- May 13, 2022
Hey man I suck at math and I had to read this a bunch of times to understand but still don't. I'm genuinely curious to understand how rational vs irrational effects character of sound in absolute terms (if that's what you mean). If you take instrument physical properties off the table, and take away any learned association between a note and it's frequency (ie., a conditioned sense of "in tune" for any given note), i don't get how all notes in the scale would sound out of tune? Not saying it won't, just jot getting why? Feel free to keep it overtly dumbed down, I won't be offended, I've been asking dumb questions my whole life, so all good). I can get the idea of relative base 12 dissonance of overtones , but not the absolute. Also, sorry but what's a neat note in the sense your use?Nerd alert View attachment 1089320
Music scale math fun:
This is an irrational number.
It's the ratio between note frequencies in an equal tempered 12 tone scale. (And also between string lengths of adjacent frets). Note that when you multiply this number by itself 12 times you get 2, which is the octave. Good for laying out a fretboard.
History of Irrational Numbers | Brilliant Math & Science WikiIrrational numbers are numbers that have a decimal expansion that neither shows periodicity (some sort of patterned recurrence) nor terminates. Let's look at their history. Hippassus of Metapontum, a Greek philosopher of the Pythagorean school of thought, is widely regarded as the first person...brilliant.org
The interval of the perfect 5th is the closest we have to a rational number.
The ratio of the open string to the length at the 7th fret (to the bridge) is 1.49830707687668... which is really close to 3/2. I think that's the reason you find something like it in most music scale systems around the world. Other notes can be all over the map.
When the frequency ratio is a rational number, the waves line up and there are no beat notes, so it sounds "in tune".
In equal temperament, transposing to any key sounds equally out of tune because the ratios stay the same.
OK I'll stop now.