|
Tag: Redirect target changed |
| (59 intermediate revisions by the same user not shown) |
| Line 1: |
Line 1: |
| '''Lefts and rights notation''' is a notation for [[just intonation]] primarily developed by [[User:CompactStar|CompactStar]].
| | #redirect [[User:CompactStar/Lefts and rights notation]] |
| == 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 simplest (with respect to [[Tenney height]]) Y whose left/right sequence starts with X and is flatter than X Y
| |
| * Xright Y = the simplest (with respect to [[Tenney height]]) 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. Here are some examples with thirds:
| |
| * Leftmajor third = [[5/4]], since it is the simplest major third flatter than 81/64
| |
| * Rightmajor third = [[9/7]], since it is the simplest major third sharper than 81/64
| |
| * Leftleftmajor third = [[16/13]], since it is the simplest major third flatter than 5/4
| |
| * Leftrightmajor third = [[24/19]], since it is the simplest major third between 5/4 and 81/64
| |
| * Rightleftmajor third = [[14/11]], since it is the simplest major third between 81/64 and 9/7
| |
| * Rightrightmajor third = [[22/17]], since it is the simplest major third sharper than 9/7
| |
| | |
| === Mapping non-Pythagorean intervals ===
| |