24-step irregular-interval single-octave tuning experiment following the Generalized Mean function (Power Mean).
The semitone intervals are determined from a set of means between 220Hz [A3] and 440Hz [A4] by applying exponents in series from -12 to 12 to the Power Mean functions.
Of note,
Exponent -1 is the Harmonic mean: D4(-2),
0 is known as the Geometric Mean: Eb4,
1 the Arithmetic mean: E4(+2),
2 the Root mean square: F4(-7),
3 the cubic mean F#4(-32),
Min/Max from exponent -12 to 12: Bb3 to Ab4.
Below is the source for the Generalized Mean formula.
https://en.wikipedia.org/wiki/Generalized_mean
Link for the tuning script using the Sevish scale workshop:
https://sevish.com/scaleworkshop/?n=220Hz_Exponential_Means_24Step_Note60Center&l=-dw.07jqp_-dm.5vber_-dc.107vt_-cz.09039_-ci.50tw8_-by.2ybxt_-b8.2ti16_-aa.3wau6_-92.1f6zw_-7f.5rwkm_-5d.xmbd_-2t.5oou1_._2t.5oou1_5d.xmbd_7f.5rwkm_92.1f6zw_aa.3wau6_b8.2ti16_by.2ybxt_ci.50tw8_cz.09039_dc.107vt_dm.5vber_dw.07jqp&f=64&m=1b&version=2.5.7
View a graphical representation of the Power Means tuning vs. standard Equal Temperament with GeoGebra:
https://www.geogebra.org/classic/y9qwb7rh
Audio Production:
DAW: Cubase Pro 15 (Steinberg)
VST: Serum2 with .tun file (Xfer Records), Drum Machine (Steinberg)
FX: Tremolo (Steinberg), Flair / Replika XT (Native Instruments), Little PrimalTap (Soundtoys), Sol (Signs of Life)
Music & Video Created, Composed, and Produced by Shawn Michael
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