I am reading the documentation of "harmonics":
"The coeff keyword can be used to manipulate the pitches by adjusting the coefficients of the sine waves that correspond to each note. For example, by increasing the coefficient of the sine wave that corresponds to the fundamental frequency of a note, the pitch of that note can be raised. Similarly, by decreasing the coefficient of a higher harmonic, the pitch can be lowered. The use of coefficients in music theory is a mathematical approach to analysing and manipulating the frequency of a note."

I have following questions:

What is "the sine wave corresponding to each note"?

I cannot change the coefficient of higher harmonics since I have only one coefficient argument. What does that mean?

Where can I find the explanation of "coefficients used in music theory"?

Where can I find the "mathematical approach" explained?

Thanks for help.

Achim

I believe this is because, in general, harmonics are multiples of the fundamental frequency, such as 2f, 3f, 4f, and so on. The coefficients allow us to stretch or compress the overall curve to obtain inharmonic stretched or compressed curves.

This technique has been and continues to be used by the spectral school. It is also available as Max patches in some IRCAM libraries, or perhaps in the Bach Max library, although I don’t recall the exact location.

I found it in one of my Max/Bach patches, but I can’t recall the source. You can see it in this screenshot.

Dear Stephane,

thanks for you answer. I understand, that the coefficient is the frequency multiplier (means if 1, it results in the harmonic row).

I just think, that the documentation is somehow misleading: sine waves, music theory, etc.

Best, Achim

Dear Achim,

I’m sure you’re well-versed in harmonics and their history, but I’ve included these explanations for users who may not have access to such information.

Best,

Stéphane