Valentine: Difference between revisions

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== Interval chain ==
== Interval chain ==
Odd harmonics and subharmonics 1–21  are in '''bold'''.  
In the following table, odd harmonics and subharmonics 1–21  are in '''bold'''.  


{| class="wikitable center-1 right-2"
{| class="wikitable center-1 right-2"
Line 27: Line 27:
|-
|-
| 1
| 1
| 77.88
| 77.9
| 21/20, 22/21, 25/24
| 21/20, 22/21, 25/24
|  
|  
Line 34: Line 34:
|-
|-
| 2
| 2
| 155.76
| 155.8
| 12/11, 11/10, 35/32
| 12/11, 11/10, 35/32
|  
|  
Line 41: Line 41:
|-
|-
| 3
| 3
| 233.64
| 233.7
| '''8/7'''
| '''8/7'''
|  
|  
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|-
|-
| 4
| 4
| 311.52
| 311.6
| 6/5
| 6/5
|  
|  
Line 55: Line 55:
|-
|-
| 5
| 5
| 389.41
| 389.5
| '''5/4'''
| '''5/4'''
|  
|  
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|-
|-
| 6
| 6
| 467.29
| 467.4
| '''21/16'''
| '''21/16'''
|  
|  
Line 69: Line 69:
|-
|-
| 7
| 7
| 545.17
| 545.3
| '''11/8''', 15/11
| '''11/8''', 15/11
|  
|  
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|-
|-
| 8
| 8
| 623.05
| 623.2
| 10/7
| 10/7
| 56/39
| 56/39
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|-
|-
| 9
| 9
| 700.93
| 701.1
| '''3/2'''
| '''3/2'''
|  
|  
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|-
|-
| 10
| 10
| 778.81
| 779.0
| 11/7, 25/16
| 11/7, 25/16
|  
|  
Line 97: Line 97:
|-
|-
| 11
| 11
| 856.69
| 856.9
| 18/11
| 18/11
| 64/39
| 64/39
Line 104: Line 104:
|-
|-
| 12
| 12
| 934.57
| 934.8
| 12/7
| 12/7
|  
|  
Line 111: Line 111:
|-
|-
| 13
| 13
| 1012.46
| 1012.7
| 9/5, 25/14
| 9/5, 25/14
|  
|  
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|-
|-
| 14
| 14
| 1090.34
| 1090.6
| '''15/8'''
| '''15/8'''
|  
|  
Line 125: Line 125:
|-
|-
| 15
| 15
| 1168.22
| 1168.5
| 63/32, 96/49, 55/28, <br>108/55, 125/64
| 55/28, 63/32, 96/49, <br>108/55, 125/64
|  
|  
| 39/20
| 39/20
Line 132: Line 132:
|-
|-
| 16
| 16
| 46.10
| 46.4
| 33/32, 36/35, 50/49
| 33/32, 36/35, 50/49
| 40/39
| 40/39
Line 139: Line 139:
|-
|-
| 17
| 17
| 123.98
| 124.3
| 15/14, 27/25
| 15/14, 27/25
| 14/13
| 14/13
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|-
|-
| 18
| 18
| 201.86
| 202.2
| '''9/8'''
| '''9/8'''
|  
|  
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|-
|-
| 19
| 19
| 279.74
| 280.1
| 33/28
| 33/28
|  
|  
Line 160: Line 160:
|-
|-
| 20
| 20
| 357.62
| 358.0
| 27/22
| 27/22
| '''16/13'''
| '''16/13'''
Line 167: Line 167:
|-
|-
| 21
| 21
| 435.51
| 435.9
| 9/7
| 9/7
|  
|  
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|-
|-
| 22
| 22
| 513.39
| 513.8
| 27/20
| 27/20
| 35/26
| 35/26
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|-
|-
| 23
| 23
| 591.27
| 591.7
| 45/32
| 45/32
|  
|  
Line 188: Line 188:
|-
|-
| 24
| 24
| 669.15
| 669.6
| 72/49
| 72/49
|  
|  
Line 195: Line 195:
|-
|-
| 25
| 25
| 747.03
| 747.5
| 54/35
| 54/35
| 20/13
| 20/13
Line 202: Line 202:
|-
|-
| 26
| 26
| 824.91
| 825.4
| 45/28
| 45/28
| 21/13
| 21/13
Line 209: Line 209:
|-
|-
| 27
| 27
| 902.79
| 903.3
| 27/16
| 27/16
| 22/13
| 22/13
Line 216: Line 216:
|-
|-
| 28
| 28
| 980.67
| 981.2
| 99/56
| 99/56
|  
|  
Line 223: Line 223:
|-
|-
| 29
| 29
| 1058.56
| 1059.1
| 90/49
| 90/49
| 24/13
| 24/13
Line 230: Line 230:
|-
|-
| 30
| 30
| 1136.44
| 1137.0
| 27/14
| 27/14
| 25/13
| 25/13
Line 237: Line 237:
|-
|-
| 31
| 31
| 14.32
| 14.9
| 81/80, 99/98
| 81/80, 99/98
|  
|  
Line 243: Line 243:
|  
|  
|}
|}
 
<nowiki/>* In 11-limit [[CWE tuning]]
<nowiki>*</nowiki> in 11-limit POTE tuning


== Chords ==
== Chords ==

Revision as of 12:21, 22 January 2025

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

In the following table, 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 77.9 21/20, 22/21, 25/24 26/25 27/26
2 155.8 12/11, 11/10, 35/32 13/12
3 233.7 8/7 15/13
4 311.6 6/5 13/11
5 389.5 5/4 26/21, 33/26
6 467.4 21/16 13/10
7 545.3 11/8, 15/11 18/13
8 623.2 10/7 56/39 13/9
9 701.1 3/2 52/35
10 779.0 11/7, 25/16 52/33
11 856.9 18/11 64/39 13/8
12 934.8 12/7 26/15
13 1012.7 9/5, 25/14
14 1090.6 15/8 13/7
15 1168.5 55/28, 63/32, 96/49,
108/55, 125/64 		39/20
16 46.4 33/32, 36/35, 50/49 40/39 27/26 26/25
17 124.3 15/14, 27/25 14/13 13/12
18 202.2 9/8
19 280.1 33/28 13/11
20 358.0 27/22 16/13 39/32 26/21
21 435.9 9/7 13/10
22 513.8 27/20 35/26
23 591.7 45/32 39/28
24 669.6 72/49 52/35
25 747.5 54/35 20/13
26 825.4 45/28 21/13 13/8
27 903.3 27/16 22/13
28 981.2 99/56
29 1059.1 90/49 24/13 13/7
30 1137.0 27/14 25/13 39/20
31 14.9 81/80, 99/98

* In 11-limit CWE 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
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