User:FloraC/Fumica's edo impressions: Difference between revisions

== Exo ==

* 1 – An exposition of pitch.  

* 2 – An exposition of consonance and dissonance.  

== Medium ==

{| class="wikitable"

|+ Tier list for medium edos (39–79)

|-

! D-tier

|-

! F-tier

=== Comma-size ===

* 39 – 1/5-comma quasisuper, most notable for tuning the minor second to 28/27 (with the 39d val) which I feel is where the tension peaks for voice leading. Such an overlooked system despite being similar to 27edo in many ways. B-tier.  

* 41 – The first of the five essential comma-level edos, and the first edo to achieve 9-odd-limit distinction and consistency. This is most significant for providing three flavors for each chromatic category: classical, Pythagorean, and septimal. In this case it is a schismic and garischismic system, so that all three kinds are separated by the same comma step and can be found on a stack of fifths. The comma step is somewhat larger than just, making the differences more pronounced, which is part of why I think this edo is pretty deep – the step isn't only a comma, but many things at once, including but not limited to the septimal dieses, as well as the chroma of the archaeotonic scale, the scale of Tetracot[7]. The best subgroup of this edo is, actually, 2.3.5.7.11.19. Prime 13 is certainly plausible, but prime 19 fits way better. There's a unique uniform tuning for the harmonic segment 18::22, a fact related to the vanish of s10 = 100/99 and s9/s11 = 243/242. The beauty of this edo goes even beyond the structure, but also to the intonation: it has a very slightly sharp 3 and a more noticeably flat 5, making a flat, more stable 15; that is ideal for my music. Finally, it's an ideal tuning for the magic temperament. I can't compliment it enough. S-tier.  

* 58 – The fourth essential comma-level edo. Being the first edo with full 11-odd-limit distinction, this one is easily adorable. Whereas 41edo tunes the fifth to 24 steps, this edo tunes the fourth to 24 steps, and the implication is its 2.3.5.7.13.29 subgroup is analogous to 41edo's 2.3.5.7.11.19 subgroup. This edo is best as a 2.3.5.7.11.13.29-subgroup system, but it has more to offer. Specifically, the harmonics 19 and 23 in the 58hi val are surprisingly convincing, and although the 17 doesn't blend quite well it at least looks good on paper. Everything considered, it is virtually the first full 23-limit system. All that bugs me is the minor fact that 11/8 and 7/5 are tuned only one comma apart. A-tier.  

* 60 – This edo has a particularly problematic fifth, in that it closes after twelve steps, tempering out the Pythagorean comma. As the first thing I leave meantone is to look for a fifth that leads to a positive Pythagorean comma, this edo is clearly not my thing. C-tier.  

* 62 – The ultimate 23-limit meantone tuning. It re-tunes harmonics 13, 17, 19, and 23 for 31edo. I find these additions to 31edo's 11-limit very favorable. A-tier.

* 63 – Similar to 56edo, nothing notable about it. D-tier.  

* 65 – As every other step of 130edo, this edo is excellent in the 2.3.5.11.19.23-subgroup, but the contrast between that and the poor approximations to 7 and 13 is fatal. Still, it allows a dual-7 dual-13 approach, not very satisfying at this level but better than nothing. C-tier.  

* 67 – A disastrous meantone tuning. F-tier.  

* 68 – While this edo contains 17edo and if we compare it with 51edo, it clearly hits more harmonic targets, it should be noted that linearly dividing the steps into four is a weaker move than into two or three, as quarter-step offsets don't tend to create new categories, unlike third- or half-step offsets. This is especially true of this edo, as 34edo hits lots of harmonic targets already. Another obvious flaw is the awkward situation with prime 11. C-tier.  

* 70 – As every other step of 140edo, this edo's structure allows lots of niche uses. Unfortunately none of them is interesting enough to make me stay very long. C-tier.  

* 73 – A strange sharp-tending hemicommatic system that seems to allow some niche uses. C-tier.  

* 74 – A good meantone tuning. Not much else to offer. D-tier.

* 77 – This edo is very sophisticated and hard to evaluate. It's an ideal tuning for the valentine temperament, obviously. It also seems to be capable of somewhat approximating the full 23-limit. Overall, the structure is a tight fit, with lots of quirks, but that's not too troublesome – they may as well be turned into advantages in the right circumstances. B-tier.  

* 79 – A disastrous non-meantone tuning. F-tier.

== Hemicomma-size ==