User:Overthink/EDO impressions
This is a page about my thoughts on various EDOs.
Ideas
In my opinion, an interval is melodically represented well if it is within ~15 cents, but harmonically represented decently only if within ~5-6 cents, the more accurate the better. It is absolutely essential for any system to approximate the perfect fifth within this 5-6 cent bound.
EDO Impressions
Note: They are by no means final!
EDOs I should try: 27, 31, 34, 43, 46, 50, 55?, 56?, 58, 62?, 72, 84, 87?, 94, 111
12: We've all heard this system thousands of times before. It has a good perfect fifth, which is essential. In my opinion, this system sounds much more like pythagorean tuning than 5-limit, though the slight tempering of the fifth reduces the dissonance of the thirds by pushing them towards the 5-limit ones, but they still hardly show 5-limit flavor. If you want true 5-limit use 53edo (or possibly a more tempered meantone system) instead. Still, the expressive possibilities are vast, though that doesn't mean you shouldn't use other systems.
17: The diatonic scale has a septimal flavor to it, with major thirds sounding nothing like 12edo ones. The minor second is the perfect size melodically, though it may take a while to get used to it. Haven't really experimented with harmony in this system.
19: Due to the flat tendency of the system, melody seems to have a melancholy feeling that you can't replicate with 12edo. Unfortunately, this includes the perfect fifth, which I feel is too off, though it may be mitigated by octave stretch. Another issue is that the minor seconds are too wide melodically.
22: The diatonic scale sounds even brighter than in 17, with thirds and sixths having a more obvious septimal flavor. The diatonic semitone is a little smaller than ideal, but still usable. I haven't looked too much into it harmonically. A possibly interesting property is that it supports pajara. The fifth is not very good though, though a compressed octave may help.
31: Haven't really tried. Seems like a good 5- and 7-limit meantone tuning, with possible 11-limit as well. The fifth sounds just close enough to be usable, but noticeably off. A little octave stretch may help here as well.
41: While this EDO has be cited as good for approximating JI, it has quite a few problems. For example, 5/4 is quite flat, making 5-limit chords sound out-of-tune, which isn't good for an EDO this size. 7/4 is also a bit flat, making septimal intervals sound more ambiguous and less concordant. Octave stretch might help, but that worsens intervals like 6/5, 9/5, 8/7, and 12/7, as well as 3/2, so it doesn't feel like a solution. In general pental and septimal intervals are too far from their nearest pythagorean intervals, as the comma step is over 29 cents. It's better to use 53edo instead.
53: Excellent 5- and 7-limit harmonies. 5/4 is now only slightly flat, compared to nearly 6 cents in 41edo. The 7/4 is a bit sharp, but this makes septimal harmonies more concordant compared to 41. The 49/48 interval is also more noticeable at 45 cents, compared to 29 cents in 41edo. Chords are significantly more consonant than in 41. Definitely would recommend.
72: Haven't really tried. This edo seems to approximate the 11-limit well. The 7th harmonic is a little flat like in 41edo, though due to the slightly flat fifth 7/6 and 9/7 may be a bit more concordant than in 41.