User:Jerdle/The Ocean

This user page is editable by any wiki editor. As a general rule, most users expect their user space to be edited only by themselves, except for minor edits (e.g. maintenance), undoing obviously harmful edits such as vandalism or disruptive editing, and user talk pages. However, by including this message box, the author of this user page has indicated that this page is open to contributions from other users (e.g. content-related edits). Author comments: This is in userspace because it is incomplete and somewhat idiosyncratic. It is missing technical data and is probably formatted in a nonstandard way.

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.