Valentine

See Starling temperaments #Valentine or Gamelismic clan #Valentine.

Interval chain

Prime harmonics are in bold.

#	Cents*	11-limit ratios (valentine mapping)	13-limit ratios (valentino mapping)	13-limit ratios (lupercalia mapping)	13-limit ratios (dwynwen mapping)
0	0.00	1/1
1	77.88	21/20, 22/21, 25/24		26/25	27/26
2	155.76	12/11, 11/10, 35/32		13/12
3	233.64	8/7		15/13
4	311.52	6/5		13/11
5	389.41	5/4		26/21, 33/26
6	467.29	21/16		13/10
7	545.17	11/8, 15/11		18/13
8	623.05	10/7	56/39		13/9
9	700.93	3/2		52/35
10	778.81	11/7, 25/16			52/33
11	856.69	18/11	64/39	13/8
12	934.57	12/7			26/15
13	1012.46	9/5, 25/14
14	1090.34	15/8		13/7
15	1168.22	63/32, 96/49, 55/28, 108/55, 125/64		39/20
16	46.10	33/32, 36/35, 50/49	40/39	27/26	26/25
17	123.98	15/14, 27/25	14/13		13/12
18	201.86	9/8
19	279.74	33/28			13/11
20	357.62	27/22	16/13	39/32	26/21
21	435.51	9/7			13/10
22	513.39	27/20	35/26
23	591.27	45/32		39/28
24	669.15	72/49			52/35
25	747.03	54/35	20/13
26	824.91	45/28	21/13		13/8
27	902.79	27/16	22/13
28	980.67
29	1058.56	90/49	24/13		13/7
30	1136.44	27/14	25/13		39/20
31	14.32	81/80, 99/98

* in 11-limit POTE tuning

Spectrum of valentine tunings by eigenmonzos

Eigenmonzo	Minor Semitone	Comments
(1\16)	75.000
12/11	75.319
8/7	77.058
7/5	77.186
5/4	77.263
(2\31)	77.419
11/9	77.508
7/6	77.761	7-odd-limit minimax
9/7	77.861	9-odd-limit minimax
(5\77)	77.922
4/3	77.995	5-odd-limit minimax, Carlos Alpha tuning
14/11	78.249	11-odd-limit minimax
(3\46)	78.261
10/9	78.277
11/8	78.760
6/5	78.910
(1\15)	80.000
11/10	82.502