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)]}

See also

• User:PiotrGrochowski/Extra-Diatonic Intervals