TAMNAMS: Difference between revisions

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The way intervals are named above (and in 12edo theory) has a problem. An interval that's n steps wide is named ''(n+1)th''. This means that adding two intervals is more complicated than it should be. Stacking two fifths makes a ninth, when naively it would make a tenth. We're used to this for the diatonic scale, but when dealing with unfamiliar scale structures, it can be very confusing.

~~For this reason the originally suggested 1-indexed interval names such as ''mos-kth'' are deprecated for non-diatonic mosses.~~ TAMNAMS ~~now prefers~~ a 0-indexed name system for non-diatonic mos intervals: First, use the term ''mosstep'' for steps of the mos, large or small. From there, an interval which is k mossteps wide is a ''k-mosstep'', short for ''k-mosstep interval''. Major, minor, perfect, etc would apply as established. The names ''mosoctave'' (or ''mosequave'' for nonoctave mosses) and ''mosunison'' could still be used, interchangeably with ''n-mosstep'' (for an n-tone mos) and ''0-mosstep'' respectively. This change makes the arithmetic needed to understand mos intervals much smoother.

Thus TAMNAMS uses a 0-indexed name system for non-diatonic mos intervals: First, use the term ''mosstep'' for steps of the mos, large or small. From there, an interval which is k mossteps wide is a ''k-mosstep'', short for ''k-mosstep interval''. Major, minor, perfect, etc would apply as established. The names ''mosoctave'' (or ''mosequave'' for nonoctave mosses) and ''mosunison'' could still be used, interchangeably with ''n-mosstep'' (for an n-tone mos) and ''0-mosstep'' respectively. This change makes the arithmetic needed to understand mos intervals much smoother.

In contexts where it doesn't cause ambiguity, ''k-mosstep'' can be shortened to ''k-step''. ''k-step'' is also generalizable to non-mos scale types such as 3-step-size scales; see below for naming in scales with 3 step sizes.

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* If you add a chroma to a perfect (Pmos) or major (Lmos) interval, it becomes ''augmented'' (A; Amos). If you add two chromas instead, it becomes ''doubly augmented'' (AA; AAmos). (Diatonic examples: augmented mos2nd (Amos2nd), augmented mos4th (Amos4th), doubly augmented mos5th (AAmos5th).)

* The pattern continues, ddd for triply diminished and AAA for triply augmented. Note that applying this operation more than 3 times is an unlikely usecase, and a shorthand notaton of d^3 and A^3 or an alternative notation or terminology entirely would likely be preferable in such circumstances, hence repetition of the corresponding letter is a sufficient system.

== Naming mos degrees ==

To denote degrees in a given mos (or altered mos) mode, we use the term ''k-mosdegree'', abbreviated as kmd (or ''k-degree'' and kd if context allows). Just like for mos interval names, we use 0-indexing, so the perfect 0-mosdegree is the tonic. The modifiers ''perfect'', ''minor'', ''major'', ''augmented'' and ''diminished'' can be used just like for mos interval names: for example, ''minor 3-mosdegree'' (m3md) denotes the degree that lies a minor 3-mosstep above the tonic. Modifiers can be omitted when clear from context.

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 The way intervals are named above (and in 12edo theory) has a problem. An interval that's n steps wide is named ''(n+1)th''. This means that adding two intervals is more complicated than it should be. Stacking two fifths makes a ninth, when naively it would make a tenth. We're used to this for the diatonic scale, but when dealing with unfamiliar scale structures, it can be very confusing.
-For this reason the originally suggested 1-indexed interval names such as ''mos-kth'' are deprecated for non-diatonic mosses. TAMNAMS now prefers a 0-indexed name system for non-diatonic mos intervals: First, use the term ''mosstep'' for steps of the mos, large or small. From there, an interval which is k mossteps wide is a ''k-mosstep'', short for ''k-mosstep interval''. Major, minor, perfect, etc would apply as established. The names ''mosoctave'' (or ''mosequave'' for nonoctave mosses) and ''mosunison'' could still be used, interchangeably with ''n-mosstep'' (for an n-tone mos) and ''0-mosstep'' respectively. This change makes the arithmetic needed to understand mos intervals much smoother.
+Thus TAMNAMS uses a 0-indexed name system for non-diatonic mos intervals: First, use the term ''mosstep'' for steps of the mos, large or small. From there, an interval which is k mossteps wide is a ''k-mosstep'', short for ''k-mosstep interval''. Major, minor, perfect, etc would apply as established. The names ''mosoctave'' (or ''mosequave'' for nonoctave mosses) and ''mosunison'' could still be used, interchangeably with ''n-mosstep'' (for an n-tone mos) and ''0-mosstep'' respectively. This change makes the arithmetic needed to understand mos intervals much smoother.
 In contexts where it doesn't cause ambiguity, ''k-mosstep'' can be shortened to ''k-step''. ''k-step'' is also generalizable to non-mos scale types such as 3-step-size scales; see below for naming in scales with 3 step sizes.
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 * If you add a chroma to a perfect (Pmos) or major (Lmos) interval, it becomes ''augmented'' (A; Amos). If you add two chromas instead, it becomes ''doubly augmented'' (AA; AAmos). (Diatonic examples: augmented mos2nd (Amos2nd), augmented mos4th (Amos4th), doubly augmented mos5th (AAmos5th).)
 * The pattern continues, ddd for triply diminished and AAA for triply augmented. Note that applying this operation more than 3 times is an unlikely usecase, and a shorthand notaton of d^3 and A^3 or an alternative notation or terminology entirely would likely be preferable in such circumstances, hence repetition of the corresponding letter is a sufficient system.
 == Naming mos degrees ==
 To denote degrees in a given mos (or altered mos) mode, we use the term ''k-mosdegree'', abbreviated as kmd (or ''k-degree'' and kd if context allows). Just like for mos interval names, we use 0-indexing, so the perfect 0-mosdegree is the tonic. The modifiers ''perfect'', ''minor'', ''major'', ''augmented'' and ''diminished'' can be used just like for mos interval names: for example, ''minor 3-mosdegree'' (m3md) denotes the degree that lies a minor 3-mosstep above the tonic. Modifiers can be omitted when clear from context.