TAMNAMS: Difference between revisions
m →Naming specific mos intervals: Added that perfect mos periods (mosperiods? as one word) can stack to form a mosoctave |
→Naming specific mos intervals: perfect is period-specific not octave-specific so it seems confusing to un-generalise and then generalise later without explaining that both are actually the same simple rule, also clarified further what is meant by "both generators have two sizes each". furthermore, the term "mosoctave" is very confusing fundamentally (think "mosnonave", etc.) so using "octave" is preferred thus "unison" is used for consistency. |
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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. | ||
===Naming specific mos intervals=== | ===Naming specific mos intervals=== | ||
The phrase ''k-mosstep'' by itself does not specify the exact size of an interval. To refer to specific intervals, the familiar modifiers of ''major'', ''minor'', ''augmented'', '' | The phrase ''k-mosstep'' by itself does not specify the exact size of an interval. To refer to specific intervals, the familiar modifiers of ''major'', ''minor'', ''augmented'',''diminished'' and ''perfect'' are used. As mosses are [[Distributional evenness|distributionally even]], every interval (except for the [[1/1|unison]] and [[2/1|octave]]) will be in no more than two sizes. | ||
To find what mos interval sizes are found in a mos, start with the patterns of large and small steps that represents the mos in its brightest mode (the following subsection explains how to do this) and its darkest mode (which is the reverse pattern for the mos's brightest mode). For our running example of 3L 4s, this is LsLsLss (brightest) and ssLsLsL (darkest). To find the large sizes of each k-mosstep, consider the first k mossteps that make up the mos pattern for the brightest mode. Repeat this process with the mos pattern for the darkest mode to find each k-mosstep's small size. 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 step pattern; this is to say that the order of L's and s's doesn't matter, rather the amount of each step size. The large and small sizes should differ by replacing one L in the large size with an s. | To find what mos interval sizes are found in a mos, start with the patterns of large and small steps that represents the mos in its brightest mode (the following subsection explains how to do this) and its darkest mode (which is the reverse pattern for the mos's brightest mode). For our running example of 3L 4s, this is LsLsLss (brightest) and ssLsLsL (darkest). To find the large sizes of each k-mosstep, consider the first k mossteps that make up the mos pattern for the brightest mode. Repeat this process with the mos pattern for the darkest mode to find each k-mosstep's small size. 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 step pattern; this is to say that the order of L's and s's doesn't matter, rather the amount of each step size. The large and small sizes should differ by replacing one L in the large size with an s. | ||
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!Sum | !Sum | ||
|- | |- | ||
|0-mosstep ( | |0-mosstep (unison) | ||
|none | |none | ||
|'''0''' | |'''0''' | ||
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|'''2L+4s''' | |'''2L+4s''' | ||
|- | |- | ||
|7-mosstep ( | |7-mosstep (octave) | ||
|LsLsLss | |LsLsLss | ||
|'''3L+4s''' | |'''3L+4s''' | ||
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|'''3L+4s''' | |'''3L+4s''' | ||
|}The modifiers of ''major'', ''minor'', ''augmented'', ''perfect'', and ''diminished'' (abbreviated as M, m, A, P, and d respectively) are given as such: | |}The modifiers of ''major'', ''minor'', ''augmented'', ''perfect'', and ''diminished'' (abbreviated as M, m, A, P, and d respectively) are given as such: | ||
* | *Integer multiples of the mosperiod, such as the unison and octave, are '''perfect''' because they only have one size each. | ||
*The generating intervals, or generators, are referred to as '''perfect'''. Note that a mos actually has two generators - a bright and dark generator - and both generators have two sizes each. For our running example of 3L 4s, the generators are a 2-mosstep and 5-mosstep (the following subsection explains how to find these). Referring to a mos's generating intervals usually implies its perfect form; specifically: | *The generating intervals, or generators, are referred to as '''perfect'''. Note that a mos actually has two generators - a bright and dark generator - and both generators have two sizes each, specifically, the only time the less common size appears is at the end of the generator chain. For our running example of 3L 4s, the generators are a 2-mosstep and 5-mosstep (the following subsection explains how to find these). Referring to a mos's generating intervals usually implies its perfect form (a.k.a the common form); 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 k-mossteps where k is greater than the number of pitches in the mos, those intervals have the same modifiers as an octave-reduced interval. Similarly, multiples of a | *For k-mossteps where k is greater than the number of pitches in the mos, those intervals have the same modifiers as an octave-reduced interval. Similarly, multiples of a octave are perfect, as are generators raised by some multiple of the octave. | ||
For multi-period mosses, | For multi-period mosses, note that both the bright and dark generators appear in every period, not just every octave, as what it means for a mos to be multi-period is that there is multiple mosperiods per octave. Therefore, generators that are raised or lowered by some integer multiple of the mos's period are also '''perfect'''. There is an important exception in interval naming for ''n''L ''n''s mosses, in which the generators are '''major''' and '''minor''' (for the bright and dark generator respectively) rather than augmented, perfect and diminished, and all other intervals (the octave, unison and multiples of the period) are perfect as would be expected. This is to prevent ambiguity over calling every interval present perfect. | ||
{| class="wikitable" | {| class="wikitable" | ||
|+Names for mos intervals for 3L 4s | |+Names for mos intervals for 3L 4s | ||
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!Gens up | !Gens up | ||
|- | |- | ||
|0-mosstep ( | |0-mosstep (unison) | ||
|Perfect | |Perfect unison | ||
|P0ms | |P0ms | ||
| 0 | | 0 | ||
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|3 | |3 | ||
|- | |- | ||
|7-mosstep ( | |7-mosstep (octave) | ||
| Perfect | | Perfect octave | ||
|P7ms | |P7ms | ||
|3L+4s | |3L+4s | ||
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*To find the mos whose order of steps represent the mos's brightest mode, follow the algorithm described here: [[Recursive structure of MOS scales|Recursive structure of MOS scales#Finding the MOS pattern from xL ys]]. | *To find the mos whose order of steps represent the mos's brightest mode, follow the algorithm described here: [[Recursive structure of MOS scales|Recursive structure of MOS scales#Finding the MOS pattern from xL ys]]. | ||
*To find the generators for a mos, follow the algorithm described here: [[Recursive structure of MOS scales#Finding a generator]]. Be sure to follow the additional instructions to produce the generators as some quantity of mossteps. Alternatively, produce an interval matrix using the instructions here ([[Interval matrix#Using step sizes]]) for making an interval matrix out of a mos pattern. The generators are the intervals that appear as one size in all but one mode. The interval that appears in its large size in all but one mode is the perfect bright generator, and the interval that appears in its small size in all but one mode is the perfect dark generator. | *To find the generators for a mos, follow the algorithm described here: [[Recursive structure of MOS scales#Finding a generator]]. Be sure to follow the additional instructions to produce the generators as some quantity of mossteps. Alternatively, produce an interval matrix using the instructions here ([[Interval matrix#Using step sizes]]) for making an interval matrix out of a mos pattern. The generators are the intervals that appear as one size in all but one mode. The interval that appears in its large size in all but one mode is the perfect bright generator, and the interval that appears in its small size in all but one mode is the perfect dark generator. | ||
===Naming alterations by a chroma=== | ===Naming alterations by a chroma=== | ||
TAMNAMS also uses the modifiers of ''augmented'' and ''diminished'' to refer to ''alterations'' of a mos interval, much like with using sharps and flats in standard notation. Mos intervals are altered by raising or lowering it by a ''moschroma'' (or simply ''chroma'', if context allows), a generalized sharp/flat that is the difference between a large step and a small step. Raising a minor mos interval by a chroma makes it major; the reverse is true. Raising a major or perfect mos interval repeatedly makes an augmented, doubly-augmented, and a triply-augmented mos interval. Likewise, lowering a minor or perfect mos interval repeatedly makes a diminished, doubly-diminished, and 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. Here, the meaning of unison and octave does not change depending on the mos pattern, but the meanings of augmented and diminished do. | TAMNAMS also uses the modifiers of ''augmented'' and ''diminished'' to refer to ''alterations'' of a mos interval, much like with using sharps and flats in standard notation. Mos intervals are altered by raising or lowering it by a ''moschroma'' (or simply ''chroma'', if context allows), a generalized sharp/flat that is the difference between a large step and a small step. Raising a minor mos interval by a chroma makes it major; the reverse is true. Raising a major or perfect mos interval repeatedly makes an augmented, doubly-augmented, and a triply-augmented mos interval. Likewise, lowering a minor or perfect mos interval repeatedly makes a diminished, doubly-diminished, and 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. Here, the meaning of unison and octave does not change depending on the mos pattern, but the meanings of augmented and diminished do. | ||