Please help! Math Music question!

Question

Calculate the Fundamental Frequency Ratio (by dividing the higher frequency by the lower

frequency), rounded if necessary to the nearest 0.000001, between D4 and G#4 under the following systems:

a) Harmonic Series (Keyed to A)

b) Just Intonation Tuning (Keyed to A)

c) Harmonic Series (Keyed to D)

d) Pythagorean Tuning

3) In your answers to 2, consider the answer 2c what you want (in other words, zero error). Calculate the error, as a percent, for each of these tuning systems in parts a, b, and d. Round to the nearest 0.001%.

Answer 1

This is a question of research and reading, then applying the math to your assigned scales.

I found a very helpful (and fascinating) read was "Music: a Mathmatical Offering" by Dave Benson: (https://homepages.abdn.ac.uk/d.j.benson/pages/html/music.pdf).

You would need to isolate each of the assigned scales, then work with the ratios offered there.

Remember, I can help with research and help you FIND the answers, but I can't ethically give you the answers.

However, I would be glad to spend some time with you helping you skim this work and find your own answers!

Let me know how I can help...