[emptybits]

IMO, the books are great but they don't go very deeply into the math of chords or relationships between chords, no. Certainly there is math coverage of intonation (JI, 12TET, etc.), which leads to "why" chords might sound the way they do as stacked intervals with more or less pure dissonance or consonance. But the "why" of progressions are a level above that yet again. So I'm sure there are better works on chords. From a guitar (but also keyboard) perspective a fascinating book is Werner Pohlert's "Basic Harmony" -- it's thick and analytical of chords and progressions. It's comprehensive though I suppose not particularly mathematical. And you probably know there is some great writing on Just Intonation which is rooted in the ratio math of "correct" intervals and chords. "The JI Primer" by David Doty is a nice short starting point on JI with references, with emphasis on the math of intervals, obviously, but it does have some coverage of stacking these into triads and beyond. If you find a pleasing rabbit hole for chord and progression math, let us know!

[alok-g]

Thanks for a detailed response. I'll check the references out.

I am a lot less knowledgeable than you have imagined here. :-) Well, I know practically all the physics and electronics part, but have not found much that connects to music theory. I could figure the mathematical why's of scales and chords ("stacked intervals with more or less pure dissonance or consonance") by myself. But ever since have been struggling to find about which chords/progressions would fit which melody. Most musicians are doing this naturally, "by the ear" as they say. :-) And music theory books I have looked at so far (including the thick ones) do not talk about mathematics at all. :-( :-)

[emptybits]

I hear you. My $0.25 ... I bet the expert authors of many music theory books would be capable of thinking in mathematical terms but (now I'm guessing) there is likely some undeserved "ew, yuck, math!" culture in the arts so rather than turn off their audience, they avoid talking about the quantitative underpinnings of why things sound the way they do.

Two more enjoyable books on the math and physics of music (though, again, probably not far enough up the tree of abstraction for chords):

"The Science of Musical Sound" by Pierce (lovely little book, not too deep though, quite coffee tableable)

"Fundamentals of Musical Acoustics" by Benade (old book, considered a classic, reads like a science text)

Good luck!

[alok-g]

Thanks a lot! :-)