User:Godtone: Difference between revisions

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* 58: Weirdly consistent tuning with a nice selection of colours. Record in [[Pepper ambiguity]] in the 13- and 15-odd-limit. The first EDO to be consistent in the 17-odd-limit. I haven't looked at this EDO very closely but suspect it may have some surprisingly accurate/good approximations hiding under its slightly meh prime error profile.

* 68: Superset of 34 that enables the 7-prime-limit. Not too remarkable for that reason alone, however my interest in this EDO was increased when I deduced that it has a step size that is close to half the size of 49/48 meaning a 7/6, an 8/7 and a semifourth can all be distinguished with accuracy. For that reason, this EDO is important as an EDO around which other EDOs have the potential for a good selection of colours which approximate these 3 intervals of interest.

* 72: [[~~385/384~~|~~Keenanismic~~]] [[~~Hemiennealimmal~~]], and thus a very nice (and ~~very accurate~~) [[11-limit]] temperament with the added convenience of being a superset of 12 EDO and a very composite EDO. The first true EDO to represent [[~~Ennealimmal~~]], and better yet, it extends it into the 11-limit well. Note ~~I linked the page for~~ 385/384, the keenanisma, ~~which is a comma it tempers~~, ~~as that page~~ has ~~lots of useful info on~~ why it is an interesting comma~~. 72 EDO has perhaps justified hate due~~ to ~~it strengthening "12 EDO centrism" but it is not to be underestimated~~.

* 72: ([[catakleismic]]) [[miracle]] [[Ragismic_microtemperaments#Octoid|octoid]] [[hemiennealimmal]] temperament, and thus a very nice [[11-limit]] (and to a lesser extent (due to inaccuracy) [[13-limit]]) temperament with the added convenience of being a superset of 12 EDO and a very composite EDO. The first true EDO to represent [[ennealimmal]], and better yet, it extends it into the 11-limit well. Note it can also be described as [[385/384|keenanismic]] hemiennealimmal, and the page for the keenanisma, [[385/384]], has some explanation for why this is a theoretically interesting comma for extending the [[7-limit]] to the [[11-limit]].

* 80: My favourite EDO. In the past, my favourite was 53 EDO. 80 EDO may be a surprising choice for favourite at first but there are a lot of reasons feeding into it which also make it unlikely to become my second favourite any time soon. I will write in depth about it and about my theories for microtonal music based on 80 EDO in the future. Tunes [[Tolermic family|17-limit Tolermic]], a strange temperament which tempers many commas I'm interested in tempering.

* 87: A good approximation of the 13-limit, with the 5-limit also good, and an alternative Tolermic tuning, so it's closely related to 80 EDO but with better fifths and harmonic sevenths. Compared to 80 EDO, 7/4 is still the worst prime but lower in both absolute and relative error, and it is tuned flatly instead of sharply. The final and most colourful EDO, but 80 EDO is more than enough colours for me. Has an interesting conceptualisation as 29 EDO representing an approximate 2.3 subgroup with 5, 7, 11 and 13 all being 1\87 flat of the 29 EDO circle, providing an elegant model of navigation. 29 EDO is itself not bad as something that sounds like a brighter 12 EDO, but it feels more elegantly and interestingly conceptualised in this superset.

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 * 58: Weirdly consistent tuning with a nice selection of colours. Record in [[Pepper ambiguity]] in the 13- and 15-odd-limit. The first EDO to be consistent in the 17-odd-limit. I haven't looked at this EDO very closely but suspect it may have some surprisingly accurate/good approximations hiding under its slightly meh prime error profile.
 * 68: Superset of 34 that enables the 7-prime-limit. Not too remarkable for that reason alone, however my interest in this EDO was increased when I deduced that it has a step size that is close to half the size of 49/48 meaning a 7/6, an 8/7 and a semifourth can all be distinguished with accuracy. For that reason, this EDO is important as an EDO around which other EDOs have the potential for a good selection of colours which approximate these 3 intervals of interest.
-* 72: [[385/384|Keenanismic]] [[Hemiennealimmal]], and thus a very nice (and very accurate) [[11-limit]] temperament with the added convenience of being a superset of 12 EDO and a very composite EDO. The first true EDO to represent [[Ennealimmal]], and better yet, it extends it into the 11-limit well. Note I linked the page for 385/384, the keenanisma, which is a comma it tempers, as that page has lots of useful info on why it is an interesting comma. 72 EDO has perhaps justified hate due to it strengthening "12 EDO centrism" but it is not to be underestimated.
+* 72: ([[catakleismic]]) [[miracle]] [[Ragismic_microtemperaments#Octoid|octoid]] [[hemiennealimmal]] temperament, and thus a very nice [[11-limit]] (and to a lesser extent (due to inaccuracy) [[13-limit]]) temperament with the added convenience of being a superset of 12 EDO and a very composite EDO. The first true EDO to represent [[ennealimmal]], and better yet, it extends it into the 11-limit well. Note it can also be described as [[385/384|keenanismic]] hemiennealimmal, and the page for the keenanisma, [[385/384]], has some explanation for why this is a theoretically interesting comma for extending the [[7-limit]] to the [[11-limit]].
 * 80: My favourite EDO. In the past, my favourite was 53 EDO. 80 EDO may be a surprising choice for favourite at first but there are a lot of reasons feeding into it which also make it unlikely to become my second favourite any time soon. I will write in depth about it and about my theories for microtonal music based on 80 EDO in the future. Tunes [[Tolermic family|17-limit Tolermic]], a strange temperament which tempers many commas I'm interested in tempering.
 * 87: A good approximation of the 13-limit, with the 5-limit also good, and an alternative Tolermic tuning, so it's closely related to 80 EDO but with better fifths and harmonic sevenths. Compared to 80 EDO, 7/4 is still the worst prime but lower in both absolute and relative error, and it is tuned flatly instead of sharply. The final and most colourful EDO, but 80 EDO is more than enough colours for me. Has an interesting conceptualisation as 29 EDO representing an approximate 2.3 subgroup with 5, 7, 11 and 13 all being 1\87 flat of the 29 EDO circle, providing an elegant model of navigation. 29 EDO is itself not bad as something that sounds like a brighter 12 EDO, but it feels more elegantly and interestingly conceptualised in this superset.