> 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.
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.