User:Eufalesio/Ultimate: Difference between revisions

is 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 (data dump)]]; 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.

* [[Apotome]] = [[77/72]] (salozoma tempered out)

* [[77/72]] = [[27/26]] * [[36/35]] (eufalesma tempered out)

* [[Pythagorean comma|Poma]] = [[64/63]] (sasaruma tempered out)

* 2 pomas = [[33/32]] (salururuma tempered out)

* [[36/35]] = [[1053/1024]] (minisma tempered out)

* 35/34 = 36/35 (subizoyoma tempered out)

* [[32/27]] = [[11/10]] * [[14/13]] (sinaisma tempered out)

* [[5120/5103]] = [[513/512]] (sanoguma tempered out)

et cetera...

Beyond that, I see no reason to use edos.

Best cassandra tuning. Since the chain takes much longer to close, a [[Buzzardsma|buzzardma]] can be used (the difference between a four-super unison and a minor second; equated in 94edo with a half-poma). 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]].   

Peak. Just like 94edo, it allows half pomas ¡/! for easier navigation. 270edo could be approached with a 2D layout using [[decoid]] layout, though this is hard to do on the Lumatone, having octaves that are very far apart. Just as 217edo, it can be approached using a subset, namely 27edo, but that's not Ultimate. That's [[ennealimmal]].

== Beyond Ultimate ==

There's a reason why I deem Ultimate ultimate. You're supposed to end there and go no further, because Ultimate is right at the limit of practicality. If you're stubborn enough to ignore my warnings and venture into the land of impossible... I still know how you can continue the sequence and add extra pairs of accidentals that are fully retrocompatible.

=== Olympic ===

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.  

=== Insanismic ===

{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, trust me.  

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.  

=== Insanismic AKA Batshit ===

But know: 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=Temperament data|2=[[Subgroup]]: 2.3.5.7.11.13

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

[[File:ULTRAOLYMPIANsymbolset.jpg|center|thumb|960x960px|The name of this notation is henceforth the ULTRAOLYMPIC notation, and the main 4 systems.Metaolympic would go in the middle of Ultimate and Batshit, with tinas but without mina accidentals. Not included since it ''kinda'' breaks the sequence.]]

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.   

The phonetic coding presented and the alterations for written text are:  

! colspan="6" |Beyond Ultimate

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

! colspan="2" |Schismina

<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.