User:Godtone: Difference between revisions

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Beyond this point, it really becomes about narrowing down EDOs based on approximative or other considerations than just 'types'/'colours'.

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=== Favourite EDOs ===

12, 13, 16, 17, 19, 20, 22, 24, 31, 32, 34, 36, 50, 53, 58, 68, 80, 87, 270, 311.<br/>

Favourite EDOs best to worst, not listed = even worse, my opinion obviously, also my opinions are still in development about many of these:<br/>

* 12: The musical language. Also the first reasonable approximation of [[Pythagorean tuning]].

* 13: Distorted 12. As such, almost xenharmonic by definition, due to maximising opportunities for alienness. The next good EDO after 12. Dreamy scales that I like a lot but I'm not sure about if that alone means they're good to use. I hope it does as 13 has huge potential if so.

* 16: The first interesting superset of 4 other than 12. Also a [[Pelogic_family#Mavila|mavila]] tuning, not that I like Mavila too much.

* 17: Notable as the first step up from 12 in colour palette. Good fifths that are slightly worse than in 12 but in the sharp direction. Kinda a bright feel.

* 19: Flattish [[meantone]] tuning. The semifourth in [[semaphore]] has a very neat sound but I wouldn't say it approximates the 7-limit. If anything, 19 is 2.3.5.37 with it representing a circle of [[37/32]]'s, thus also being the first good approximation of the 2.37 subgroup, and thus of [[37/32]], which represents probably my favourite interval of 19.

* 20: The first EDO to have both the 5L5s and 4L4s symmetrical scales, and significant for that reason alone. Can sound quite atonal, however:

** Its 10 EDO subset has a very strong circle of [[16/13]]'s and a strong circle of [[15/14]]'s.

** Its 5 EDO subset has a strong (and remarkably small) circle of [[23/20]]'s.

** Its 4 EDO subset has a strong (and remarkably small) circle of [[19/16]]'s.

** [[10/9]] is approximated well by 3\20 and [[14/11]] is approximated well by 7\20. Has a flattish approximation of [[7/4]] and some higher (octave-reduced) harmonics but I don't think I'd use it to approximate those higher harmonics.

This gives it the (additional) remarkable property that all its flavours of seconds are arguably consonant other than 1\20.

* 22: The first EDO that melodically approximates the 11-limit, and very tone efficient for that purpose. Sounds harmonically complex. [[Superpyth]] + [[Orwell]] tuning. Not a fan of porcupine to be honest.

* 24: I think neutral intervals and semifourths are kinda cool and unexpected root movement is cool, so acts as a nice stepping stone into microtonality with a strong base of familiarity to build off of. Alternate tuning for [[semaphore]]. I also include it because I like highly composite EDOs, and this is very clearly one. Represents the 2.3.11.19.37 subgroup particularly well.

* 31: The next EDO that melodically approximates the 11-limit, and considerably better. Extremely nice arrangement of intervals that feels weirdly intuitive and ideal. Colourful EDO. Basically ideal meantone tuning as more notes than this is overkill for meantone if you don't specifically want meantone.

* 34: The first good approximation of the 5-prime-limit due to being the first reasonably accurate tuning of [[Kleismic family|Hanson AKA kleismic]]. 19 is also a tuning for kleismic but feels like it doesn't do justice to the accuracy and pristineness of kleismic to me. Has the sharp 3/2's of 17 EDO, and as 17 EDO is a good colour system, 34 EDO is a natural extension.

* 36: Because of being a superset of 12, quite overlooked. It is actually a very good subgroup temperament! A natural extension of 12 EDO's colour palette, preferring to avoid the neutral and semi- intervals of 24 EDO. I should note though that while both 24 and 36 are reasonably good systems, I do not think they should be used together, as there are preferable EDOs in the high end range, such as 80 EDO.

* 50: The last meantone EDO that should ever be considered because it is the last EDO to consistently map 9/8 and 10/9, 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 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.

* 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.

* 80: My favourite EDO. My previous 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.

=== Philosophy ===

@@ Line 66: / Line 66: @@
 Beyond this point, it really becomes about narrowing down EDOs based on approximative or other considerations than just 'types'/'colours'.
 <br/>
+=== Favourite EDOs ===
+, 13, 16, 17, 19, 20, 22, 24, 31, 32, 34, 36, 50, 53, 58, 68, 80, 87, 270, 311.<br/>
+Favourite EDOs best to worst, not listed = even worse, my opinion obviously, also my opinions are still in development about many of these:<br/>
+* 12: The musical language. Also the first reasonable approximation of [[Pythagorean tuning]].
+* 13: Distorted 12. As such, almost xenharmonic by definition, due to maximising opportunities for alienness. The next good EDO after 12. Dreamy scales that I like a lot but I'm not sure about if that alone means they're good to use. I hope it does as 13 has huge potential if so.
+* 16: The first interesting superset of 4 other than 12. Also a [[Pelogic_family#Mavila|mavila]] tuning, not that I like Mavila too much.
+* 17: Notable as the first step up from 12 in colour palette. Good fifths that are slightly worse than in 12 but in the sharp direction. Kinda a bright feel.
+* 19: Flattish [[meantone]] tuning. The semifourth in [[semaphore]] has a very neat sound but I wouldn't say it approximates the 7-limit. If anything, 19 is 2.3.5.37 with it representing a circle of [[37/32]]'s, thus also being the first good approximation of the 2.37 subgroup, and thus of [[37/32]], which represents probably my favourite interval of 19.
+* 20: The first EDO to have both the 5L5s and 4L4s symmetrical scales, and significant for that reason alone. Can sound quite atonal, however:
+** Its 10 EDO subset has a very strong circle of [[16/13]]'s and a strong circle of [[15/14]]'s.
+** Its 5 EDO subset has a strong (and remarkably small) circle of [[23/20]]'s.
+** Its 4 EDO subset has a strong (and remarkably small) circle of [[19/16]]'s.
+** [[10/9]] is approximated well by 3\20 and [[14/11]] is approximated well by 7\20. Has a flattish approximation of [[7/4]] and some higher (octave-reduced) harmonics but I don't think I'd use it to approximate those higher harmonics.
+This gives it the (additional) remarkable property that all its flavours of seconds are arguably consonant other than 1\20.
+* 22: The first EDO that melodically approximates the 11-limit, and very tone efficient for that purpose. Sounds harmonically complex. [[Superpyth]] + [[Orwell]] tuning. Not a fan of porcupine to be honest.
+* 24: I think neutral intervals and semifourths are kinda cool and unexpected root movement is cool, so acts as a nice stepping stone into microtonality with a strong base of familiarity to build off of. Alternate tuning for [[semaphore]]. I also include it because I like highly composite EDOs, and this is very clearly one. Represents the 2.3.11.19.37 subgroup particularly well.
+* 31: The next EDO that melodically approximates the 11-limit, and considerably better. Extremely nice arrangement of intervals that feels weirdly intuitive and ideal. Colourful EDO. Basically ideal meantone tuning as more notes than this is overkill for meantone if you don't specifically want meantone.
+* 34: The first good approximation of the 5-prime-limit due to being the first reasonably accurate tuning of [[Kleismic family|Hanson AKA kleismic]]. 19 is also a tuning for kleismic but feels like it doesn't do justice to the accuracy and pristineness of kleismic to me. Has the sharp 3/2's of 17 EDO, and as 17 EDO is a good colour system, 34 EDO is a natural extension.
+* 36: Because of being a superset of 12, quite overlooked. It is actually a very good subgroup temperament! A natural extension of 12 EDO's colour palette, preferring to avoid the neutral and semi- intervals of 24 EDO. I should note though that while both 24 and 36 are reasonably good systems, I do not think they should be used together, as there are preferable EDOs in the high end range, such as 80 EDO.
+* 50: The last meantone EDO that should ever be considered because it is the last EDO to consistently map 9/8 and 10/9, 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 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.
+* 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.
+* 80: My favourite EDO. My previous 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.
 === Philosophy ===