8edo: Difference between revisions

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=== 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, in the 5-limit 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 [[~~Jubilismic_clan#Walid|Walid~~]] or a much less accurate [[~~Dimipent_family#Diminished~~|~~Diminished~~]] scale.

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, in the 5-limit this is best interpreted as [[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 [[mother]], but the ideal tuning for that is much closer to [[5edo]]. The 8d val supports septimal father and [[pater]], and is much closer to the ideal tuning for both, as the extremely sharp 7 works better with the {{nowrap| 3 & 5 }}. In terms of multi-period temperaments, it makes for a near perfect [[walid]] or a much less accurate [[diminished (temperament)|diminished]] scale.

== Instruments ==

@@ Line 511: / Line 511: @@
 === Temperaments ===
-edo 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,  in the 5-limit 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 [[Jubilismic_clan#Walid|Walid]] or a much less accurate [[Dimipent_family#Diminished|Diminished]] scale.
+edo 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, in the 5-limit this is best interpreted as [[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 [[mother]], but the ideal tuning for that is much closer to [[5edo]]. The 8d val supports septimal father and [[pater]], and is much closer to the ideal tuning for both, as the extremely sharp 7 works better with the {{nowrap| 3 & 5 }}. In terms of multi-period temperaments, it makes for a near perfect [[walid]] or a much less accurate [[diminished (temperament)|diminished]] scale.
 == Instruments ==