87edo: Difference between revisions

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The '''87 equal temperament''', often abbreviated '''87-tET''', '''87-EDO''', or '''87-ET''', is the scale derived by dividing the octave into 87 equally-sized steps, where each step represents a frequency ratio of 13.79 [[cent|cents]]. It is solid as both a [[13-limit]] (or [[15 odd limit]]) and as a [[5-limit]] system, and of course does well enough in any limit in between. It represents the [[13-limit]] [[tonality diamond]] both uniquely and [[consistent|consistently]], and is the smallest equal temperament to do so.

The '''87 equal temperament''', often abbreviated '''87-tET''', '''87-EDO''', or '''87-ET''', is the scale derived by dividing the octave into 87 equally-sized steps, where each step represents a frequency ratio of 13.79 [[cent|cents]]. It is solid as both a [[13-limit]] (or [[15 odd limit]]) and as a [[5-limit]] system, and of course does well enough in any limit in between. It represents the [[13-limit]] [[tonality diamond]] both uniquely and [[consistent|consistently]] (see [[87edo/13-limit detempering]]), and is the smallest equal temperament to do so.

87et [[tempering out|tempers out]] 196/195, 325/324, 352/351, 364/363, 385/384, 441/440, 625/624, 676/675, and 1001/1000 as well as the 29-comma, <46 -29|, the misty comma, <26 -12 -3|, the kleisma, 15625/15552, 245/243, 1029/1024, 3136/3125, and 5120/5103.

Revision as of 14:58, 12 June 2020 view source FloraC (talk \| contribs) autopatrolled, Bureaucrats, Interface administrators, Sysops 18,328 edits Move the detempering table somewhere else and replace w/ a normal one Tag: Visual edit: Switched ← Older edit		Revision as of 16:25, 12 June 2020 view source Xenwolf (talk \| contribs) autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops 8,705 edits the (now detached) table is important for this page: it shows the relevance of 87edo Newer edit →
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	The '''87 equal temperament''', often abbreviated '''87-tET''', '''87-EDO''', or '''87-ET''', is the scale derived by dividing the octave into 87 equally-sized steps, where each step represents a frequency ratio of 13.79 [[cent\|cents]]. It is solid as both a [[13-limit]] (or [[15 odd limit]]) and as a [[5-limit]] system, and of course does well enough in any limit in between. It represents the [[13-limit]] [[tonality diamond]] both uniquely and [[consistent\|consistently]], and is the smallest equal temperament to do so.		The '''87 equal temperament''', often abbreviated '''87-tET''', '''87-EDO''', or '''87-ET''', is the scale derived by dividing the octave into 87 equally-sized steps, where each step represents a frequency ratio of 13.79 [[cent\|cents]]. It is solid as both a [[13-limit]] (or [[15 odd limit]]) and as a [[5-limit]] system, and of course does well enough in any limit in between. It represents the [[13-limit]] [[tonality diamond]] both uniquely and [[consistent\|consistently]] (see [[87edo/13-limit detempering]]), and is the smallest equal temperament to do so.

	87et [[tempering out\|tempers out]] 196/195, 325/324, 352/351, 364/363, 385/384, 441/440, 625/624, 676/675, and 1001/1000 as well as the 29-comma, <46 -29\|, the misty comma, <26 -12 -3\|, the kleisma, 15625/15552, 245/243, 1029/1024, 3136/3125, and 5120/5103.		87et [[tempering out\|tempers out]] 196/195, 325/324, 352/351, 364/363, 385/384, 441/440, 625/624, 676/675, and 1001/1000 as well as the 29-comma, <46 -29\|, the misty comma, <26 -12 -3\|, the kleisma, 15625/15552, 245/243, 1029/1024, 3136/3125, and 5120/5103.