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 stretched 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 warm 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)