205edo: Difference between revisions

205EDO divides the octave into 205 parts of 5.854 cents each. It can serve as a tuning for various temperaments, such as [[Ragismic_microtemperaments|amity]] or [[Hemifamity_family|laka]], and supplies the optimal patent val for [[Hemifamity_temperaments#Quanic|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 [[Gamelismic_clan|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 [[mina|minas]].

205et tempers out 540/539, so that it allows [[swetismic_chords|swetismic chords]]; 640/637, so that it allows [[huntmic_chords|huntmic chords]]; 352/351, so that it allows [[minthmic_chords|minthmic chords]]; 1188/1183 and 540/539, so that it allows [[kestrel_chords|kestrel chords]]; and 847/845, so that it allows the [[cuthbert_triad|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 [http://hpi.zentral.zone/tonalplexus Tonal Plexus midi controller]. See the [http://musictheory.zentral.zone/huntsystem1.html 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|meantone]] fifth in 119\205, an excellent [[Myna|myna]] generator in 53\205, and a very good [[Porcupine|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 [http://en.wikipedia.org/wiki/Nicola_Vicentino Nicola Vicentino]'s [http://www.tonalsoft.com/monzo/vicentino/vicentino.aspx 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=

 

===17 note===

===26 note===

==Amity (58\205) MOS==

===11 note===

===18 note===

===25 note===

==Hemithirds (33\205) MOS==

===13 note===

===19 note===

===25 note===

===31 notes===

==Meantone (119\205) MOS==

===12 note===

===19 note===

===31 notes===

==Myna (53\205) MOS==

===11 note===

===15 note===

===19 note===

===23 note===

===27 note===

===31 notes===

==Porcupine (28\205) MOS==

===15 note===

===22 note===

===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

[[Category:amity]]

[[Category:hemithirds]]

[[Category:laka]]

[[Category:quanic]]