Sensi

Sensi is a regular temperament for the 2.3.5.7.13 subgroup 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, 27edo, and 46edo.

In the language of regular temperaments, it is the rank-2 temperament defined by tempering out the zozoyo (245/243), zotrigu (126/125), and thozogu (91/90) commas.

See Sensipent family #Sensi or Starling temperaments #Sensi for more technical data. For full 13-limit extensions of sensi, see Sensi extensions.

Interval chain

In the following table, odd harmonics are in bold.

Generators	Cents*	Approximate ratios†
0	0.000	1/1
1	443.322	9/7, 13/10
2	886.644	5/3, 42/25
3	129.966	13/12, 14/13, 15/14, 27/25
4	573.288	7/5, 18/13, 25/18
5	1016.610	9/5, 70/39
6	259.932	7/6, 15/13
7	703.253	3/2
8	1146.576	27/14, 35/18
9	389.896	5/4
10	833.220	13/8, 21/13
11	76.542	21/20, 25/24
12	519.864	27/20
13	963.185	7/4
14	206.507	9/8
15	649.829	35/24 (close to 16/11)
16	1093.151	15/8
17	336.473	39/32 (close to 17/14)
18	779.795	25/16
19	23.117	49/48, 65/64, 81/80
20	466.439	21/16

^* in 2.3.5.7.13 POTE tuning

^† 2.3.5.7.13 ratio interpretations

Chords

Main article: Chords of sensus

The most common consonant triad in sensi is the 6:10:13 triad, which spans 3 generators. Sensi[8] 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 and consonant chords without roots (fundamentals), 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[8] 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-mos5th-mos8th chords in sensi[8] usually spell 5:7:9 and 7:10:13 chords (shown in the Anti-Dylathian mode QJKLMNOPQ = ssLssLsL):

• Q M P = ssLs sLs L = 5:7:9
• J N Q = sLss LsL s = 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

Visualizations

A Diagram of Sensi[5], [8], [11], and [19] with intervals named in relation to the L and s of Sensi[8]:

Note that X, M and Z are not standard, but d and A are; they are short for "diminished" and "augmented".

A Diagram relating the Sensi generator chain (horizontal axis) to the steps within the octave (vertical axis) for Sensi[8] and [11]:

A Diagram showing 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[5]. 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[8]. The Large step of Sensi[8] is represented by a move straight down, so this pattern is a little more zig-zaggy than the pattern for Sensi[5]. Add the white hexes and you have Sensi[11]. The small step of Sensi[11] (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.

A Sensi[19] Guitar (one octave):

SOMEONE PLEASE MAKE ONE OF THESE AND SEND IT TO DUSTIN SCHALLERT!

Music

• Technical Notes for Newbeams #Tumbledown Stew by Andrew Heathwaite
• Technical Notes for Newbeams #Hypnocloudsmack 3 by Andrew Heathwaite