197ed12: Difference between revisions

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'''[[Ed12|Division of the twelfth harmonic]] into 197 equal parts''' (197ED12) is very nearly identical to [[55edo|55 EDO]], but with the [[12/1]] rather than the 2/1 being just. The octave is about 1.05 [[cent]]s stretched and the step size is about 21.84 cents.

== Theory ==

This tuning ~~tempers out~~ [[~~81/80~~]] in the ~~5-limit;~~ [[~~121~~/~~120~~]] ~~in the 11-limit; 91/90 and 169/168 in the 13-limit; 154/153 in the 17-limit; 133/132 and 76/75 in the 19-limit; 117/115~~, ~~161~~/~~160~~, and ~~162/161 in the 23-limit;~~ [[~~116~~/~~115~~]], ~~117~~/~~116, and 147/145 in~~ the 29-limit~~; 93/92 and 156/155 in~~ the 31-limit~~; 111/110 in~~ the [[~~37-limit~~]]~~; 86/85 and 129/128 in~~ the ~~43-limit; 141/140~~ in the 47-limit~~; 123/122 in the 61-limit; 143/142 in the 71-limit; 146/145~~ and ~~147/146 in the 73-limit; 166/165 in~~ the ~~83-limit; 98/97~~ in the ~~97-limit; 101/100 in the 101-limit; 103/102 in the 103-limit; 107/106 in the 107-limit; 114/113 in the 113-limit; and 127/125 in the 127~~-limit.

This tuning serves as a stretched version of [[55edo]], improving the accuracy of primes [[3/1|3]], [[7/1|7]], and [[11/1|11]], though prime [[5/1|5]] becomes worse. The [[patent val]]s match through the [[11-limit]], with the [[13-limit]] corresponding to the 55f [[val]] (written with [[wart notation]]). It thus tempers out the same [[comma]]s as 55edo in the 11-limit, and the same commas as 55f in the [[13-limit]].

==Harmonics==

== Harmonics ==

~~[[Category:Edonoi]]~~

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 {{Infobox ET}}
-'''[[Ed12|Division of the twelfth harmonic]] into 197 equal parts''' (197ED12) is very nearly identical to [[55edo|55 EDO]], but with the [[12/1]] rather than the 2/1 being just. The octave is about 1.05 [[cent]]s stretched and the step size is about 21.84 cents.
+{{ED intro}}
 == Theory ==
-This tuning tempers out [[81/80]] in the 5-limit; [[121/120]] in the 11-limit; 91/90 and 169/168 in the 13-limit; 154/153 in the 17-limit; 133/132 and 76/75 in the 19-limit; 117/115, 161/160, and 162/161 in the 23-limit; [[116/115]], 117/116, and 147/145 in the 29-limit; 93/92 and 156/155 in the 31-limit; 111/110 in the [[37-limit]]; 86/85 and 129/128 in the 43-limit; 141/140 in the 47-limit; 123/122 in the 61-limit; 143/142 in the 71-limit; 146/145 and 147/146 in the 73-limit; 166/165 in the 83-limit; 98/97 in the 97-limit; 101/100 in the 101-limit; 103/102 in the 103-limit; 107/106 in the 107-limit; 114/113 in the 113-limit; and 127/125 in the 127-limit.
+This tuning serves as a stretched version of [[55edo]], improving the accuracy of primes [[3/1|3]], [[7/1|7]], and [[11/1|11]], though prime [[5/1|5]] becomes worse. The [[patent val]]s match through the [[11-limit]], with the [[13-limit]] corresponding to the 55f [[val]] (written with [[wart notation]]). It thus tempers out the same [[comma]]s as 55edo in the 11-limit, and the same commas as 55f in the [[13-limit]].
-==Harmonics==
+== Harmonics ==
-{{Harmonics in equal|197|12|1|prec=2|columns=15}}
+{{Harmonics in equal|197|12|1|prec=2|columns=11}}
+{{Harmonics in equal|197|12|1|prec=2|columns=11|start=12}}
-[[Category:Edonoi]]