1200edo: Difference between revisions
removed cat notation, made link to temperament more specific via redirect, added some links, switched from inline val coding to template:val |
m Moving from Category:Edo to Category:Equal divisions of the octave using Cat-a-lot |
||
| Line 3: | Line 3: | ||
1200edo is uniquely [[consistent]] through the [[11-limit]], which means the intervals of the 11-limit [[tonality diamond]], and hence their size in cents rounded to the nearest integer, can be found by applying the 11-limit [[patent val]] {{val| 1200 1902 2786 3369 4151 }}. It is [[contorted]] in the [[5-limit]], having the same mapping as 600edo. In the [[7-limit]], it tempers out 2460375/2458624 and 95703125/95551488, leading to a temperament it supports with a period of 1/3 octave and a generator which is an approximate 225/224 of 7\1200, also supported by [[171edo]]. In the 11-limit, it tempers out 9801/9800, 234375/234256 and 825000/823543, leading to a temperament with a half-octave period and an approximate 99/98 generator of 17\1200, also supported by [[494edo]]. In the 7-limit, it provides a val, 1200ccd, which is extremely closely close to the 7-limit [[POTE tuning]] of [[quadritikleismic temperament]]: {{val| 1200 1902 2785 3368 }}. It also provides the optimal patent val for the 224&752 temperament tempering out 2200/2197, 4096/4095, 9801/9800 and 35750/35721. | 1200edo is uniquely [[consistent]] through the [[11-limit]], which means the intervals of the 11-limit [[tonality diamond]], and hence their size in cents rounded to the nearest integer, can be found by applying the 11-limit [[patent val]] {{val| 1200 1902 2786 3369 4151 }}. It is [[contorted]] in the [[5-limit]], having the same mapping as 600edo. In the [[7-limit]], it tempers out 2460375/2458624 and 95703125/95551488, leading to a temperament it supports with a period of 1/3 octave and a generator which is an approximate 225/224 of 7\1200, also supported by [[171edo]]. In the 11-limit, it tempers out 9801/9800, 234375/234256 and 825000/823543, leading to a temperament with a half-octave period and an approximate 99/98 generator of 17\1200, also supported by [[494edo]]. In the 7-limit, it provides a val, 1200ccd, which is extremely closely close to the 7-limit [[POTE tuning]] of [[quadritikleismic temperament]]: {{val| 1200 1902 2785 3368 }}. It also provides the optimal patent val for the 224&752 temperament tempering out 2200/2197, 4096/4095, 9801/9800 and 35750/35721. | ||
[[Category: | [[Category:Equal divisions of the octave]] | ||
[[Category:theory]] | [[Category:theory]] | ||