Miracle/Chords: Difference between revisions
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Below are listed the [[ | Below are listed the [[dyadic chord]]s of 11-limit [[Gamelismic clan#Miracle|miracle temperament]]. They are listed in order of increasing [[Graham complexity]], with [[hash complexity]] used to break ties. For any linear temperament, if we chose a generator, we may put any octave-equivalent chord of the temperament in a canonical form by representing it as a set of nonnegative integers, starting with 0, which are the number of generator steps giving an octave-equivalent note class in the chord. If S is such a set, the sum Σ 2^s for all s∊S provides a unique odd number encoding the chord, and the logarithm base two of this number is the hash complexity, listed under the heading "Hash" below. The floor of hash complexity, that is, the greatest integer less than the hash complexity, is equal to the Graham complexity. | ||
The heading "transversal" shows a JI chord whose intervals temper to the marvel chord. Under "type" it says otonal if it is an essentially just chord best understood in terms of the overtone series, utonal if it is the inversion of an otonal chord, and ambitonal if it can equally well be seen as otonal or utonal. | The heading "transversal" shows a JI chord whose intervals temper to the marvel chord. Under "type" it says otonal if it is an essentially just chord best understood in terms of the overtone series, utonal if it is the inversion of an otonal chord, and ambitonal if it can equally well be seen as otonal or utonal. | ||
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[[Category: | [[Category:Chords]] | ||
[[Category: | [[Category:Listen]] | ||
[[Category: | [[Category:Miracle]] | ||
[[Category: | [[Category:Pentad]] | ||
[[Category: | [[Category:Tetrad]] | ||
[[Category: | [[Category:Triad]] | ||