Ed5/3
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author JosephRuhf and made on 2016-12-02 10:16:00 UTC.
- The original revision id was 601220128.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
<span style="font-size: 19.5px;">Division of a sixth (e. g. 5/3 or 11/7) into n equal parts</span> Division of e. g. the 5:3 or the 11:7 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 5:3 or 11:7 or another sixth as a base though, is apparent by being named directly in the standard definition of such as the octave based [[Sensi|sensi]] temperament. Many, though not all, of these scales have a pseudo (false) octave, with various degrees of accuracy, but which context(s), if any, it is very perceptually important in is as yet an open question. Incidentally, one way to treat 5/3 or 11/7 as an equivalence is the use of the 6:7:8:(10) or 7:8:9:(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 four 4/3 to get to 8/7 (tempering out the comma 225/224) or four 9/7 to get to 9/8 (tempering out the comma 5929/5832). So, doing this yields 7, 9, and 16 note MOS either way, the 16 note MOS of the two temperaments being mirror images of each other (7L 9s for ed(5/3)s vs 9L 7s for ed(11/7)s). While the notes are rather closer together, the scheme is uncannily similar to meantone. "Microdiatonic" might be a good term for it (even better than for edfs as the generator it uses is an excellent fit for heptatonic MOS) if it hasn't been named yet.
Original HTML content:
<html><head><title>edVI</title></head><body><span style="font-size: 19.5px;">Division of a sixth (e. g. 5/3 or 11/7) into n equal parts</span><br /> <br /> <br /> Division of e. g. the 5:3 or the 11:7 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of <a class="wiki_link" href="/equivalence">equivalence</a> has not even been posed yet. The utility of 5:3 or 11:7 or another sixth as a base though, is apparent by being named directly in the standard definition of such as the octave based <a class="wiki_link" href="/Sensi">sensi</a> temperament. Many, though not all, of these scales have a pseudo (false) octave, with various degrees of accuracy, but which context(s), if any, it is very perceptually important in is as yet an open question.<br /> <br /> Incidentally, one way to treat 5/3 or 11/7 as an equivalence is the use of the 6:7:8:(10) or 7:8:9:(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 four 4/3 to get to 8/7 (tempering out the comma 225/224) or four 9/7 to get to 9/8 (tempering out the comma 5929/5832). So, doing this yields 7, 9, and 16 note MOS either way, the 16 note MOS of the two temperaments being mirror images of each other (7L 9s for ed(5/3)s vs 9L 7s for ed(11/7)s). While the notes are rather closer together, the scheme is uncannily similar to meantone. "Microdiatonic" might be a good term for it (even better than for edfs as the generator it uses is an excellent fit for heptatonic MOS) if it hasn't been named yet.</body></html>