Valentine: Difference between revisions
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'''Valentine''' is a regular temperament for 7 and 11 | '''Valentine''' is a [[regular temperament]] for the [[7-limit|7-]] and [[11-limit]], which tempers out [[121/120]], [[126/125]], and [[176/175]]. | ||
See [[Starling temperaments #Valentine]] for more technical data. | See [[Starling temperaments #Valentine]] for more technical data. | ||
== Interval chain == | == Interval chain == | ||
Odd harmonics and subharmonics 1–21 are in '''bold'''. | |||
{| class="wikitable center-1 right-2" | {| class="wikitable center-1 right-2" | ||
| Line 11: | Line 11: | ||
! rowspan="2" | Cents* | ! rowspan="2" | Cents* | ||
! rowspan="2" | 11-limit ratios | ! rowspan="2" | 11-limit ratios | ||
! colspan="3" | 13-limit | ! colspan="3" | 13-limit extension | ||
|- | |- | ||
! Valentino | ! Valentino | ||
| Line 19: | Line 19: | ||
| 0 | | 0 | ||
| 0.00 | | 0.00 | ||
| 1/1 | | '''1/1''' | ||
| | | | ||
| | | | ||
| Line 61: | Line 61: | ||
| 6 | | 6 | ||
| 467.29 | | 467.29 | ||
| 21/16 | | '''21/16''' | ||
| | | | ||
| 13/10 | | 13/10 | ||
| Line 117: | Line 117: | ||
| 14 | | 14 | ||
| 1090.34 | | 1090.34 | ||
| 15/8 | | '''15/8''' | ||
| | | | ||
| 13/7 | | 13/7 | ||
| Line 145: | Line 145: | ||
| 18 | | 18 | ||
| 201.86 | | 201.86 | ||
| 9/8 | | '''9/8''' | ||
| | | | ||
| | | | ||
| Line 215: | Line 215: | ||
| 28 | | 28 | ||
| 980.67 | | 980.67 | ||
| | | 99/56 | ||
| | | | ||
| | | | ||
| Line 247: | Line 247: | ||
{{main| Chords of valentine }} | {{main| Chords of valentine }} | ||
== Tuning spectrum == | == Tunings == | ||
=== Tuning spectrum === | |||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|- | |- | ||
! | ! Edo<br>generator | ||
! [[ | ! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval]]) | ||
! | ! Generator (¢) | ||
! | ! Comments | ||
|- | |- | ||
| [[16edo|1\16]] | | [[16edo|1\16]] | ||
| Line 309: | Line 309: | ||
| 4/3 | | 4/3 | ||
| 77.995 | | 77.995 | ||
| 5-odd-limit minimax | | 5-odd-limit minimax | ||
|- | |- | ||
| | | | ||
Revision as of 11:43, 22 January 2025
Valentine is a regular temperament for the 7- and 11-limit, which tempers out 121/120, 126/125, and 176/175.
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
Tunings
Tuning spectrum
| Edo generator |
Eigenmonzo (unchanged-interval) |
Generator (¢) | 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 | |
| 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 |