MODMOS scale: Difference between revisions

Mike Battaglia (talk | contribs)
Ways of Looking at MODMOS Scales: better formatting and added basic proof sketch for why there aren't infinitely many monotonic MODMOS's
Mike Battaglia (talk | contribs)
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Another important note is that the more alterations are made, the less the resulting scale will resemble the original MOS. Thus, it can be very useful, when trying to "organize" the universe of MODMOS's generated by an MOS, to sort them by the total number of alterations that have been made. Thus one can look at '''single-alteration''' MODMOS's, '''double-alteration''' MODMOS's, and so on, each of which gets further from the character of the core MOS. Similarly, one can look at the maximum number of chroma-alterations that has been made to any particular note at a time: are all notes formed by one chroma alteration, or do we have any notes which have been doubly adjusted? Or triply adjusted? etc.
Another important note is that the more alterations are made, the less the resulting scale will resemble the original MOS. Thus, it can be very useful, when trying to "organize" the universe of MODMOS's generated by an MOS, to sort them by the total number of alterations that have been made. Thus one can look at '''single-alteration''' MODMOS's, '''double-alteration''' MODMOS's, and so on, each of which gets further from the character of the core MOS. Similarly, one can look at the maximum number of chroma-alterations that has been made to any particular note at a time: are all notes formed by one chroma alteration, or do we have any notes which have been doubly adjusted? Or triply adjusted? etc.


It is also important to look at, for some MODMOS, how many generators the entire thing will span, which is called the '''coverage''' of the MODMOS. For instance, the diatonic scale requires 7 contiguous generators, whereas the melodic minor requires 9, the harmonic minor and major scales require 10, and the double harmonic scale requires 11. It can be quite useful to look at the "coverage" of a MODMOS on the generator chain, particularly if one want the MODMOS to fit into a single larger "chromatic" or "enharmonic" sized MOS.
It is also important to look at, for some MODMOS, how many generators the entire thing will span, which is called the '''generator span''' or '''coverage''' of the MODMOS. For instance, the diatonic scale requires 7 contiguous generators, whereas the melodic minor requires 9, the harmonic minor and major scales require 10, and the double harmonic scale requires 11. It can be quite useful to look at the "coverage" of a MODMOS on the generator chain, particularly if one want the MODMOS to fit into a single larger "chromatic" or "enharmonic" sized MOS.


There are doubtless many other useful ways in which one can analyze the MODMOS universe associated to an MOS. As a baseline definition, however, all of these scales are still MODMOS scales.
There are doubtless many other useful ways in which one can analyze the MODMOS universe associated to an MOS. As a baseline definition, however, all of these scales are still MODMOS scales.