9edt
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 2016-09-12 00:21:19 UTC.
- The original revision id was 591640954.
- 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:
The 9 equal division of 3, the tritave, divides it into 9 equal steps of size 211.328 cents each. It has a decent 7 and an excellent 13, but a 5 which is 39 cents flat; if octaves were added and it was a third, it would count as a neutral third. The corresponding 5/3 is 845 cents, which is a neutral sixth between 8/5 and 5/3, which is really more a 13/8, though this is allegedly a no-twos tuning. The 3.7.13 subgroup tempers out 351/343 and 2197/2187. 9edt is the third [[@The Riemann Zeta Function and Tuning#Removing%20primes|no-twos zeta peak edt]]. Following [[@4edt]], this is the next "Lambda" (BP related) equal division of the tritave; in a certain sense analogous to [[@7edo]] in diatonic music. This scale is also related to [[@17edo]] by which it may be approximated by playing every third step (the 17edo non-octave whole-tone scale), the discrepancy is only about four cents when it gets to 3/1. 0: 1/1 1: 211.328 cents 9/8 2: 422.657 cents 9/7 3: 633.985 cents 13/9 4: 845.313 cents 5/3 5: 1056.642 cents 9/5 6: 1267.970 cents 7: 1479.298 cents 7/3 8: 1690.627 cents 8/3 9: 3/1
Original HTML content:
<html><head><title>9edt</title></head><body>The 9 equal division of 3, the tritave, divides it into 9 equal steps of size 211.328 cents each. It has a decent 7 and an excellent 13, but a 5 which is 39 cents flat; if octaves were added and it was a third, it would count as a neutral third. The corresponding 5/3 is 845 cents, which is a neutral sixth between 8/5 and 5/3, which is really more a 13/8, though this is allegedly a no-twos tuning. The 3.7.13 subgroup tempers out 351/343 and 2197/2187. 9edt is the third <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Removing%20primes" target="_blank">no-twos zeta peak edt</a>.<br /> <br /> Following <a class="wiki_link" href="/4edt" target="_blank">4edt</a>, this is the next "Lambda" (BP related) equal division of the tritave; in a certain sense analogous to <a class="wiki_link" href="/7edo" target="_blank">7edo</a> in diatonic music.<br /> <br /> This scale is also related to <a class="wiki_link" href="/17edo" target="_blank">17edo</a> by which it may be approximated by playing every third step (the 17edo non-octave whole-tone scale), the discrepancy is only about four cents when it gets to 3/1.<br /> <br /> 0: 1/1<br /> 1: 211.328 cents 9/8<br /> 2: 422.657 cents 9/7<br /> 3: 633.985 cents 13/9<br /> 4: 845.313 cents 5/3<br /> 5: 1056.642 cents 9/5<br /> 6: 1267.970 cents<br /> 7: 1479.298 cents 7/3<br /> 8: 1690.627 cents 8/3<br /> 9: 3/1</body></html>