> up to the octave ... well, up to the thirteenth, at least... I suppose one could continue to name diatonic intervals above that for really convoluted chords.

> up to the octave ... well, up to the thirteenth, at least... I suppose one could continue to name diatonic intervals above that for really convoluted chords. Without the off-by one error, one could do interval arithmetics in a way that intuitively makes sense... It's really weird such a bad convention caught on to begin with. Edit: going down the rabbit hole... It looks like the off-by-one error for diatonic intervals goes back to the greek antiquity. The Romans named the fourth and fifth diatessaon and diapente, which have greek roots, but their chromatic intervals start a zero (tonus, ditonus, tritonus which gave the (semi-)tone and the tritone). The "semi" prefix means "subtract half a tone", not divide by two... https://en.wikipedia.org/wiki/Interval_(music)#Latin_nomenclature https://en.wikipedia.org/wiki/Interval_(music)#Latin_nomencl... Neither the Greeks nor the Romans had a concept of zero, so it starts to make sense as to why we started with a crooked convention. Inertia and habbit made it stick around. There's another rabbit hole for microtonal interval names... https://en.wikipedia.org/wiki/List_of_pitch_intervals#List https://en.wikipedia.org/wiki/List_of_pitch_intervals#List