User:Eufalesio/Ultimate - Revision history

Eufalesio: /* Easy tables */

2026-06-06T15:30:36Z

Easy tables

← Older revision		Revision as of 15:30, 6 June 2026
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	The [[pergen]] is (P8, P5, ^1), where ^1 is the "minicomma" (from this point forward refered to as "MC"); a 3~5c interval that represents 385/384, 352/351, 5120/5103, 513/512, the layoma, etc. 4:5:6:7:9:11:13:15:17:19 octave reduced is notated as:		The [[pergen]] is (P8, P5, ^1), where ^1 is the "minicomma" (from this point forward refered to as "MC"); a 3~5c interval that represents 385/384, 352/351, 5120/5103, 513/512, the layoma, etc. 4:5:6:7:9:11:13:15:17:19 octave reduced is notated as:

	P1 – ^'''↓'''M3 – P5 – '''↓'''m7 – M2 – ⇑4 – v⇑m6 – ^'''↓'''M7 – ~~vv↑↑↑↑M2~~ – ^m3		P1 – ^'''↓'''M3 – P5 – '''↓'''m7 – M2 – ⇑4 – v⇑m6 – ^'''↓'''M7 – ^^'''⇓⇓'''M2 – ^m3

	Using pomas (pythagorean commas, [↑/'''↓''']) improves this notation for reasons that will be exposed later.		Using pomas (pythagorean commas, [↑/'''↓''']) improves this notation for reasons that will be exposed later.
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	\|↑		\|↑
	\|'''↓'''		\|'''↓'''
	\|^		\| rowspan="2" \|^
	\|v		\| rowspan="2" \|v
	\| rowspan="2" \|<nowiki>◿ \| ◺</nowiki>		\| rowspan="2" \|<nowiki>◿ \| ◺</nowiki>
	\| rowspan="2" \|<nowiki>◹ \| ◸</nowiki>		\| rowspan="2" \|<nowiki>◹ \| ◸</nowiki>
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	\|⇑		\|⇑
	\|'''⇓'''		\|'''⇓'''
	\|M
	\|W
	\|\		\|\
	\|-		\|-
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	{\| class="wikitable"		{\| class="wikitable"
	!Extra accidentals		!Extra accidentals
			! colspan="2" \|Mercator comma*
	! colspan="2" \|Fwiwisma		! colspan="2" \|Fwiwisma
	! colspan="2" \|Half-apotome		! colspan="2" \|Half-apotome
	! colspan="2" \|Non-gary poma*
	\|-		\|-
	\| rowspan="2" \|Symbols		\| rowspan="2" \|Symbols
			\| rowspan="2" \|M
			\| rowspan="2" \|W
	\| rowspan="2" \|¡		\| rowspan="2" \|¡
	\| rowspan="2" \|!		\| rowspan="2" \|!
	\|{{Sagittal\|t}}		\|{{Sagittal\|t}}
	\|{{Sagittal\|d}}		\|{{Sagittal\|d}}
	\|p
	\|q
	\|-		\|-
	\|{{Sagittal\|t#}}		\|{{Sagittal\|t#}}
	\|{{Sagittal\|db}}		\|{{Sagittal\|db}}
	~~\|pp~~
	~~\|qq~~
	\|-		\|-
	\| rowspan="2" \|Spoken		\| rowspan="2" \|Spoken
			\| rowspan="2" \|mo
			\| rowspan="2" \|mu
	\| rowspan="2" \|halfpo		\| rowspan="2" \|halfpo
	\| rowspan="2" \|halfqu		\| rowspan="2" \|halfqu
	\|halfsharp		\|halfsharp
	\|halfflat		\|halfflat
	~~\|po~~
	~~\|qu~~
	\|-		\|-
	\|sesquisharp		\|sesquisharp
	\|sesquiflat		\|sesquiflat
	~~\|pop(o)~~
	~~\|quq(u)~~
	\|}		\|}
	<nowiki>*</nowiki>Not necessary ~~in Ultimate. This can prevent filling the page with garischismas. Logically~~, ~~here the arrow is spoken ru/zo like in color~~ notation, ~~while~~ the p/q is ~~po/qu~~.		<nowiki>*</nowiki>Not strictly necessary, but it does simplify notation immensely, specially for ultra-long chains of fifths and notating p17, which requires at least four pomas. A mercator comma follows the following equation: ⇑⇑P1 = Mm2, ⇑⇑m2 = W'''↓'''M2; 17/16 is then ^^W↑m2.

	=== Syntax ===		=== Syntax ===

Eufalesio: I hid a temp page in here lol, to justify the insanity and hyperultramega accuracy of this sequence

2026-06-04T17:45:52Z

I hid a temp page in here lol, to justify the insanity and hyperultramega accuracy of this sequence

Show changes

Eufalesio: /* Olympic */

2026-05-24T20:48:12Z

Olympic

← Older revision		Revision as of 20:48, 24 May 2026
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	Everything else is the same. v↑ for 81/80, ⇑ for 33/32, v⇑ for 1053/1024. It'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.		Everything else is the same. v↑ for 81/80, ⇑ for 33/32, v⇑ for 1053/1024. It'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 yazalathana are bad: the strong ones keep either of 1540/1539 or 1729/1728, and a decent but weak one adding 5776/5775 needs you to split the septimal comma in halves, which is not ideal. Acknowledgements to [[Flora Canou]] for this insight. In short: Olympic kinda sucks, it is better, not ''way'' better than Ultimate, which		Extensions to the yazalathana are bad: the strong ones keep either of 1540/1539 or 1729/1728, and a decent but weak one adding 5776/5775 needs you to split the septimal comma in halves, which is not ideal. Acknowledgements to [[Flora Canou]] for this insight. In short: Olympic kinda sucks: it is better, but not ''way'' better than Ultimate, which for a new dimension to worry about is not justifiable; unlike the jump from cassandra to Ultimate being a quantum leap.
	=== Insanic ===		=== Insanic ===
	Olympic STILL not enough? Split your losses and use [[5767168/5767125\|{S64/S65}]]. Now you observe the olympia and get a schismina accidental. An olympia is 3 of these schisminas. You could write this as dots above or below the accidentals but this is possibly getting a tad crowded. ↑ is 64/63 and 81/80 is v↑. ⇑̱ is 33/32 whilst ⇑ is 4096/3969. v̇⇑ 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''.		Olympic STILL not enough? Split your losses and use [[5767168/5767125\|{S64/S65}]]. Now you observe the olympia and get a schismina accidental. An olympia is 3 of these schisminas. You could write this as dots above or below the accidentals but this is possibly getting a tad crowded. ↑ is 64/63 and 81/80 is v↑. ⇑̱ is 33/32 whilst ⇑ is 4096/3969. v̇⇑ 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''.

Eufalesio: /* Ultimate still not enough? */

2026-05-22T12:12:56Z

Ultimate still not enough?

← Older revision		Revision as of 12:12, 22 May 2026
Line 208:		Line 208:

	Everything else is the same. v↑ for 81/80, ⇑ for 33/32, v⇑ for 1053/1024. It'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.		Everything else is the same. v↑ for 81/80, ⇑ for 33/32, v⇑ for 1053/1024. It'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.
	~~{{Note\|Find good extensions to the 19-limit.}}~~

			Extensions to the yazalathana are bad: the strong ones keep either of 1540/1539 or 1729/1728, and a decent but weak one adding 5776/5775 needs you to split the septimal comma in halves, which is not ideal. Acknowledgements to [[Flora Canou]] for this insight. In short: Olympic kinda sucks, it is better, not ''way'' better than Ultimate, which
	=== Insanic ===		=== Insanic ===
	Olympic STILL not enough? Split your losses and use [[5767168/5767125\|{S64/S65}]]. Now you observe the olympia and get a schismina accidental. An olympia is 3 of these schisminas. You could write this as dots above or below the accidentals but this is possibly getting a tad crowded. ↑ is 64/63 and 81/80 is v↑. ⇑̱ is 33/32 whilst ⇑ is 4096/3969. ~~v̈⇑~~ 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''.		Olympic STILL not enough? Split your losses and use [[5767168/5767125\|{S64/S65}]]. Now you observe the olympia and get a schismina accidental. An olympia is 3 of these schisminas. You could write this as dots above or below the accidentals but this is possibly getting a tad crowded. ↑ is 64/63 and 81/80 is v↑. ⇑̱ is 33/32 whilst ⇑ is 4096/3969. v̇⇑ 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''.
	{~~{Note~~\|~~Find good extensions~~ to the ~~whatever limit~~.}}
			Unlike Olympic, this one is undeniably '''WAY''' more accurate. Supposedly, It can be extended to the no-17 19-limit by doing {S64/S65, [[228096/228095\|S96/S98]]} and p17 can be added by tempering out S324/S351. I'll leave the question of how to write 17/16 and 19/16 as an excercise left to the reader to figure out, because I know it's going to be extremely contrived. My notation is not going to serve you well here.

	To recap: 12edo (apotomes), Cassandra (+pomas), Ultimate (+saruyomas), Olympic (+sasarumas), {S64/S65} (+schisminas).		To recap: 12edo (apotomes), Cassandra (+pomas), Ultimate (+saruyomas), Olympic (+sasarumas), {S64/S65} (+schisminas).

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	\|quq(u)		\|quq(u)
	\|}		\|}
	<nowiki>*</nowiki>Not necessary in Ultimate. This can prevent filling the page with garischismas. Logically, here the arrow is spoken ru/zo like in color notation, while the ~~slashed arrow~~ is po/qu.		<nowiki>*</nowiki>Not necessary in Ultimate. This can prevent filling the page with garischismas. Logically, here the arrow is spoken ru/zo like in color notation, while the p/q is po/qu.

	=== Syntax ===		=== Syntax ===
			For an accidental: (schismina) + (sasaruma) + [saruyoma] + [poma] + [apotome]

			* v# = downsharp
			* M'''⇓''' = dupquq

			For intervals: [accidental] + [5L 7s 6\|5 nominal]

			* '''↓'''M2 = qumajor second
			* ^'''↓'''M3 = upqumajor third
			* v⇑m6 = downpopominor sixth

			For pitches: [5L 7s 6\|5 nominal] + [accidental] + [octave number]

	* ~~For an accidental: (schismina) + (sasaruma) + [saruyoma] + [poma] + [apotome] v#~~ = ~~downsharp, M'''⇓''' = dupquq~~		* D4 = dee four
	* ~~For intervals: [accidental] + [5L 7s 6\|5 nominal] '''↓'''M2, ^'''↓'''M3, v⇑m6; qumajor second, upqumajor third, downpopominor sixth~~		* E⇑b4 = e popoflat four
	* ~~For pitches: [5L 7s 6\|5 nominal] + [accidental] + [octave number] Example: D4, E⇑b4,~~ F^'''↓'''#5~~; dee four, e popoflat four,~~ ef upqusharp five		* F^'''↓'''#5 = ef upqusharp five

Eufalesio: Hotfixes!

2026-05-18T22:14:53Z

Hotfixes!

← Older revision		Revision as of 22:14, 18 May 2026
Line 272:		Line 272:
	\| colspan="2" \|11-limit JI		\| colspan="2" \|11-limit JI
	\|}		\|}
	The following accidentals only ~~make sense in~~ rank-2s and edos~~. For instance, fwismas in gariwizmic, half-apotomes in newt~~.		The following accidentals are not part of the main bunch because they are either only part of rank-2s and edos or ligatures.
	{\| class="wikitable"		{\| class="wikitable"
	!Extra accidentals		!Extra accidentals

Eufalesio: Final things on notation

2026-05-18T22:13:56Z

Final things on notation

← Older revision		Revision as of 22:13, 18 May 2026
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	==== 94 ====		==== 94 ====
	Best cassandra tuning. Since the chain takes much longer to close, ¡ and ! may be used to raise or lower by a ~~half-poma.~~ (~~Note that~~ a half-poma ~~implies~~ a ~~half-octave,~~ and thus an even-numbered edo). This tuning is optimal and technically usable in the Lumatone, but only as a subset, requiring more than one preset to reach within the [[Standard Lumatone mapping for Pythagorean]]. The cassandra layout can be used in a guitar with the [[skip fretting system 94 7 16]]. However, in a 6-string guitar there will be no other unisons.		Best cassandra tuning. Since the chain takes much longer to close, ¡ and ! may be used to raise or lower by a [[2835/2816\|fwiwisma]] (a half-poma, as a result of tempering out kalisma and thus an even-numbered edo). This tuning is optimal and technically usable in the Lumatone, but only as a subset, requiring more than one preset to reach within the [[Standard Lumatone mapping for Pythagorean]]. The cassandra layout can be used in a guitar with the [[skip fretting system 94 7 16]]. However, in a 6-string guitar there will be no other unisons.

	Note that 94edo is already quite fine for most real instruments, and though its step is very much discernible, human error can begin to slip pitches into the wrong edostep even in very skilled musicians.		Note that 94edo is already quite fine for most real instruments, and though its step is very much discernible, human error can begin to slip pitches into the wrong edostep even in very skilled musicians.
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	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 into a schisma (◿/◹) and a garischisma (◺/◸). Unlike in JI, where the schisma is around half the garischisma, here the schisma is ~1.6x LARGER, not smaller.		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 into a schisma (◿/◹) and a garischisma (◺/◸). Unlike in JI, where the schisma is around half the garischisma, here the schisma is ~1.6x LARGER, not smaller.

	The simplest choice is to make ↑ 64/63; the poma is ◸↑ now, or if you want to be sleek, ↑̵.		The simplest choice is to make ↑ 64/63; the poma is ◸↑ now, or if you want to be sleek, '''p'''.

	Everything else is the same. v↑ for 81/80, ⇑ for 33/32, v⇑ for 1053/1024. It'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.		Everything else is the same. v↑ for 81/80, ⇑ for 33/32, v⇑ for 1053/1024. It'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.
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	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. What's beyond Ultimate, not my problem.		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. What's beyond Ultimate, not my problem.

	=== Easy ~~table~~ ===		=== Easy tables ===
			These are all the accidentals you need to know to write in Ultimate, and even beyond it. For most cases, there is no need to go beyond two of anything, in the case of pomas however, you can end up using three or even more if you don't respell enharmonically (if possible), or go too far down the chain of fifths. One instance is writing 5/4 above a 16/11, which is 20/11. Above a C, this is '''⇓'''G - ^'''↓⇓'''B.
	{\| class="wikitable"		{\| class="wikitable"
	\|+		\|+
	! rowspan="2" \|~~Accidental type~~		! rowspan="2" \|Main accidentals
	! colspan="7" \|Ultimate		! colspan="7" \|Ultimate
	! colspan="4" \|Beyond Ultimate		! colspan="4" \|Beyond Ultimate
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	!Natural		!Natural
	! colspan="2" \|Apotome		! colspan="2" \|Apotome
	! colspan="2" \|Poma/''Ruma''		! colspan="2" \|Poma/Ruma
	! colspan="2" \|Saruyoma		! colspan="2" \|Saruyoma
	! colspan="2" \|Sasaruma		! colspan="2" \|Sasaruma
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	\|-		\|-
	\| rowspan="2" \|Symbols		\| rowspan="2" \|Symbols
	\| rowspan="2" \|♮		\| rowspan="2" \|{{Sagittal\|h}}
	\|♯		\|{{Sagittal\|#}}
	\|♭		\|{{Sagittal\|b}}
	\|↑		\|↑
	\|'''↓'''		\|'''↓'''
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	\| rowspan="2" \|Ọ O̤ O̱		\| rowspan="2" \|Ọ O̤ O̱
	\|-		\|-
	\|𝄪		\|{{Sagittal\|x}}
	\|𝄫		\|{{Sagittal\|bb}}
	\|⇑		\|⇑
	\|'''⇓'''		\|'''⇓'''
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	\| colspan="2" \|11-limit JI		\| colspan="2" \|11-limit JI
	\|}		\|}
			The following accidentals only make sense in rank-2s and edos. For instance, fwismas in gariwizmic, half-apotomes in newt.
			{\| class="wikitable"
			!Extra accidentals
			! colspan="2" \|Fwiwisma
			! colspan="2" \|Half-apotome
			! colspan="2" \|Non-gary poma*
			\|-
			\| rowspan="2" \|Symbols
			\| rowspan="2" \|¡
			\| rowspan="2" \|!
			\|{{Sagittal\|t}}
			\|{{Sagittal\|d}}
			\|p
			\|q
			\|-
			\|{{Sagittal\|t#}}
			\|{{Sagittal\|db}}
			\|pp
			\|qq
			\|-
			\| rowspan="2" \|Spoken
			\| rowspan="2" \|halfpo
			\| rowspan="2" \|halfqu
			\|halfsharp
			\|halfflat
			\|po
			\|qu
			\|-
			\|sesquisharp
			\|sesquiflat
			\|pop(o)
			\|quq(u)
			\|}
			<nowiki>*</nowiki>Not necessary in Ultimate. This can prevent filling the page with garischismas. Logically, here the arrow is spoken ru/zo like in color notation, while the slashed arrow is po/qu.

	=== Syntax ===		=== Syntax ===

Eufalesio: Nomenclature!

2026-05-18T19:27:22Z

Nomenclature!

@@ Line 1: / Line 1: @@
-is 41&53&217, with mapping {{Mapping|1 0 0 25 -33 -13|0 1 0 -14 23 12|0 0 1 0 0 -1}}. It's otherwise known by in the wiki as ''[[cassaschismic]]'' (tad less rambly), also [[User:Eufalesio/Important Tables#Temperament properties of Ultimate edos (I care about)|here]]; but we will simply call it '''Ultimate'''. Our reasoning of this will become clear. Or at least, we expect you to understand why it's clear in our mind.
+iis 41&53&217, with mapping {{Mapping|1 0 0 25 -33 -13|0 1 0 -14 23 12|0 0 1 0 0 -1}}. It's otherwise known by in the wiki as ''[[cassaschismic]]'' (tad less rambly), also [[User:Eufalesio/Important Tables#Temperament properties of Ultimate edos (I care about)|here]]; but we will simply call it '''Ultimate'''. Our reasoning of this will become clear. Or at least, we expect you to understand why it's clear in our mind.
 Special thanks for [[Kite Giedraitis]] for feedback and edits.
@@ Line 157: / Line 157: @@
 ==== 12e ====
-The coarsest tuning that makes sense. It can be written just with sharps and flats, since the poma and the MC are tempered out in all its possible expressions. 12e because patent val tunes 11/8 as a tritone, not fourth. The cassandra mapping is based on 11/8 as a kind of fourth, not tritone. Either way, p11 is NOT there. Consider it an extremely coarse [[yazatha]] tuning. 24edo '''can't''' be used, as it uses a new mapping disjoint from the circle of fitfths and the poma is still tempered out.
+The coarsest tuning that makes sense. It can be written just with apotomes, since the poma and the MC are tempered out in all its possible expressions. 12e because patent val tunes 11/8 as a tritone, not fourth. The cassandra mapping is based on 11/8 as a kind of fourth, not tritone. Either way, p11 is NOT there. Consider it an extremely coarse [[yazatha]] tuning. 24edo '''can't''' be used, as it uses a new mapping disjoint from the circle of fitfths and the poma is still tempered out.
 === Cassandra edos ===
-They are the simplest of the bunch and the easiest to work with. They can be written with sharps and flats, ↑/'''↓''' for the pomas reaching qualites of p5 and p7, and ⇑/'''⇓''' for doubled pomas reaching qualities of p11 and p13.
+They are the simplest of the bunch and the easiest to work with. They can be written with apotomes, ↑/'''↓''' for the pomas reaching qualites of p5 and p7, and ⇑/'''⇓''' for doubled pomas reaching qualities of p11 and p13.
 ==== 41 ====
@@ Line 174: / Line 174: @@
 === Non-cassandra Ultimate ===
-They are very fine and likely impossible to implement into real instruments with an Ultimate layout. They can be written with sharps and flats, ↑/'''↓''' for the pomas, ⇑/'''⇓''' for doubled pomas, and the addition of ^/v for the MC, taken directly from the [[Kite's ups and downs notation|ups-and-downs notation.]] This is completely unfeasible to use with a Lumatone or with any acoustic instrument. Though, it can still be used in a DAW without much problem. Because Ultimate is rank-3, the layout is 3D and thus it is impossible to play on a flat surface, requiring some sort of eldritch holographic "keyspace".
+They are very fine and likely impossible to implement into real instruments with an Ultimate layout. They can be written with apotomes, ↑/'''↓''' for the pomas, ⇑/'''⇓''' for doubled pomas, and the addition of ^/v for the MC, taken directly from the [[Kite's ups and downs notation|ups-and-downs notation.]] This is completely unfeasible to use with a Lumatone or with any acoustic instrument. Though, it can still be used in a DAW without much problem. Because Ultimate is rank-3, the layout is 3D and thus it is impossible to play on a flat surface, requiring some sort of eldritch holographic "keyspace".
 ==== 217 ====
@@ Line 213: / Line 213: @@
 Olympic STILL not enough? Split your losses and use [[5767168/5767125|{S64/S65}]]. Now you observe the olympia and get a schismina accidental. An olympia is 3 of these schisminas. You could write this as dots above or below the accidentals but this is possibly getting a tad crowded. ↑ is 64/63 and 81/80 is v↑. ⇑̱ is 33/32 whilst ⇑ is 4096/3969. v̈⇑ 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''.
 {{Note|Find good extensions to the whatever limit.}}
-To recap: 12edo (sharps/flats), Cassandra (+pomas), Ultimate (+saruyomas), Olympic (+sasarumas), {S64/S65} (+schisminas).
+To recap: 12edo (apotomes), Cassandra (+pomas), Ultimate (+saruyomas), Olympic (+sasarumas), {S64/S65} (+schisminas).

Eufalesio: Added the logical extension to absolute insanity! Theorists, do your worst!

2026-05-18T15:57:43Z

Added the logical extension to absolute insanity! Theorists, do your worst!

@@ Line 1: / Line 1: @@
-is 41&53&217, with mapping {{Mapping|1 0 0 25 -33 -13|0 1 0 -14 23 12|0 0 1 0 0 -1}}. It's otherwise known by in the wiki as ''[[cassaschismic]]'' (technical info inside), also [[User:Eufalesio/Important Tables#Temperament properties of Ultimate edos (I care about)|here]]; but we will simply call it '''Ultimate'''. Our reasoning of this will become clear. Or at least, we expect you to understand why it's clear in our mind.
+is 41&53&217, with mapping {{Mapping|1 0 0 25 -33 -13|0 1 0 -14 23 12|0 0 1 0 0 -1}}. It's otherwise known by in the wiki as ''[[cassaschismic]]'' (tad less rambly), also [[User:Eufalesio/Important Tables#Temperament properties of Ultimate edos (I care about)|here]]; but we will simply call it '''Ultimate'''. Our reasoning of this will become clear. Or at least, we expect you to understand why it's clear in our mind.
 Special thanks for [[Kite Giedraitis]] for feedback and edits.
@@ Line 198: / Line 198: @@
 edo and 270edo have the key property of being even, tempering out the [[kalisma]] and allowing the poma to be halved. Using them this way is reminiscent of [[Gariwizmic]], a very similar subset of Ultimate, but with the MC found deep in the generator chain, not independent. This is useful for easier navigation within a DAW. It's possible to use Gariwizmic wholesale, though it only slightly improves 270edo in precision, Newt is a much better choice for accuracy's sake, though 94edo does ''not'' support it. Gariwizmic provides structure, not the tuning.

Eufalesio: /* Interval list */

2026-05-18T12:15:18Z

Interval list

← Older revision		Revision as of 12:15, 18 May 2026
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	\|-		\|-
	!0		!0
	\|~~720~~/~~361~~		\|351/176
	\|1/1		\|'''1/1'''
	\|-		\|-
	!1		!1
Line 49:		Line 49:
	!4		!4
	\|24/19		\|24/19
	\|81/64		\|19/15
	\|-		\|-
	!5		!5
	\|36/19		\|36/19
	\|~~243~~/~~128~~		\|19/10
	\|-		\|-
	!6		!6
	\|64/45		\|27/19
	\|~~729~~/~~512~~		\|57/40
	\|-		\|-
	!7		!7
Line 84:		Line 84:
	\|-		\|-
	!13		!13
	\|~~243~~/~~160~~		\|38/25
	\|32/21		\|'''32/21'''
	\|-		\|-
	!14		!14
	\|~~729~~/~~640~~		\|57/50
	\|'''8/7'''		\|'''8/7'''
	\|-		\|-
	!15		!15
	\|~~416~~/~~243~~		\|77/45
	\|12/7		\|12/7
	\|-		\|-
	!16		!16
	\|~~104~~/81		\|77/60
	\|9/7		\|9/7
	\|-		\|-

Eufalesio: 176edo sucks lol

2026-05-17T18:22:57Z

176edo sucks lol

← Older revision		Revision as of 18:22, 17 May 2026
Line 145:		Line 145:
	However, if you forgo p5 and p13 for the chain of fifths, you end up with [[gary]]. Gary is a serendipitous temperament, the same as cassandra but optimized for the [[zala]]. 135edo is an essentially perfect tuning, reaching sub-cent levels of error in the subgroup, with a poma of 26.{{Overline\|6}} c.		However, if you forgo p5 and p13 for the chain of fifths, you end up with [[gary]]. Gary is a serendipitous temperament, the same as cassandra but optimized for the [[zala]]. 135edo is an essentially perfect tuning, reaching sub-cent levels of error in the subgroup, with a poma of 26.{{Overline\|6}} c.

	Ultimate is not just an extension of the concept, but what I believe to be the '''end''' of that extension. Ultimate adds an independent "minicomma" generator for p5 and p13, which acts as 385/384, ~352/351, ~5120/5103, layoma, ... etc, being around 4.4c. It doesn't begin to ~~make sense~~ up until 217edo, but 270edo and 311edo are arguably the best tunings. 217edo is alright, but not the best, which would make it a waste of time if it weren't a multiple of 31edo.		Ultimate is not just an extension of the concept, but what I believe to be the '''end''' of that extension. Ultimate adds an independent "minicomma" generator for p5 and p13, which acts as 385/384, ~352/351, ~5120/5103, layoma, ... etc, being around 4.4c. It doesn't begin to be fully useful up until 217edo, but 270edo and 311edo are arguably the best tunings. 217edo is alright, but not the best, which would make it a waste of time if it weren't a multiple of 31edo.

			[[176edo]] also supports it earlier at full structure, but it kinda blows as an equal tuning because the MC is too wide.

	'''The key reasons''' on why Ultimate is ultimate, is ultimately due to the fact that 270edo and 311edo are inside the supported equal tunings, because going any further would make the edosteps not discernible, and because no other edo in their vicinity is as good as them. Beyond that, I see no reason to use edos.		'''The key reasons''' on why Ultimate is ultimate, is ultimately due to the fact that 270edo and 311edo are inside the supported equal tunings, because going any further would make the edosteps not discernible, and because no other edo in their vicinity is as good as them. Beyond that, I see no reason to use edos.