Valentine: Difference between revisions

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→Spectrum of valentine tunings by eigenmonzos: improve and standardize tuning spectra tables
Line 247: Line 247:
{{main| Chords of valentine }}
{{main| Chords of valentine }}


== Spectrum of valentine tunings by eigenmonzos ==
== Tuning spectrum ==


{| class="wikitable center-1 right-2"
{| class="wikitable center-all"
|-
|-
! Eigenmonzo
! ET<br>generator
! Minor<br>Semitone
! [[eigenmonzo|eigenmonzo<br>(unchanged interval]])
! Comments
! minor<br>semitone (¢)
! comments
|-
|-
| ([[16edo|1\16]])
| [[16edo|1\16]]
|
| 75.000
| 75.000
|
|-
|  
|  
|-
| 12/11
| 12/11
| 75.319
| 75.319
|
|-
|  
|  
|-
| 8/7
| 8/7
| 77.058
| 77.058
|
|-
|  
|  
|-
| 7/5
| 7/5
| 77.186
| 77.186
|
|-
|  
|  
|-
| 5/4
| 5/4
| 77.263
| 77.263
|
|-
| [[31edo|2\31]]
|  
|  
| 77.419
|
|-
|-
| ([[31edo|2\31]])
| 77.419
|  
|  
|-
| 11/9
| 11/9
| 77.508
| 77.508
|
|-
|  
|  
|-
| 7/6
| 7/6
| 77.761
| 77.761
| 7-odd-limit minimax
| 7-odd-limit minimax
|-
|-
|
| 9/7
| 9/7
| 77.861
| 77.861
| 9-odd-limit minimax
| 9-odd-limit minimax
|-
|-
| ([[77edo|5\77]])
| [[77edo|5\77]]
|
| 77.922
| 77.922
|
|-
|  
|  
|-
| 4/3
| 4/3
| 77.995
| 77.995
| 5-odd-limit minimax, Carlos Alpha tuning
| 5-odd-limit minimax, Carlos Alpha tuning
|-
|-
|
| 14/11
| 14/11
| 78.249
| 78.249
| 11-odd-limit minimax
| 11-odd-limit minimax
|-
|-
| ([[46edo|3\46]])
| [[46edo|3\46]]
|
| 78.261
| 78.261
|
|-
|  
|  
|-
| 10/9
| 10/9
| 78.277
| 78.277
|
|-
|  
|  
|-
| 11/8
| 11/8
| 78.760
| 78.760
|
|-
|  
|  
|-
| 6/5
| 6/5
| 78.910
| 78.910
|
|-
| [[15edo|1\15]]
|  
|  
| 80.000
|
|-
|-
| ([[15edo|1\15]])
| 80.000
|  
|  
|-
| 11/10
| 11/10
| 82.502
| 82.502
|  
|
|}
|}


Revision as of 00:28, 30 September 2021

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

See Starling temperaments #Valentine for more technical data.

Interval chain

Prime harmonics 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
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

Tuning spectrum

ET
generator 		eigenmonzo
(unchanged interval) 		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

Template:IoT

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