It can be seen as implying a rank-2 tuning which is generated by an extremely sharp major third of about 443 cents which represents both 9/7 and 13/10. It is so named because the generator is a "semisixth": two generators make a major sixth which approximates 5/3, which cannot occur in 12edo. Equal temperaments that support sensi include 19edo (generator 7\19; soft sensoid), 27edo (generator 10\27; supersoft sensoid), and 46edo (generator 17\46; L/s = 7/5, more optimized for sensi temperament).
In the following table, odd harmonics and subharmonics are in bold.
|3||129.966||13/12, 14/13, 15/14, 27/25|
|4||573.288||7/5, 18/13, 25/18|
|15||649.829||35/24 (close to 16/11)|
|17||336.473||39/32 (close to 17/14)|
|19||23.117||49/48, 65/64, 81/80|
- * in 22.214.171.124.13 POTE tuning
- † 126.96.36.199.13 ratio interpretations
Sortable table of sensi's major and minor intervals in various sensi tunings:
|Degree||Size in 19edo (soft)||Size in 27edo (supersoft)||Size in 46edo||Approximate ratios||#Gens up|
|unison||0\19, 0.00||0\27, 0.00||0\46, 0.00||1/1||0|
|min. sen2nd||2\19, 126.3||3\27, 133.3||5\46, 130.4||14/13||+3|
|maj. sen2nd||3\19, 189.5||4\27, 177.8||7\46, 182.6||10/9||-5|
|min. sen3rd||4\19, 252.6||6\27, 266.7||10\46, 260.9||7/6||+6|
|maj. sen3rd||5\19, 315.8||7\27, 311.1||12\46, 313.0||6/5||-2|
|perf. sen4th||7\19, 442.1||10\27, 444.4||17\46, 443.5||9/7, 13/10||+1|
|aug. sen4th||8\19, 505.3||11\27, 488.9||19\46, 495.7||4/3||-7|
|min. sen5th||9\19, 568.4||13\27, 577.8||22\46, 573.9||7/5, 18/13||+4|
|maj. sen5th||10\19, 631.6||14\27, 622.2||24\46, 626.1||10/7, 13/9||-4|
|dim. sen6th||11\19, 694.7||16\27, 711.1||27\46, 704.3||3/2||+7|
|perf. sen6th||12\19, 757.9||17\27, 755.6||20\46, 756.5||14/9, 20/13||-1|
|min. sen7th||14\19, 884.2||20\27, 888.9||34\46, 887.0||5/3||+2|
|maj. sen7th||15\19, 947.4||21\27, 933.3||36\46, 939.1||12/7||-6|
|min. sen8th||16\19, 1010.5||23\27, 1022.2||39\46, 1017.4||9/5||+5|
|maj. sen8th||17\19, 1073.7||24\27, 1066.7||41\46, 1069.6||13/7||-3|
- Main article: Chords of sensus
The "fundamental otonal consonance" of sensi (in this article's definition of sensi) is 4:5:6:7:9:13. However, the full chord isn't available in the 8-note MOS.
One of the most common consonant triads in sensi is the 6:10:13 triad, which spans 3 generators. Sensi has five 6:10:13 triads, four 7:9:13 triads, three 5:6:7:9 tetrads and one 5:6:7:9:13 pentad. Having many diminished triads, it is similar to the 12edo diminished scale in some ways. Sensi is interesting mainly because it gives new 13-limit interpretations to fairly familiar (in the sense of extended meantone-like) intervals. Restricted to the 8-note MOS, it is essentially a non-over-1 temperament.
Melodically, sensi sounds fairly familiar because many intervals are either 5-limit or have familiar categorical interpretations, being represented in the meantone tuning 19edo. For example, the small step of about 130 cents categorizes pretty well as a large semitone (except at places in the scale where two of them make a flat subminor third); the large step is a small whole tone representing 10/9.
The root-sen5th-sen8th chords in sensi usually spell 5:7:9 (root-minor sen5th-minor sen8th) and 7:10:13 (root-major sen5th-major sen8th) chords (shown in the Anti-Dylathian mode QJKLMNOPQ = ssLssLsL):
- Q M P = ssLs sLs L ≈ 5:7:9
- J N Q = sLss LsL s is the odd one out
- K O J = LssL sLs s ≈ 7:10:13
- L P K = ssLs Lss L ≈ 5:7:9
- M Q L = sLsL ssL s ≈ 7:10:13
- N J M = LsLs sLs s ≈ 7:10:13
- O K N = sLss Lss L ≈ 5:7:9
- P L O = LssL ssL s ≈ 7:10:13
Other otonal chords approximated in the 8-note MOS include:
- root - maj. sen7th - maj. sen8th ≈ 7:12:13
- root - maj. sen2nd - maj. sen5th ≈ 9:10:13
- root - min. sen3rd - dim. sen6th ≈ 6:7:9
- root - perf. sen4th - dim. sen6th ≈ 10:13:15 (ultramajor triad)
- root - perf. sen4th - maj. sen7th ≈ 7:9:13
- root - perf. sen4th - maj. sen5th - maj. sen7th ≈ 7:9:10:13
- root - perf. sen4th - min. sen7th ≈ 10:13:18
- root - perf. sen4th - min. sen5th - min. sen7th ≈ 10:13:14:18
- root - min. sen7th - min. sen3rd (+ octave) ≈ 3:5:7
- root - min. sen7th - min. sen2nd (+ octave) ≈ 6:10:13
- root - dim. sen6th - min. sen7th ≈ 6:9:10
- root - dim. sen6th - min. sen2nd (+octave) ≈ 6:9:13
Steps of sensi
This diagram shows sensi, , , and  with intervals named in relation to the L and s of sensi.
Note that X, M and Z are not standard, but d and A are; they are short for "diminished" and "augmented".
Map of sensi
These diagrams relate the sensi generator chain (horizontal axis) to the steps within the octave (vertical axis) for sensi and .
- See also: Lumatone mapping for sensi
This diagram shows a layout for playing sensi temperament on an isomorphic keyboard.
The darkest hexagons represent the same note (eg. C), but offset by octaves. The next-darkest hexagons show the notes of Sensi. Imagine stepping from hex to hex as you move across the keyboard from left to right, landing only on the darkest and next-darkest hexes. The light red hexagons show additional notes needed to play Sensi. The Large step of Sensi is represented by a move straight down, so this pattern is a little more zig-zaggy than the pattern for Sensi. Add the white hexes and you have Sensi. The small step of Sensi (indicated in the diagram as "c" for chroma), is represented by a move straight down and down-left. This pattern actually involves moving backward in the horizontal direction, and is therefore more zig-zaggy.
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