User:Eufalesio/Ultimate: Difference between revisions

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

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 ^/v 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 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, '''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.

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''. 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 /◿̄m3. 17/16 is \M'''⇓⇓̱'''M2.

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.

! colspan="5" |Beyond Ultimate

! colspan="2" |<nowiki>Layoma | Sasaruma</nowiki>

!Tina

| rowspan="2" |^

| rowspan="2" |v

| rowspan="2" |<nowiki>◿ | ◺</nowiki>

| rowspan="2" |<nowiki>◹ | ◸</nowiki>

|/

| colspan="5" |Color notation, or some other JI phonetic coding

| colspan="2" |11-limit JI ?

|???

! colspan="2" |Mercator comma*

! colspan="2" |Fwiwisma

! colspan="2" |Half-apotome

| rowspan="2" |M

| rowspan="2" |W

<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.

* ^'''↓'''M3 = upqumajor third

* F^'''↓'''#5 = ef upqusharp five