198edo: Difference between revisions

Line 7:

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 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 triad]], [[sinbadmic chords]], and [[petrmic triad]] 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.

Line 16:

=== ~~Miscellany~~ ===

=== Subsets and supersets ===

198 factors into 2 × 3<sup>2</sup> × 11, and has divisors {{EDOs| 2, 3, 6, 9, 11, 18, 22, 33, 66 and 99 }}.

A step of 198edo is exactly 50 [[purdal]]s or 62 [[prima]]s.

== Intervals ==

@@ Line 7: / Line 7: @@
 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 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 triad]], [[sinbadmic chords]], and [[petrmic triad]] 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.
@@ Line 16: / Line 16: @@
 {{Harmonics in equal|198|columns=11}}
-=== Miscellany ===
+=== Subsets and supersets ===
 factors into 2 × 3<sup>2</sup> × 11, and has divisors {{EDOs| 2, 3, 6, 9, 11, 18, 22, 33, 66 and 99 }}.
+A step of 198edo is exactly 50 [[purdal]]s or 62 [[prima]]s.
 == Intervals ==