User:Eufalesio/Ultimate: Difference between revisions

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=== Olympic ===

[[Olympic|This]]. The best course of action for detempering Ultimate is to observe the garischisma, resulting in rank-4 olympic, which is just {S64, S65}. Notationwise, this results in spliting the saruyoma being observed. Unlike in JI, where the schisma is around half the garischisma, here the schisma is ~1.6x LARGER, not smaller. A [[10241/10240|tina]] is required to reach prime 17 and 19.

[[Olympic|This]]. The best course of action for detempering Ultimate is to observe the garischisma, resulting in rank-4 olympic, which is just {S64, S65}. Notationwise, this results in spliting the saruyoma being observed. Unlike in JI, where the schisma is around half the garischisma, here the schisma is ~1.6x LARGER, not smaller. A [[10241/10240|tina (~10241/10240)]] is required to reach prime 17 and 19.

Olympic decouples 64/63 from the chain of fifths; 64/63 is now its own thing, and the poma is \|↑. (\| is a garischisma down)

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t's something I don't think I'll ever see myself doing because this accuracy is enough to represent highly fine edos such as 494, 764, or 935edo, which is already too much for me.

Extensions to the 19-limit are bad: the strong one keeps 1729/1728 and 1216/1215, [[Catalog of rank-4 temperaments#Metaolympic|'''Meta'''olympic]] works, and though it's a weak extension; it can still be written retrocompatibly. Acknowledgements to [[Flora Canou]] for this insight.

Extensions to the 19-limit are bad: the strong one keeps 1729/1728 and 1216/1215, [[Catalog of rank-4 temperaments#Metaolympic|'''Meta'''olympic]] works, and though it's a weak extension; it can still be written retrocompatibly. Acknowledgements to [[Flora Canou]] for this great insight.

Here, 19/16 is †|\m3. 17/16 is 𐕣^|\'''⇊⇊'''M2. (|\ is a schisma up, † is a heavily inflated tina~~; 10241/10240~~)

Here, 19/16 is †|\m3. 17/16 is 𐕣^|\'''⇊⇊'''M2. (|\ is a schisma up, † is a heavily inflated tina)

=== ~~Insanic~~ ===

=== Insanismic ===

Olympic STILL not enough? Split your losses and use [[5767168/5767125|{S64/S65}]]. Now you observe the olympia and get a schismina accidental.

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* v⇈̇ is 1053/1024 whilst v⇈ is 36/35.

{S64/S65} is at a level of precision comparable to 8539edo and much finer. The people at sagittal.org had already declared its own version of this notation to be of "Insane" precision, ~~so if you need anything finer, you are~~ ''~~beyond~~ insane''. ~~Or, to be more crude... '''batshit''' insane~~.

{S64/S65} is at a level of precision comparable to 8539edo and much, MUCH finer. The people at sagittal.org had already declared its own version of this notation to be of "Insane" precision. Personally, ''insane'' is way too nice of a descriptor. This is is beyond your grasp of perfection.

Unlike Olympic, this one is undeniably '''WAY''' more accurate, at least 100 times more accurate. It can be extended to the whole 19-limit by adding S76/S77 and S2431 (or the [[devicisma]]) to the comma list, however, a tina is required to reach prime 17 and 19, which is close, but not equal to a third of a schismina~~. The tina is 10241/10240~~. 19/16 is †|̈\m3. 17/16 is 𐕣^^'''⇊⇊̱'''M2.

With an average tuning error of -0.000234c, let's be frank, this is JI. Approachable, thanks to it being part of the sequence and thus retrocompatible, but approachable nontheless. You are quite frankly, batshit insane if you require this precision, but I still give you the tools to express that insanity.

Wouldn't I be also batshit insane by having researched it? No. I know I won't use it. But, knowing about it is important; how much '''JI'''uice I can squeeze out of 12edo... taking it to insanity? Well, here is the answer!

Unlike Olympic, this one is undeniably '''WAY''' more accurate, at least 100 times more accurate. It can be weakly extended to the whole 19-limit by adding S76/S77 and S2431 (or the [[devicisma]]) to the comma list, however, a tina is required to reach prime 17 and 19, which is close, but not equal to a third of a schismina. 19/16 is †|̈\m3. 17/16 is 𐕣^^'''⇊⇊̱'''M2.

Look how goddamn accurate this temp is! Look, I even made a technical temp data section! [expandable]

=== ~~Batshit~~ AKA Batshit-Insanic or simply call it Insanic if profanity is not allowed ===

Many thanks to Flora Canou for help with all the temp stuff... she's the real heroine here behind the numbers.

{{Databox|1=[[Subgroup]]: 2.3.5.7.11.13

=== Insanismic AKA Batshit ===

I'm aware temps can't have NSFW names. "Insanismic" is the SFW, clean term. The one for the front page. The ''correct'' mask. But really, the ''real'' name is '''batshit.''' Because that's what this temperament is. Batshit insane. Yes, I like crude, evocative names. The English language has a beautiful expression for this special obsession that I will not '''not''' use. The unfathomable precision it bestows. The madness that ensues upon the search of perfection. Here is perfection! GO CRAZY!{{Databox|1=[[Subgroup]]: 2.3.5.7.11.13

[[Comma list]]: [[5767168/5767125]]

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⟨ 0 0 1 0 0 -1 ],

⟨ 0 0 0 1 1 0 ],

Mapping generators: ~2, ~3, ~5, ~7, ~128~~/65~~

Mapping generators: ~2, ~3, ~5, ~7, ~65/128

[[Optimal tuning|Optimal tunings]]? ~~(the calculator isn't very helpful here...)~~

[[Optimal tuning|Optimal tunings]]?

: [[~~CWE~~]]: ~2 = ~~1200~~.~~000 ¢~~, ~3/2 = 701.~~956 ¢~~, ~5/4 = 386.~~315 ¢~~, ~7/4 = 968.~~827 ¢~~, ~128~~/65~~ = 1173.~~154¢~~

: [[WE]]: ~2 = 1199.9995¢, ~3/2 = 701.9556¢, ~5/4 = 386.3147¢, ~7/4 = 968.8271¢, ~65/128 = -1173.1542¢

: error map: -0.~~000,~~ 0.~~001,~~ 0.~~001,~~ 0.~~001,~~ 0.~~001,~~ 0.~~003~~

: error map: -0.0005 0.0001 0.0000 0.0002 -0.0003 0.001

Optimal ET sequence: {{EDOs|7, 10e, 12e, 30b, 31e, 34, 36, 41, 46, 53, 84, 87, 130, 183, 217, 224, 270, 494, 764, 935, 1075, 1205, 1609, 1696, 1920, 2190, 2684, 3395, 5144, 5585, 6079, 8269, 8539, 11664, 14124, 14348, 14618, 20203}}

Badness (~~[[User:FloraC#Tools|Flora]]~~): 0.~~241077 [Sintel Badness gives me NA, thanks Flora for having a calculator that gives a usable value...]~~

Badness (Sintel): 0.241

==== Subgroup: 2.3.5.7.11.13.17.19 ====

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[[Optimal tuning|Optimal tunings]]?

: [[~~CWE~~]]: ~2 = 1200.000 ¢, ~3/2 = 701.~~956 ¢~~, ~5/4 = 386.~~316 ¢~~, ~7/4 = 968.~~828 ¢~~, ~608~~/385~~ = 791.~~052¢~~

: [[WE]]: ~2 = 1200.000 ¢, ~3/2 = 701.9561¢, ~5/4 = 386.3149¢, ~7/4 = 968.828¢, ~385/608 = -791.0513¢

: error map 0.~~000,~~ 0.~~001,~~ 0.~~002,~~ 0.~~002,~~ 0.~~001,~~ 0.~~002,~~ 0.~~001,~~ 0.~~001~~

: error map -0.0006 0.0005 0.0000 0.0009 -0.0004 0.0001 -0.0012 -0.0008

'''Optimal''' ET sequence: {{EDOs|41g, 53, 94, 176g, 217, 270, 311, 487, 581, 1115g, 1385, 1696, 1966, 2597, 2814, 3084, 3178, 3395, 5144, 6573, 7958, 8269, 8539, 11934, 16808, 20203}}.

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== Nomenclature and notation ==

This notation can be easily spoken as well as written, adapting Kite's color notation and ups and downs into a nice collage. At least, the part of Ultimate. For the things beyond Ultimate I <s>stole</s> borrowed some Sagittal nomenclature of the Magrathean symbol set that had the same comma functions. Behold!

[[File:ULTRAOLYMPIANsymbolset.jpg|center|thumb|960x960px|The name of this notation is henceforth ~~Ultraolympic~~ notation~~. If swear words can't be used~~, ~~use ''Insanic'' instead of ''Batshit'' or ''Batshit-Insanic''.~~

[[File:ULTRAOLYMPIANsymbolset.jpg|center|thumb|960x960px|The name of this notation is henceforth the ULTRAOLYMPIC notation, and the main 4 systems.]]

~~What can I say... I like crude, powerful language. The English language has a beautiful expression for this special obsession that I will not '''not''' use~~.]]

=== Easy tables ===

@@ Line 205: / Line 205: @@
 === Olympic ===
-[[Olympic|This]]. The best course of action for detempering Ultimate is to observe the garischisma, resulting in rank-4 olympic, which is just {S64, S65}. Notationwise, this results in spliting the saruyoma being observed. Unlike in JI, where the schisma is around half the garischisma, here the schisma is ~1.6x LARGER, not smaller. A [[10241/10240|tina]] is required to reach prime 17 and 19.
+[[Olympic|This]]. The best course of action for detempering Ultimate is to observe the garischisma, resulting in rank-4 olympic, which is just {S64, S65}. Notationwise, this results in spliting the saruyoma being observed. Unlike in JI, where the schisma is around half the garischisma, here the schisma is ~1.6x LARGER, not smaller. A [[10241/10240|tina (~10241/10240)]] is required to reach prime 17 and 19.
 Olympic decouples 64/63 from the chain of fifths; 64/63 is now its own thing, and the poma is \|↑. (\| is a garischisma down)
@@ Line 218: / Line 218: @@
 t's something I don't think I'll ever see myself doing because this accuracy is enough to represent highly fine edos such as 494, 764, or 935edo, which is already too much for me.
-Extensions to the 19-limit are bad: the strong one keeps 1729/1728 and 1216/1215, [[Catalog of rank-4 temperaments#Metaolympic|'''Meta'''olympic]] works, and though it's a weak extension; it can still be written retrocompatibly. Acknowledgements to [[Flora Canou]] for this insight.
+Extensions to the 19-limit are bad: the strong one keeps 1729/1728 and 1216/1215, [[Catalog of rank-4 temperaments#Metaolympic|'''Meta'''olympic]] works, and though it's a weak extension; it can still be written retrocompatibly. Acknowledgements to [[Flora Canou]] for this great insight.
-Here, 19/16 is †|\m3. 17/16 is 𐕣^|\'''⇊⇊'''M2. (|\ is a schisma up, † is a heavily inflated tina; 10241/10240)
+Here, 19/16 is †|\m3. 17/16 is 𐕣^|\'''⇊⇊'''M2. (|\ is a schisma up, † is a heavily inflated tina)
-=== Insanic ===
+=== Insanismic ===
 Olympic STILL not enough? Split your losses and use [[5767168/5767125|{S64/S65}]]. Now you observe the olympia and get a schismina accidental.
@@ Line 232: / Line 232: @@
 * v⇈̇ is 1053/1024 whilst v⇈ is 36/35.
-{S64/S65} is at a level of precision comparable to 8539edo and much finer. The people at sagittal.org had already declared its own version of this notation to be of "Insane" precision, so if you need anything finer, you are ''beyond insane''. Or, to be more crude... '''batshit''' insane.
+{S64/S65} is at a level of precision comparable to 8539edo and much, MUCH finer. The people at sagittal.org had already declared its own version of this notation to be of "Insane" precision. Personally, ''insane'' is way too nice of a descriptor. This is is beyond your grasp of perfection.
-Unlike Olympic, this one is undeniably '''WAY''' more accurate, at least 100 times more accurate. It can be extended to the whole 19-limit by adding S76/S77 and S2431 (or the [[devicisma]]) to the comma list, however, a tina is required to reach prime 17 and 19, which is close, but not equal to a third of a schismina. The tina is 10241/10240. 19/16 is †|̈\m3. 17/16 is 𐕣^^'''⇊⇊̱'''M2.
+With an average tuning error of -0.000234c, let's be frank, this is JI. Approachable, thanks to it being part of the sequence and thus retrocompatible, but approachable nontheless. You are quite frankly, batshit insane if you require this precision, but I still give you the tools to express that insanity.
+Wouldn't I be also batshit insane by having researched it? No. I know I won't use it. But, knowing about it is important; how much '''JI'''uice I can squeeze out of 12edo... taking it to insanity? Well, here is the answer!
+Unlike Olympic, this one is undeniably '''WAY''' more accurate, at least 100 times more accurate. It can be weakly extended to the whole 19-limit by adding S76/S77 and S2431 (or the [[devicisma]]) to the comma list, however, a tina is required to reach prime 17 and 19, which is close, but not equal to a third of a schismina. 19/16 is †|̈\m3. 17/16 is 𐕣^^'''⇊⇊̱'''M2.
 Look how goddamn accurate this temp is! Look, I even made a technical temp data section! [expandable]
-=== Batshit AKA Batshit-Insanic <small><small><small><small><small>or simply call it</small></small></small></small></small> Insanic<small><small><small><small><small> if profanity is not allowed</small></small></small></small></small> ===
+Many thanks to Flora Canou for help with all the temp stuff... she's the real heroine here behind the numbers.
-{{Databox|1=[[Subgroup]]: 2.3.5.7.11.13
+=== Insanismic AKA Batshit ===
+I'm aware temps can't have NSFW names. "Insanismic" is the SFW, clean term. The one for the front page. The ''correct'' mask. But really, the ''real'' name is '''batshit.''' Because that's what this temperament is. Batshit insane. Yes, I like crude, evocative names. The English language has a beautiful expression for this special obsession that I will not '''not''' use. The unfathomable precision it bestows. The madness that ensues upon the search of perfection. Here is perfection! GO CRAZY!{{Databox|1=[[Subgroup]]: 2.3.5.7.11.13
 [[Comma list]]: [[5767168/5767125]]
@@ Line 247: / Line 253: @@
 ⟨	0	0	1	0	0	-1	],
 ⟨	0	0	0	1	1	0	],
-<nowiki>⟨	0	0	0	0	-3	-1	]]</nowiki>
+<nowiki>⟨	0	0	0	0	3	1	]]</nowiki>
-Mapping generators: ~2, ~3, ~5, ~7, ~128/65
+Mapping generators: ~2, ~3, ~5, ~7, ~65/128
-[[Optimal tuning|Optimal tunings]]? (the calculator isn't very helpful here...)
+[[Optimal tuning|Optimal tunings]]?
-: [[CWE]]: ~2 = 1200.000 ¢, ~3/2 = 701.956 ¢, ~5/4 = 386.315 ¢, ~7/4 = 968.827 ¢, ~128/65 = 1173.154¢
+: [[WE]]: ~2 = 1199.9995¢, ~3/2 = 701.9556¢, ~5/4 = 386.3147¢, ~7/4 = 968.8271¢, ~65/128 = -1173.1542¢
-: error map: -0.000, 0.001, 0.001, 0.001, 0.001, 0.003
+: error map: -0.0005  0.0001  0.0000  0.0002 -0.0003  0.001
 Optimal ET sequence: {{EDOs|7, 10e, 12e, 30b, 31e, 34, 36, 41, 46, 53, 84, 87, 130, 183, 217, 224, 270, 494, 764, 935, 1075, 1205, 1609, 1696, 1920, 2190, 2684, 3395, 5144, 5585, 6079, 8269, 8539, 11664, 14124, 14348, 14618, 20203}}
-Badness ([[User:FloraC#Tools|Flora]]): 0.241077 [Sintel Badness gives me NA, thanks Flora for having a calculator that gives a usable value...]
+Badness (Sintel): 0.241
 ==== Subgroup: 2.3.5.7.11.13.17.19 ====
@@ Line 271: / Line 277: @@
 [[Optimal tuning|Optimal tunings]]?
-: [[CWE]]: ~2 = 1200.000 ¢, ~3/2 = 701.956 ¢, ~5/4 = 386.316 ¢, ~7/4 = 968.828 ¢, ~608/385 = 791.052¢
+: [[WE]]: ~2 = 1200.000 ¢, ~3/2 = 701.9561¢, ~5/4 = 386.3149¢, ~7/4 = 968.828¢, ~385/608 = -791.0513¢
-: error map 0.000, 0.001, 0.002, 0.002, 0.001, 0.002, 0.001, 0.001
+: error map -0.0006  0.0005  0.0000  0.0009 -0.0004  0.0001 -0.0012 -0.0008
 '''Optimal''' ET sequence: {{EDOs|41g, 53, 94, 176g, 217, 270, 311, 487, 581, 1115g, 1385, 1696, 1966, 2597, 2814, 3084, 3178, 3395, 5144, 6573, 7958, 8269, 8539, 11934, 16808, 20203}}.
@@ Line 284: / Line 290: @@
 == Nomenclature and notation ==
 This notation can be easily spoken as well as written, adapting Kite's color notation and ups and downs into a nice collage. At least, the part of Ultimate. For the things beyond Ultimate I <s>stole</s> borrowed some Sagittal nomenclature of the Magrathean symbol set that had the same comma functions. Behold!
-[[File:ULTRAOLYMPIANsymbolset.jpg|center|thumb|960x960px|The name of this notation is henceforth Ultraolympic notation. If swear words can't be used, use ''Insanic'' instead of ''Batshit'' or ''Batshit-Insanic''.
+[[File:ULTRAOLYMPIANsymbolset.jpg|center|thumb|960x960px|The name of this notation is henceforth the ULTRAOLYMPIC notation, and the main 4 systems.]]
-What can I say... I like crude, powerful language. The English language has a beautiful expression for this special obsession that I will not '''not''' use.]]
 === Easy tables ===