User:CompactStar/Ordinal interval notation: Difference between revisions
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'''Lefts and rights notation''' is a notation for [[just intonation]] primarily developed by [[User:CompactStar|CompactStar]]. | '''Lefts and rights notation''' is a notation for [[just intonation]] primarily developed by [[User:CompactStar|CompactStar]]. | ||
== Explanation == | == Explanation == | ||
Regular interval names corresponds to [[Pythagorean]] intervals, e.g. [[32/27]] is a minor third. To name non-Pythagorean intervals, they are given the name of a nearby Pythagorean interval (see [[#Mapping non-Pythagorean intervals]]), then prefixed with a sequence of lefts and rights (abbreviated as < and > respectively) | Regular interval names corresponds to [[Pythagorean]] intervals, e.g. [[32/27]] is a minor third. To name non-Pythagorean intervals, they are given the name of a nearby Pythagorean interval (see [[#Mapping non-Pythagorean intervals]]), then prefixed with a sequence of lefts and rights (abbreviated as < and > respectively). Left and right have the following meaning (where X is any left/right sequence, and Y is a regular interval category like "major third"): | ||
* | * Xleft Y = the smallest Y whose left/right sequence starts with X and is flatter than X Y | ||
* Xright Y = the smallest Y whose left/right sequence starts with X and is sharper than X Y | |||
For example, [[5/4]] | More simply, left means to find the simplest flatter interval, and right means to find the simplest sharper interval, with each new left/right having less and less of an impact. For example, [[5/4]] is a leftmajor third, since it is the simplest major third flatter than [[81/64]]. | ||
=== Mapping non-Pythagorean intervals === | === Mapping non-Pythagorean intervals === | ||
Revision as of 02:51, 20 July 2023
Lefts and rights notation is a notation for just intonation primarily developed by CompactStar.
Explanation
Regular interval names corresponds to Pythagorean intervals, e.g. 32/27 is a minor third. To name non-Pythagorean intervals, they are given the name of a nearby Pythagorean interval (see #Mapping non-Pythagorean intervals), then prefixed with a sequence of lefts and rights (abbreviated as < and > respectively). Left and right have the following meaning (where X is any left/right sequence, and Y is a regular interval category like "major third"):
- Xleft Y = the smallest Y whose left/right sequence starts with X and is flatter than X Y
- Xright Y = the smallest Y whose left/right sequence starts with X and is sharper than X Y
More simply, left means to find the simplest flatter interval, and right means to find the simplest sharper interval, with each new left/right having less and less of an impact. For example, 5/4 is a leftmajor third, since it is the simplest major third flatter than 81/64.