MODMOS scale: Difference between revisions
add some notes about useful ways to look at MODMOS's |
|||
| Line 22: | Line 22: | ||
== Gene's Terminology == | == Gene's Terminology == | ||
The name comes from the fact that if the period is an octave and the number of notes in the MOS scale is N, then a chroma moves a note along the chain of generators by ±N, so that a MODMOS, reduced modulo N on the generator chain, becomes a MOS. In all cases the Graham complexity of the chroma c is N, since this is the number of generator steps needed to reach c times P, the number of periods to an octave. | The name comes from the fact that if the period is an octave and the number of notes in the MOS scale is N, then a chroma moves a note along the chain of generators by ±N, so that a MODMOS, reduced modulo N on the generator chain, becomes a MOS. In all cases the Graham complexity of the chroma c is N, since this is the number of generator steps needed to reach c times P, the number of periods to an octave. | ||
If the steps of the MODMOS have a complexity no more than N, we may call it a chromatic MODMOS; these have all steps the same as Otherwise, the steps may be of complexity greater than N, for instance by having steps of size d = |s-c|; these we may call enharmonic MODMOS. If we were to limit ourselves to note adjustments of one chroma, then in no case can the complexity be more than 2N. | If the steps of the MODMOS have a complexity no more than N, we may call it a chromatic MODMOS; these have all steps the same as Otherwise, the steps may be of complexity greater than N, for instance by having steps of size d = |s-c|; these we may call enharmonic MODMOS. If we were to limit ourselves to note adjustments of one chroma, then in no case can the complexity be more than 2N. | ||
== Melisse Series == | |||
One particular way of generating MODMOS is via the Melisse series. For a MOS of size N with octave period, we may put the 1/1 at the base of the generator chain, so that it can be represented by 0, 1, 2 ... N-1. The Melisse series now consists of the N-1 MODMOS 0, 1, 2 ... N-1-k, 2N-k, 2N-k+1 ... 2N-1 for each k 0 < k < N. Since the 1/1 can be any note, we may then pick the desired note and subtract generators so as to make that note correspond to 0, giving the desired mode of the MODMOS. | One particular way of generating MODMOS is via the Melisse series. For a MOS of size N with octave period, we may put the 1/1 at the base of the generator chain, so that it can be represented by 0, 1, 2 ... N-1. The Melisse series now consists of the N-1 MODMOS 0, 1, 2 ... N-1-k, 2N-k, 2N-k+1 ... 2N-1 for each k 0 < k < N. Since the 1/1 can be any note, we may then pick the desired note and subtract generators so as to make that note correspond to 0, giving the desired mode of the MODMOS. | ||