365edo/Eliora's approach
Theory
As 365 is the number of days in the common year, and there is a way to implement such a fact into music. An octave stretch of -0.796 cents would compress 365edo to an interesting intepretation: the pure 2/1 would represent 365.24219edo, which is the length of solar days in a tropical year. In 23-limit, 365eeffgghiii val's octave stretch of -0.79428 cents is very close, and makes 2/1 correspond to 365.241917 days, or 365 days 5h 48m 21.7s, which is only about 20 seconds short of the tropical year in the present era.
This approach will cover what is essentially "tropical year"-EDO, that is 365.2422edo using the 365eeffgghiii val. Therefore, each step is equal to 3.2854936 cents, and there are common octaves consisting of 365 steps and leap octaves consisting of 366 steps.
In the 7-limit, the val is the same as patent val for 365edo, and hence it supports the hemiwürschmidt temperament just like the unstretched pure-octave 365edo does.
Mapping used
| 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | |
|---|---|---|---|---|---|---|---|---|---|
| Map | 365 | 579 | 848 | 1025 | 1264 | 1352 | 1493 | 1551 | 1653 |
| Reduced | 365 | 214 | 118 | 295 | 169 | 257 | 33 | 91 | 193 |
Table of intervals
| Step | Note name | Interval name | Associated Ratio
based on 365eeffgghiii |
|---|---|---|---|
| 0 | January 1 | Prime, unison | 1/1 |
| 32 | February 1 | Dodecaphonic semitone | |
| 33 | February 2 | Septendecimal semitone | 17/16 |
| 59 | February 28 | ||
| 59 II | February 29 | inserted once every 4 octaves | accumulating octave stretch |
| 60 | March 1 | Dodecaphonic major second | |
| 63 | March 4 | Classical major second, meantone | 9/8 |
| 91 | April 1 | Undevicesimal minor third, dodecaphonic minor third | 19/16 |
| 118 | April 28 | Classical major third | 5/4 |
| 169 | June 18 | Undecimal superfourth | 11/8 |
| 182 | July 1 | Dodecaphonic tritone | |
| 193 | July 12 | Vicesimotertial lalala | 23/16 |
| 214 | August 2 | Perfect fifth | 3/2 |
| 257 | September 14 | Tridecimal neutral sixth | 13/8 |
| 295 | October 22 | Harmonic seventh | 7/4 |
| 365 | January 1 | Octave | 2/1 |
Rank two temperaments by generator
| Generator
(reduced) |
Temperament | Calendar name |
|---|---|---|
| 181\365 | 121i & 365eeffgghiii | June 30 |
| 59\365 | 99ef & 365eeffgghiii | February 28 |
| 172\365 | 87 & 365eeffgghiii | June 21 |
| 107\365 | 58hi & 365eeffgghiii | April 17 |