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

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* 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.

* 43 – 1/5-comma meantone, basically the optimal meantone tuning in the 5-limit. The 3 and 5 are equally off, making up a beautifully pure 15. Unfortunately the diesis is too small to achieve good septimal and undecimal harmony. B-tier.

* 44 – This edo adds decent approximation to harmonic 13 on top of 22edo's 11-limit, which is pretty tense to start with. At this point it just all breaks down. D-tier.

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* 45 – The only legit edo tuning for flattone. Otherwise it has little utility. It has this weird structure of 9/8~10/9~11/10 all tempered together as a characteristic of flattone, but meanwhile the septimal comma is tuned to two steps, which feels a bit ugly. D-tier.

* 46 – The second essential comma-level edo. Five more notes than 41edo, offering the distinction of two types of neutral intervals at the cost of a narrower septimal diesis. As an eighth-tone system, it has a true quartertone. With that and all the accurate approximations, the expressive possibilities are endless. Best as a 2.3.5.7.11.17.23-subgroup temperament. A-tier.

* 46 – The second essential comma-level edo. Five more notes than 41edo, offering the distinction of two types of neutral intervals at the cost of a narrower septimal diesis. As an eighth-tone system, it has a true quartertone. With that and all the accurate approximations, the expressive possibilities are endless. Best as a 2.3.5.7.11.17.23 subgroup temperament. A-tier.

* 48 – More appropriate as an interval category scheme than anything else. C-tier.

* 50 – Close to 2/7-comma meantone so it has a niche. Has the same problem as 45edo, though less severe. C-tier.

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 * 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.
 * 43 – 1/5-comma meantone, basically the optimal meantone tuning in the 5-limit. The 3 and 5 are equally off, making up a beautifully pure 15. Unfortunately the diesis is too small to achieve good septimal and undecimal harmony. B-tier.
+* 44 – This edo adds decent approximation to harmonic 13 on top of 22edo's 11-limit, which is pretty tense to start with. At this point it just all breaks down. D-tier.
-…
+* 45 – The only legit edo tuning for flattone. Otherwise it has little utility. It has this weird structure of 9/8~10/9~11/10 all tempered together as a characteristic of flattone, but meanwhile the septimal comma is tuned to two steps, which feels a bit ugly. D-tier.
+* 46 – The second essential comma-level edo. Five more notes than 41edo, offering the distinction of two types of neutral intervals at the cost of a narrower septimal diesis. As an eighth-tone system, it has a true quartertone. With that and all the accurate approximations, the expressive possibilities are endless. Best as a 2.3.5.7.11.17.23-subgroup temperament. A-tier.
-* 46 – The second essential comma-level edo. Five more notes than 41edo, offering the distinction of two types of neutral intervals at the cost of a narrower septimal diesis. As an eighth-tone system, it has a true quartertone. With that and all the accurate approximations, the expressive possibilities are endless. Best as a 2.3.5.7.11.17.23 subgroup temperament. A-tier.
 * 48 – More appropriate as an interval category scheme than anything else. C-tier.
+* 50 – Close to 2/7-comma meantone so it has a niche. Has the same problem as 45edo, though less severe. C-tier.
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