TAMNAMS: Difference between revisions

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== Naming MOS intervals ==

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.'' ~~Alternatively, the terminology "(major/minor/etc.) ''k''-shift" can be used where ''k'' is number of steps (unison = 0); so a mos3rd is a 2-shift.~~

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.''

~~TAMNAMS uses the following modifiers to denote different interval sizes within a MOS interval class:~~

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" 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.

* For multiples of the period plus or minus 0 or 1 generators: ''perfect''. (Diatonic examples: perfect mos4th (Pmos4th), perfect mos5th (Pmos5th), perfect mos8th (Pmos8th), perfect mos12th (Pmos12th), etc.)

* For generic interval classes with 2 specific sizes of intervals therein (which are therefore separated by a chroma of c = L - s), ''major'' and ''minor'' are used to distinguish the larger (L) and smaller (s) intervals. Note that the generator, its period-equivalents, and the generator's period-complement and its period-equivalents are the only intervals excluded from this rule due to their inclusion in the previous rule. Diatonic examples: major mos2nd (abbreviated Lmos2nd), minor mos3rd (abbreviated smos3rd), major mos3rd (Lmos3rd), etc.)

* 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.)

* 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.

~~=== Alternate non-ordinal names ===~~

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.

~~I (SupahstarSaga)~~ propose a variant name system~~. (This is similar to the "k-shift" suggestion above.)~~ 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" 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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TAMNAMS uses the following modifiers to denote different interval sizes within a MOS interval class:

* For multiples of the period plus or minus 0 or 1 generators: ''perfect''. (Diatonic examples: perfect mos4th (Pmos4th), perfect mos5th (Pmos5th), perfect mos8th (Pmos8th), perfect mos12th (Pmos12th), etc.)

* For generic interval classes with 2 specific sizes of intervals therein (which are therefore separated by a chroma of c = L - s), ''major'' and ''minor'' are used to distinguish the larger (L) and smaller (s) intervals. Note that the generator, its period-equivalents, and the generator's period-complement and its period-equivalents are the only intervals excluded from this rule due to their inclusion in the previous rule. Diatonic examples: major mos2nd (abbreviated Lmos2nd), minor mos3rd (abbreviated smos3rd), major mos3rd (Lmos3rd), etc.)

* 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.)

* 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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== MOS pattern names ==

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 == Naming MOS intervals ==
-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.'' Alternatively, the terminology "(major/minor/etc.) ''k''-shift" can be used where ''k'' is number of steps (unison = 0); so a mos3rd is a 2-shift.
+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.''
-TAMNAMS uses the following modifiers to denote different interval sizes within a MOS interval class:
+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" 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.
-* For multiples of the period plus or minus 0 or 1 generators: ''perfect''. (Diatonic examples: perfect mos4th (Pmos4th), perfect mos5th (Pmos5th), perfect mos8th (Pmos8th), perfect mos12th (Pmos12th), etc.)
-* For generic interval classes with 2 specific sizes of intervals therein (which are therefore separated by a chroma of c = L - s), ''major'' and ''minor'' are used to distinguish the larger (L) and smaller (s) intervals. Note that the generator, its period-equivalents, and the generator's period-complement and its period-equivalents are the only intervals excluded from this rule due to their inclusion in the previous rule. Diatonic examples: major mos2nd (abbreviated Lmos2nd), minor mos3rd (abbreviated smos3rd), major mos3rd (Lmos3rd), etc.)
-* 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.)
-* 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.
-=== Alternate non-ordinal names ===
-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.
-I (SupahstarSaga) propose a variant name system. (This is similar to the "k-shift" suggestion above.) 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" 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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 |}
+TAMNAMS uses the following modifiers to denote different interval sizes within a MOS interval class:
+* For multiples of the period plus or minus 0 or 1 generators: ''perfect''. (Diatonic examples: perfect mos4th (Pmos4th), perfect mos5th (Pmos5th), perfect mos8th (Pmos8th), perfect mos12th (Pmos12th), etc.)
+* For generic interval classes with 2 specific sizes of intervals therein (which are therefore separated by a chroma of c = L - s), ''major'' and ''minor'' are used to distinguish the larger (L) and smaller (s) intervals. Note that the generator, its period-equivalents, and the generator's period-complement and its period-equivalents are the only intervals excluded from this rule due to their inclusion in the previous rule. Diatonic examples: major mos2nd (abbreviated Lmos2nd), minor mos3rd (abbreviated smos3rd), major mos3rd (Lmos3rd), etc.)
+* 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.)
+* 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.
+l
 == MOS pattern names ==

TAMNAMS: Difference between revisions

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