User:Eufalesio/Ultimate: Difference between revisions

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==== 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.

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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 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.

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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.

=== 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"

|+

! rowspan="2" |~~Accidental type~~

! rowspan="2" |Main accidentals

! colspan="7" |Ultimate

! colspan="4" |Beyond Ultimate

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!Natural

! colspan="2" |Apotome

! colspan="2" |Poma/''Ruma''

! colspan="2" |Poma/Ruma

! colspan="2" |Saruyoma

! colspan="2" |Sasaruma

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|-

| rowspan="2" |Symbols

| rowspan="2" |♮

| rowspan="2" |{{Sagittal|h}}

|♯

|{{Sagittal|#}}

|♭

|{{Sagittal|b}}

|↑

|'''↓'''

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| rowspan="2" |Ọ O̤ O̱

|-

|𝄪

|{{Sagittal|x}}

|𝄫

|{{Sagittal|bb}}

|⇑

|'''⇓'''

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| 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 ===

@@ Line 169: / Line 169: @@
 ==== 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.
@@ Line 205: / Line 205: @@
 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.
@@ Line 218: / Line 218: @@
 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"
 |+
-! rowspan="2" |Accidental type
+! rowspan="2" |Main accidentals
 ! colspan="7" |Ultimate
 ! colspan="4" |Beyond Ultimate
@@ Line 227: / Line 228: @@
 !Natural
 ! colspan="2" |Apotome
-! colspan="2" |Poma/''Ruma''
+! colspan="2" |Poma/Ruma
 ! colspan="2" |Saruyoma
 ! colspan="2" |Sasaruma
@@ Line 233: / Line 234: @@
 |-
 | rowspan="2" |Symbols
-| rowspan="2" |♮
+| rowspan="2" |{{Sagittal|h}}
-|♯
+|{{Sagittal|#}}
-|♭
+|{{Sagittal|b}}
 |↑
 |'''↓'''
@@ Line 245: / Line 246: @@
 | rowspan="2" |Ọ O̤ O̱
 |-
-|𝄪
+|{{Sagittal|x}}
-|𝄫
+|{{Sagittal|bb}}
 |⇑
 |'''⇓'''
@@ Line 271: / Line 272: @@
 | 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 ===