Firedance

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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

Music