User:Eufalesio/Ultimate: Difference between revisions

iis 53 & 94 & 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.

Ultimate can be easily defined in the 13-limit as nullifying the [[2080/2079|sinaisma]], [[minisma]], and [[eufalesma]]. This indirectly means that the [[Symbiotic comma|salozo]], [[Nexus comma|tribilo]], [[Wilschisma|sathoyo]], [[Olympia|salururu]], [[Garischisma|sasaru]], [[Argyria|lolotrizo]] commas, among an infinitude more, are all nullified too. In the 19-limit, it also tempers out the [[1225/1224|subizoyoma]] and [[1216/1215|sanoguma]].

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 – ^^'''⇊⇊'''M2 – ^m3

 

Using pomas (pythagorean commas, [↑/'''↓''']) improves this notation for reasons that will be exposed later.

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.  

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.

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".

[[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.

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. 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.

 

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.

 

 

 

 

 

 

 

 

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...)

 

 

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

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''.

 

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.]]

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 with buzzardsmas, 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. The phonetic coding presented and the alterations are

! colspan="9" |Ultimate

! colspan="6" |Beyond Ultimate

! colspan="2" |[[Buzzardsma|Buzzardsma*]]

! colspan="4" |<small><nowiki>Saruyoma - Sasaruma | Layoma</nowiki></small>

| rowspan="2" |h

|#

|b

|S

|s

| rowspan="2" |M

| rowspan="2" |^

| rowspan="2" |v

| rowspan="2" |<nowiki>Y | X</nowiki>

| rowspan="2" |. .. …

| rowspan="2" | †

| rowspan="2" | ‡

|##

|bb

|H

|h

|super

|sub

| rowspan="2" |<nowiki>gi | bi</nowiki>

|hyper

|hypo

!Edo accidentals

! colspan="2" |[[2835/2816|Fwiwisma]]

! colspan="2" |[[Sqrt(2187/2048)|Half-apotome]]

|¡

|!

|t

|d

|S¡

|t#

|db

|semiper

|semisub

|semiaug

|semidim

|sesquiper

|sesquisub

|sesquiaug

|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: ⇈⇈P1 = mm2, ⇈⇈m2 = m'''↓'''M2; 17/16 is then |\^μ↑m2.

 

<big>Of course, you can use whatever phonetic coding you want, as long as it's not ''too bespoke''. IFYKYK.</big>

For an accidental: (tina) + (schismina) + (sasaruma/layoma) + [saruyoma] + [poma] + [apotome]  

* ^^'''⇊''' = duphypo

* '''↓'''M2 = submajor second

* ^'''↓'''M3 = upsubmajor third

* v⇈m6 = downhyperminor sixth

For pitches: [5L 7s 6|5 nominal] + [accidental] + [octave number] <small>(scientific please, A4=440Hz)</small>

* E⇈b4 = e hyperflat four

* F^'''↓'''#5 = ef upsubsharp five