Non-over-1 temperament
A non-over-2 temperament, or non-/2 temperament, is a regular temperament that tempers a subgroup corresponding to a harmonic series chord r:n1:...:nk where r ≠ 2, but is not meant to approximate a chord of the form 2:m1:...:mk. 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:m1:...:mk (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 x31eq data page.)
| Generators | Cents* | Approximate ratios† |
|---|---|---|
| 0 | 0.000 | 1/1 |
| 1 | 443.322 | 13/10~9/7 |
| 2 | 886.644 | 42/25~5/3 |
| 3 | 129.966 | 13/12~14/13~15/14~27/25 |
| 4 | 573.288 | 7/5~25/18~18/13 |
| 5 | 1016.610 | 9/5~70/39 |
| 6 | 259.932 | 7/6~15/13 |
| 7 | 703.253 | 3/2 |
- * in 2.3.5.7.13 POTE tuning
- † 2.3.5.7.13 ratio interpretations