i have a user page now :)
music theory that does not have a name yet
A number of things bother me about the way tuning is done on this wiki and in general, in particular octave/tritave equivalence, generators, and the excessive use of hard-to-understand vocabulary and math which often isn't even all that relevant or helpful. The last one should not be a surprise; the first two might be. I find generators extremely unintuitive, and while they may be useful for things, that does not mean I have to like them. I also dislike the concept of equivalence in general. I think *every* pitch should be considered its own thing.
So I decided to formalize the ideas that I have been exploring into a music theory, inspired by Caftaphata.
Terms
Most of these terms are widely-used but I might be using them slightly differently than most people.
- Interval
The frequency ratio between two notes. Can be a measurement of specific notes or just a ratio.
- Harmonic
An interval which is an integer ratio (including 1/1). Also, a note which is a harmonic interval above another note.
- Harmonic Series
The set of notes which are harmonics of the fundamental, including the fundamental itself.
- Overtone
A tone produced with the fundamental, forming the timbre of a single note.
Explanation
The simplest interval is the unison, 1/1. This is the interval between a note and itself. Stacking it multiple times doesn't do anything, which isn't very interesting, so let's consider the next simplest interval: the octave, 2/1. Although notes an octave apart are not considered equivalent, they do have a special relationship: the higher note is a harmonic of the lower. 3/1 is also a harmonic interval. Stacking these gives us intervals like 4/1, 6/1, and 8/1, which are also harmonics. Since only harmonics can be created, this does not allow for much progression, since every note only contains overtones from the root note. So we will now allow intervals to be subtracted from each other, creating nonharmonic intervals like 3/2 which have new overtones. Going up by harmonics removes some overtones and strengthens the remaining ones; going down by harmonics weakens existing overtones and adds new ones in the gaps. Combining these gives us nonharmonic intervals.