User:TromboneBoi9/JDN Interval Names

JDN stands for "Just-intonation Descriptive Names," and is a system of interval names that works somewhat similarly to the HEJI notation system. It aims to name distinct JI intervals up to the 13-limit one-to-one, enough to work as a naming system for corresponding EDO intervals.

That being said, I'm unsure of its efficacy as a system for pure JI, but things can be altered if needed.

3-limit, perfect

Intervals in the 3-limit are always referred to as "perfect" intervals, and the base names "unison," "second," etc. always refer to intervals in the major scale. Thus, a perfect second is 9/8, a perfect third is 81/64, a perfect sixth is 27/16 and so on.

Intervals in the 3-limit beyond these use the words "sharp" or "flat," which describe alterations of a Pythagorean apotome up or down. A perfect flat-seventh is 16/9.

For brevity, the word "perfect" may be removed, making names such as second, third, flat-seventh, etc.

5-limit, major and minor

The word "major" replaces the word "perfect" and lowers an interval by a syntonic comma. Thus a major third strictly refers to 5/4. Note that this allows 9/8 and 10/9 intervals to be distinguished, as they are the perfect second and the major second respectively.

The word "minor" also replaces the word "perfect" and lowers an interval by 135/128 (down an apotome and up a syntonic comma), which means a minor third is 6/5.

"Augmented" or "diminished" alters an interval by 25/24 up or down, which means the augmented fourth is 25/18 and the diminished fifth is 36/25.

7-limit, super- and sub-

The prefixes "super-" and "sub-" (when appended to "perfect," "major," "minor," etc.) refer to an alteration of 36/35 up or down respectively. This makes the supermajor second 8/7 and the subminor third 7/6.

11-limit, up- and down-

The prefixes "up-" and "down-" (when appended in the same way as "super-" or "sub-") refer to an alteration of 33/32 up or down respectively. This makes the upperfect fourth or upfourth 11/8.