User:CompactStar/Ordinal interval notation

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 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. For example, 5/4 is the leftmajor third, since it is the simplest major third flatter than 81/64, and 9/7 is the rightmajor third,.