Sensi: Difference between revisions
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'''Sensi''', 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). | '''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). | ||
== Interval chain == | == Interval chain == | ||
| Line 106: | Line 106: | ||
|} | |} | ||
<nowiki/>* In 2.3.5.7.13 CWE tuning | <nowiki/>* 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. | |||
{| class="wikitable sortable" | |||
!|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 | |||
|} | |||
{{Navbox regtemp}} | {{Navbox regtemp}} | ||
{{Cat|temperaments}} | {{Cat|temperaments}} | ||
Latest revision as of 14:08, 14 April 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 |
| View • Talk • EditRegular temperaments | |
|---|---|
| Rank-2 | |
| Acot | Blackwood (1/5-octave) • Whitewood (1/7-octave) • Compton (1/12-octave) |
| Monocot | Meantone • Schismic • Gentle-fifth temperaments • Archy |
| Complexity 2 | Diaschismic (diploid monocot) • Pajara (diploid monocot) • Injera (diploid monocot) • Rastmatic (dicot) • Mohajira (dicot) • Intertridecimal (dicot) • Interseptimal (alpha-dicot) |
| Complexity 3 | Augmented (triploid) • Misty (triploid) • Slendric (tricot) • Porcupine (omega-tricot) |
| Complexity 4 | Diminished (tetraploid) • Tetracot (tetracot) • Buzzard (alpha-tetracot) • Squares (beta-tetracot) • Negri (omega-tetracot) |
| Complexity 5-6 | Magic (alpha-pentacot) • Amity (gamma-pentacot) • Kleismic (alpha-hexacot) • Miracle (hexacot) |
| Higher complexity | Orwell (alpha-heptacot) • Sensi (beta-heptacot) • Octacot (octacot) • Wurschmidt (beta-octacot) • Valentine (enneacot) • Ammonite (epsilon-enneacot) • Myna (beta-decacot) • Ennealimmal (enneaploid dicot) |
| Straddle-3 | A-Team (alter-tricot) • Machine (alter-monocot) |
| No-3 | Mabilic (alpha-triseph) • Orgone (trimech) • Didacus (diseph) |
| No-octaves | Sensamagic (monogem) |
| Exotemperaments | Dicot • Mavila • Father |
| Higher-rank | |
| Rank-3 | Hemifamity • Marvel • Parapyth |
