365edo/Eliora's approach
Main article: 365edo
365 is the number of days in the common year, and as such this proposes some interesting intereprations.
This approach will cover what is essentially "tropical year"-EDO, that is 365.2422edo using the 365eeffgghiii val.
Mapping:
| 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 |
Theory
365eeffgghiii val shares rank two temperaments with the following vals: 121i, 99ef, 68e, 27egi, 41i, 46p, 58hi, 87, 50, 94.
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 |