8edo: Difference between revisions
m Infobox ET now computes most parameters automatically |
Create temperament section, expand commas. |
||
| Line 207: | Line 207: | ||
! [[Color name]] | ! [[Color name]] | ||
! Name(s) | ! Name(s) | ||
|- | |||
| 3 | |||
| [[8192/6561]] | |||
| {{monzo| 13 -8 }} | |||
| 384.35 | |||
| sawa 4th | |||
| Pythagorean diminished fourth | |||
|- | |||
| 5 | |||
| [[16/15]] | |||
| {{monzo| 4 -1 -1 }} | |||
| 111.73 | |||
| gu 2nd | |||
| Classic minor second | |||
|- | |- | ||
| 5 | | 5 | ||
| Line 298: | Line 312: | ||
| Triluyo | | Triluyo | ||
| Wizardharry | | Wizardharry | ||
|- | |||
| 13 | |||
| [[40/39]] | |||
| {{monzo| 3 -1 1 0 0 -1 }} | |||
| 43.83 | |||
| Thuyo unison | |||
| tridecimal minor diesis | |||
|} | |} | ||
<references/> | <references/> | ||
| Line 321: | Line 342: | ||
</pre> | </pre> | ||
=== | === Temperaments === | ||
8edo is fairly composite, so the only step that generates a [[mos]] scale that covers every interval other than the 1 is the 3, producing scales of 332 and [[3L_2s|21212]]. In terms of temperaments, this is best interpreted as [[Father_family|Father]], as 8edo is the highest edo that tempers out the diatonic semitone in it's [[patent val]], merging 5/4 and 4/3 into a single interval, which is also the generator. This means major and minor chords are rotations of each other, making them inaccurate but very simple, with even the 5 note mos having 3 of both and providing a functional skeleton of 5-limit harmony, albeit with some very strange enharmonic equivalences. In terms of 7-limit extensions things get even more inaccurate, as the patent val supports [[Father_family#Mother|Mother]], but the ideal tuning for that is much closer to [[5edo]]. The d val supports septimal father and [[Father_family#Pater|Pater]], and is much closer to the ideal tuning for both, as the extremely sharp 7 works better with the 3&5. In terms of multi-period temperaments, it makes for a near perfect [[Father_family#Walid|Walid]] or a much less accurate [[Dimipent_family#Diminished|Diminished]] scale. | |||
== Music == | == Music == | ||