Another TIL: The ratio of one equally tempered half step is the twelfth root of 2.

Maybe, sometime these days, I will even understand the math behind equal temperament (which, to this day, I don't, but I guess it was just never explained to me in a way I understand).

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it's an average

you need a bit of acoustics (physics)
to understand the "harmonic series"

then examine just intonation (and hear the results when trying to modulate to a different (more harmonically distant) key)

it started from an effort to make keyboard instruments that would sound in tune in all keys of chromatic scale ...

piano tuners (and associated literature) may also help

maybe you knew all this already ...

good luck

@js0000 yeah, I know the history behind it and I have heard one or two recordings of music in just and mean-tone intonation. I guess I'll need to sit down with a notebook and do all the math myself (and maybe code a few examples in Supercollider) once so I understand the differences.


the eureka moment for me
was playing an e major triad
on a keyboard tuned to just intonation off of c


in some way, a computer and a keyboard should be able to do this

i just don't know how

also, i feel confident that if you put sufficient effort in, you will soon understand what you presently do not ...

viel glück

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