User:Godtone: Difference between revisions

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Note however that the supertonic may in some cases be above the antitonic (and correspondingly the subtonic may in some cases be below the antitonic). This leaves '''3''' (the mediant) and '''7''' (the contramediant) as gap-fillers for below and above '''5''' (the antitonic) respectively. This does however point to the next place to investigate: when is the supertonic above the antitonic? This would imply that twice the dominant is above 1.5 octaves, or that the dominant is above 900 cents while being below the contralead, thus implying that an EDO approximation must be 9 or above to support such a MOSS (as there must be space for the contralead to be distinct).

Another interesting observation is that this system suggests an at-least-7-note-per-period MOSS because in order for all of the functions '''0, 1, 2, 4, 6, 8, 9''' to be present ~~and distinct from each-other~~, there must be at least 7 notes. (Note that the ~~only~~ digits absent are '''3, 5, 7''' where '''3, 7''' are context-dependent gap-filler functions while '''5''' is a function unrelated to the generator and instead related to the period-complement symmetry of the functions suggesting a midpoint between adjacent instances of the tonic.~~) However~~, ~~yet~~ more interestingly, ~~if you have a 5-note MOSS~~, ~~it naturally implies using the~~ 7-, ~~8- or~~ 9~~-note~~ child MOSS as the basis for analysing a 5-note MOSS ~~with a~~ small step ~~that~~ is too large to serve as a true (contra)lead ~~as that child MOSS will instead have the contralead be the chroma of that MOSS~~. Meanwhile, if the small step is small enough to serve as a (contra)lead, it will necessarily be confused with either a supertonic or a subtonic, implying an interesting musical reality for such MOSSes. This system thus also suggests that modes which have at least two generators from the tonic in each direction have a unique musical capability and thus modes that do not satisfy this restriction have emergent musical properties based on their very lack of some of those functions.

Another interesting observation is that this system suggests an at-least-5-note-per-period MOSS because in order for all of the functions '''0, 1, 2, 4, 6, 8, 9''' to be present, there must be at least 5 notes. That way, there exists at least one mode where the dominant, serviant, supertonic and subtonic are all present relative to the tonic, with the (contra)lead being - at minimum - a reality of the (chromatic) extension of the MOSS, which is always important as it acts as melodic background. Note that the digits whose functions are potentially absent from the minimum MOSS are '''1, 3, 5, 7, 9''' which is to say all the odd digits, and where '''3''' and '''7''' are context-dependent gap-filler functions while '''5''' is a function unrelated to the generator and instead related to the period-complement symmetry of the functions suggesting a midpoint between adjacent instances of the tonic. Also note that for 5-note MOSSes, the mediant and contramediant necessarily cannot exist in the same mode where the dominant, serviant, supertonic and subtonic are simultaneously present. Yet more interestingly, the desire to include the functions '''1, 3, 7, 9''' suggests using the child MOSS as the basis for analysing a 5-note and sometimes 6-note (and even 7-note) MOSS in cases where the small step is too large to serve as a true (contra)lead. Meanwhile, if the small step is small enough to serve as a (contra)lead, it will necessarily be confused with either a supertonic or a subtonic, implying an interesting musical reality for such MOSSes. This system thus also suggests that modes which have at least two generators from the tonic in each direction have a unique musical capability and thus modes that do not satisfy this restriction have emergent musical properties based on their very lack of some of those functions.

== Examples of functions ==

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 Note however that the supertonic may in some cases be above the antitonic (and correspondingly the subtonic may in some cases be below the antitonic). This leaves '''3''' (the mediant) and '''7''' (the contramediant) as gap-fillers for below and above '''5''' (the antitonic) respectively. This does however point to the next place to investigate: when is the supertonic above the antitonic? This would imply that twice the dominant is above 1.5 octaves, or that the dominant is above 900 cents while being below the contralead, thus implying that an EDO approximation must be 9 or above to support such a MOSS (as there must be space for the contralead to be distinct).
-Another interesting observation is that this system suggests an at-least-7-note-per-period MOSS because in order for all of the functions '''0, 1, 2, 4, 6, 8, 9''' to be present and distinct from each-other, there must be at least 7 notes. (Note that the only digits absent are '''3, 5, 7''' where '''3, 7''' are context-dependent gap-filler functions while '''5''' is a function unrelated to the generator and instead related to the period-complement symmetry of the functions suggesting a midpoint between adjacent instances of the tonic.) However, yet more interestingly, if you have a 5-note MOSS, it naturally implies using the 7-, 8- or 9-note child MOSS as the basis for analysing a 5-note MOSS with a small step that is too large to serve as a true (contra)lead as that child MOSS will instead have the contralead be the chroma of that MOSS. Meanwhile, if the small step is small enough to serve as a (contra)lead, it will necessarily be confused with either a supertonic or a subtonic, implying an interesting musical reality for such MOSSes. This system thus also suggests that modes which have at least two generators from the tonic in each direction have a unique musical capability and thus modes that do not satisfy this restriction have emergent musical properties based on their very lack of some of those functions.
+Another interesting observation is that this system suggests an at-least-5-note-per-period MOSS because in order for all of the functions '''0, 1, 2, 4, 6, 8, 9''' to be present, there must be at least 5 notes. That way, there exists at least one mode where the dominant, serviant, supertonic and subtonic are all present relative to the tonic, with the (contra)lead being - at minimum - a reality of the (chromatic) extension of the MOSS, which is always important as it acts as melodic background. Note that the digits whose functions are potentially absent from the minimum MOSS are '''1, 3, 5, 7, 9''' which is to say all the odd digits, and where '''3''' and '''7''' are context-dependent gap-filler functions while '''5''' is a function unrelated to the generator and instead related to the period-complement symmetry of the functions suggesting a midpoint between adjacent instances of the tonic. Also note that for 5-note MOSSes, the mediant and contramediant necessarily cannot exist in the same mode where the dominant, serviant, supertonic and subtonic are simultaneously present. Yet more interestingly, the desire to include the functions '''1, 3, 7, 9''' suggests using the child MOSS as the basis for analysing a 5-note and sometimes 6-note (and even 7-note) MOSS in cases where the small step is too large to serve as a true (contra)lead. Meanwhile, if the small step is small enough to serve as a (contra)lead, it will necessarily be confused with either a supertonic or a subtonic, implying an interesting musical reality for such MOSSes. This system thus also suggests that modes which have at least two generators from the tonic in each direction have a unique musical capability and thus modes that do not satisfy this restriction have emergent musical properties based on their very lack of some of those functions.
 == Examples of functions ==