How to derive scales and chords based on physics?

[theholygideons]

What are some music theory textbooks which show how scales and chords are derived mathematically and through the overtone series? I've always taken the scales and chords in classical music for granted. Now, I want to understand the logic behind their formation so that I can branch out into more modern music.

[lostinidlewonder]

Isn't this sort of thinking more appropriate for tuners?

[jimf12]

There is a book I got on my Kindle for free I think (or like $1) called Music Theory: From Beginner to Expert - The Ultimate Step-By-Step to Understanding and Learning Music Theory Effortlessly by Nicolas Carter.    He does have a section on this where he explains where the different tuning systems came into play.   I'm not sure if it's the detail you want, but if you want a primer on the overtone series and how they are used then it does that.   It's really a good book overall, definitely more in depth than most theory books I have seen. 

https://www.amazon.com/Music-Theory-Step-Step-Understanding/dp/1986061833/ref=asc_df_1986061833/?tag=hyprod-20&linkCode=df0&hvadid=266059698431&hvpos=&hvnetw=g&hvrand=18094026749868485693&hvpone=&hvptwo=&hvqmt=&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=9021604&hvtargid=pla-450275079965&psc=1

[arda152]

I have "Harmonic Experience: Tonal Harmony from Its Natural Origins to Its Modern Expression" from W. A. Mathieu sitting in my bookshelf, but I only had time to skim through it a little bit until now. From what I saw, it seems to be explaining harmony using overtone relationships and complex graphs which I still have to decipher. I thought it may be helpful for you, so maybe you can take a look at it 

[sharpie]

I tried the link provided above and was tickled to find it available at no cost under my kindle unlimited subscription.  Thanks for this posted question. I would like to do the same.

[jimf12]

I tried the link provided above and was tickled to find it available at no cost under my kindle unlimited subscription.  Thanks for this posted question. I would like to do the same.

I knew it was cheap, forgot it was free.    I hope you find it useful, I certainly did.   If you read the reviews, some love it and some think it's terrible.   Mostly the people that don't like it are overwhelmed, and I think that is a valid criticism.   The title should be something like From Early Intermerdiate to Late Intermediate, because if you pick this up a complete beginner you are going to probably find it pretty daunting.    On the flip side, you aren't going to be an expert at music theory after absorbing the material.   

[kony]

I know some basics.

For example, an octave's frequency is always exactly 2x relationship between the higher and lower note.

And a perfect fifth is 1.5x.

And a perfect fourth is 2/1.5 = 4/3.

However, in the western scale, a lot of the notes are not perfectly mathematical. The scale is tuned to the closest integers instead of left in the original, logarithmic forms.

Given a complete scale of 12 semitone intervals, if it were mathematical we should have (1+K)^12 = 2, where K is the semitone interval. As such we can see K is irrational.

Therefore different scales have different "feels".

[gipsypiano]

See
Johannes Kepler harmonices mundi theres a lot about music in there.
The man lived in the same village as I was born.
https://en.wikipedia.org/wiki/Harmonices_Mundi

https://microcosmos.uchicago.edu/microcosmos_new/kepler/harmonicesmundi/music.html

good luck

[sharpie]

@kony Thank you!!! Just what I wished to know.  Sharpie