Valentine

Valentine is a regular temperament for the 7- and 11-limit, which tempers out 121/120, 126/125, and 176/175.

Valentine is very closely related to Carlos Alpha, the rank-1 non-octave temperament of Wendy Carlos, as the generator chain of valentine is the same thing as Carlos Alpha. Indeed, the way Carlos uses Alpha in Beauty in the Beast suggests that she really intended Alpha to be the same thing as valentine, and that it is misdescribed as a rank-1 temperament. Carlos tells us that "[t]he melodic motions of Alpha are amazingly exotic and fresh, like you've never heard before", and since Alpha lives inside valentine this comment carries over and applies to it if you stick close melodically to generator steps, which is almost impossible not to do since the generator step is so small. Mos scales of 15, 16, 31 and 46 notes are available to explore these exotic and fresh melodies, or the less exotic ones you might cook up otherwise.

See Starling temperaments #Valentine for more technical data.

Interval chain

Odd harmonics and subharmonics 1–21 are in bold.

#	Cents*	11-limit ratios	13-limit extension
			Valentino	Lupercalia	Dwynwen
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	99/56
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

Chords

Main article: Chords of valentine

Tunings

Tuning spectrum

Edo generator	Eigenmonzo (unchanged-interval)	Generator (¢)	Comments
1\16		75.000	Lower bound of 7-odd-limit diamond monotone
	11/6	75.319
	15/11	76.707
	7/4	77.058
	7/5	77.186
	5/4	77.263
2\31		77.419	Lower bound of 9- and 11-odd-limit, 11-limit 15-, and 21-odd-limit diamond monotone
	11/9	77.508
	15/14	77.614
	15/8	77.733
	7/6	77.761	7-odd-limit minimax
	9/7	77.861	9-odd-limit minimax
5\77		77.922
	3/2	77.995	5-odd-limit minimax
	11/7	78.249	11-odd-limit minimax
3\46		78.261
	9/5	78.277
	21/16	78.463
	11/8	78.760
	5/3	78.910
1\15		80.000	Upper bound of 7-, 9- and 11-odd-limit, 11-limit 15-, and 21-odd-limti diamond monotone
	21/11	80.537
	11/10	82.502
	21/20	84.867