3 ms·

I wish this was even more "from first principles." I wish the "harmony" section would point out that the "simple ratios" they initially show both have powers of

by baddox 10y ago

I wish this was even more "from first principles." I wish the "harmony" section would point out that the "simple ratios" they initially show both have powers of two in their denominators, and thus are just octave adjustments of the harmonic series. I wish the "chords" section would derive the major triad as the fundamental frequency combined with the first two (non-octave) frequencies in the harmonic series octave-adjusted down to be close to the fundamental.

meowface 10y ago
Do you have any simple resources (similar to the OP link) to help learn a bit more of the math behind musical ratios?
- baddox 10y ago
  Sadly, I really don't. I've picked it up over a long time, and I still probably have plenty of misconceptions and less-than-rigorous understandings.
  - meowface 10y ago
    The thing I don't quite understand is why many seem to argue that major chords aren't inherently more "consonant" than minor chords, and that it's just psychological/cultural, despite the mathematical consonance that seems to be inherent of major triads.
    - nandemo 10y ago
      "Consonant" vs "dissonant" is subjective: it's a matter of perception, taste. The way you test the hypothesis "This chord is more consonant/more pleasant than that other chord" is by asking a lot of people. Just like "steak tastes better medium-rare than well-done". Physics & chemistry can inform the discussion but it cannot prove or refute the hypothesis.
- elihu 10y ago
  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.

by baddox 10y ago

meowface 10y ago

Do you have any simple resources (similar to the OP link) to help learn a bit more of the math behind musical ratios?

baddox 10y ago
Sadly, I really don't. I've picked it up over a long time, and I still probably have plenty of misconceptions and less-than-rigorous understandings.
- meowface 10y ago
  The thing I don't quite understand is why many seem to argue that major chords aren't inherently more "consonant" than minor chords, and that it's just psychological/cultural, despite the mathematical consonance that seems to be inherent of major triads.
  - nandemo 10y ago
    "Consonant" vs "dissonant" is subjective: it's a matter of perception, taste. The way you test the hypothesis "This chord is more consonant/more pleasant than that other chord" is by asking a lot of people. Just like "steak tastes better medium-rare than well-done". Physics & chemistry can inform the discussion but it cannot prove or refute the hypothesis.
elihu 10y ago
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.