Ed8/3: Difference between revisions

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== 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 does not necessarily imply directly using this interval as an [[equivalence]].~~ The ~~question of equivalence has not even been posed yet. Many, though not all, of these scales have a false~~ [[~~octave~~]]~~, with various degrees of accuracy. The eleventh is also the highest equivalence~~ where composers do not need to go beyond the 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]]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.

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''.

=== Temperament areas ===

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

[[Category:Ed8/3| ]]

== Individual pages for ed8/3's ==

~~[[Category:Edonoi]]~~

{| class="wikitable center-all"

|+ style=white-space:nowrap | 0…49

| [[0ed8/3|0]]

| [[1ed8/3|1]]

| [[2ed8/3|2]]

| [[3ed8/3|3]]

| [[4ed8/3|4]]

| [[5ed8/3|5]]

| [[6ed8/3|6]]

| [[7ed8/3|7]]

| [[8ed8/3|8]]

| [[9ed8/3|9]]

|-

| [[10ed8/3|10]]

| [[11ed8/3|11]]

| [[12ed8/3|12]]

| [[13ed8/3|13]]

| [[14ed8/3|14]]

| [[15ed8/3|15]]

| [[16ed8/3|16]]

| [[17ed8/3|17]]

| [[18ed8/3|18]]

| [[19ed8/3|19]]

|-

| [[20ed8/3|20]]

| [[21ed8/3|21]]

| [[22ed8/3|22]]

| [[23ed8/3|23]]

| [[24ed8/3|24]]

| [[25ed8/3|25]]

| [[26ed8/3|26]]

| [[27ed8/3|27]]

| [[28ed8/3|28]]

| [[29ed8/3|29]]

|-

| [[30ed8/3|30]]

| [[31ed8/3|31]]

| [[32ed8/3|32]]

| [[33ed8/3|33]]

| [[34ed8/3|34]]

| [[35ed8/3|35]]

| [[36ed8/3|36]]

| [[37ed8/3|37]]

| [[38ed8/3|38]]

| [[39ed8/3|39]]

|-

| [[40ed8/3|40]]

| [[41ed8/3|41]]

| [[42ed8/3|42]]

| [[43ed8/3|43]]

| [[44ed8/3|44]]

| [[45ed8/3|45]]

| [[46ed8/3|46]]

| [[47ed8/3|47]]

| [[48ed8/3|48]]

| [[49ed8/3|49]]

|}

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

[[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 2: / Line 2: @@
 == 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 does not necessarily imply directly using this interval as an [[equivalence]]. The question of equivalence has not even been posed yet. Many, though not all, of these scales have a false [[octave]], with various degrees of accuracy. The eleventh is also the highest equivalence where composers do not need to go beyond the 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]]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.
+{{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''.
 === Temperament areas ===
@@ Line 24: / Line 26: @@
 * Perfect Ionian through Pluperfect/Abundant Phrygian[9i]: Montréal
-[[Category:Ed8/3| ]] <!-- main article -->
+== Individual pages for ed8/3's ==
-[[Category:Edonoi]]
+{| class="wikitable center-all"
+|+ style=white-space:nowrap | 0…49
+| [[0ed8/3|0]]
+| [[1ed8/3|1]]
+| [[2ed8/3|2]]
+| [[3ed8/3|3]]
+| [[4ed8/3|4]]
+| [[5ed8/3|5]]
+| [[6ed8/3|6]]
+| [[7ed8/3|7]]
+| [[8ed8/3|8]]
+| [[9ed8/3|9]]
+|-
+| [[10ed8/3|10]]
+| [[11ed8/3|11]]
+| [[12ed8/3|12]]
+| [[13ed8/3|13]]
+| [[14ed8/3|14]]
+| [[15ed8/3|15]]
+| [[16ed8/3|16]]
+| [[17ed8/3|17]]
+| [[18ed8/3|18]]
+| [[19ed8/3|19]]
+|-
+| [[20ed8/3|20]]
+| [[21ed8/3|21]]
+| [[22ed8/3|22]]
+| [[23ed8/3|23]]
+| [[24ed8/3|24]]
+| [[25ed8/3|25]]
+| [[26ed8/3|26]]
+| [[27ed8/3|27]]
+| [[28ed8/3|28]]
+| [[29ed8/3|29]]
+|-
+| [[30ed8/3|30]]
+| [[31ed8/3|31]]
+| [[32ed8/3|32]]
+| [[33ed8/3|33]]
+| [[34ed8/3|34]]
+| [[35ed8/3|35]]
+| [[36ed8/3|36]]
+| [[37ed8/3|37]]
+| [[38ed8/3|38]]
+| [[39ed8/3|39]]
+|-
+| [[40ed8/3|40]]
+| [[41ed8/3|41]]
+| [[42ed8/3|42]]
+| [[43ed8/3|43]]
+| [[44ed8/3|44]]
+| [[45ed8/3|45]]
+| [[46ed8/3|46]]
+| [[47ed8/3|47]]
+| [[48ed8/3|48]]
+| [[49ed8/3|49]]
+|}
+[[Category:Ed8/3's| ]]
+<!-- main article -->
 [[Category:Lists of scales]]
-{{Todo| review }}
+{{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.}}