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User:TromboneBoi9/Approaches to weird EDOs: Difference between revisions

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Small edits in 13edo section, started 8edo section
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!Note name
!Note name
![[26edo]] name
![[26edo]] name
!Pseudo-diatonic name
!Pseudo-diatonic interval name
|-
|-
|0\13
|0\13
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[[8edo]] is best taken free and atonally, and is far and above best notated as a [[24edo]] subset.
[[8edo]] is best taken free and atonally, and is far and above best notated as a [[24edo]] subset.


The usage of 8edo—or rather, the three-quartertone scale—requires the acceptance of dissonant altered intervals, since the only pure prime it approximates with any decency is [[19/16|19]] (in the form of 2\8, which is the same as 3\12). Even so, 8edo is so small that it is best treated as a scale within a whole ''24edo'' framework.
The usage of 8edo—or rather, the three-quartertone scale—requires the acceptance of strangely altered intervals, since the only pure prime it approximates with any decency is [[19/16|19]] (in the form of 2\8, which is the same as 3\12). Even so, 8edo is so small that it is best treated as a scale within a whole ''24edo'' framework. [[MOS scales]] are certainly possible—albeit sparse since 8 is a small composite number—but it's already a reasonably-sized scale at its own size.
 
That being said, if we were to whittle a simpler scale out of 8edo, [[3L 2s|3L2s]] is the natural choice, generated by 5\8, the 750¢ "fifthoid."


{| class="wikitable"
{| class="wikitable"
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!Cents
!Cents
!24edo name
!24edo name
!3L2s name
!Interval name
|-
|-
|0\8
|0\8
|0
|0
|C
|C
|C
|Perfect unison
|-
|-
|1\8
|1\8
|150
|150
|vD
|vD
|C♯
|Neutral second
|-
|-
|2\8
|2\8
|300
|300
|E♭
|E♭
|D
|Minor third
|-
|-
|3\8
|3\8
|450
|450
|vF
|^E, vF
|D♯
|Supermajor third, Subfourth
|-
|-
|4\8
|4\8
|600
|600
|F♯
|F♯, G♭
|E
|Tritone
|-
|-
|5\8
|5\8
|750
|750
|^G
|^G, vA♭
|G
|Superfifth, Subminor sixth
|-
|-
|6\8
|6\8
|900
|900
|A
|A
|G♯
|Major sixth
|-
|-
|7\8
|7\8
|1050
|1050
|vB
|vB
|A
|Neutral seventh
|-
|-
|8\8
|8\8
|1200
|1200
|C
|C
|C
|Perfect octave
|}
|}


The 3L2s notation system you see here uses a pentatonic CDEGA nominal scheme with the 4|0 mode.
That being said, by themselves, many of the intervals aren't terrible. Connoisseurs of 24edo ([[Wyschnegradsky]], anyone?) would obviously find 8edo rather stimulating, with a perfect one-to-one mixture of traditional intervals and quartertonally-altered intervals.
 
Here's a progression similar to the "V - i"-esque progression I demonstrated in 13edo but in 8edo (24edo subset notation with Stein-Zimmerman quartertone accidentals, numbers show edosteps in 8edo):
 
[[File:8edo-dem1.png|360px]]
[[File:8edo-dem1.mp3]]
 
Like the 13edo progression, this progression largely receives its cohesion melodically. This progression moves the bass by 5\8, the 750¢ superfifth, still recognizable in this instance as a fifth despite its intrusion into the minor sixth interval space. Steps are larger, so the progression must start on the 2\8 minor third rather than any kind of major third.
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