For example, what would be a four note chord the intervals of which were all major 2nds? Or all minor 2nds? Or a combination of major 2nd, major 2nd, minor 2nd? Is there a reference you might recommend for me to look at who has already figured this all out? Ideally they would include all the permutations from unison, unison, unison and then through m2, m2, m2* and all the way through perf octave, perf octave, perf octave. Thank you for your kind assistance. - J.D.C.
Answer: Really the naming conventions of traditional music theory are based on triadic harmony, so they will not provide a logical name for every possible combination of 4 pitch classes. For non-triadic harmony it would make more sense to use an arbitrary naming system using numbers, like 2,2,2 for 4 notes each separated by major seconds (measuring in half steps). In a system like that, the arbitrary combination of F, G#, A, B could be called 3,1,2.
And in the context of basically triadic music the ear will tend to interpret even arbitrary chords as triadic if it can. For instance, a supposedly "quartal" harmony like C, F, Bb (5,5 in the number system) is going to be heard as a C7 with a suspended fourth if the ear is at all tempted by the context.
A combination like C,D,E is ambiguous enough not to have any particular meaning in harmony. But if it were to be analyzed as triadic harmony you'd rearrange its pitch classes in triadic order: D,C,E. Then it could be seen as a D9 lacking a third (and a fifth, though higher-order chords often leave out the 5th).
So: to find the triadic analysis of any combination of tones, arrange its pitches in triadic order, where they fall along the continuum A C E G B D F... but in many cases there will be no meaningful name from triadic naming conventions. Such combinations would not be seen as traditional functional harmony, but as passing combinations formed by counterpoint.
