I'm away from my piano for 4 months. I've been sublimating my desire to improvise on that instrument by finally learning a bunch of basic harmony theory, which I practice just by singing or whistling. For example I'm getting into modes. These 7 modes are all obtained by taking the major scale and starting it at different points, but I find that's *not* the good way for me to understand the individual flavor of each one. 🧵
Much better for me is to think of each mode as the major scale (= Dorian mode) with some notes raised or lowered a half-step - since I already have an intuitive sense of what that will do to the sound. For example, anything with the third lowered a half-step (♭3) will have a minor feel. And Aeolian, which also has the 6th and 7th lowered (♭6 and ♭7), is nothing but my old friend the harmonic minor scale!
A more interesting mode is Dorian, which has just the 3rd and 7th notes lowered a half-step (3♭ and 7♭). Since this 6th is not lowered this is not as sad as minor. You can play happy tunes in minor, but it's easier to play really lugubrious tear-jerkers, which I find annoying. The major 6th of Dorian changes the sound to something more emotionally subtle. Listen to a bunch of examples here:
Some argue that the Dorian mode gets a peculiarly 'neutral' quality by being palindromic: the pattern of whole and half steps when you go *up* this mode is the same as when you go *down*:
w h w w w h w
This may seem crazily mathematical, but Pascal said "Music is the pleasure the human mind experiences from counting without being aware that it is counting."
For more, try this:
One reason I'm having fun learning music theory is that there's now a wealth of resources online, especially on YouTube with some very nice people clearly explaining things.
For something more theoretical on the Dorian mode, try this blog:
https://mynewmicrophone.com/dorian-mode/
or for something extremely practical, try this video:
@johncarlosbaez Have you heard of the strong connection between the Riemann zeta function and "good" equal temperaments? https://en.xen.wiki/w/The_Riemann_zeta_function_and_tuning
@keenanpepper @johncarlosbaez heh, I was just thinking of tweeting this at some prominent math people on here. Yes, magically the Riemann Zeta Function, known for its role in the Riemann hypothesis, happens to magically tell you how well different equal temperaments approximate the harmonic series (and the rational numbers). Of course from this standpoint we care about the peaks rather than the zeros.
Any idea how we can interpret some of the other special functions in number theory within this paradigm?
(Also I joined here on QOTO; should I join on Mathstodon instead?)
