TAMNAMS: Difference between revisions

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To denote interval classes within the MOS, TAMNAMS uses the generic prefix ''mos-'', or the specific prefixes and abbreviations listed under "MOS pattern names". Usage example: ''In 31edo's ultrasoft [[mosh]] scale, the perfect mosthird (aka Pmosh3rd) is a neutral third and the major mosfifth (aka Lmosh5th) is a perfect fifth.''

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. Thus we propose a variant name system: 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. Equivalently "mosdiminished" and "mosaugmented" could be used for chroma alterations of multiples of the equave (e.g. "mosdiminished octave"), because the part that changes meaning depending on the mos pattern is not the unison or the equave. This change makes the arithmetic needed to understand mos intervals much smoother.

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. Thus we propose a variant name system: 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".

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* For nL ns scales, there's an exception to the above two rules. Only multiples of the period (1\n) are called "perfect". Other intervals are called major or minor, despite being period-equivalent to a generator. The reason for this exception is that otherwise all intervals would be called "perfect", leading to ambiguity.

* If you subtract a chroma from a perfect (Pmos) or minor (smos) interval, it becomes ''diminished'' (d; dmos). If you subtract two chromas instead, it becomes ''doubly diminished'' (dd; ddmos). (Diatonic examples: diminished mos3rd (dmos3rd), diminished mos4th (dmos4th), doubly diminished mos5th (ddmos5th), etc.)

** When modifying unisons or equave multiples, "mosdiminished" and "mosaugmented" could be used (e.g. "mosdiminished octave" instead of "diminished mosoctave"), because the part that changes meaning depending on the mos pattern is not the unison or the equave.

* 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.

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 To denote interval classes within the MOS, TAMNAMS uses the generic prefix ''mos-'', or the specific prefixes and abbreviations listed under "MOS pattern names". Usage example: ''In 31edo's ultrasoft [[mosh]] scale, the perfect mosthird (aka Pmosh3rd) is a neutral third and the major mosfifth (aka Lmosh5th) is a perfect fifth.''
-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. Thus we propose a variant name system: 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. Equivalently "mosdiminished" and "mosaugmented" could be used for chroma alterations of multiples of the equave (e.g. "mosdiminished octave"), because the part that changes meaning depending on the mos pattern is not the unison or the equave. This change makes the arithmetic needed to understand mos intervals much smoother.
+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. Thus we propose a variant name system: 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".
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 * For nL ns scales, there's an exception to the above two rules. Only multiples of the period (1\n) are called "perfect". Other intervals are called major or minor, despite being period-equivalent to a generator. The reason for this exception is that otherwise all intervals would be called "perfect", leading to ambiguity.
 * If you subtract a chroma from a perfect (Pmos) or minor (smos) interval, it becomes ''diminished'' (d; dmos). If you subtract two chromas instead, it becomes ''doubly diminished'' (dd; ddmos). (Diatonic examples: diminished mos3rd (dmos3rd), diminished mos4th (dmos4th), doubly diminished mos5th (ddmos5th), etc.)
+** When modifying unisons or equave multiples, "mosdiminished" and "mosaugmented" could be used (e.g. "mosdiminished octave" instead of "diminished mosoctave"), because the part that changes meaning depending on the mos pattern is not the unison or the equave.
 * 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.

TAMNAMS: Difference between revisions

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