Sensi

Sensi is a regular temperament for the 2.3.5.7.13 subgroup. EDOs that support sensi include 19edo, 27edo, and 46edo.

See Sensipent family #Sensi for more information.

Interval chain

Generators	Cents*	Approximate ratios†
0	0.000	1/1
1	443.322	13/10~9/7
2	886.644	42/25~5/3
3	129.966	13/12~14/13~15/14
4	573.288	7/5~25/18~18/13
5	1016.610	9/5~70/39
6	259.932	7/6~15/13
7	703.253	3/2
8	1146.576	35/18~27/14
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

Harmony in sensi

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.

Sensi[8] sounds fairly familiar because many intervals are either 5-limit or have familiar categorical interpretations. For example, the small step of about 130 cents categorizes pretty well as a large semitone; the large step is a small whole tone representing 10/9. It's abundant in diminished triads and has a dramatic, restless flair because its consonant chords lack the root or fundamental. Sensi is interesting mainly because it gives new 13-limit interpretations to fairly familiar intervals.

Sensi 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