Spectral Mappings for CARLOS BETA
19 September 2011 Filed in: Tuning Theory
This article is a follow-up to my article Spectral Mappings for CARLOS GAMMA. The reader should refer to it for more details. This article comes a bit late because I have already dismantled the note layout for Carlos Beta on my Chameleon that is getting ready to be played in Carlos Alpha and 15ED2.
I had created a possible list of ratios to calculate the frequency of the first sixteen partials of a “spectrally mapped” sound to be played with Carlos Beta tuning system but never tried to apply it to a real sound. So, it remains only as a reminder of a way to calculate similar spectral mappings.
One step of Carlos Beta is the 11th root of 3:2 = 1.037548235794 or , said another way, 1.037548235794^11 = 1.5
caret (^) is computerese for “raised to the power of”
Using this coefficient (1.037548235794) to approximate ratios of a harmonic sounds results in a similar list:
The frequency ratios of the 16 partials were chosen in order to minimize the “perceptual change” of the “destination” spectrum compared to a harmonic “source” spectrum (the frequency of the 2nd partial is close to 2 times the frequency of the fundamental, the 3rd to 3 times it et cetera).
All partials are powers of the 11th root of 3/2 = 1.037548235794