# Ed8/3

**EdXI** means **Division of an eleventh interval into n equal parts**.

Division of an eleventh (e. g. 8/3) into n equal parts

Division of e. g. the 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 or 11/4 as an equivalence is the use of the 3:4:5:6:(8)/4:5:6:8:(11) 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) or 1071794405/262144 (tempering out the comma |-29 0 8 0 8>). 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) and Magic (within 11/4) temperaments. The terms for it are the "Macromohajira"/"Macromagic" Bolivarian mode (get your mind out of the *other* gutter, they don't have to do with *that country that is there right now*, at least not particularly directly). Rather, they refer to a place that is slightly cleaner:

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