210edo: Difference between revisions

Cleanup
Rework
Line 3: Line 3:


== Theory ==
== Theory ==
210et [[tempering out|tempers out]] 67108864/66430125 ([[misty comma]]) and 30958682112/30517578125 ([[trisedodge comma]]) in the 5-limit; [[3136/3125]], [[5120/5103]], and 118098/117649 in the 7-limit. It is [[consistent]] to the [[9-odd-limit]], but there is a sharp tendency for [[harmonic]]s [[3/1|3]], [[5/1|5]], and [[7/1|7]].  
210 = 3 × 70, and 210edo shares its [[3/2|fifth]] with [[70edo]]. It is [[consistent]] to the [[9-odd-limit]], but there is a sharp tendency in the lower [[harmonic]]s. The equal temperament [[tempering out|tempers out]] 67108864/66430125 ([[misty comma]]) and 30958682112/30517578125 (trisedodge comma) in the 5-limit; [[3136/3125]], [[5120/5103]], and 118098/117649 in the 7-limit.  


Using the patent val, it tempers out [[176/175]], 1375/1372, [[8019/8000]], and 41503/41472 in the 11-limit; [[351/350]], [[352/351]], [[847/845]], 2197/2187, and 16900/16807 in the 13-limit. Using the 210e val, it tempers out [[540/539]], [[4000/3993]], 6912/6875, and 15488/15435 in the 11-limit; [[351/350]], [[364/363]], [[1001/1000]], [[2197/2187]], and 3584/3575 in the 13-limit.  
Using the 210e val, which does the best, it tempers out [[540/539]], [[4000/3993]], 6912/6875, and 15488/15435 in the 11-limit; [[351/350]], [[364/363]], [[1001/1000]], [[2197/2187]], and 3584/3575 in the 13-limit. Using the patent val, it tempers out [[176/175]], 1375/1372, [[8019/8000]], and 41503/41472 in the 11-limit; [[351/350]], [[352/351]], [[847/845]], 2197/2187, and 16900/16807 in the 13-limit.  


=== Odd harmonics ===
=== Odd harmonics ===
Line 51: Line 51:
| 123\210<br>(17\210)
| 123\210<br>(17\210)
| 702.86<br>(97.14)
| 702.86<br>(97.14)
| 3/2<br>(135\128)
| 3/2<br>(18/17)
| [[Misty]]
| [[Misty]] (210gh)
|-
|-
| 5
| 5
| 98\210<br>(13\210)
| 13\210
| 560.00<br>(74.29)
| 74.29
| 864/625<br>(25/24)
| 25/24
| [[Trisedodge]]
| [[Countdown]] (210e)
|}
|}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct