
|- | |||
| [[28edo]] | |||
| [[56edo]] | |||
|- | |||
| [[30edo]] | |||
| [[60edo]] | |||
|- | |||
| [[35edo]] | |||
| [[70edo]] | |||
|- | |||
|} | |} | ||
{{Navbox notation}} | |||