User:BudjarnLambeth/Firedance: Difference between revisions

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: [[The Riemann Zeta Function and Tuning#Optimal octave stretch|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:

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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]]:

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.