> 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. That

> 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.