Found in 5 comments on Hacker News
tshaddox · 2025-10-22 · Original thread
I first became aware of this concept many years on Gary Garrett's blog, where he primarily refers to it as "the lattice." His introduction to the concept gives a brief history:

https://www.garygarrett.me/?p=342

More introduction to the lattice:

https://www.garygarrett.me/?p=995

https://www.garygarrett.me/?p=1632

https://www.garygarrett.me/?p=1696

Some comparison audio between equal temperament and just intonation:

https://www.garygarrett.me/?p=1812

Some songs with lattice animations:

https://www.garygarrett.me/?p=103

https://www.garygarrett.me/?p=1253

I also like this book which Gary recommends, although it's very challenging and I never made it all the way through:

https://www.amazon.com/Harmonic-Experience-Harmony-Natural-E...

A book that I came across the other day (via a recommendation from YT-ber Adam Neely): "Harmonic Experience" by W.A. Mathieu. It's a little expensive as a first dive into this stuff, but it does look like a very natural way to lead you into and through the actual experience of western tonal harmony, often by singing along with a drone (easy to generate on today's computers).

https://www.amazon.com/Harmonic-Experience-Harmony-Natural-E...

chubot · 2020-01-19 · Original thread
I remember getting Semiology of Graphics from the Palo Alto library around 2006. At the time it was sort of legendary and out of print, but it looks like it's since been reprinted. I think you can get most of the ideas from newer books, but it's well done and clearly ahead of its time.

https://www.amazon.com/Semiology-Graphics-Diagrams-Networks-...

https://medium.com/@karlsluis/before-tufte-there-was-bertin-...

Interestingly another relatively unknown book I like (and bought/read 20 years ago) is also about harmony:

https://www.amazon.com/Harmonic-Experience-Harmony-Natural-E...

I would say there's two kinds of harmony: harmony in equal temperament, and "alternative" harmonies based on physics, and this is about the latter. I can't tell from the link what the other harmony book is about. What's good about it?

As far as computer books, I've read a lot of recommendations here over the years like "thinking forth", "Computer Lib" by Ted Nelson, etc. They are well known to some audiences but not others.

----

I also enjoy reading what people though the computing future would be like. I have "Superdistribution" by Brad Cox:

https://news.ycombinator.com/item?id=21833331

And "Mirror Worlds" by Gelertner:

https://www.amazon.com/Mirror-Worlds-Software-Universe-Shoeb...

I'm pretty sure Gelertner claims that the Facebook feed is identical to his "life streams". I guess taken literally it's hard not to see the current Internet as a "mirror world" that's becoming the real world.

baddox · 2015-01-19 · Original thread
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...

baddox · 2014-10-17 · Original thread
Out of curiosity, have you studied just intonation? I'm currently reading the mostly excellent Haromonic Experience [0]. I'm reasonably well educated on music theory, but I had never looked into just intonation and the way frequency relates to our perception of pitch and harmony. I'm finding this stuff enlightening.

An ideal string (or any oscillator) when disturbed (e.g. plucked) will tend to vibrate at a fundamental frequency of x Hz as well as modes of 2x, 3x, 4x, etc. These higher frequencies at integer multiples of the fundamental frequency are called harmonic partials. This is a physical phenomena unrelated to music and human hearing.

But the basic elements of harmony come from the fact that our auditory system seems to be "tuned" to identify harmonic partials.

If we start with a fundamental frequency x Hz (let's call it C), the first partial is 2x Hz, and it is another C an octave above (multiplying or dividing a pitch by a power of 2 will give you the same pitch in another octave).

The next partial is 3x Hz, and it sounds like a G. This is the interval called a perfect fifth, and is the strongest, most stable sounding interval (other than the octave). The next partial is 4x Hz, which is just another C, two octaves above the C we started with.

The next partial is 5x Hz, which sounds like an E. This is a major third, which is another strong and stable interval which is ubiquitous in most music.

[0] http://www.amazon.com/gp/product/0892815604/ref=oh_aui_detai...