User:Ganaram inukshuk/Notes/TAMNAMS: Difference between revisions

TAMNAMS uses the designations of '''major''', '''minor''', '''perfect''', '''augmented''', and '''diminished''' to refer to mos intervals. To find what mos intervals are found in a mos xL ys, start with the pattern of large and small steps that represents the mos in its brightest mode. This section's running example will be 3L 4s, with the pattern (or string) LsLsLss as its brightest mode. A k-mosstep is reached by going up k mossteps up from the root, and can be represented as the first k steps of the pattern. Note that a mosunison, or 0-mosstep, is reached by going up 0 steps, so the pattern for that is no steps. Similarly, a mosoctave is reached by going up x+y steps up from the root, which encompasses the entire mos step pattern. This process finds the specific sizes for all the mos intervals. Repeat the process as described with the pattern that represents the mos in its darkest mode, which can be obtained by reversing the order of steps for the brightest mode. This produces all of the mos intervals in their specific sizes, where the process using the brightest mode produces the large, or major intervals, and the process using the darkest mode produces the small, or minor intervals.

To make these sizes more clear, the mosintervals produced this way can be rewritten as a sum of large and small steps iL+js, where i and j are the number of L's and s's in the interval's subpattern. Note that the difference in size between an interval's large and small size is basically the replacement of one L with one s.

!Steps

!Steps

The mosunison and mosoctave appear as only one size, as 0L+0s and xL+ys respectively, and are referred to as perfect. All other k-mossteps produced this way should be in one of two sizes; the smaller of the two sizes is referred to as a minor k-mosstep, and the larger of the two a major k-mosstep. However, the generating intervals of a mos use the labels augmented, perfect, and diminished instead. Every mos has a pair of generators known as the bright and dark generator, and can be found using this algorithm. (Add link to algorithm). The bright generator will have a large size that's referred to as perfect and a small size that's referred to as diminished. Similarly, the dark generator will have a large size that's referred to as augmented and a small size that's referred to as perfect. These are named such because, for the bright and dark generators, there will be only one mode that contains an augmented generator and only one, different mode that contains a diminished generator. In other words, across all modes, the generators will appear as one size in all but one mode each.

 

Intervals that are more than x+y mossteps above the root share the same designation as the same mosstep that is octave-reduced. Given our example of 3L 4s, if there is a 10-mosstep, it is the same designation (in this case, either major or minor) as a 3-mosstep. Octave-reduction on a general k-mosstep can be done by finding the remainder of k divided by (x+y).

TAMNAMS also uses the designations of augmented and diminished to refer to alterations of a mos interval, much like with using sharps and flats in standard notation. However, mos intervals are altered by raising or lowering it by a moschroma, the difference between a large step and a small step. Raising a minor mos interval by a chroma makes it major, and lowering a major mos interval makes it minor. A major or perfect mos interval can be raised by a chroma repeatedly to produce an augmented, doubly-augmented, and (uncommonly) a triply-augmented mos interval. Likewise, a minor or perfect mos interval can be lowered by a chroma repeatedly to produce a diminished, doubly-diminished, and (uncommonly) a triply-diminished mos interval. The names of alterations also apply to mos degrees.