User:Jerdle/The Ocean: Difference between revisions
Created page with "The ocean is a set of temperaments related to schismic in the same way deeptone relates 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. 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. The name "ocean" is due to 7c suppo..." Tags: Mobile edit Mobile web edit Advanced mobile edit |
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{{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.}} | |||
'''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. | |||
The name "ocean" | 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. | ||
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]] | |||
Latest revision as of 14:26, 12 January 2026
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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, as all of these temperaments are supported by 7c, the term "ocean" works.
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.
| 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 | [-26 15 1⟩ | Flattone |
| 3 | Bathy | 26 & 33 | [-37 22 1⟩ | Flattertone |
| 4 | Abyss | 33c & 40 | [-48 29 1⟩ | Deeptone |
| 5 | Hadal | 40c & 47 | [-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.