Lydian mixolydian scale on the harmonic series

 Recently I am writing for a piano trio (violin, cello, and piano). First, I work out the harmonics on the string. I found the two adjacent strings of the pitch of A string on the cello and G string on the violin. The harmonic series, the natural vibration of the string, finds the 4th to  7th harmonic form a dominant 7th chord. Combining the natural harmonics of A and G strings, it forms a Lydian-Mixolydian scale on G, sees the example.

Sound an octave higher

The natural harmonic is played on the string, thus, the tunning deviates from the equal temperament and the digit shows how many cents deviated. It is quite special that the G octave is different. Although I can lower the g string a bit by -31 cents to get a perfect octave, I wonder it is hard to tune with the piano's ET. Composers worked with bitonality, polyrhythm, but I work with bi-tuning systems, equal temperament, and overtone tuning.

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