178edo: Difference between revisions

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'''178edo''' is the [[EDO|equal division of the octave]] into 178 parts of 6.7416 cents each. It tempers out 15625/15555 (kleisma) and 571919811374025/562949953421312 in the 5-limit. Using the patent val, it tempers out 225/224, 4375/4374, and 40960000/40353607 in the 7-limit; 243/242, 3025/3024, 4375/4356, and 16896/16807 in the 11-limit; 640/637, 1188/1183, 1625/1617, 1716/1715, and 4096/4095 in the 13-limit. Using the 178def val, it tempers out 10976/10935, 33075/32768, and 50421/50000 in the 7-limit; 441/440, 3388/3375, 4125/4096, and 8019/8000 in the 11-limit; 325/324, 625/624, 847/845, 1287/1280, and 1573/1568 in the 13-limit.

[[~~Category:Edo~~]]

178et [[tempering out|tempers out]] 15625/15552 ([[15625/15552|kleisma]]) and {{monzo| -49 28 2 }} in the 5-limit. Using the [[patent val]], it tempers out [[225/224]], [[4375/4374]], and 40960000/40353607 in the 7-limit; [[243/242]], [[3025/3024]], 4375/4356, and 16896/16807 in the 11-limit; [[640/637]], [[1188/1183]], 1625/1617, [[1716/1715]], and [[4096/4095]] in the 13-limit. Using the 178def val, it tempers out [[10976/10935]], 33075/32768, and [[50421/50000]] in the 7-limit; [[441/440]], [[3388/3375]], [[4125/4096]], and [[8019/8000]] in the 11-limit; [[325/324]], [[625/624]], [[847/845]], [[1287/1280]], and [[1573/1568]] in the 13-limit.

=== Prime harmonics ===

=== Subsets and supersets ===

Since 178 factors into {{factorization|178}}, 178edo contains [[2edo]] and [[89edo]] as its subsets.

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-'''178edo''' is the [[EDO|equal division of the octave]] into 178 parts of 6.7416 cents each. It tempers out 15625/15555 (kleisma) and 571919811374025/562949953421312 in the 5-limit. Using the patent val, it tempers out 225/224, 4375/4374, and 40960000/40353607 in the 7-limit; 243/242, 3025/3024, 4375/4356, and 16896/16807 in the 11-limit; 640/637, 1188/1183, 1625/1617, 1716/1715, and 4096/4095 in the 13-limit. Using the 178def val, it tempers out 10976/10935, 33075/32768, and 50421/50000 in the 7-limit; 441/440, 3388/3375, 4125/4096, and 8019/8000 in the 11-limit; 325/324, 625/624, 847/845, 1287/1280, and 1573/1568 in the 13-limit.
+{{Infobox ET}}
+{{ED intro}}
-[[Category:Edo]]
+et [[tempering out|tempers out]] 15625/15552 ([[15625/15552|kleisma]]) and {{monzo| -49 28 2 }} in the 5-limit. Using the [[patent val]], it tempers out [[225/224]], [[4375/4374]], and 40960000/40353607 in the 7-limit; [[243/242]], [[3025/3024]], 4375/4356, and 16896/16807 in the 11-limit; [[640/637]], [[1188/1183]], 1625/1617, [[1716/1715]], and [[4096/4095]] in the 13-limit. Using the 178def val, it tempers out [[10976/10935]], 33075/32768, and [[50421/50000]] in the 7-limit; [[441/440]], [[3388/3375]], [[4125/4096]], and [[8019/8000]] in the 11-limit; [[325/324]], [[625/624]], [[847/845]], [[1287/1280]], and [[1573/1568]] in the 13-limit.
+=== Prime harmonics ===
+{{Harmonics in equal|178}}
+=== Subsets and supersets ===
+Since 178 factors into {{factorization|178}}, 178edo contains [[2edo]] and [[89edo]] as its subsets.