13edo: Difference between revisions
m →Theory: Piloting a table that uses odd harmonics instead of prime harmonics. there's little reason to have fifth span since 13edo is non-diatonic |
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[[:File:13ed2-001.svg|13ed2-001.svg]] | [[:File:13ed2-001.svg|13ed2-001.svg]] | ||
===Differences between distributionally-even scales and smaller edos=== | |||
{| class="wikitable" | |||
|+ | |||
!N | |||
! L-Nedo | |||
!s-Nedo | |||
|- | |||
|2 | |||
|46.154¢ | |||
| -46.154¢ | |||
|- | |||
|3 | |||
|61.5385¢ | |||
| -30.769¢ | |||
|- | |||
|4 | |||
| 69.231¢ | |||
| -23.077¢ | |||
|- | |||
|5 | |||
|36.923¢ | |||
| -65.615¢ | |||
|- | |||
|6 | |||
| 76.923¢ | |||
| -23.077¢ | |||
|- | |||
|7 | |||
|13.187¢ | |||
| -79.121¢ | |||
|- | |||
|8 | |||
|34.615¢ | |||
| -57.385¢ | |||
|- | |||
|9 | |||
| 51.282¢ | |||
| -41.026¢ | |||
|- | |||
|10 | |||
|64.615¢ | |||
| -27.385¢ | |||
|- | |||
|11 | |||
|75.5245¢ | |||
| -16.783¢ | |||
|- | |||
|12 | |||
|84.615¢ | |||
| -7.385¢ | |||
|} | |||
== Tuning by ear == | == Tuning by ear == | ||
13-EDO can be approximated by a circle of [[64/49]] subminor fourths (which can be tuned by tuning two [[7/4]] subminor sevenths). A stack of 13 of these subfourths closes with an error of +10.526432c, or +11% of 13-EDO's step size. | 13-EDO can be approximated by a circle of [[64/49]] subminor fourths (which can be tuned by tuning two [[7/4]] subminor sevenths). A stack of 13 of these subfourths closes with an error of +10.526432c, or +11% of 13-EDO's step size. | ||
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== Mapping to Standard Keyboards == | == Mapping to Standard Keyboards == | ||
The 5L+3s scale (Oneirotonic) can be mapped to the standard keyboard effectively, although somewhat awkwardly. Consider the sequence of 730-cent intervals that it derives from: 1 6 11 3 8 (13) 5 10 2 7 12 4 9 1/1. One of these must be absent, so it might as well be the last. So, there are at most five of the full octatonic scales on different keys. Of the four mappings that keep the major pentatonic on the white keys, which ironically look like ordinary minor-pentatonics, the latter which begins on B might be the most straightforward to learn and use. | The 5L+3s scale (Oneirotonic) can be mapped to the standard keyboard effectively, although somewhat awkwardly. Consider the sequence of 730-cent intervals that it derives from: 1 6 11 3 [[Tel:8 (13) 5 10 2 7 12 4 9 1|8 (13) 5 10 2 7 12 4 9 1]]/1. One of these must be absent, so it might as well be the last. So, there are at most five of the full octatonic scales on different keys. Of the four mappings that keep the major pentatonic on the white keys, which ironically look like ordinary minor-pentatonics, the latter which begins on B might be the most straightforward to learn and use. | ||
{| class="wikitable" | {| class="wikitable" | ||