Interval summary
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PiotrGrochowski's summary[edit]
Meantone intervals:
| interval | meantone fifths | description (example ratios) |
|---|---|---|
| unison | 0 | 1/1, or 0 cents in any tuning |
| inverse doubly diminished second (meantone kleisma) | +19 | 875/864, 686/675, 3125/3072, 49/48, 525/512 |
| diminished second (meantone diesis) | −12 | 64/63, 50/49, 128/125 |
| augmented unison (chromatic semitone) | +7 | 28/27, 25/24, 21/20, 135/128 |
| minor second (diatonic semitone) | −5 | 16/15, 15/14, 27/25 |
| major second | +2 | 10/9, 9/8 |
| diminished third | −10 | 8/7, 144/125 |
| augmented second | +9 | 7/6, 75/64 |
| minor third | −3 | 32/27, 6/5 |
| major third | +4 | 5/4, 81/64 |
| diminished fourth | −8 | 32/25, 9/7 |
| augmented third | +11 | 125/96, 98/75, 21/16 |
| fourth | −1 | 4/3 |
| augmented fourth | +6 | 25/18, 7/5, 45/32 |
| diminished fifth | −6 | 64/45, 10/7, 36/25 |
| fifth | +1 | The perfect fifth is 3/2, or 701.955 cents. 1/4 comma meantone: 696.578 cents 12edo: 700 cents 17edo: 705.882 cents 19edo: 694.737 cents 22edo: 709.091 cents |
| diminished sixth | −11 | 32/21, 75/49, 192/125 |
| augmented fifth | +8 | 14/9, 25/16 |
| minor sixth | −4 | 128/81, 8/5 |
| major sixth | +3 | 5/3, 27/16 |
| diminished seventh | −9 | 128/75, 12/7 |
| augmented sixth | +10 | 125/72, 7/4 |
| minor seventh | −2 | 16/9, 9/5 |
| major seventh | +5 | 50/27, 28/15, 15/8 |
| diminished octave | −7 | 256/135, 40/21, 48/25, 27/14 |
| augmented seventh | +12 | 125/64, 49/25, 63/32 |
| octave | 0 | 2/1 |
Below is me trying to name all the 15-odd-limit intervals.
10/9, 182.404 cents – lesser major second 9/5
9/8, 203.910 cents — greater major second 16/9
8/7, 231.174 cents — septimal supermajor second 7/4
7/6, 266.871 cents — septimal subminor third 12/7
6/5, 315.641 cents — perfect minor third 5/3
5/4, 386.314 cents — perfect major third 8/5
9/7, 435.084 cents — septimal supermajor third 14/9
4/3, 498.045 cents — perfect fourth
7/5, 582.512 cents — septimal augmented fourth
10/7, 617.488 cents — septimal diminished fifth
3/2, 701.955 cents — perfect fifth
Xenwolf's summary[edit]
Mike Battaglia's summary[edit]
Diatonic, Chromatic, Enharmonic, Subchromatic's summary[edit]
0 cents unison 20 cents potato unison 40 cents xencomma 60 cents potato augmented unison 80 cents augmented unison 100 cents semitone 120 cents minor second 140 cents xeneutral second 160 cents xeneutral second II 180 cents potato major second 200 cents major second