Ed8/3: Difference between revisions
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''' | 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. | |||
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. | |||
[[Category: | 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 == | |||
{{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 === | |||
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 == | |||
{| 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|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 | 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. |