198edo: Difference between revisions

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~~The '''~~198 equal divisions of the octave''' ('''198edo'''), or the '''198(-tone) equal temperament''' ('''198tet''', '''198et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 198 parts of about 6.06 [[cent]]s each.

== Theory ==

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Like 99, it tempers out [[2401/2400]], [[3136/3125]], [[4375/4374]], [[5120/5103]], [[6144/6125]] and [[10976/10935]] in the 7-limit. In the 11-limit, [[3025/3024]], [[3388/3375]], [[9801/9800]], [[14641/14580]], and [[16384/16335]]; in the 13-limit, [[352/351]], [[676/675]], [[847/845]], [[1001/1000]], [[1716/1715]], [[2080/2079]], [[2200/2197]] and [[6656/6655]].

It provides the [[optimal patent val]] for the 13-limit rank-5 temperament tempering out 352/351, plus other temperaments of lower rank also tempering it out, such as [[hemimist]] and [[namaka]]. Besides [[minthmic chords]], it enables [[essentially tempered chords]] including [[cuthbert ~~triad~~]], [[sinbadmic chords]], and [[petrmic ~~triad~~]] in the 13-odd-limit, in addition to [[island chords]] in the 15-odd-limit.

It provides the [[optimal patent val]] for the 13-limit rank-5 temperament tempering out 352/351, plus other temperaments of lower rank also tempering it out, such as [[hemimist]] and [[namaka]]. Besides [[minthmic chords]], it enables [[essentially tempered chords]] including [[cuthbert chords]], [[sinbadmic chords]], and [[petrmic chords]] in the 13-odd-limit, in addition to [[island chords]] in the 15-odd-limit.

Notably, it is the last edo to map [[64/63]] and [[81/80]] to the same step consistently.

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 {{Infobox ET}}
-The '''198 equal divisions of the octave''' ('''198edo'''), or the '''198(-tone) equal temperament''' ('''198tet''', '''198et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 198 parts of about 6.06 [[cent]]s each.
+{{EDO intro|198}}
 == Theory ==
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 Like 99, it tempers out [[2401/2400]], [[3136/3125]], [[4375/4374]], [[5120/5103]], [[6144/6125]] and [[10976/10935]] in the 7-limit. In the 11-limit, [[3025/3024]], [[3388/3375]], [[9801/9800]], [[14641/14580]], and [[16384/16335]]; in the 13-limit, [[352/351]], [[676/675]], [[847/845]], [[1001/1000]], [[1716/1715]], [[2080/2079]], [[2200/2197]] and [[6656/6655]].
-It provides the [[optimal patent val]] for the 13-limit rank-5 temperament tempering out 352/351, plus other temperaments of lower rank also tempering it out, such as [[hemimist]] and [[namaka]]. Besides [[minthmic chords]], it enables [[essentially tempered chords]] including [[cuthbert triad]], [[sinbadmic chords]], and [[petrmic triad]] in the 13-odd-limit, in addition to [[island chords]] in the 15-odd-limit.
+It provides the [[optimal patent val]] for the 13-limit rank-5 temperament tempering out 352/351, plus other temperaments of lower rank also tempering it out, such as [[hemimist]] and [[namaka]]. Besides [[minthmic chords]], it enables [[essentially tempered chords]] including [[cuthbert chords]], [[sinbadmic chords]], and [[petrmic chords]] in the 13-odd-limit, in addition to [[island chords]] in the 15-odd-limit.
 Notably, it is the last edo to map [[64/63]] and [[81/80]] to the same step consistently.