User:Dummy index/Random lists of temperaments by generator size

12ET-complementary comma pairs (e.g. syntonic-schismatic relation)

M3 or d4	A: 4*P5=M3+2*P8	B: 8*P5+d4=5*P8	Remarks
32/27	2187/2048=[-11 7⟩	256/243=[8 -5⟩	A/B=[-19 12⟩, A: (7edo), B: (5edo)
6/5	135/128=[-7 3 1⟩	(64/63)^2*(245/243)=[12 -9 1⟩	A/B=[-19 12⟩, A: Mavila, B: Superpyth
11/9	729/704=[-6 6 0 0 -1⟩	(64/63)^2/(99/98)=[13 -6 0 0 -1⟩	A/B=[-19 12⟩, A: Flattone, B: Supra
8192/6561	531441/524288=[-19 12⟩	1/1	A: (12edo)
5/4	81/80=[-4 4 -1⟩	32805/32768=[-15 8 1⟩	A*B=[-19 12⟩, A: Meantone, B: Schismatic
81/64	1/1	531441/524288=[-19 12⟩	B: (12edo)
9/7	64/63=[6 -2 0 -1⟩	59049/57344=[-13 10 0 -1⟩	B/A=[-19 12⟩, A: Archytas clan, B: Septimal meantone
4/3	256/243=[8 -5⟩	2187/2048=[-11 7⟩	B/A=[-19 12⟩, A: (5edo), B: (7edo)

Q: Mavila must have the fifth flatter than 7edo's, why be placed between 7edo and 5edo?

A: I wrote the 32/27 in this table as a monzo-ish nominal ratio. 32/27 constructed of P5 & P8 will much sharper when flatter P5 situation.

(3/2)^(1/2)	2187/2048=[-11 7⟩	17-comma=[27 -17⟩	A/B=[-38 24⟩, A: (7edo), B: (17edo)
(3/2)^(4/7)	531441/524288=[-19 12⟩	531441/524288=[-19 12⟩	A*B=[-38 24⟩, A: (12edo), B: (12edo)
(3/2)^(2/3)	256/243=[8 -5⟩	[-41 26⟩	B/A=[-49 31⟩, A: (5edo), B: (26edo)

Temperaments spectrum

Respect to 5L 2s/Temperaments and Epic Table 1.

For diatonic range

and some Neutral thirds.

	Ratios				Remarks	Mapping development
Fifthspan	-8	-6	4	6
Pelogic	25/18	14/9	6/5 8/7	9/7		[⟨1 0 ...], ⟨0 1 -3 -4 -1]]
Armodue	10/7	11/7	6/5 7/6	14/11		[⟨1 0 ...], ⟨0 1 -3 5 -1]] +9
Septimal mavila	7/5	25/16	6/5	32/25		[⟨1 0 ...], ⟨0 1 -3 -11 -1]] -16
Hornbostel	25/18 48/35	25/16	6/5	32/25		[⟨1 0 ...], ⟨0 1 -3 12]] +23
Plutus	32/25 48/35	16/11	5/4 7/6	11/8	105/64 is at 10 fifthspan -> 7edo	[⟨1 0 ...], ⟨0 1 4 5 6]] +7-7
Flattone	21/16	16/11	5/4 11/9	11/8		[⟨1 0 ...], ⟨0 1 4 -9 6]] -14
Meanenneadecal	9/7	16/11	5/4 11/9	11/8		[⟨1 0 ...], ⟨0 1 4 10 6]] +19
Septimal meantone	9/7	10/7	5/4	7/5	Good 4:5:7 in 10 fifthspanp-p	[⟨1 0 ...], ⟨0 1 4 10]]
Mohajira	14/11		5/4		7/5 is at -9.5 fifthspan	[⟨1 0 ...], ⟨0 2 8 -11]] *2-31
Undecimal meantone	14/11	10/7	5/4	7/5	Good 4:5:7 in 10 fifthspanp-p	[⟨1 0 ...], ⟨0 1 4 10 18]] +12
Dominant	32/25	7/5	5/4 9/7	10/7	inaccurate	[⟨1 0 ...], ⟨0 1 4 -2]] -12
Schism	5/4	10/7	81/64 9/7	7/5	inaccurate	[⟨1 0 ...], ⟨0 1 -8 -2]] -12
Grackle	5/4		81/64		7/5 is at -18 fifthspan	[⟨1 0 ...], ⟨0 1 -8 -26]] -24
Garibaldi	5/4	7/5	81/64 80/63	10/7	Good 4:5:6:7 in 15 fifthspanp-p Good 4:6 & 5:7 in 6 fifthspanp-p	[⟨1 0 ...], ⟨0 1 -8 -14]] +12
Andromeda	5/4	7/5	14/11	10/7	11/9 is at -20 fifthspan -> 41edo	[⟨1 0 ...], ⟨0 1 -8 -14 -18 -21]]
Hemififths		7/5	14/11	10/7	5/4 is at 12.5 fifthspan	[⟨1 0 ...], ⟨0 2 25 13 5]] *2+41
Edson		7/5	14/11	10/7	-> 29edo	[⟨1 0 ...], ⟨0 1 no-five -14-(-8) -18-(-8) -21-(-8)]]
Gentle region Leapfrog	27/22		14/11			[⟨1 0 ...], ⟨0 1 no-five 15 11 8]] +29
Supra	11/9	11/8	9/7 14/11	16/11		[⟨1 0 ...], ⟨0 1 no-five -2 -6]] -17
Superpyth	6/5	15/11	9/7	22/15		[⟨1 0 ...], ⟨0 1 9 -2 16]] +22
Ultrapyth	33/28	112/81	9/7	81/56		[⟨1 0 ...], ⟨0 1 14 -2 -11]] +5-25

For 600 cents to 800 cents

	Generator	Ratios		Remarks	Mapping
Fifth(?)span		1	2
Pluto	7/5	10/7	81/80		[⟨1 0 ...], ⟨0 -7 -26 -25]]
Tritonic	7/5	10/7,64/45	64/63		[⟨1 0 ...], ⟨0 -5 11 12]]
Liese	10/7	10/7,81/56	21/20,28/27		[⟨1 0 ...], ⟨0 3 12 11]]
Maquila	15/11	22/15,35/24	77/72		[⟨1 0 ...], ⟨0 17 -6 22 10]]
Pelogic	3/2	3/2,10/7,64/45	9/8,16/15,15/14,28/25,64/63		[⟨1 0 ...], ⟨0 1 -3 -4]]
Septimal mavila	3/2	3/2,16/11,22/15,64/45	12/11,11/10,9/8,16/15		[⟨1 0 ...], ⟨0 1 -3 -11 -1]]
Larry	40/27	40/27	11/10		[⟨1 0 ...], ⟨0 -6 -17 no-seven -15]]
Flattone	3/2	3/2,40/27	9/8,10/9		[⟨1 0 ...], ⟨0 1 4 -9]]
Septimal meantone	3/2	3/2,40/27	9/8,10/9,28/25		[⟨1 0 ...], ⟨0 1 4 10]]
Garibaldi	3/2	3/2	9/8,28/25		[⟨1 0 ...], ⟨0 1 -8 -14]]
Leapday	3/2	3/2	9/8		[⟨1 0 ...], ⟨0 1 21 15]]
Superpyth	3/2	3/2,32/21	8/7,9/8		[⟨1 0 ...], ⟨0 1 9 -2]]
Hemiseven	320/243	243/160	8/7,55/48		[⟨1 0 ...], ⟨0 -6 -29 2 21]]
Father	3/2	3/2,8/5,14/9,45/32,81/56	6/5,7/6,9/8,32/25,56/45		[⟨1 0 ...], ⟨0 1 -1 3]]
Sidi	9/7	14/9,45/28	5/4,6/5		[⟨1 0 ...], ⟨0 -4 -2 -9]]
Magic	5/4	8/5,45/28	9/7,32/25		[⟨1 0 ...], ⟨0 5 1 12]]

Pan-5L2s tuning spectrum

Eigenmonzo (unchanged interval)	at (fifthspan)	Generator (cents)	in this temperament (e.g.)
5/4	-3(m3)	671.229	Mavila
6/5	+4(M3)	678.910	Mavila
11/9	+4(M3)	686.852	Flattone
11/8	+6(A4)	691.886	Flattone
6/5	-3(m3)	694.786	Meantone (1/3 comma)
9/7	-8(d4)	695.614	Septimal meantone
7/6	+9(A2)	696.319	Septimal meantone
5/4	+4(M3)	696.578	Meantone (1/4 comma)
7/5	+6(A4)	697.085	Septimal meantone
11/8	+18(AA3)	697.295	Undecimal meantone
14/11	-8(d4)	697.812	Undecimal meantone
7/5	-18(dd6)	700.972	Grackle
5/4	-8(d4)	701.711	Schismatic
6/5	+9(A2)	701.738	Schismatic
3/2	+1(P5)	701.955	Pythagorean
11/8	-18(dd6)	702.705	Andromeda
7/5	-6(d5)	702.915	Garibaldi
13/11	-3(m3)	703.597	Leapfrog
14/11	+4(M3)	704.377	Leapfrog
27/22	-8(d4)	705.682	Leapfrog
11/9	-8(d4)	706.574	Supra
11/8	-6(d5)	708.114	Supra
9/7	+4(M3)	708.771	Archy (1/4 comma)
5/4	+9(A2)	709.590	Superpyth
6/5	-8(d4)	710.545	Superpyth
7/6	-3(m3)	711.043	Archy (1/3 comma)

Clarify Meantone#Tuning spectrum

19/17	at +2(M2)	696.279	for regular temperament with nominal 19/17 at M2, see some 19-limit variation in Meantone family (search ⟨0 1 * * * * -5 -3] in mappings.)
18/17	at +7(A1)	699.850	for regular temperament with nominal 18/17 at A1, see some 17-limit variation in Meantone family (search ⟨0 1 * * * * -5] in mappings.)
18/17	at -5(m2)	700.209	for regular temperament with nominal 18/17 at m2, see No-sevens subgroup temperaments#Photia for example.
17/16	at -5(m2)	699.009	for regular temperament with nominal 17/16 at m2, see some 17-limit variation in Meantone family (search ⟨0 1 * * * * -5] in mappings.)
19/16	at -3(m3)	700.829	for regular temperament with nominal 19/16 at m3, see some 19-limit variation in Meantone family (search ⟨0 1 * * * * * -3] in mappings.)
45/34	at +11(A3)	698.661	for regular temperament with nominal 45/34 at A3, see some 17-limit variation in Meantone family (search ⟨0 1 4 * * * -5] in mappings.)
17/15	at -10(d3)	698.331	for regular temperament with nominal 17/15 at d3, see some 17-limit variation in Meantone family (search ⟨0 1 4 * * * -5] in mappings.)
51/38	at -1(P4)	690.673	for regular temperament with nominal 51/38 at P4, see some 19-limit variation in Meantone family (search ⟨0 1 * * * * -5 -3] in mappings.)
81/80	at 0(P1)	---	81/80 is tempered out, return to 1/1, anyway.
81/80	at +12(A7)	701.792	this interpretation is by the schismatic temperament.
81/80	at +19(AA7)	695.869	this interpretation is by the Lalayo.
256/243	at -5(m2)	701.955	any 3-limit eigenmonzo results in the pythagorean tuning.
1024/729	at -6(d5)
2187/2048	at +7(A1)
8192/6561	at -8(d4)
[27 -17⟩	at -17(dd3)
256/243	at +7(A1)	698.604	flatten 2187/2048 of +7(A1) by [-19 12⟩. (-1 pythagorean comma / +7 step)
1024/729	at +6(A4)	698.045	flatten 729/512 of +6(A4) by [-19 12⟩. (-1 pythagorean comma / +6 step)
2187/2048	at -5(m2)	697.263	sharpen 256/243 of -5(m2) by [-19 12⟩. (+1 pythagorean comma / -5 step)
8192/6561	at +4(M3)	696.090	flatten 81/64 of +4(M3) by [-19 12⟩. (-1 pythagorean comma / +4 step)
[27 -17⟩	at +7(A1)	695.252	flatten 2187/2048 of +7(A1) by two [-19 12⟩. (-2 pythagorean comma / +7 step)