4 ms·

An “oct”ave is 8 intervals not 8 notes. The 1 is the root, and the 8 is the same note as the 1 again (2:1). There’s no specific reason to have 8, or 12, or 7,

An “oct”ave is 8 intervals not 8 notes. The 1 is the root, and the 8 is the same note as the 1 again (2:1). There’s no specific reason to have 8, or 12, or 7, we just decided that way, same as we decided to count intervals not notes, and to start with 1 not 0. You could just as well say “let’s divide the frequency range between x and 2x by 10 instead of 12”. Or we do something between x and 3x instead. We just don’t. For what it’s worth, most guitarists (probably the largest group of amateur musicians in the west) use tab notation to begin with and many never graduate to standard notation. As others have said, music notation is often not much more than a “paint by numbers” - experienced musicians can “paint” the picture without reading every single number.

feoren 3y ago
> You could just as well say “let’s divide the frequency range between x and 2x by 10 instead of 12”. Or we do something between x and 3x instead. We just don’t. The reasons for this are much much more complicated than "we just don't", and include "we sometimes do". The history of tunings and the emergence and dominance of 12-TET is fascinating and rooted in both math and myth.
josephg 3y ago
> An “oct”ave is 8 intervals not 8 notes. The 1 is the root, and the 8 is the same note as the 1 again (2:1). Double counting the root note is ridiculous. Thats like saying there's 11 numbers in decimal - 0, 1, 2, 3 all the way to 10. You end up with weird distortions like "8 notes in 1 octave, 15 notes in 2 octaves". It makes way more sense to just admit there are 7 notes in each octave (in diatonic scales), and then we can just multiply like we do everywhere else. Also, thats not what "interval" means - at least not in common parlance. An interval implies we're measuring the gap between 2 things. We usually measure intervals by subtraction. The interval between 10 and 15 is 5. The interval between 12:10 and 12:15 is 5 minutes. Likewise, we should count the interval between two notes by subtraction. The interval between the tonic and itself is 0. The interval between the tonic and the "major 2nd" (ugh) is a gap of 1 (diatonically) or 2 (chromatically). In music's defense, I think the notation system might predate the number 0. But keeping and defending the status quo seems ridiculous. There are clearly real improvements to be made.

feoren 3y ago

> You could just as well say “let’s divide the frequency range between x and 2x by 10 instead of 12”. Or we do something between x and 3x instead. We just don’t. The reasons for this are much much more complicated than "we just don't", and include "we sometimes do". The history of tunings and the emergence and dominance of 12-TET is fascinating and rooted in both math and myth.

josephg 3y ago

> An “oct”ave is 8 intervals not 8 notes. The 1 is the root, and the 8 is the same note as the 1 again (2:1). Double counting the root note is ridiculous. Thats like saying there's 11 numbers in decimal - 0, 1, 2, 3 all the way to 10. You end up with weird distortions like "8 notes in 1 octave, 15 notes in 2 octaves". It makes way more sense to just admit there are 7 notes in each octave (in diatonic scales), and then we can just multiply like we do everywhere else. Also, thats not what "interval" means - at least not in common parlance. An interval implies we're measuring the gap between 2 things. We usually measure intervals by subtraction. The interval between 10 and 15 is 5. The interval between 12:10 and 12:15 is 5 minutes. Likewise, we should count the interval between two notes by subtraction. The interval between the tonic and itself is 0. The interval between the tonic and the "major 2nd" (ugh) is a gap of 1 (diatonically) or 2 (chromatically). In music's defense, I think the notation system might predate the number 0. But keeping and defending the status quo seems ridiculous. There are clearly real improvements to be made.