User:Eufalesio/Ultimate: Difference between revisions
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et cetera... | et cetera... | ||
The [[pergen]] is (P8, P5, | 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 – | 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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=== Interval list === | === Interval list === | ||
Here is a quick compressed cheat sheet of octave-reduced intervals. This is a | Here is a quick compressed cheat sheet of octave-reduced intervals. This is a MASSIvE simplification with many (infinitely many) intervals left out for the sake of brevity. For every entry here, ratios here represent pitch-classes and their pitch class inverses; so for instance 8/5 pitch class is mapped to +8 fifths -1 MC, being the octave inverse of 5/4 pitch class negates the mappings so it is found at -8 fifths + 1 MC. There are no octave reduced primes or prime inverses with positive fifth-span and MC-span. | ||
{| class="wikitable" | {| class="wikitable" | ||
! | ! | ||
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=== Cassandra edos === | === Cassandra edos === | ||
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 | 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 ==== | ==== 41 ==== | ||
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=== Non-cassandra Ultimate === | === Non-cassandra Ultimate === | ||
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 (qualities of p7), | 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 (qualities of p7), ⇈/'''⇊''' for doubled pomas (qualities of p11), and the addition of /vv for the MC (for qualities of p5, p13, p17, p19 aside from pomas) 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 ==== | ==== 217 ==== | ||
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Olympic decouples 64/63 from the chain of fifths; 64/63 is now its own thing, and the poma is ◸↑. | Olympic decouples 64/63 from the chain of fifths; 64/63 is now its own thing, and the poma is ◸↑. | ||
Everything else is the same. | 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 19-limit are bad: the strong one keeps 1729/1728 and 1216/1215, and a decent but weak one adding 5776/5775 and 4200/4199 needs you to split the septimal comma in halves, which is not ideal and also breaks the sequence. Acknowledgements to [[Flora Canou]] for this insight. This means, 19/16 is still | Extensions to the 19-limit are bad: the strong one keeps 1729/1728 and 1216/1215, and a decent but weak one adding 5776/5775 and 4200/4199 needs you to split the septimal comma in halves, which is not ideal and also breaks the sequence. Acknowledgements to [[Flora Canou]] for this insight. This means, 19/16 is still ^m3. 17/16 is vv\'''⇊⇊'''M2. | ||
=== 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 | 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. 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. | ||
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 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 | 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 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. | ||
Look how goddamn accurate this temp is! Look, I even made a technical temp data section! | Look how goddamn accurate this temp is! Look, I even made a technical temp data section! | ||
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: [[CWE]]: ~2 = 1200.000 ¢, ~3/2 = 701.956 ¢, ~5/4 = 386.316 ¢, ~7/4 = 968.828 ¢, ~608/385 = 791.052¢ | : [[CWE]]: ~2 = 1200.000 ¢, ~3/2 = 701.956 ¢, ~5/4 = 386.316 ¢, ~7/4 = 968.828 ¢, ~608/385 = 791.052¢ | ||
'''Optimal''' ET sequence: {{EDOs|53,94,270,???,3395,???, | '''Optimal''' ET sequence: {{EDOs|53,94,270,???,3395,???,8539,16808,20203}} (I have no idea what follows.) | ||
CWE errors: 0.000, 0.001, 0.002, 0.002, 0.001, 0.002, 0.001, 0.001 (the calculator isn't very helpful here...) | CWE errors: 0.000, 0.001, 0.002, 0.002, 0.001, 0.002, 0.001, 0.001 (the calculator isn't very helpful here...) | ||
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=== Easy tables === | === 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 ''' | 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" |Main accidentals | ! rowspan="2" |Main accidentals | ||
! colspan=" | ! colspan="9" |Ultimate | ||
! colspan=" | ! colspan="8" |Beyond Ultimate | ||
|- | |- | ||
!Natural | !Natural | ||
! colspan="2" |Apotome | ! colspan="2" |Apotome | ||
! colspan="2" |Poma/Ruma | ! colspan="2" |Poma/Ruma | ||
! colspan="2" | | ! colspan="2" |[[Buzzardsma|Buzzardsma*]] | ||
! colspan=" | ! colspan="6" |<small><nowiki>Saruyoma - Sasaruma | Layoma</nowiki></small> | ||
! colspan="2" |Schismina | ! colspan="2" |Schismina | ||
! colspan="2" |Tina | ! colspan="2" |Tina | ||
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|↑ | |↑ | ||
|'''↓''' | |'''↓''' | ||
| rowspan="2" | | | rowspan="2" |m | ||
| rowspan="2" | | | rowspan="2" |μ | ||
| rowspan="2" |/ | | rowspan="2" |^ | ||
| | | rowspan="2" |v | ||
| colspan="2" |<nowiki>/| |\</nowiki> | |||
| colspan="2" |<nowiki>\| |/</nowiki> | |||
| rowspan="2" |Ȯ Ö Ō | | rowspan="2" |Ȯ Ö Ō | ||
| rowspan="2" |Ọ O̤ O̱ | | rowspan="2" |Ọ O̤ O̱ | ||
| rowspan="2" | | | rowspan="2" | † | ||
| rowspan="2" | | | rowspan="2" | 𐕣 | ||
|- | |- | ||
|{{Sagittal|x}} | |{{Sagittal|x}} | ||
|{{Sagittal|bb}} | |{{Sagittal|bb}} | ||
| | |⇈ | ||
| | |⇊ | ||
|<nowiki>/|^</nowiki> | |||
<nowiki>|</nowiki>\^ | |||
|<nowiki>/|v</nowiki> | |||
<nowiki>|</nowiki>\v | |||
|<nowiki>\|^ </nowiki> | |||
<nowiki>|</nowiki>/^ | |||
|<nowiki>\|v</nowiki> | |||
<nowiki>|</nowiki>/v | |||
|- | |- | ||
| rowspan="2" |Spoken | | rowspan="2" |Spoken | ||
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|flat | |flat | ||
|po | |po | ||
super | |||
|qu | |qu | ||
sub | |||
| rowspan="2" |me | |||
| rowspan="2" |mu | |||
|up | |up | ||
|down | |down | ||
| colspan=" | | colspan="8" rowspan="2" |??? | ||
|- | |- | ||
|– | |– | ||
|– | |– | ||
|pop(o) | |pop(o) | ||
hyper | |||
|quq(u) | |quq(u) | ||
hypo | |||
|dup | |dup | ||
|dud | |dud | ||
|} | |} | ||
The following accidentals are not part of the main bunch because they are either only part of rank-2s and edos or ligatures. | 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" | ||
! | !Edo accidentals | ||
! colspan="2" |[[2835/2816|Fwiwisma]] | ! colspan="2" |[[2835/2816|Fwiwisma]] | ||
! colspan="2" |[[Sqrt(2187/2048)|Half-apotome]] | ! colspan="2" |[[Sqrt(2187/2048)|Half-apotome]] | ||
|- | |- | ||
| rowspan="2" |Symbols | | rowspan="2" |Symbols | ||
|¡ | |||
|! | |||
|{{Sagittal|t}} | |{{Sagittal|t}} | ||
|{{Sagittal|d}} | |{{Sagittal|d}} | ||
|- | |- | ||
|¡↑ | |||
|'''!↓''' | |||
|{{Sagittal|t#}} | |{{Sagittal|t#}} | ||
|{{Sagittal|db}} | |{{Sagittal|db}} | ||
|- | |- | ||
| rowspan="2" |Spoken | | rowspan="2" |Spoken | ||
| | |halfpo | ||
semiper | |||
| | |halfqu | ||
semisub | |||
|halfsharp | |halfsharp | ||
semiaug | |||
|halfflat | |halfflat | ||
semidim | |||
|- | |- | ||
|sesquipo | |||
sesquiper | |||
|sesquiqu | |||
sesquisub | |||
|sesquisharp | |sesquisharp | ||
sesquiaug | |||
|sesquiflat | |sesquiflat | ||
sesquidim | |||
|} | |} | ||
<nowiki>*</nowiki>Not strictly necessary, but it does simplify notation immensely. The buzzardsma equals the mercator comma in Ultimate (also being tempered out in 53edo), but not beyond it. It is useful for ultra-long chains of fifths and notating p17, which requires at least four rumas. It follows the following equation: | <nowiki>*</nowiki>Not strictly necessary, but it does simplify notation immensely. The buzzardsma equals the mercator comma in Ultimate (also being tempered out in 53edo), but not beyond it. It is useful for ultra-long chains of fifths and notating p17, which requires at least four rumas. It follows the following equation: ⇈⇈P1 = mm2, ⇈⇈m2 = m'''↓'''M2; 17/16 is then |\^μ↑m2. | ||
=== Syntax === | === Syntax === | ||
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* v# = downsharp | * v# = downsharp | ||
* | * ^^'''⇊''' = dupquq | ||
For intervals: [accidental] + [5L 7s 6|5 nominal] | For intervals: [accidental] + [5L 7s 6|5 nominal] | ||
* '''↓'''M2 = qumajor second | * '''↓'''M2 = qumajor second | ||
* | * ^'''↓'''M3 = upqumajor third | ||
* | * v⇈m6 = downpopominor sixth | ||
For pitches: [5L 7s 6|5 nominal] + [accidental] + [octave number] | For pitches: [5L 7s 6|5 nominal] + [accidental] + [octave number] | ||
* D4 = dee four | * D4 = dee four | ||
* | * E⇈b4 = e popoflat four | ||
* F | * F^'''↓'''#5 = ef upqusharp five | ||