Ed8/3: Difference between revisions

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'''~~Ed8~~/3''' ~~means division of~~ [[8/3]] ~~into n~~ equal ~~parts~~.

The '''equal division of 8/3''' ('''ed8/3''') is a [[tuning]] obtained by dividing the [[8/3|Pythagorean perfect eleventh (8/3)]] in a certain number of [[equal]] steps.

== Equivalence ==

Division of 8/3 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed8/3 scales have a perceptually important [[Pseudo-octave|false octave]], with various degrees of accuracy.

~~Division of 8/3 into equal parts can be conceived of as to directly use this interval as an equivalence, or not.~~ The ~~question of [[equivalence]] has not even been posed yet. Many, though not all, of these scales have a pseudo (false)~~ [[~~octave~~]]~~, with various degrees of accuracy. The eleventh is also the highest equivalence~~ where composers do not need to go beyond the ~~pseudo (~~false) octave just to have a reasonably complete chordal harmony. ~~However, the~~ utility of 8:3 or another eleventh as a ~~base is complicated~~ by the fact that 8:3 is the avoid note in a major modality ~~although this~~ matters less in Mixolydian than it does in Ionian given that the former is the natural dominant scale anyway.

The eleventh is the highest [[period]] where composers do not need to go beyond the false octave just to have a reasonably complete chordal harmony. The structural utility of 8/3 or another eleventh as a period may be undermined, though, by the fact that 8/3 is the {{w|avoid note}} in a major modality. This matters less in Mixolydian than it does in Ionian given that the former is the natural dominant scale anyway.

~~Incidentally, one way~~ to ~~treat 8~~/3 ~~as an equivalence~~ is the use of the 3:4:5:6:(8) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in [[meantone]].

One approach to ed8/3 tunings is the use of the 3:4:5:6:(8) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in [[meantone]].

== ~~Regular temperament approaches~~ ==

== Joseph Ruhf's approach ==

Whereas in meantone it takes four [[3/2]] to get to [[5/1]], here it takes twelve octaves to get to [[134217718/98415]] (tempering out the schisma). So, doing this yields 7, 10 and 17 or 13, 16 or 19 note [[~~MOS~~ scale~~|MOS~~]]. While the notes are rather farther apart, the scheme is uncannily similar to the [[~~Mohajira~~]] (within 8/3) temperaments.

Whereas in meantone it takes four [[3/2]] to get to [[5/1]], here it takes twelve octaves to get to [[134217718/98415]] (tempering out the schisma). So, doing this yields 7-, 10- and 17- or 13-, 16- or 19-note [[mos scale]]s. While the notes are rather farther apart, the scheme is uncannily similar to the [[mohajira]] (within 8/3) temperaments. [[Joseph Ruhf]] calls this the ''Macromohajira Bolivarian mode''.

~~The terms for it are~~ the "Macromohajira" Bolivarian mode ~~(get your mind out of the ''other'' gutter, they don't have to do with~~ ''~~[[wikipedia:Venezuela|that country that is there right now]]'', at least not particularly directly)~~. ~~Rather, they refer to a place that is slightly cleaner:~~

=== Temperament areas ===

Galveston Bay Temperament Area

* 2L 8s and 8L 2s, 5L 5s - Galveston Symmetric, Pentachordal Major, Macro-Blackwood

* 4L 6s and 6L 4s - Baytown

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The similar decatonic scales in edIXs and edXs belong to the Chesapeake Bay Temperament Area:

* Double Neapolitan[10i]: Scala Mariae/Notre Dame

* Neapolitan/Middletown Valley Dorian[10i]: Annapolis

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* Locrian and Pluperfect/Abundant Phrygian[10i]/Lydian and Perfect Ionian[11i]: Scala Francisci

* Perfect Ionian through Pluperfect/Abundant Phrygian[9i]: Montréal

[[Category:~~Equal-step tuning~~]]

[[Category:~~Todo:cleanup~~]]

[[Category:Ed8/3's| ]]

~~[[Category:Todo:improve layout]]~~

~~[[Category:Todo:improve readability]]~~

[[Category:Lists of scales]]

{{todo|inline=1|cleanup|explain edonoi|text=Most people do not think 8/3 sounds like an equivalence, so there must be some other reason why people are dividing it — some property ''other than'' equivalence that makes people want to divide it. Please add to this page an explanation of what that reason is... The page also needs a general overall cleanup.}}

@@ Line 1: / Line 1: @@
-'''Ed8/3''' means division of [[8/3]] into n equal parts.
+The '''equal division of 8/3''' ('''ed8/3''') is a [[tuning]] obtained by dividing the [[8/3|Pythagorean perfect eleventh (8/3)]] in a certain number of [[equal]] steps.
 == Equivalence ==
+Division of 8/3 into equal parts does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed8/3 scales have a perceptually important [[Pseudo-octave|false octave]], with various degrees of accuracy.
-Division of 8/3 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of [[equivalence]] has not even been posed yet. Many, though not all, of these scales have a pseudo (false) [[octave]], with various degrees of accuracy. The eleventh is also the highest equivalence where composers do not need to go beyond the pseudo (false) octave just to have a reasonably complete chordal harmony. However, the utility of 8:3 or another eleventh as a base is complicated by the fact that 8:3 is the avoid note in a major modality although this matters less in Mixolydian than it does in Ionian given that the former is the natural dominant scale anyway.
+The eleventh is the highest [[period]] where composers do not need to go beyond the false octave just to have a reasonably complete chordal harmony. The structural utility of 8/3 or another eleventh as a period may be undermined, though, by the fact that 8/3 is the {{w|avoid note}} in a major modality. This matters less in Mixolydian than it does in Ionian given that the former is the natural dominant scale anyway.
-Incidentally, one way to treat 8/3 as an equivalence is the use of the 3:4:5:6:(8) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in [[meantone]].
+One approach to ed8/3 tunings is the use of the 3:4:5:6:(8) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in [[meantone]].
-== Regular temperament approaches ==
+== Joseph Ruhf's approach ==
-Whereas in meantone it takes four [[3/2]] to get to [[5/1]], here it takes twelve octaves to get to [[134217718/98415]] (tempering out the schisma). So, doing this yields 7, 10 and 17 or 13, 16 or 19 note [[MOS scale|MOS]]. While the notes are rather farther apart, the scheme is uncannily similar to the [[Mohajira]] (within 8/3) temperaments.
+{{idiosyncratic terms}}
+Whereas in meantone it takes four [[3/2]] to get to [[5/1]], here it takes twelve octaves to get to [[134217718/98415]] (tempering out the schisma). So, doing this yields 7-, 10- and 17- or 13-, 16- or 19-note [[mos scale]]s. While the notes are rather farther apart, the scheme is uncannily similar to the [[mohajira]] (within 8/3) temperaments. [[Joseph Ruhf]] calls this the ''Macromohajira Bolivarian mode''.
-The terms for it are the "Macromohajira" Bolivarian mode (get your mind out of the ''other'' gutter, they don't have to do with ''[[wikipedia:Venezuela|that country that is there right now]]'', at least not particularly directly). Rather, they refer to a place that is slightly cleaner:
+=== Temperament areas ===
 Galveston Bay Temperament Area
 * 2L 8s and 8L 2s, 5L 5s - Galveston Symmetric, Pentachordal Major, Macro-Blackwood
 * 4L 6s and 6L 4s - Baytown
@@ Line 19: / Line 19: @@
 The similar decatonic scales in edIXs and edXs belong to the Chesapeake Bay Temperament Area:
 * Double Neapolitan[10i]: Scala Mariae/Notre Dame
 * Neapolitan/Middletown Valley Dorian[10i]: Annapolis
@@ Line 26: / Line 25: @@
 * Locrian and Pluperfect/Abundant Phrygian[10i]/Lydian and Perfect Ionian[11i]: Scala Francisci
 * Perfect Ionian through Pluperfect/Abundant Phrygian[9i]: Montréal
-[[Category:Equal-step tuning]]
-[[Category:Todo:cleanup]]
+[[Category:Ed8/3's| ]]
-[[Category:Todo:improve layout]]
+<!-- main article -->
-[[Category:Todo:improve readability]]
+[[Category:Lists of scales]]
+{{todo|inline=1|cleanup|explain edonoi|text=Most people do not think 8/3 sounds like an equivalence, so there must be some other reason why people are dividing it — some property ''other than'' equivalence that makes people want to divide it. Please add to this page an explanation of what that reason is... The page also needs a general overall cleanup.}}