15edo/Interval names
| Degree | Cents | Aaron's Answer | Igs' Input | Kite's Correction | Keenan Category | Margo's Method | SagiSpeak | Ups and downs | Gareth's Go | Extra-diatonic 2 | Represented Ratios |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 0 | P1 | Unison | Unison | P1 | Unison | P1 | P1, m2 | P1 | P1 | 1/1 |
| 1 | 80 | m2 | Subminor 2nd | Subminor 2nd | m2 | Minor 2nd | pai-P1 | ^1, ^m2 | m2 | S1 | 25/24, 21/20, 16/15 |
| 2 | 160 | NM2 (Narrow M2) | Neutral 2nd | Neutral 2nd | M2 | Large Neutral 2nd | pao-M2 | vM2 | M2 | sM2 | 11/10, 12/11, 10/9 |
| 3 | 240 | LM2 | Supermajor 2nd | Supermajor 2nd | A2/d3 | Large Major 2nd | M2 | M2, m3 | Serd* | M2, m3 (Serd) | 8/7, 7/6, 9/8 |
| 4 | 320 | Lm3 | Minor 3rd | Minor 3rd | m3 | Large Minor 3rd | pai-m3 | ^m3 | m3 | Sm3 | 6/5, 11/9 |
| 5 | 400 | M3 | Major 3rd | Major 3rd | M3 | Major 3rd | pao-M3 | vM3 | M3 | sM3 | 5/4, 14/11 |
| 6 | 480 | S4 (Small 4) | Sub 4th | Sub 4th | P4 | Small Perfect 4th | P4 | M3, P4, d5 | P4 | M3, P4 (Thourth) | 4/3, 9/7, 21/16 |
| 7 | 560 | Na4/Sd5 | Narrow Tritone | Super 4th | A4 | Small Tritone | pai-P4 | ^4, ^d5 | A4 | S4 | 11/8, 7/5 |
| 8 | 640 | La4/Wd5 | Wide Tritone | Sub 5th | d5 | Large Tritone | pao-P5 | vA4, v5 | d5 | s5 | 16/11, 10/7 |
| 9 | 720 | L5 | Super 5th | Super 5th | P5 | Large Perfect 5th | P5 | A4, P5, m6 | P5 | P5, m6 (Fixth) | 3/2, 14/9, 32/21 |
| 10 | 800 | m6 | Minor 6th | Minor 6th | m6 | Minor 6th | pai-m6 | ^5, ^m6 | m6 | Sm6 | 8/5, 11/7 |
| 11 | 880 | SM6 | Major 6th | Major 6th | M6 | Small Major 6th | pao-M6 | vA5, vM6 | M6 | sM6 | 5/3, 18/11 |
| 12 | 960 | SM7 | Subminor 7th | Subminor 7th | A6/d7 | Small Minor 7th | m7 | M6, m7 | Sinth* | M6, m7 (Sinth) | 7/4, 12/7, 16/9 |
| 13 | 1040 | Wm7 | Neutral 7th | Neutral 7th | m7 | Small Neutral 7th | pai-m7 | ^m7 | m7 | Sm7 | 20/11, 11/6, 9/5 |
| 14 | 1120 | M7 | Supermajor 7th | Supermajor 7th | M7 | Major 7th | pao-P8 | vM7, v8 | M7 | sM7 | 48/25, 40/21, 15/8 |
| 15 | 1200 | P8 | Octave | Octave | P8 | Octave | P8 | M7, P8 | P8 | P8 | 2/1 |
*'Serd' and 'Sinth' are Portmanteaux of Second and Third; and Sixth and Seventh respectively. These intervals represent exact half Perfect 4ths and Perfect 5ths, and replace the "regular" interval name. I have put them in there to gain functionality at the cost of losing familiarity/introducing novelty in addition to 'HO', the half-octave. My (Gareth's) system at this stage is the same as Dave Keenan's but for the addition of these. I suppose they could just be optional additional names for those steps. I was led to this after not finding any reason to change Dave's system, but not liking that it led to A2/d3 for the 240c interval in 5n-edos, and A6/d7 for the 960c interval. Seems weird.
Sagi-Speak, Ups and Downs, and Colours are all great, but are completely new ideas that can be linked to on the pages. Sagi-Speak and Ups are directly linked to the two main options for notation.
I like Igs' and Dave's systems the best I think. They are very different. Both are 'size' based rather than 'function', but the point of reference for Igs' is 12edo, which would be more familiar to new readers. Dave's uses JI / 72edo alterations two short chains of the edos best fifth - giving the perfect and neutral intervals, so is malleable in it's application to edos, and more able to reflect the 'function' of the intervals in an edo. I've added a few functional labels to it. Might be best to have those in brackets. At this stage I would like to see both on every edo page. Igs' has a point that his extra-diatonic names need not or perhaps should not be associated with ratios. Dave's on the other hand benifit from such an association. Perhaps an edo page could start with Igs' in the intervals section without ratios as he first edits, and in the temperament section Dave's names can be included.
I've done this for 72edo as well. [author: Gareth.hearne (talk)]