User:Jerdle/The Ocean: Difference between revisions

Revision as of 09:43, 30 June 2025

The ocean is a group of temperaments related to schismic in the same way deeptone and mavila relate to meantone.

While mavila, meantone and deeptone equate 5/4 to a third, ocean temperaments equate it to a (usually diminished) fourth. The number of times the fourth must be diminished to get to ~5/4 is known as the depth of the temperament.

As such, this is an equivalence continuum. The natural name for it would be something like diatonic-chromatic, due to its equating a certain number of 2187/2048 Pythagorean chromatic semitones to a 16/15 pental diatonic semitone, but that is already taken by the father-3 equivalence continuum. It could be apotome-diatonic, but the ocean just sounds like a better name.

Some of these temperaments are already named (especially those with low depth), but those with higher depth are not.


Depth (d)	Name	EDO join	Comma
0	Father	3 & 5	16/15
1	Schismic	5 & 12	32805/32768
2	Dusk	19 & 64	[-26 15 1⟩
3	Midnight	26 & 33	[-37 22 1⟩
4	Abyss	33c & 40	[-48 29 1⟩
5	Hadal	40c & 47	[-59 36 1⟩
∞	7c	7c	2187/2048

While, with positive depth, the fifth gets flatter and flatter, with negative depth, it gets sharper and sharper, converging to 4\7 in each case.

@@ Line 1: / Line 1: @@
-The ocean is a set of temperaments related to schismic in the same way deeptone relates to meantone.
+'''The ocean''' is a group of temperaments related to [[schismic]] in the same way [[deeptone]] and [[mavila]] relate to [[meantone]].
-More precisely, these temperaments equate 5/4 to a kind of fourth. There is a single parameter d such that 5/4 is equated to a d-fold diminished fourth.
+While mavila, meantone and deeptone equate [[5/4]] to a third, ocean temperaments equate it to a (usually diminished) fourth. The number of times the fourth must be diminished to get to ~5/4 is known as the depth of the temperament.
-The temperaments with small d are already named. 0 gets you father, 1 gets you schismic. And as d tends to infinity, this tends to 7c-edo, which is a tuning of all temperaments here.
+As such, this is an [[equivalence continuum]]. The natural name for it would be something like diatonic-chromatic, due to its equating a certain number of [[2187/2048]] Pythagorean chromatic semitones to a [[16/15]] pental diatonic semitone, but that is already taken by the [[father-3 equivalence continuum]]. It could be apotome-diatonic, but the ocean just sounds like a better name.
-The name "ocean" is due to 7c supporting all of these temperaments. Think seven seas.
+Some of these temperaments are already named (especially those with low depth), but those with higher depth are not.
+{| class="wikitable"
-This is actually an equivalence continuum, and equates Pythagorean chromatic semitones of 2187/2048 to a 16/15 classical diatonic semitone. However, the term "diatonic-chromatic equivalence continuum" is taken, so this is simply the ocean.
+|+
+!Depth (d)
+!Name
+!EDO join
+!Comma
+|-
+|0
+|[[Father]]
+|3 & 5
+|[[16/15]]
+|-
+|1
+|[[Schismic]]
+|5 & 12
+|[[32805/32768]]
+|-
+|2
+|Dusk
+|19 & 64
+|{{monzo| -26 15 1 }}
+|-
+|3
+|Midnight
+|26 & 33
+|{{monzo| -37 22 1 }}
+|-
+|4
+|Abyss
+|33c & 40
+|{{monzo| -48 29 1 }}
+|-
+|5
+|Hadal
+|40c & 47
+|{{monzo| -59 36 1 }}
+|-
+|∞
+|[[7edo|7c]]
+|7c
+|[[2187/2048]]
+|}
+While, with positive depth, the fifth gets flatter and flatter, with negative depth, it gets sharper and sharper, converging to 4\7 in each case.

User:Jerdle/The Ocean: Difference between revisions

Revision as of 09:43, 30 June 2025

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