Hacker News Books

Yes. See Harmonic Experience: Tonal Harmony from Its Natural Origins to Its Modern Expression by W.A. Mathieu

https://www.goodreads.com/book/show/114365.Harmonic_Experien...

Perhaps Harmonic Experience by W.A. Mathieu.

Which book are you reading, out of curiosity? I recently bought Harmonic Experience, the physical book, and thought it was funny that it is even offered in the Kindle format.

(By the way, it's not at all an introductory or comprehensive music theory book. It's about the history of harmony, temperament systems, and psychoacoustics.)

http://www.amazon.com/Harmonic-Experience-Harmony-Natural-Ex...

> Isn't most tolerable trade-off between multually-incompatible requirements another way of saying "best overall"?

I could have said that better. What I meant was that standard notation isn't better than every other system according to every metric we could use to compare such things.

Gary Garrett has more lattice demos on Youtube. Here's one that's an animation of an example in Harmonic Experience by W. A. Mathieu (which uses lattices extensively to explain harmony and is the best reference I know of for explaining how to understand them): https://www.youtube.com/watch?v=I49bj-X7fH0

A 3-5 lattice is a grid where one axis is fifths (powers of 3 in just intonation) and another axis is major thirds (powers of 5). Garrett implies a third axis for septimal flatted seventh (i.e. barbershop 7th) intervals. Since the grid is leaning to the right, the diagonals that lean the left are minor thirds. Powers of 2 (octaves) are usually ignored. Triangles that are flat on the bottom are major triads. Triangles that are flat on top are minor triads.

There isn't an obvious way to encode a whole song onto a single lattice diagram in a way that could be printed on a page and still be readable. They seem to work pretty well as animations or as static illustrations to explain chord transitions, though.

I don't have any good web links, but a couple of books that I've found useful are The Science of Musical Sound by John R. Pierce and Harmonic Experience by W. Mathieu. (The former is more focused on sound and scientific theory, whereas the latter is more focused on understanding music in a way that would be useful to a musician or composer.)

On the Sensation of Tone by Helmholtz is also worth checking out if you want to understand where a lot of the modern understanding of just intonation comes from.