User:Jerdle/The Ocean: Difference between revisions

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-The ocean is a set of temperaments related to schismic in the same way deeptone relates to meantone.
+{{Editable user page|This is in userspace because it is incomplete and somewhat idiosyncratic. It is missing technical data and is probably formatted in a nonstandard way.}}
-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.
+'''The ocean''' is a group of temperaments related to [[schismic]] in the same way [[deeptone]] and [[mavila]] relate to [[meantone]].
-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.
+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 name "ocean" is due to 7c supporting all of these temperaments. Think seven seas.
+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, as all of these temperaments are supported by 7c, the term "ocean" works.
-This is actually a temperament continuum, and equates Pythagorean chromatic semitones of 2187/2048 to a 16/15 classical diatonic semitone. However, the term "diatonic-chromatic temperament continuum" is taken.
+Some of these temperaments are already named (especially those with low depth), but those with higher depth are not. As such, a series of names based on ocean stratification has been chosen.
+{| class="wikitable"
+|+
+!Depth (d)
+!Name
+!EDO join
+!Comma
+!Temperament with similar generator size
+|-
+|0
+|[[Father]]
+|3 & 5
+|[[16/15]]
+|
+|-
+|1
+|[[Schismic]]
+|5 & 12
+|[[32805/32768]]
+|
+|-
+|2
+|Meso
+|19 & 64
+|{{monzo| -26 15 1 }}
+|[[Flattone]]
+|-
+|3
+|Bathy
+|26 & 33
+|{{monzo| -37 22 1 }}
+|[[Flattertone]]
+|-
+|4
+|Abyss
+|33c & 40
+|{{monzo| -48 29 1 }}
+| rowspan="2" |[[Deeptone]]
+|-
+|5
+|Hadal
+|40c & 47
+|{{monzo| -59 36 1 }}
+|-
+|…
+|…
+|…
+|…
+|
+|-
+|∞
+|[[Whitewood]]
+|7c
+|[[2187/2048]]
+|
+|}
+Beyond hadal, there are no more patent vals (the next temperament being the vaguely ridiculous 47cc & 54b). As such, it is a natural place to stop.
+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. I could use atmosphere names here, but really those seem like they'd be better for an alternative to superpyth rather than to mavila.
+[[Category:Equivalence continua]]