Non-over-1 temperament: Difference between revisions
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A '''non-over-2 temperament''', or '''non-/2 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 ≠ 2, but is not meant to approximate a chord of the form 2:m<sub>1</sub>:...:m<sub>k</sub>. Non-over-2 temperaments give regular-temperament interpretations to edos that approximate over-2 chords such as 4:5:6:7:11 poorly, such as [[14edo]], [[18edo]], [[23edo]] and [[29edo]]. | A '''non-over-2 temperament''', or '''non-/2 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 ≠ 2, but is not meant to approximate a chord of the form 2:m<sub>1</sub>:...:m<sub>k</sub>. Non-over-2 temperaments give regular-temperament interpretations to edos that approximate over-2 chords such as 4:5:6:7:11 poorly, such as [[14edo]], [[18edo]], [[23edo]] and [[29edo]]. | ||
== Example == | |||
[[Sensi]] is ''effectively'' a non-over-2 temperament provided you restrict yourself to the sensi[8] MOS. The sensi[8] MOS only has a 5:6:7:9:13 chord, but no chord of the form 2:m<sub>1</sub>:...:m<sub>k</sub> (except 2:3). Thus sensi can be viewed as a 2.6/5.7/5.9/5.13/10 or 2.3.6/5.7/5.13/10 temperament. (See [http://x31eq.com/cgi-bin/rt.cgi?limit=2_6%2F5_7%2F5_9%2F5_13%2F10&ets=19_27&tuning=po&subgroup=on x31eq data page].) | |||
{| class="wikitable" | |||
|- | |||
! style="text-align:right" | Generators | |||
! | Cents<sup>*</sup> | |||
! | Approximate ratios<sup>†</sup> | |||
|- | |||
| | 0 | |||
| style="text-align:right;" | 0.000 | |||
| | 1/1 | |||
|- | |||
| | 1 | |||
| style="text-align:right;" | 443.322 | |||
| | 13/10~9/7 | |||
|- | |||
| | 2 | |||
| style="text-align:right;" | 886.644 | |||
| | 42/25~5/3 | |||
|- | |||
| | 3 | |||
| style="text-align:right;" | 129.966 | |||
| | 13/12~14/13~15/14~27/25 | |||
|- | |||
| | 4 | |||
| style="text-align:right;" | 573.288 | |||
| | 7/5~25/18~18/13 | |||
|- | |||
| | 5 | |||
| style="text-align:right;" | 1016.610 | |||
| | 9/5~70/39 | |||
|- | |||
| | 6 | |||
| style="text-align:right;" | 259.932 | |||
| | 7/6~15/13 | |||
|- | |||
| | 7 | |||
| style="text-align:right;" | 703.253 | |||
| | '''3/2''' | |||
|} | |||
: <sup>*</sup> in 2.3.5.7.13 POTE tuning | |||
: <sup>†</sup> 2.3.5.7.13 ratio interpretations | |||
[[Category:Temperament]] | [[Category:Temperament]] | ||