Ed8/3: Difference between revisions

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<font style="font-size: 19.5px;">Division of an eleventh (e. g. 8/3) into n equal parts</font>

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~~. The utility of 8:3 or another eleventh as a base though, is apparent by being used at the base of so much modern tonal harmony~~. Many, though not all, of these scales have a pseudo (false) octave, with various degrees of accuracy.

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:(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 ''[[wikipedia:Venezuela|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'''

[[Category:Equal-step tuning]]

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 <font style="font-size: 19.5px;">Division of an eleventh (e. g. 8/3) into n equal parts</font>
-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. The utility of 8:3 or another eleventh as a base though, is apparent by being used at the base of so much modern tonal harmony. Many, though not all, of these scales have a pseudo (false) octave, with various degrees of accuracy.
+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:(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 ''[[wikipedia:Venezuela|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
+L 8s and 8L 2s, 5L 5s - Galveston Symmetric, Pentachordal Major, Macro-Blackwood
+L 6s and 6L 4s - Baytown
+'''3L 7s and 7L 3s - Bolivar'''
 [[Category:Equal-step tuning]]