> Then it’s easy to see that your “major + minor = perfect” formula only works for some intervals, Etc.
Where does it go wrong? Do those cases come up in practice?
Counting up and down the scale is a core use case for a notation for intervals. It absolutely needs to be well-supported. A 12-semitone approach is never going to match the usability of even the existing system.
Re:Music theory for nerds
by komponisto on Tuesday September 20, 2016 @05:05AM
(#12538116)
>A 12-semitone approach is never going to match the usability of even the existing system
I am obliged to point out that a 12-semitone approach is in fact part of the "existing system" (see: pitch-class set theory).
(Mind you, I of course think its usefulness is overrated, because I think the "atonal" repertory is tonal.)
If instead you used digits from –5 to 6, using arithmetic mod 12, it becomes obvious that e.g.:
The “perfect” intervals are just ±5 (ratios very close to 3:2 and 4:3). The “major” intervals are –3, –1, 2, 4 (approx. ratios of 5:3, 15:8, 9:8, 5:4). The “minor” intervals are –4, –2, 1, 3 (approx. ratios of 8:5, 16:9, 16:15, 6:5).Then it’s easy to see that your “major + minor = perfect” formula only works for some intervals, Etc. Overall the simple heuristics are more obfuscatory than helpful IMO.