Experiences

I thought about Ernest Levy’s A Theory of Harmony where he said that all harmony can exist in any chord and any chord has an opposite pole. So, if the, in a hypothetic way, the harmonic series is a chord it must have an opposite pole (experience 1 - image 1 and image 2)


Image 1 - Harmonic Series in D - positive pole - 1/2 approximation



Image 2 - Harmonic Series in D - negative pole - 1/2 approximation


This opposite pole is made by intervals but also by mathematic calculation. Therefore, for the harmonic series positive pole the formula to know perfectly each partial is Y x Hz, so: 1st partial = 1 x 36.71Hz; 2nd partial = 2 x 36.71Hz; 3rd partial = 3 x 36.71; etc. For the harmonic series negative pole the formula to know perfectly each partial is HZ ÷ Y, so: 1st partial = 1174.659Hz ÷ 1; 2nd partial = 1174.659Hz ÷ 2; 3rd partial = 1174.659Hz ÷ 3; etc.

Using the formula it is possible to have an approximation, in each harmonic series poles of, 1/4; 1/6 or even 1/8 (image 3 and image 4)

Image 3 - Harmonic Series in D - positive pole - 1/4 approximation

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Image 4 - Harmonic Series in D - negative pole - 1/4 approximation