Firedance
The firedance scale is a subset of zeta-stretched 15edo described by Budjarn Lambeth in 2023.
Zeta-stretched 15edo (also known as 47zpi, the 47th zeta peak index), is 15edo with octaves compressed according to this process: Optimal octave stretch.
You can also stretch 15edo using Paul Erlich's TOP tuning, or using TE tuning, and get a very similar (but not exactly identical) result. Or even just use plain old pure-octaves 15edo. All are considered acceptable tunings.
The firedance scale was designed by starting with 5edo, and then just tweaking intervals up and down by individual edo-steps of 15edo, by ear, until it sounded good.
Attached is Scale Workshop's table of interval relationships in the firedance scale:
| 0 | 1 | 2 | 3 | 4 | (5) | |
|---|---|---|---|---|---|---|
| 0 | 0 | 239.147 | 558.010 | 717.441 | 956.588 | 1195.7 |
| 239.147 | 0 | 318.9 | 478.3 | 717.4 | 956.6 | 1195.7 |
| 558.010 | 0 | 159.4 | 398.6 | 637.7 | 876.9 | 1195.7 |
| 717.441 | 0 | 239.1 | 478.3 | 717.4 | 1036.3 | 1195.7 |
| 956.588 | 0 | 239.1 | 478.3 | 797.2 | 956.6 | 1195.7 |
Although it wasn't consciously designed this way, you can see that a lot of septimal harmonies occur in the intervals between the intervals. Most notably, all those 717's are decent approximations of 3/2, all those 239's are decent approximations of 8/7, and all those 956's are decent approximations of 7/4.
On top of that, the firedance scale is a very close approximation to this primodal over-7 scale. A subset of 56afdo:
- 64/56
- 77/56
- 84/56
- 98/56
- 112/56
56 just being a higher octave of 7 in the harmonic series.
So from both a regular temperament theory point of view and also a primodality point of view, it's quite a nifty little scale with lots of xen harmonies baked into it.
Scala file
! Firedance scale 47zpi.scl ! Created using Scale Workshop 2.5.7 ! Firedance scale (47zpi) 5 ! 239.147000 558.010000 717.441000 956.588000 1195.735000