11edt: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro}} | |||
== Theory == | |||
== | From a no-two point of view, 11edt has a [[5/3]] major sixth that is 19.8 cents flat. However, 11edt has an extremely inaccurate seventh harmonic [[7/1]], which is off by almost half a step (or about a semitone), which causes it to temper out [[49/45]] in the 7-limit. 11edt is at the extreme end of [[arcturus]] temperament, defined by tempering out [[15625/15309]] in the 3.5.7 subgroup. It gives an equalized interpretation for the [[9L 2s (3/1-equivalent)|sub-arcturus]] [[MOS]] scale. | ||
The 11th harmonic, [[11/1]], only 1.6 cents flat, is very close to just. By exploiting the badly tuned seventh harmonic, 11edt tempers out [[35/33]] and [[77/75]] in the 11-limit. In the 3.5.11 subgroup, it tempers out [[125/121]]. | |||
=== Relation to edos === | |||
11edt can be seen as a very stretched version of [[7edo]], with octaves sharpened by 10.3 cents. The octave stretching makes the [[3/2]] perfect fifth in better tune, while preserving a just [[3/1]] tritave. | |||
=== Prime harmonics === | |||
{{Harmonics in equal|11|3|1}} | |||
{{Harmonics in equal|11|3|1|intervals=prime}} | |||
=== Interval table === | |||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
! # | ! # | ||
! | ! [[Cent]]s | ||
! | ! [[Hekt]]s | ||
! Approximate ratios | ! Approximate ratios | ||
! [[Arcturus]] nonatonic notation (J = 1/1) | ! [[Arcturus]] nonatonic notation (J = 1/1) | ||
| Line 83: | Line 93: | ||
| J | | J | ||
|} | |} | ||
== Pieces == | == Pieces == | ||