Ed8/3
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
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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
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| 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 |
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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. |