11edt: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == 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. | 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. | ||
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=== Relation to edos === | === 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. | 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 === | === Prime harmonics === | ||
{{Harmonics in equal|11|3|1}} | {{Harmonics in equal|11|3|1}} | ||
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=== Interval table === | === Interval table === | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|- | |||
! # | ! # | ||
! [[Cent]]s | ! [[Cent]]s | ||
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== Pieces == | == Pieces == | ||
Mozart's [http://micro.soonlabel.com/6th-comma-meantone/K331-period/k331-walter-piano-11edt.mp3 sonata #11 in A Major K331 in 11 EDT] (using a 11 => 12 key mapping so octaves become tritaves) | Mozart's [http://micro.soonlabel.com/6th-comma-meantone/K331-period/k331-walter-piano-11edt.mp3 sonata #11 in A Major K331 in 11 EDT] (using a 11 => 12 key mapping so octaves become tritaves) | ||