User:Eufalesio/Ultimate: Difference between revisions

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is 41&53&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.

iis 41&53&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.

Special thanks for [[Kite Giedraitis]] for feedback and edits.

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==== 12e ====

The coarsest tuning that makes sense. It can be written just with ~~sharps and flats~~, since the poma and the MC are tempered out in all its possible expressions. 12e because patent val tunes 11/8 as a tritone, not fourth. The cassandra mapping is based on 11/8 as a kind of fourth, not tritone. Either way, p11 is NOT there. Consider it an extremely coarse [[yazatha]] tuning. 24edo '''can't''' be used, as it uses a new mapping disjoint from the circle of fitfths and the poma is still tempered out.

The coarsest tuning that makes sense. It can be written just with apotomes, since the poma and the MC are tempered out in all its possible expressions. 12e because patent val tunes 11/8 as a tritone, not fourth. The cassandra mapping is based on 11/8 as a kind of fourth, not tritone. Either way, p11 is NOT there. Consider it an extremely coarse [[yazatha]] tuning. 24edo '''can't''' be used, as it uses a new mapping disjoint from the circle of fitfths and the poma is still tempered out.

=== Cassandra edos ===

They are the simplest of the bunch and the easiest to work with. They can be written with ~~sharps and flats~~, ↑/'''↓''' for the pomas reaching qualites of p5 and p7, and ⇑/'''⇓''' for doubled pomas reaching qualities of p11 and p13.

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 ====

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=== Non-cassandra Ultimate ===

They are very fine and likely impossible to implement into real instruments with an Ultimate layout. They can be written with ~~sharps and flats~~, ↑/'''↓''' for the pomas, ⇑/'''⇓''' for doubled pomas, and the addition of ^/v for the MC, 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".

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, ⇑/'''⇓''' for doubled pomas, and the addition of ^/v for the MC, 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 ====

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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. v̈⇑ 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''.

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

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

== Nomenclature and notation ==

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 ===

{| class="wikitable"

|+

! rowspan="2" |Accidental type

! colspan="7" |Ultimate

! colspan="4" |Beyond Ultimate

|-

!Natural

! colspan="2" |Apotome

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

! colspan="2" |Saruyoma

! colspan="2" |Sasaruma

! colspan="2" |Schismina

|-

| rowspan="2" |Symbols

| rowspan="2" |♮

|♯

|♭

|↑

|'''↓'''

|^

|v

| rowspan="2" |◺

| rowspan="2" |◸

| rowspan="2" |Ȯ Ö Ō

| rowspan="2" |Ọ O̤ O̱

|-

|𝄪

|𝄫

|⇑

|'''⇓'''

|M

|W

|-

| rowspan="2" |Spoken

| rowspan="2" |natural

|sharp

|flat

|po

|qu

|up

|down

| colspan="4" |Color notation, or some other JI phonetic coding

|-

|–

|pop(o)

|quq(u)

|dup

|dud

| colspan="2" |7-limit JI

| colspan="2" |11-limit JI

|}

=== Syntax ===

* For an accidental: (schismina) + (sasaruma) + [saruyoma] + [poma] + [apotome] v# = downsharp, M'''⇓''' = dupquq

* For intervals: [accidental] + [5L 7s 6|5 nominal] '''↓'''M2, ^'''↓'''M3, v⇑m6; qumajor second, upqumajor third, downpopominor sixth

* For pitches: [5L 7s 6|5 nominal] + [accidental] + [octave number] Example: D4, E⇑b4, F^'''↓'''#5; dee four, e popoflat four, ef upqusharp five

@@ Line 1: / Line 1: @@
-is 41&53&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.
+iis 41&53&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.
 Special thanks for [[Kite Giedraitis]] for feedback and edits.
@@ Line 157: / Line 157: @@
 ==== 12e ====
-The coarsest tuning that makes sense. It can be written just with sharps and flats, since the poma and the MC are tempered out in all its possible expressions. 12e because patent val tunes 11/8 as a tritone, not fourth. The cassandra mapping is based on 11/8 as a kind of fourth, not tritone. Either way, p11 is NOT there. Consider it an extremely coarse [[yazatha]] tuning. 24edo '''can't''' be used, as it uses a new mapping disjoint from the circle of fitfths and the poma is still tempered out.
+The coarsest tuning that makes sense. It can be written just with apotomes, since the poma and the MC are tempered out in all its possible expressions. 12e because patent val tunes 11/8 as a tritone, not fourth. The cassandra mapping is based on 11/8 as a kind of fourth, not tritone. Either way, p11 is NOT there. Consider it an extremely coarse [[yazatha]] tuning. 24edo '''can't''' be used, as it uses a new mapping disjoint from the circle of fitfths and the poma is still tempered out.
 === Cassandra edos ===
-They are the simplest of the bunch and the easiest to work with. They can be written with sharps and flats, ↑/'''↓''' for the pomas reaching qualites of p5 and p7, and ⇑/'''⇓''' for doubled pomas reaching qualities of p11 and p13.
+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 ====
@@ Line 174: / Line 174: @@
 === Non-cassandra Ultimate ===
-They are very fine and likely impossible to implement into real instruments with an Ultimate layout. They can be written with sharps and flats, ↑/'''↓''' for the pomas, ⇑/'''⇓''' for doubled pomas, and the addition of ^/v for the MC, 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".
+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, ⇑/'''⇓''' for doubled pomas, and the addition of ^/v for the MC, 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 ====
@@ Line 213: / Line 213: @@
 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. v̈⇑ 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''.
 {{Note|Find good extensions to the whatever limit.}}
-To recap: 12edo (sharps/flats), Cassandra (+pomas), Ultimate (+saruyomas), Olympic (+sasarumas), {S64/S65} (+schisminas).
+To recap: 12edo (apotomes), Cassandra (+pomas), Ultimate (+saruyomas), Olympic (+sasarumas), {S64/S65} (+schisminas).
+== Nomenclature and notation ==
+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 ===
+{| class="wikitable"
+|+
+! rowspan="2" |Accidental type
+! colspan="7" |Ultimate
+! colspan="4" |Beyond Ultimate
+|-
+!Natural
+! colspan="2" |Apotome
+! colspan="2" |Poma/''Ruma''
+! colspan="2" |Saruyoma
+! colspan="2" |Sasaruma
+! colspan="2" |Schismina
+|-
+| rowspan="2" |Symbols
+| rowspan="2" |♮
+|♯
+|♭
+|↑
+|'''↓'''
+|^
+|v
+| rowspan="2" |◺
+| rowspan="2" |◸
+| rowspan="2" |Ȯ Ö Ō
+| rowspan="2" |Ọ O̤ O̱
+|-
+|𝄪
+|𝄫
+|⇑
+|'''⇓'''
+|M
+|W
+|-
+| rowspan="2" |Spoken
+| rowspan="2" |natural
+|sharp
+|flat
+|po
+|qu
+|up
+|down
+| colspan="4" |Color notation, or some other JI phonetic coding
+|-
+|–
+|–
+|pop(o)
+|quq(u)
+|dup
+|dud
+| colspan="2" |7-limit JI
+| colspan="2" |11-limit JI
+|}
+=== Syntax ===
+* For an accidental: (schismina) + (sasaruma) + [saruyoma] + [poma] + [apotome] v# = downsharp, M'''⇓''' = dupquq
+* For intervals: [accidental] + [5L 7s 6|5 nominal] '''↓'''M2, ^'''↓'''M3, v⇑m6; qumajor second, upqumajor third, downpopominor sixth
+* For pitches: [5L 7s 6|5 nominal] + [accidental] + [octave number] Example: D4, E⇑b4, F^'''↓'''#5; dee four, e popoflat four, ef upqusharp five