A Musical Scale in Simple Ratios of the Harmonic Series Converted to Cents of Twelve-tone Equal Temperament for Digital Synthesis

Abstract: – Intervals between harmonics in the frequency spectra of pitched sounds occur in a pattern of simple ratios. New musical scales have now been invented with intervals in these ratios, and series of scales sharing common tones allowing for musical modulation. Twelve-tone equal temperament (12Tet) is standard for Euro-genic musical instruments. It divides the octave—the interval between frequencies having a 2:1 ratio—into twelve equal, smaller intervals. Each smaller interval (semitone or half-step) is divided into 100 cents for tuning, resulting in division of the octave into 1,200 fine increments. The simple ratios of the harmonic series, the basis for the new scales, do not conform to the twelve semitones of 12Tet. Digital sound synthesis is very flexible, but writing programs is a tedious distraction from composing music. User interfaces of commercial digital synthesizers and graphic interfaces of virtual digital synthesizer applications tend to correlate fine-tuning with the 1,200 cents of 12Tet. Octave frequencies being a ratio of two, 12Tet dividing octaves into twelve equal intervals, the value of any one thus being the twelfth root of two, a logarithmic equation must be used to calculate values in cents for simple-ratio intervals. Commercial synthesis equipment can be adjusted accordingly, and new music composed with the new scales. Key-Words:- music, microtonal, computer music, music theory, music acoustic