User:Ganaram inukshuk/Notes/TAMNAMS: Difference between revisions
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=== Finding and naming mos intervals === | === Finding and naming 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. | 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. | 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. | ||
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==== Naming alterations by a chroma ==== | ==== Naming alterations by a chroma ==== | ||
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. | |||
A mosunison or mosoctave that is itself augmented or diminished may also be referred to a mosaugmented or mosdiminished unison or octave. | A mosunison or mosoctave that is itself augmented or diminished may also be referred to a mosaugmented or mosdiminished unison or octave. | ||
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==== | ==== Mos intervals smaller than a chroma ==== | ||
* Mosdiesis (a generalization of the diesis as commonly found in meantone theories): |L - 2s| | * Mosdiesis (a generalization of the diesis as commonly found in meantone theories): |L - 2s| | ||