Sensi

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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 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 13/12~14/13~15/14~27/25
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

Introduction

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.

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.

Sensi Visualizations

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

steps_of_sensi.png

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]:

map_of_sensi[8].pngmap_of_sensi[11]_correction2.png

A Diagram showing a layout for playing Sensi Temperament on an Isomorphic Keyboard:

sensi_isomorphic_layout.png

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):

sensi[19]in46.jpg

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

Music