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: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>. Non-over-1 temperaments give regular-temperament interpretations to edos that approximate [[Overtone scales|over-1]] chords 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]]. | 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>. 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]]. | ||
== Examples == | == Examples == | ||