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]]'' (~~technical info inside~~), 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.

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.

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

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94edo and 270edo have the key property of being even, tempering out the [[kalisma]] and allowing the poma to be halved. Using them this way is reminiscent of [[Gariwizmic]], a very similar subset of Ultimate, but with the MC found deep in the generator chain, not independent. This is useful for easier navigation within a DAW. It's possible to use Gariwizmic wholesale, though it only slightly improves 270edo in precision, Newt is a much better choice for accuracy's sake, though 94edo does ''not'' support it. Gariwizmic provides structure, not the tuning.

== Ultimate still not enough? ==

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 following the same path of reasoning, and add extra pairs of accidentals that are fully retrocompatible.

=== Olympic ===

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, ↑̵.

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.

=== Insanic ===

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).

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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]]'' (technical info inside), 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.
+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.
 Special thanks for [[Kite Giedraitis]] for feedback and edits.
@@ Line 198: / Line 198: @@
 edo and 270edo have the key property of being even, tempering out the [[kalisma]] and allowing the poma to be halved. Using them this way is reminiscent of [[Gariwizmic]], a very similar subset of Ultimate, but with the MC found deep in the generator chain, not independent. This is useful for easier navigation within a DAW. It's possible to use Gariwizmic wholesale, though it only slightly improves 270edo in precision, Newt is a much better choice for accuracy's sake, though 94edo does ''not'' support it. Gariwizmic provides structure, not the tuning.
+== Ultimate still not enough? ==
+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 following the same path of reasoning, and add extra pairs of accidentals that are fully retrocompatible.
+=== Olympic ===
+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, ↑̵.
+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.
+{{Note|Find good extensions to the 19-limit.}}
+=== Insanic ===
+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).