User:Eufalesio/12edo detemperament sequences: Difference between revisions

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The path through cassandra into septischismic is the easiest, as it keeps the chain of fifths, and a pythseptimal comma ([[gary]]) with a hyper accurate [[zala]], but adds an independent generator for 5 and 13, a "minicomma" that works as aberschisma ~ major minthma. Thus, the mappings of 5 and 13 can be thought as the same as cassandra, but altered by +1 / -1 minicomma. It can be detempered further into rank-4 [[olympic]] and finally, the goddamn-fucking-insanely Absolute [[5767168/5767125#Insanismic|Batshit AKA ''Insanismic for the prudes.'']]

It can instead be detempered into [[hecate]], which either cassandra or compton through the shit extension 12e & 72 can do. But I do not recommend going into hecate. It's decent, but it ~~decouples the generic comma of cassandra from the chain of fifths and thus the garischisma is observed, and can~~'~~t be detempered further into hyper~~-~~accurate temperaments~~.

It can instead be detempered into [[hecate]], which either cassandra or compton through the shit extension 12e & 72 can do. But I do not recommend going into hecate. It's decent, but it's a Rug-Sweeper.

=== 12f ===

Maps 11/8 to a tritone, 13/8 to a major sixth. It is the best val temperament wise. All the corrections of primes 5 to 13 are in the same direction. There are two good paths to consider, through tridecimal compton and through diaschismic. Through tridecimal compton, the path ends at [[Marvel family#Helios|helios]], yet another marvel temperament, which either way is very similar to compton still... so just use 72edo.

Through diaschismic, things get brighter. I don't really like diaschismic, but it can be detempered into, 46 & 58 & 270, 12f Ultimate, which is more accurate than 12e Ultimate, altering primes 5-13 by -2, -3, -5, -6 half-[[176/175|valinorsmas]]. It can be detempered into the ultra-accurate [[Catalog of rank-4 temperaments#Kalimera|Kalimera]] by subtracting an [[ibnsinma]] to primes 7,11,13, and ends at rank-5 [[chalmersic]], ~~both arguably~~ Absolute.

Through diaschismic, things get brighter. I don't really like diaschismic, but it can be detempered into, 46 & 58 & 270, 12f Ultimate, which is more accurate than 12e Ultimate, altering primes 5-13 by -2, -3, -5, -6 half-[[176/175|valinorsmas]]. It can be detempered into the ultra-accurate [[Catalog of rank-4 temperaments#Kalimera|Kalimera]] by subtracting an [[ibnsinma]] to primes 7,11,13, and ends at rank-5 [[chalmersic]]. Chalmersic is Absolute, but Kalimera is also a sane point to stop, so I'm also deeming it an Absolute, though a lesser one.

=== 12de ===

Maps 7/4 to a major sixth, 11/8 to a fourth, 13/8 to a minor sixth. It is an [[exotemperament]]; but... if you can stomach the weirdly mapped 7/4, you can go places. The diaschisma is also tempered out but you go through [[srutal]], and this can be dempered into the best 13-limit temperament: [[donar]], 12de Ultimate. It is much more accurate than 12e Ultimate and 12f Ultimate. It alters primes 5-13 by -2, +8, +6, +5 half-valinorsmas. Donar then can be detempered into Kalimera or [https://sintel.pythonanywhere.com/result?subgroup=2.3.5.7.11.13&reduce=off&weights=unweighted&target=&edos=46+%26+58+%26+270+%26+2460&commas=4375%2F4374%0D%0AS65&submit_comma=submit {4375/4374, 4225/4224}], both to chalmersic.

Through the pontiac route you get [[Schismatic family#Quadrapont|Quadrapont]], pontiac with 4th octaves, You either way can detemper into donar, or whatever the hell 12de & 53 & 171 is. That thing can only detemper into {4375/4374, 4225/4224} by observing the schisma, and then to chalmersic.

Through the pontiac route you get [[Schismatic family#Quadrapont|Quadrapont]], pontiac with 4th octaves, You either way can detemper into donar, or whatever the hell 12de & 53 & 171 is. That thing can only detemper into {4375/4374, 4225/4224} by observing the schisma, and then to chalmersic. Notice here that Chalmersic is both 12f and 12de Absolute, however, the notation will be different depending whether or not choose the 12f path or the 12de path, because all primes beyond 5 have fundamentally different mappings.

== 19-limit ==

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17 is more complex and less accurately tuned, but still within reasonable use and accuracy... though, it needs the 12e'''g''' val. This can mitigated if you use [[Buzzardsma|saquarumas]] as accidentals... but still, kinda sorta not the best.

In Olympic, you '''must''' use the weak extension [[Catalog of rank-4 temperaments#Metaolympic|Metaolympic]], in which your garischisma is split in two heavily inflated [[10241/10240]] halves, and you use one of these halves to reach 17/16 and 19/16, -1 and +1 respectively. Through [[~~User:Eufalesio/Ultimate#~~Insatinismic ~~AKA Batshittin|Batshittin~~]] ~~(a weak extension of Batshit~~), you use the same 10241/10240 and [[Mina|minas]]; 4096/4095 ~ 4225/4224, with of course perfect precision.

In Olympic, you '''must''' use the weak extension [[Catalog of rank-4 temperaments#Metaolympic|Metaolympic]], in which your garischisma is split in two heavily inflated [[10241/10240]] halves, and you use one of these halves to reach 17/16 and 19/16, -1 and +1 respectively. Through Batshittin (aka [[Insatinismic]] for the prudes), you use the same 10241/10240 and [[Mina|minas]]; 4096/4095 ~ 4225/4224, with of course perfect precision.

=== 12f ===

@@ Line 93: / Line 93: @@
 The path through cassandra into septischismic is the easiest, as it keeps the chain of fifths, and a pythseptimal comma ([[gary]]) with a hyper accurate [[zala]], but adds an independent generator for 5 and 13, a "minicomma" that works as aberschisma ~ major minthma. Thus, the mappings of 5 and 13 can be thought as the same as cassandra, but altered by +1 / -1 minicomma. It can be detempered further into rank-4 [[olympic]] and finally, the goddamn-fucking-insanely Absolute [[5767168/5767125#Insanismic|Batshit AKA ''Insanismic for the prudes.'']]
-It can instead be detempered into [[hecate]], which either cassandra or compton through the shit extension 12e & 72 can do. But I do not recommend going into hecate. It's decent, but it decouples the generic comma of cassandra from the chain of fifths and thus the garischisma is observed, and can't be detempered further into hyper-accurate temperaments.
+It can instead be detempered into [[hecate]], which either cassandra or compton through the shit extension 12e & 72 can do. But I do not recommend going into hecate. It's decent, but it's a Rug-Sweeper.
 === 12f ===
 Maps 11/8 to a tritone, 13/8 to a major sixth. It is the best val temperament wise. All the corrections of primes 5 to 13 are in the same direction. There are two good paths to consider, through tridecimal compton and through diaschismic. Through tridecimal compton, the path ends at [[Marvel family#Helios|helios]], yet another marvel temperament, which either way is very similar to compton still... so just use 72edo.
-Through diaschismic, things get brighter. I don't really like diaschismic, but it can be detempered into, 46 & 58 & 270, 12f Ultimate, which is more accurate than 12e Ultimate, altering primes 5-13 by -2, -3, -5, -6 half-[[176/175|valinorsmas]]. It can be detempered into the ultra-accurate [[Catalog of rank-4 temperaments#Kalimera|Kalimera]] by subtracting an [[ibnsinma]] to primes 7,11,13, and ends at rank-5 [[chalmersic]], both arguably Absolute.
+Through diaschismic, things get brighter. I don't really like diaschismic, but it can be detempered into, 46 & 58 & 270, 12f Ultimate, which is more accurate than 12e Ultimate, altering primes 5-13 by -2, -3, -5, -6 half-[[176/175|valinorsmas]]. It can be detempered into the ultra-accurate [[Catalog of rank-4 temperaments#Kalimera|Kalimera]] by subtracting an [[ibnsinma]] to primes 7,11,13, and ends at rank-5 [[chalmersic]]. Chalmersic is Absolute, but Kalimera is also a sane point to stop, so I'm also deeming it an Absolute, though a lesser one.
 === 12de ===
 Maps 7/4 to a major sixth, 11/8 to a fourth, 13/8 to a minor sixth. It is an [[exotemperament]]; but... if you can stomach the weirdly mapped 7/4, you can go places. The diaschisma is also tempered out but you go through [[srutal]], and this can be dempered into the best 13-limit temperament: [[donar]], 12de Ultimate. It is much more accurate than 12e Ultimate and 12f Ultimate. It alters primes 5-13 by -2, +8, +6, +5 half-valinorsmas. Donar then can be detempered into Kalimera or [https://sintel.pythonanywhere.com/result?subgroup=2.3.5.7.11.13&reduce=off&weights=unweighted&target=&edos=46+%26+58+%26+270+%26+2460&commas=4375%2F4374%0D%0AS65&submit_comma=submit {4375/4374, 4225/4224}], both to chalmersic.
-Through the pontiac route you get [[Schismatic family#Quadrapont|Quadrapont]], pontiac with 4th octaves, You either way can detemper into donar, or whatever the hell 12de & 53 & 171 is. That thing can only detemper into {4375/4374, 4225/4224} by observing the schisma, and then to chalmersic.
+Through the pontiac route you get [[Schismatic family#Quadrapont|Quadrapont]], pontiac with 4th octaves, You either way can detemper into donar, or whatever the hell 12de & 53 & 171 is. That thing can only detemper into {4375/4374, 4225/4224} by observing the schisma, and then to chalmersic. Notice here that Chalmersic is both 12f and 12de Absolute, however, the notation will be different depending whether or not choose the 12f path or the 12de path, because all primes beyond 5 have fundamentally different mappings.
 == 19-limit ==
@@ Line 113: / Line 113: @@
 is more complex and less accurately tuned, but still within reasonable use and accuracy... though, it needs the 12e'''g''' val. This can mitigated if you use [[Buzzardsma|saquarumas]] as accidentals... but still, kinda sorta not the best.
-In Olympic, you '''must''' use the weak extension [[Catalog of rank-4 temperaments#Metaolympic|Metaolympic]], in which your garischisma is split in two heavily inflated [[10241/10240]] halves, and you use one of these halves to reach 17/16 and 19/16, -1 and +1 respectively. Through [[User:Eufalesio/Ultimate#Insatinismic AKA Batshittin|Batshittin]] (a weak extension of Batshit), you use the same 10241/10240 and [[Mina|minas]]; 4096/4095 ~ 4225/4224, with of course perfect precision.
+In Olympic, you '''must''' use the weak extension [[Catalog of rank-4 temperaments#Metaolympic|Metaolympic]], in which your garischisma is split in two heavily inflated [[10241/10240]] halves, and you use one of these halves to reach 17/16 and 19/16, -1 and +1 respectively. Through Batshittin (aka [[Insatinismic]] for the prudes), you use the same 10241/10240 and [[Mina|minas]]; 4096/4095 ~ 4225/4224, with of course perfect precision.
 === 12f ===