Ed8/3: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,264 edits
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,264 edits
mNo edit summary
 
(15 intermediate revisions by 5 users not shown)
Line 2: Line 2:


== Equivalence ==
== 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 ==
{{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''.
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''.


Line 24: Line 26:
* Perfect Ionian through Pluperfect/Abundant Phrygian[9i]: Montréal
* 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]]
[[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.}}

Latest revision as of 07:29, 5 October 2025

The equal division of 8/3 (ed8/3) is a tuning obtained by dividing the 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 false octave, with various degrees of accuracy.

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 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.

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.

Joseph Ruhf's approach

This article or section contains multiple idiosyncratic terms. Such terms are used by only a few people and are not regularly used within the community.

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 scales. 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

Galveston Bay Temperament Area

  • 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
  • Neapolitan/Middletown Valley Dorian[10i]: Annapolis
  • Middletown Valley Mixolydian[10i]: Oriole
  • 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

Individual pages for ed8/3's

0…49
0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49


Todo: cleanup, explain edonoi

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.

Retrieved from "https://en.xen.wiki/index.php?title=Ed8/3&oldid=211986"