8edo: Difference between revisions

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== Notation ==

=== Ups and downs notation ===

8edo can be notated as a subset of 24edo, using [[Ups and ~~Downs Notation~~|ups and downs]]. It can also be notated as a subset of 16edo, but this is a less intuitive notation.

8edo can be notated as a subset of 24edo, using [[Ups and downs notation|ups and downs]]. It can also be notated as a subset of 16edo, but this is a less intuitive notation.

{| class="wikitable center-all"

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== Chord names ==

[[Ups and ~~Downs Notation~~ #Chords and Chord Progressions|Ups and downs]] can name any 8edo chord. Alterations are always enclosed in parentheses, additions never are. An up, down or mid immediately after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13).

[[Ups and downs notation #Chords and Chord Progressions|Ups and downs]] can name any 8edo chord. Alterations are always enclosed in parentheses, additions never are. An up, down or mid immediately after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13).

8edo chords are very ambiguous, with many chord homonyms. Even the major and minor triads are [[Chord homonym|homonyms]]. Chord components usually default to M2, M3, P4, P5, M6, m7, M9, P11 and M13. Thus D7 has a M3, P5 and m7. 8-edo chord names using 24edo subset names are greatly simplified by using different defaults: instead of the conventional M2, M3, P4, P5, M6, m7, M9, P11 and M13, we have ~2, ^M3, v4, ^5, M6, ~7, ~9, v11 and M13. Thus D7 becomes ^M3, ^5 and ~7.

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== Approximation to JI ==

[[File:~~8ed2-001.svg|alt=alt : Your browser has no SVG support.]]~~

[[File:8ed2-001.svg]]

~~[[:File:8ed2-001.svg|~~8ed2-001.svg]]

== Regular temperament properties ==

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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 ==

A [[Lumatone mapping for 8edo]] is available.

== Music ==

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; [[Randy Winchester]]

* [https://archive.org/details/jamendo-005173/07.mp3 "7. 8 / octave"], from ''[[Comets Over Flatland]]'' (2007)

; [[User:Fitzgerald_Lee|Fitzgerald Lee]]

* [https://youtu.be/zwRDfjLzXkU Jonky Jazz] (2025)

== Ear training ==

@@ Line 121: / Line 121: @@
 == Notation ==
 === Ups and downs notation ===
-edo can be notated as a subset of 24edo, using [[Ups and Downs Notation|ups and downs]]. It can also be notated as a subset of 16edo, but this is a less intuitive notation.
+edo can be notated as a subset of 24edo, using [[Ups and downs notation|ups and downs]]. It can also be notated as a subset of 16edo, but this is a less intuitive notation.
 {| class="wikitable center-all"
@@ Line 303: / Line 303: @@
 == Chord names ==
-[[Ups and Downs Notation #Chords and Chord Progressions|Ups and downs]] can name any 8edo chord. Alterations are always enclosed in parentheses, additions never are. An up, down or mid immediately after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13).
+[[Ups and downs notation #Chords and Chord Progressions|Ups and downs]] can name any 8edo chord. Alterations are always enclosed in parentheses, additions never are. An up, down or mid immediately after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13).
 edo chords are very ambiguous, with many chord homonyms. Even the major and minor triads are [[Chord homonym|homonyms]]. Chord components usually default to M2, M3, P4, P5, M6, m7, M9, P11 and M13. Thus D7 has a M3, P5 and m7. 8-edo chord names using 24edo subset names are greatly simplified by using different defaults: instead of the conventional M2, M3, P4, P5, M6, m7, M9, P11 and M13, we have  ~2, ^M3, v4, ^5, M6, ~7, ~9, v11 and M13. Thus D7 becomes ^M3, ^5 and ~7.
@@ Line 359: / Line 359: @@
 == Approximation to JI ==
-[[File:8ed2-001.svg|alt=alt : Your browser has no SVG support.]]
+[[File:8ed2-001.svg]]
-[[:File:8ed2-001.svg|8ed2-001.svg]]
 == Regular temperament properties ==
@@ Line 513: / 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 ==
+A [[Lumatone mapping for 8edo]] is available.
 == Music ==
@@ Line 566: / Line 567: @@
 ; [[Randy Winchester]]
 * [https://archive.org/details/jamendo-005173/07.mp3 "7. 8 / octave"], from ''[[Comets Over Flatland]]'' (2007)
+; [[User:Fitzgerald_Lee|Fitzgerald Lee]]
+* [https://youtu.be/zwRDfjLzXkU Jonky Jazz] (2025)
 == Ear training ==