User:Godtone: Difference between revisions

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* 37: Truly an excellent no-3's [[13-limit]] system. Ridiculously overlooked just because of its not so great approximation of prime 3 (which is at least [[5L 2s|diatonic]] and sounds convincing enough especially in context). A logical system for building on it is [[111edo]] which keeps this 13-limit mapping (but improves the 3).

* 50: The last meantone EDO that should ever be considered because it is the last EDO to consistently map 9/8 and 10/9 to the same step and because 81/80 is a rather large comma to temper at this scale and thus costs you a lot of accuracy. It is surprisingly consistent in the higher limits, and that it is quite composite is appealing to me, especially given that it is a superset of 10 EDO.

* 53: [[Kleismic family#Catakleismic|Catakleismic]] [[Pythagorean tuning|Pythagorean]] [[Orwell]]. If that description doesn't sound epic I don't really know what will. Very colourful EDO. Near-perfect 5-limit JI with good 7-limit, passable 11-limit through Orwell and good no-17's 19-limit. Normally I wouldn't like large prime EDOs but this is a rare exception as in this case it's a practically perfect representation of the [[3-limit|2.3]] subgroup.

* 53: [[Kleismic family#Catakleismic|Catakleismic]] [[Pythagorean tuning|Pythagorean]] [[Orwell]] [[Buzzard]]. If that description doesn't sound epic I don't really know what will. Very colourful EDO. Near-perfect 5-limit JI with good 7-limit, passable 11-limit through Orwell and good no-17's 19-limit. Normally I wouldn't like large prime EDOs but this is a rare exception as in this case it's a practically perfect representation of the [[3-limit|2.3]] subgroup.

* 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. It supports hemipyth thru 16/13 = 11/9, a questionable equivalence but arguably 58 is the only EDO to make it work/make sense. I like its organisation of intervals/colours a lot.

* 58: Weirdly consistent tuning with a nice selection of colours. Also supports the important 53&58 temperament [[Buzzard]]. 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. It supports hemipyth thru 16/13 = 11/9, a questionable equivalence but arguably 58 is the only EDO to make it work/make sense. I like its organisation of intervals/colours a lot.

* 65: Very cool. Underappreciated. Good [[nestoria]] + [[wurschmidt]] tuning, but more importantly, it is in some surprisingly exact sense the "dual" to what 53 EDO's schismic offers harmonically, including the fact that its subgroup is larger and involves larger primes at the cost of some accuracy (depending on how strict you wanna be about which primes you consider approximated for the purposes of interpreting harmony). Also has a very cool superset, [[130edo]], but I implore people to explore what 65 EDO has to offer first, being 5 * 13 with lots of cool xen stuff deriving from the implications of that.

* 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. It also performs well as a no-11's no-29's [[31-limit]] temperament, although it shares the idiosyncracy of 80 EDO of splitting the [[81/80|syntonic comma]] into two [[64/63]]'s.

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 * 37: Truly an excellent no-3's [[13-limit]] system. Ridiculously overlooked just because of its not so great approximation of prime 3 (which is at least [[5L 2s|diatonic]] and sounds convincing enough especially in context). A logical system for building on it is [[111edo]] which keeps this 13-limit mapping (but improves the 3).
 * 50: The last meantone EDO that should ever be considered because it is the last EDO to consistently map 9/8 and 10/9 to the same step and because 81/80 is a rather large comma to temper at this scale and thus costs you a lot of accuracy. It is surprisingly consistent in the higher limits, and that it is quite composite is appealing to me, especially given that it is a superset of 10 EDO.
-* 53: [[Kleismic family#Catakleismic|Catakleismic]] [[Pythagorean tuning|Pythagorean]] [[Orwell]]. If that description doesn't sound epic I don't really know what will. Very colourful EDO. Near-perfect 5-limit JI with good 7-limit, passable 11-limit through Orwell and good no-17's 19-limit. Normally I wouldn't like large prime EDOs but this is a rare exception as in this case it's a practically perfect representation of the [[3-limit|2.3]] subgroup.
+* 53: [[Kleismic family#Catakleismic|Catakleismic]] [[Pythagorean tuning|Pythagorean]] [[Orwell]] [[Buzzard]]. If that description doesn't sound epic I don't really know what will. Very colourful EDO. Near-perfect 5-limit JI with good 7-limit, passable 11-limit through Orwell and good no-17's 19-limit. Normally I wouldn't like large prime EDOs but this is a rare exception as in this case it's a practically perfect representation of the [[3-limit|2.3]] subgroup.
-* 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. It supports hemipyth thru 16/13 = 11/9, a questionable equivalence but arguably 58 is the only EDO to make it work/make sense. I like its organisation of intervals/colours a lot.
+* 58: Weirdly consistent tuning with a nice selection of colours. Also supports the important 53&58 temperament [[Buzzard]]. 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. It supports hemipyth thru 16/13 = 11/9, a questionable equivalence but arguably 58 is the only EDO to make it work/make sense. I like its organisation of intervals/colours a lot.
 * 65: Very cool. Underappreciated. Good [[nestoria]] + [[wurschmidt]] tuning, but more importantly, it is in some surprisingly exact sense the "dual" to what 53 EDO's schismic offers harmonically, including the fact that its subgroup is larger and involves larger primes at the cost of some accuracy (depending on how strict you wanna be about which primes you consider approximated for the purposes of interpreting harmony). Also has a very cool superset, [[130edo]], but I implore people to explore what 65 EDO has to offer first, being 5 * 13 with lots of cool xen stuff deriving from the implications of that.
 * 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. It also performs well as a no-11's no-29's [[31-limit]] temperament, although it shares the idiosyncracy of 80 EDO of splitting the [[81/80|syntonic comma]] into two [[64/63]]'s.

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