205edo

205EDO divides the octave into 205 parts of 5.854 cents each. It can serve as a tuning for various temperaments, such as amity or laka, and supplies the optimal patent val for quanic in the 7-, 11-, 13-, 17- and 19-limits, and for 13-limit amity, as well as other temperaments tempering out the huntma, 640/637, the rank five temperament for which it also supplies the optimal patent val. In the 5-limit it tempers out 1600000/1594323, the amity comma, and |38 -2 -15>, the hemithirds comma, and is an excellent tuning for 5-limit amity. The patent val tempers out 4375/4374, 5120/5103, 6144/6125 and 540/539. Using its alternative mapping <205 325 476 525| it can also be used for hemithirds temperament; the 13-limit version of this, <205 325 476 575 709 759|, is especially noteworthy. It factors into primes as 5 \* 41, a fact some advocates of the division make use of; it is also 2460/12, so that a single step is precisely 12 minas.

205et tempers out 540/539, so that it allows swetismic chords; 640/637, so that it allows huntmic chords; 352/351, so that it allows minthmic chords; 1188/1183 and 540/539, so that it allows kestrel chords; and 847/845, so that it allows the cuthbert triad. This makes it a tuning of exceptional fludity for its degree of accuracy.

# Temperament generators and Tonal Plexus

205edo is the default tuning for the Tonal Plexus midi controller. See the theory part on the same website. Aside from the 24\205 generator of quanic, the 58\205 generator of amity, and the 33\205 generator of hemithirds, 205edo supplies an excellent meantone fifth in 119\205, an excellent myna generator in 53\205, and a very good porcupine generator with 28\205, which is also an excellent generator for the higher-limit extension porky, and when sliced in half to 14\205, can even be used for nautilus. These facts are all potentially of significance to anyone using a 205edo based system such as the Tonal Plexus.

The 119\205 meantone fifth is extremely close to the 1/4-comma fifth, being only 0.007 cents sharp of it. Moreover the steps are half a cent flat of 1/4 of a syntonic comma. This makes the Tonal Plexus keyboard potentially of use in implementing Nicola Vicentino's adaptive-JI scheme of 1555. It also means that authentic 1/4-comma meantone tuning is, for practical purposes, available in 205 and allows for historically authentic performances of 1/4-comma music on the historically newfangled Tonal Plexus.

# 205edo MOS

## Quanic (24\205) MOS

### 17 note

11 13 11 13 11 13 11 13 11 13 11 13 11 13 11 13 13

### 26 note

11 11 2 11 11 2 11 11 2 11 11 2 11 11 2 11 11 2 11 11 2 11 11 2 11 2

## Amity (58\205) MOS

### 18 note

23 4 23 4 4 23 4 23 4 4 23 4 23 4 4 23 4 4

### 25 note

19 4 4 19 4 4 4 19 4 4 19 4 4 4 19 4 4 19 4 4 4 19 4 4 4

## Hemithirds (33\205) MOS

### 19 note

19 7 7 19 7 7 19 7 7 19 7 7 19 7 7 19 7 7 7

### 25 note

12 7 7 7 12 7 7 7 12 7 7 7 12 7 7 7 12 7 7 7 12 7 7 7 7

### 31 notes

5 7 7 7 7 5 7 7 7 7 5 7 7 7 7 5 7 7 7 7 5 7 7 7 7 5 7 7 7 7 7

## Meantone (119\205) MOS

### 19 note

13 13 7 13 13 7 13 13 7 13 7 13 13 7 13 13 7 13 7

### 31 notes

6 7 6 7 7 6 7 6 7 7 6 7 6 7 7 6 7 7 6 7 6 7 7 6 7 6 7 7 6 7 7

## Myna (53\205) MOS

### 19 note

7 7 7 7 25 7 7 7 7 25 7 7 7 7 25 7 7 7 25

### 23 note

7 7 7 7 7 18 7 7 7 7 7 18 7 7 7 7 7 18 7 7 7 7 18

### 27 note

7 7 7 7 7 7 11 7 7 7 7 7 7 11 7 7 7 7 7 7 11 7 7 7 7 7 11

### 31 notes

7 7 7 7 7 7 7 4 7 7 7 7 7 7 7 4 7 7 7 7 7 7 7 4 7 7 7 7 7 7 4

## Porcupine (28\205) MOS

### 22 note

10 9 9 10 9 9 10 9 9 10 9 9 10 9 9 10 9 9 10 9 9 9

### 29 note

1 9 9 9 1 9 9 9 1 9 9 9 1 9 9 9 1 9 9 9 1 9 9 9 1 9 9 9 9