EDe: Difference between revisions
equivalences |
|||
| Line 1: | Line 1: | ||
Equal divisions of the [[natave]], which is the mathematical constant e used as a musical interval. e is of particular interest because of its relationship with logarithms, the fact that pitch is perceived logarithmically, and the fact that equal divisions are logarithmic. | Equal divisions of the [[natave]], which is the mathematical constant e used as a musical interval. e is of particular interest because of its relationship with logarithms, the fact that pitch is perceived logarithmically, and the fact that equal divisions are logarithmic. | ||
== 10-EDN == | == Correspondence of EDN to EDO == | ||
{| class="wikitable" | |||
|+ | |||
!Tuning | |||
!Equivalent edo | |||
!Comment | |||
|- | |||
|2edn | |||
| | |||
|A stack of two major sixths | |||
|- | |||
|3edn | |||
|[[2edo]] | |||
| | |||
|- | |||
|4edn | |||
| | |||
| rowspan="2" |Neither are equivalent with [[3edo]] | |||
|- | |||
|5edn | |||
| | |||
|- | |||
|6edn | |||
|[[4edo]] | |||
|With a stretch | |||
|- | |||
|7edn | |||
|[[5edo]] | |||
| | |||
|- | |||
|8edn | |||
| | |||
|Entirely misses 2/1, falling halfway between 5edo and 6edo | |||
|- | |||
|9edn | |||
|[[6edo]] | |||
|With a considerable stretch | |||
|- | |||
|10edn | |||
|[[7edo]] | |||
| | |||
|- | |||
|11edn | |||
| | |||
| rowspan="2" |Neither are equivalent to 8edo | |||
|- | |||
|12edn | |||
| | |||
|- | |||
|13edn | |||
|[[9edo]] | |||
| | |||
|- | |||
|14edn | |||
| | |||
| rowspan="2" |Neither are equivalent to 10edo | |||
|- | |||
|15edn | |||
| | |||
|- | |||
|16edn | |||
|[[11edo]] | |||
| | |||
|- | |||
|17edn | |||
|[[12edo]] | |||
|With a noticeable stretch, given the dominance of 12edo this is more likely to sound like like out of tune 12edo than it's own tuning | |||
|- | |||
|18edn | |||
| | |||
|Entirely misses 2/1, falling halfway between 12 and 13edo | |||
|- | |||
|19edn | |||
|[[13edo]] | |||
|Noticeably compressed | |||
|- | |||
|20edn | |||
|[[14edo]] | |||
|Noticeably stretched | |||
|- | |||
|21edn | |||
| | |||
|Entirely misses 2/1, falling halfway between 14edo and 15edo | |||
|- | |||
|22edn | |||
| | |||
|Cannot be considered equivalent to [[15edo]] | |||
|- | |||
|23edn | |||
|[[16edo]] | |||
| | |||
|- | |||
|24edn | |||
|[[17edo]] | |||
|Some equivalences can be spotted due to 17edo's fame but it's a heavy stretch amounting to 40% | |||
|} | |||
== Selected divisions == | |||
=== 10-EDN === | |||
{| class="wikitable" | {| class="wikitable" | ||
|+Intervals of 10-EDN | |+Intervals of 10-EDN | ||
| Line 82: | Line 181: | ||
20-EDN is a doubling of 10-EDN with intervals closer to semitones. | 20-EDN is a doubling of 10-EDN with intervals closer to semitones. | ||
== 17-EDN == | === 17-EDN === | ||
17-EDN is very close to 12-EDO but with slightly sharp semitones (101.84 cents). This causes the octave to be far too sharp (1222.05 cents; essentially double a Pythagorean large tritone) and gives it a rather pleasant sharp fifth of 712.86 cents. | 17-EDN is very close to 12-EDO but with slightly sharp semitones (101.84 cents). This causes the octave to be far too sharp (1222.05 cents; essentially double a Pythagorean large tritone) and gives it a rather pleasant sharp fifth of 712.86 cents. | ||
== 24-EDN == | === 24-EDN === | ||
24-EDN has third tones so far sharp of 17-EDO that it becomes a stretched 50-ED8 (50\24 is 2406.74 cents). However, 43\24 is essentially the 6th harmonic (1514.83+1586.965=3101.79 cents).. | 24-EDN has third tones so far sharp of 17-EDO that it becomes a stretched 50-ED8 (50\24 is 2406.74 cents). However, 43\24 is essentially the 6th harmonic (1514.83+1586.965=3101.79 cents).. | ||