Sensi: Difference between revisions
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| Odd limit 1 = 7 | Mistuning 1 = 7.5 | Complexity 1 = 19 | | Odd limit 1 = 7 | Mistuning 1 = 7.5 | Complexity 1 = 19 | ||
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[[File:Sentry11.png|thumb|Sensi 11-note MOS]] | |||
'''Sensi''', 2.3.5.7[{{e|19}} & {{e|27}}], is a rank-2 temperament generated by a sharpened 9/7 such that two of them are equated to 5/3. Distinctly from other sensamagic temperaments, 3/2 is also found at 7 generators, or equivalently the octave is found at 125/63. It is most accurately extended to add prime 31 (by equating the generator with 31/24), but less accurately prime 13 is canonically added (by equating the generator with 13/10). | '''Sensi''', 2.3.5.7[{{e|19}} & {{e|27}}], is a rank-2 temperament generated by a sharpened 9/7 such that two of them are equated to 5/3. Distinctly from other sensamagic temperaments, 3/2 is also found at 7 generators, or equivalently the octave is found at 125/63. It is most accurately extended to add prime 31 (by equating the generator with 31/24), but less accurately prime 13 is canonically added (by equating the generator with 13/10). | ||
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== Patent vals == | == Patent vals == | ||
The following patent vals support 2.3.5.7 Sensi. Vals contorted in the 7-limit are not included. | The following patent vals support 2.3.5.7 Sensi. Vals contorted in the 7-limit are not included. | ||
{ class="wikitable sortable" | {| class="wikitable sortable" | ||
!|Edo!!13 extension!!Generator!!3/2 tuning!!5/4 tuning!!13/8 tuning | !|Edo!!13 extension!!Generator!!3/2 tuning!!5/4 tuning!!7/4 tuning!!13/8 tuning | ||
|- | |- | ||
||19||19 & 27||442.105||694.737||378.947||947.368||821.053 | ||19||19 & 27||442.105||694.737||378.947||947.368||821.053 | ||
Latest revision as of 02:00, 2 June 2026
| Sensi |
Sensi, 2.3.5.7[19 & 27], is a rank-2 temperament generated by a sharpened 9/7 such that two of them are equated to 5/3. Distinctly from other sensamagic temperaments, 3/2 is also found at 7 generators, or equivalently the octave is found at 125/63. It is most accurately extended to add prime 31 (by equating the generator with 31/24), but less accurately prime 13 is canonically added (by equating the generator with 13/10).
Interval chain
In the following table, odd harmonics and subharmonics 1–21 are in bold.
| # | Cents* | Approximate ratios |
|---|---|---|
| 0 | 0.0 | 1/1 |
| 1 | 443.4 | 9/7, 13/10 |
| 2 | 886.7 | 5/3, 42/25 |
| 3 | 130.1 | 13/12, 14/13, 15/14, 27/25 |
| 4 | 573.4 | 7/5, 18/13, 25/18 |
| 5 | 1016.8 | 9/5 |
| 6 | 260.1 | 7/6, 15/13 |
| 7 | 703.5 | 3/2 |
| 8 | 1146.9 | 27/14, 35/18 |
| 9 | 390.2 | 5/4 |
| 10 | 833.6 | 13/8, 21/13 |
| 11 | 76.9 | 21/20, 25/24 |
| 12 | 520.3 | 27/20 |
| 13 | 963.7 | 7/4 |
| 14 | 207.0 | 9/8 |
| 15 | 650.4 | 35/24 |
| 16 | 1093.7 | 15/8 |
| 17 | 337.1 | 39/32 |
| 18 | 780.4 | 25/16 |
| 19 | 23.8 | 49/48, 65/64, 81/80 |
| 20 | 467.2 | 21/16 |
* In 2.3.5.7.13 CWE tuning
Patent vals
The following patent vals support 2.3.5.7 Sensi. Vals contorted in the 7-limit are not included.
| Edo | 13 extension | Generator | 3/2 tuning | 5/4 tuning | 7/4 tuning | 13/8 tuning |
|---|---|---|---|---|---|---|
| 19 | 19 & 27 | 442.105 | 694.737 | 378.947 | 947.368 | 821.053 |
| 65 | 443.077 | 701.538 | 387.692 | 960.000 | 849.231 | |
| 46 | 19 & 27 | 443.478 | 704.348 | 391.304 | 965.217 | 834.783 |
| 73 | 19 & 27 | 443.836 | 706.849 | 394.521 | 969.863 | 838.356 |
| 27 | 19 & 27 | 444.444 | 711.111 | 400.000 | 977.778 | 844.444 |
