User:Ganaram inukshuk/Notes/TAMNAMS: Difference between revisions
→Sandboxed rewrite: Naming mos intervals and mos degrees: Rewrote naming mos degrees/intervals section a lot; still wip and not ready for deployment |
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The ordinal names could still be suggestive for e.g. (tunings of) heptatonic mosses where the ordinal names tend to match up well with diatonic ordinal categories. | The ordinal names could still be suggestive for e.g. (tunings of) heptatonic mosses where the ordinal names tend to match up well with diatonic ordinal categories. | ||
=== | === Specific mos intervals === | ||
Note that the phrase ''k-mosstep'' by itself does not specify whether an interval is major or minor. To refer to specific intervals, the familiar designations of '''major''', '''minor''', '''augment''', '''perfect''', and '''diminished''' are used. As mosses are [[Distributional evenness|distributionally even]], every interval will be in no more than two sizes, except for the mosoctave and mosunison, which only has one size. | Note that the phrase ''k-mosstep'' by itself does not specify whether an interval is major or minor. To refer to specific intervals, the familiar designations of '''major''', '''minor''', '''augment''', '''perfect''', and '''diminished''' are used. As mosses are [[Distributional evenness|distributionally even]], every interval will be in no more than two sizes, except for the mosoctave and mosunison, which only has one size. | ||
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. Since a k-mosstep is reached by going up k mossteps up from the root, to find every mos interval, we consider the first k steps of the mos pattern to find each interval's large size. To find the intervals' small size, we repeat the same process of finding mos intervals | ==== How to find 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. Since a k-mosstep is reached by going up k mossteps up from the root, to find every mos interval, we consider the first k steps of the mos pattern to find each interval's large size. To find the intervals' small size, we repeat the same process of finding mos intervals using the step pattern in the mos's darkest mode, which is the pattern of steps in the brightest mode reversed. To make these sizes more clear, we can denote the mos intervals 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 pattern. Note that the size difference between a large interval and small interval corresponds with replacing an L with an s. | |||
{| class="wikitable" | {| class="wikitable" | ||
|+Specific interval sizes for 3L 4s | |+Specific interval sizes for 3L 4s | ||
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|'''3L+4s''' | |'''3L+4s''' | ||
|} | |} | ||
==== How to label specific mos intervals ==== | |||
The labels of major, minor, augmented, perfect, and diminished are assigned in the following manner: | The labels of major, minor, augmented, perfect, and diminished are assigned in the following manner: | ||
* The | * The mosunison and mosoctave are '''perfect''' because they only have one size each. | ||
* The | * The generators are referred to as '''perfect''' by default. However, the generators have two interval sizes, and all mosses actually have two generators: a bright and dark generator. The following subsection explains how to find the generators for a mos. For our running example of 3L 4s, the generators are a 2-mosstep and 5-mosstep. Specifically: | ||
** The large size of the bright generator is '''perfect''', and the small size is '''diminished'''. | ** The large size of the bright generator is '''perfect''', and the small size is '''diminished'''. | ||
** The large size of the dark generator is '''augmented''', and the small size is '''perfect'''. | ** The large size of the dark generator is '''augmented''', and the small size is '''perfect'''. | ||
* For all other intervals, the large size is '''major''' and the small size is '''minor'''. | * For all other intervals, the large size is '''major''' and the small size is '''minor'''. | ||
* For multi-period mosses not of the form nL ns, there is an additional interval that occurs periodically that only appears as one size. This interval is perfect. Additionally: | * For k-mossteps where k is greater than the number of pitches in the mos, those intervals have the same categories as an octave-reduced interval. Similarly, multiples of a mosoctave are perfect, as are generators raised by some multiple of the mosperiod. | ||
** Multiples of the period are perfect, | * For multi-period mosses not of the form nL ns, there is an additional interval that occurs periodically that only appears as one size. This interval, the mos's period, is '''perfect'''. Additionally: | ||
** Generators that are raised some multiple of the | ** Multiples of the period are '''perfect''', as with multiples of a mosoctave. | ||
** Both the bright and dark generators appear in every period, not just every octave. Generators that are raised some multiple of the mos's period are also '''perfect''', as with generators raised by some multiple of the mosoctave. | |||
* For multi-period mosses that are of the form nL ns, the generators are '''major''' and '''minor''', rather than augmented, perfect, and diminished. This is to prevent ambiguity over calling every interval perfect. | * For multi-period mosses that are of the form nL ns, the generators are '''major''' and '''minor''', rather than augmented, perfect, and diminished. This is to prevent ambiguity over calling every interval perfect. | ||
{| class="wikitable" | {| class="wikitable" | ||