User:BudjarnLambeth/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

Music

• Improvisation in Zeta-Stretched 15-Tone Equal Temperament (15 EDO) - Budjarn Lambeth (2024)