Ed8/3: Difference between revisions

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

== ~~Division of 8/3 into n equal parts~~ ==

== Equivalence ==

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.

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.

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. 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. While the notes are rather farther apart, the scheme is uncannily similar to the [[Mohajira]] (within 8/3) ) temperaments. 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:~~

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]].

~~Galveston Bay Temperament Area~~

== Regular temperament approaches ==

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.

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

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:

~~4L 6s and 6L 4s - Baytown~~

Galveston Bay Temperament Area

'''3L 7s and 7L 3s - Bolivar'''

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

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

* '''3L 7s and 7L 3s - Bolivar'''

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

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

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

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

Neapolitan/Middletown Valley Dorian[10i]: Annapolis

* Middletown Valley Mixolydian[10i]: Oriole

* Other similar decatonic ± 1 scales have the following names:

Middletown Valley Mixolydian[10i]: Oriole

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

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

Other similar decatonic ± 1 scales have the following names:

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:Todo:improve layout]]

[[Category:Todo:improve readability]]

@@ Line 1: / Line 1: @@
 '''Ed8/3''' means division of [[8/3]] into n equal parts.
-== Division of 8/3 into n equal parts ==
+== Equivalence ==
-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.
+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.
-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. 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. While the notes are rather farther apart, the scheme is uncannily similar to the [[Mohajira]] (within 8/3) ) temperaments. 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:
+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]].
-Galveston Bay Temperament Area
+== Regular temperament approaches ==
+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.
-L 8s and 8L 2s, 5L 5s - Galveston Symmetric, Pentachordal Major, Macro-Blackwood
+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:
-L 6s and 6L 4s - Baytown
+Galveston Bay Temperament Area
-'''3L 7s and 7L 3s - Bolivar'''
+* 2L 8s and 8L 2s, 5L 5s - Galveston Symmetric, Pentachordal Major, Macro-Blackwood
+* 4L 6s and 6L 4s - Baytown
+* '''3L 7s and 7L 3s - Bolivar'''
 The similar decatonic scales in edIXs and edXs belong to the Chesapeake Bay Temperament Area:
-Double Neapolitan[10i]: Scala Mariae/Notre Dame
+* Double Neapolitan[10i]: Scala Mariae/Notre Dame
+* Neapolitan/Middletown Valley Dorian[10i]: Annapolis
-Neapolitan/Middletown Valley Dorian[10i]: Annapolis
+* Middletown Valley Mixolydian[10i]: Oriole
+* Other similar decatonic ± 1 scales have the following names:
-Middletown Valley Mixolydian[10i]: Oriole
+* Locrian and Pluperfect/Abundant Phrygian[10i]/Lydian and Perfect Ionian[11i]: Scala Francisci
+* Perfect Ionian through Pluperfect/Abundant Phrygian[9i]: Montréal
-Other similar decatonic ± 1 scales have the following names:
-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:Todo:improve layout]]
 [[Category:Todo:improve readability]]