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

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== Diesis-size ==

* 27 – The cyberpunk edo. Good sharp-tending tuning profile in the 2.3.5.7.13 subgroup with the sole exception of ~~the~~ harmonic 15, which is way too sharp ~~for my taste.~~ I prefer a flat tuning of 15 or at least no sharper than 12edo's, so as to improve its stability as a consonant major seventh. Other than that it is pretty good. B-tier.

* 27 – The cyberpunk edo. Good sharp-tending tuning profile in the 2.3.5.7.13 subgroup with the sole exception of harmonic 15, which is way too sharp, as I prefer a flat tuning of 15 or at least no sharper than 12edo's, so as to improve its stability as a consonant major seventh. Other than that it is pretty good. B-tier.

* 28 – Potentially useful as every other step of 56edo. D-tier.

* 29 – The first edo that sounds like Pythagorean tuning with distinct chromatic and diatonic semitones, by which I mean most contemporary 12edo music will sound alright if retempered to this through dominant. The patent-val interpretation is pretty underwhelming. Otherwise it's a good framework as every other step of 58edo and every third step of 87edo. C-tier.

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== Comma-size ==

~~Starting~~ from here, all edos have at least one diatonic scale (35edo being the last nondiatonic edo). I'm only listing those which have a good fifth (relative error < 1/3). For the rest, expect

The sense of uniqueness of each edo begins to diminish in this range. As the steps get smaller, more and more intervals start to be reasonably approximated, and the edos feel more and more like free pitch. For one thing, starting from here, all edos have at least one diatonic scale (35edo being the last nondiatonic edo). For this reason I'm only listing those which have a good fifth (relative error < 1/3). For the rest, expect

* ''n''-edo – Potentially useful as every other step of 2''n''-edo. D-tier.

: ''n''-edo – Potentially useful as every other step of 2''n''-edo. D-tier.

* 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.

* 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.

…

@@ Line 32: / Line 32: @@
 == Diesis-size ==
-* 27 – The cyberpunk edo. Good sharp-tending tuning profile in the 2.3.5.7.13 subgroup with the sole exception of the harmonic 15, which is way too sharp for my taste. I prefer a flat tuning of 15 or at least no sharper than 12edo's, so as to improve its stability as a consonant major seventh. Other than that it is pretty good. B-tier.
+* 27 – The cyberpunk edo. Good sharp-tending tuning profile in the 2.3.5.7.13 subgroup with the sole exception of harmonic 15, which is way too sharp, as I prefer a flat tuning of 15 or at least no sharper than 12edo's, so as to improve its stability as a consonant major seventh. Other than that it is pretty good. B-tier.
 * 28 – Potentially useful as every other step of 56edo. D-tier.
 * 29 – The first edo that sounds like Pythagorean tuning with distinct chromatic and diatonic semitones, by which I mean most contemporary 12edo music will sound alright if retempered to this through dominant. The patent-val interpretation is pretty underwhelming. Otherwise it's a good framework as every other step of 58edo and every third step of 87edo. C-tier.
@@ Line 46: / Line 46: @@
 == Comma-size ==
-Starting from here, all edos have at least one diatonic scale (35edo being the last nondiatonic edo). I'm only listing those which have a good fifth (relative error < 1/3). For the rest, expect
+The sense of uniqueness of each edo begins to diminish in this range. As the steps get smaller, more and more intervals start to be reasonably approximated, and the edos feel more and more like free pitch. For one thing, starting from here, all edos have at least one diatonic scale (35edo being the last nondiatonic edo). For this reason I'm only listing those which have a good fifth (relative error < 1/3). For the rest, expect
-* ''n''-edo – Potentially useful as every other step of 2''n''-edo. D-tier.
+: ''n''-edo – Potentially useful as every other step of 2''n''-edo. D-tier.
+* 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.
+* 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.
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