Non-over-1 temperament: Difference between revisions

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A '''non-over-1 temperament''' is a [[regular temperament]] that tempers a [[subgroup]] corresponding to a harmonic series chord r:n1:...:nk where r ≠ 1, but is not meant to approximate a chord of the form 1:m1:...:mk. Assuming octave equivalence, this means a subgroup of the form 2.k1/f.[...].k1/f, where f:k1:...:kr is a JI chord none of whose notes is a power of 2.

A '''non-over-1 temperament''' is a [[regular temperament]] that tempers a [[subgroup]] corresponding to a harmonic series chord r:n1:...:nk where r ≠ 1, but is not meant to approximate a chord of the form 1:m1:...:mk. Assuming octave equivalence, this means a subgroup of the form 2.k1/f.[...].kr/f, where f:k1:...:kr is a JI chord none of whose notes is a power of 2.

Non-over-1 temperaments give regular-temperament interpretations to edos that approximate [[Overtone scales|over-1]] chords (assuming [[octave equivalence]]) such as [[4:5:6:7:11]] poorly, such as [[14edo]], [[18edo]], [[23edo]] and [[29edo]], thus may have much xenharmonic potential. Many of these temperaments have an [[octatonic]] structure, as [[8edo]] represents non-over-1 intervals well for its size as far as the [[17-limit]].

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	A '''non-over-1 temperament''' is a [[regular temperament]] that tempers a [[subgroup]] corresponding to a harmonic series chord r:n<sub>1</sub>:...:n<sub>k</sub> where r ≠ 1, but is not meant to approximate a chord of the form 1:m<sub>1</sub>:...:m<sub>k</sub>. Assuming octave equivalence, this means a subgroup of the form 2.k<sub>1</sub>/f.[...].k<sub>1</sub>/f, where f:k<sub>1</sub>:...:k<sub>r</sub> is a JI chord none of whose notes is a power of 2.		A '''non-over-1 temperament''' is a [[regular temperament]] that tempers a [[subgroup]] corresponding to a harmonic series chord r:n<sub>1</sub>:...:n<sub>k</sub> where r ≠ 1, but is not meant to approximate a chord of the form 1:m<sub>1</sub>:...:m<sub>k</sub>. Assuming octave equivalence, this means a subgroup of the form 2.k<sub>1</sub>/f.[...].k<sub>r</sub>/f, where f:k<sub>1</sub>:...:k<sub>r</sub> is a JI chord none of whose notes is a power of 2.

	Non-over-1 temperaments give regular-temperament interpretations to edos that approximate [[Overtone scales\|over-1]] chords (assuming [[octave equivalence]]) such as [[4:5:6:7:11]] poorly, such as [[14edo]], [[18edo]], [[23edo]] and [[29edo]], thus may have much xenharmonic potential. Many of these temperaments have an [[octatonic]] structure, as [[8edo]] represents non-over-1 intervals well for its size as far as the [[17-limit]].		Non-over-1 temperaments give regular-temperament interpretations to edos that approximate [[Overtone scales\|over-1]] chords (assuming [[octave equivalence]]) such as [[4:5:6:7:11]] poorly, such as [[14edo]], [[18edo]], [[23edo]] and [[29edo]], thus may have much xenharmonic potential. Many of these temperaments have an [[octatonic]] structure, as [[8edo]] represents non-over-1 intervals well for its size as far as the [[17-limit]].