Sensi

From Xenharmonic Reference
Sensi
Subgroups 2.3.5.7
Reduced mapping ⟨1; 7 9 13]
ET join 19 & 27
Generators (CWE) ~9/7 = 443.3¢
MOS scales 3L 2s, 3L 5s, 8L 3s, 8L 11s
Ploidacot beta-heptacot
Comma basis 126/125, 245/243 (7-limit)
Minimax error 7-odd-limit: 7.5¢
Target scale size 7-odd-limit: 19 notes

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).

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


ViewTalkEditRegular temperaments
Rank-2
Acot Blackwood (1/5-octave) • Whitewood (1/7-octave) • Compton (1/12-octave)
Monocot MeantoneSchismicLeapdayArchy
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 Trismegistus (alpha-triseph) • Orgone (trimech) • Didacus (diseph)
No-octaves Sensamagic (monogem)
Exotemperament DicotMavilaFather
Higher-rank
Rank-3 HemifamityMarvelParapyth