User:Ganaram inukshuk/Notes/TAMNAMS: Difference between revisions

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==== Finding a mos's generators ====

To find the generators for a mos, follow the algorithm described [[Recursive structure of MOS scales#Finding a generator|here]], and follow the additional instructions to produce the generators as some quantity of mossteps. Alternatively, produce an interval matrix using the instructions [[Interval matrix#Using step sizes|here]] 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 mos degrees ===~~

Individual mos degrees are based on the labels assigned to intervals using the process for naming mos intervals. Mos degrees are enumerated starting at the 0-mosdegree, the tonic. For example, if you go up a major k-mosstep up from the root, then the mos degree reached this way is a major k-mosdegree. Much like "k-mossteps" being shortened to "k-steps" if context allows, k-mosdegrees may also be shortened to "k-degrees". The modifiers of major/minor or augmented/perfect/diminished may also be omitted when clear from context.

~~==== Naming mos chords ====~~

To denote a chord or a mode on a given degree, write the chord or the mode in parentheses after the degree symbol. The most explicit option is to write out the chord in cents, edosteps or mossteps (e.g. in [[13edo]] [[5L 3s]], the 0-369-646 chord can be written 0-4-7\13, P0ms-M2ms-M4ms or 7|0 0-2-4ms) and to write the mode. To save space, you can use whatever names or abbreviations for the chord or mode you have defined for the reader. For example, in the LsLLsLLs mode of 5L 3s, we have m2md(0-369-646), or the chord 0-369-646 on the 2-mosdegree which is a minor 2-mosstep. The LsLLsLLs mode also has m2md(7|), meaning that we have the 7| (LLsLLsLs) mode on the 2-mosdegree which is a minor 2-mosstep in LsLLsLLs (see [[TAMNAMS#Proposal:%20Naming%20mos%20modes|below]] for the convention we have used to name the mode).

=== Naming alterations by a chroma ===

TAMNAMS also uses the designations of augmented and diminished to refer to alterations of a mos interval, much like with using sharps and flats in standard notation. However, mos intervals are altered by raising or lowering it by a moschroma, 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, and lowering a major mos interval makes it minor. A major or perfect mos interval can be raised by a chroma repeatedly to produce an augmented, doubly-augmented, and (uncommonly) a triply-augmented mos interval. Likewise, a minor or perfect mos interval can be lowered by a chroma repeatedly to produce a diminished, doubly-diminished, and (uncommonly) a triply-diminished mos interval~~. The names of alterations also apply to mos degrees~~.

TAMNAMS also uses the designations of augmented and diminished to refer to alterations of a mos interval, much like with using sharps and flats in standard notation. However, mos intervals are altered by raising or lowering it by a moschroma, 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, and lowering a major mos interval makes it minor. A major or perfect mos interval can be raised by a chroma repeatedly to produce an augmented, doubly-augmented, and (uncommonly) a triply-augmented mos interval. Likewise, a minor or perfect mos interval can be lowered by a chroma repeatedly to produce a diminished, doubly-diminished, and (uncommonly) 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.

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|-

!Number of chromas

!Perfect intervals ~~and degrees~~

!Perfect intervals

!Major/minor intervals ~~and degrees~~

!Major/minor intervals

|-

|3 chromas

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* Mosdiesis (a generalized diesis for use with mosses): |L - 2s|

* Moskleisma (a generalized kleisma for use with mosses): |L - 3s|

=== Naming mos degrees ===

Individual mos degrees are based on the labels assigned to intervals using the process for naming mos intervals, including naming alterations. Mos degrees are enumerated starting at the 0-mosdegree, the tonic. For example, if you go up a major k-mosstep up from the root, then the mos degree reached this way is a major k-mosdegree. Much like "k-mossteps" being shortened to "k-steps" if context allows, k-mosdegrees may also be shortened to "k-degrees". The modifiers of major/minor or augmented/perfect/diminished may also be omitted when clear from context.

==== Naming mos chords ====

To denote a chord or a mode on a given degree, write the chord or the mode in parentheses after the degree symbol. The most explicit option is to write out the chord in cents, edosteps or mossteps (e.g. in [[13edo]] [[5L 3s]], the 0-369-646 chord can be written 0-4-7\13, P0ms-M2ms-M4ms or 7|0 0-2-4ms) and to write the mode. To save space, you can use whatever names or abbreviations for the chord or mode you have defined for the reader. For example, in the LsLLsLLs mode of 5L 3s, we have m2md(0-369-646), or the chord 0-369-646 on the 2-mosdegree which is a minor 2-mosstep. The LsLLsLLs mode also has m2md(7|), meaning that we have the 7| (LLsLLsLs) mode on the 2-mosdegree which is a minor 2-mosstep in LsLLsLLs (see [[TAMNAMS#Proposal:%20Naming%20mos%20modes|below]] for the convention we have used to name the mode).

== Other sandboxed rewrites ==

@@ Line 164: / Line 164: @@
 ==== Finding a mos's generators ====
 To find the generators for a mos, follow the algorithm described [[Recursive structure of MOS scales#Finding a generator|here]], and follow the additional instructions to produce the generators as some quantity of mossteps. Alternatively, produce an interval matrix using the instructions [[Interval matrix#Using step sizes|here]] 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 mos degrees ===
-Individual mos degrees are based on the labels assigned to intervals using the process for naming mos intervals. Mos degrees are enumerated starting at the 0-mosdegree, the tonic. For example, if you go up a major k-mosstep up from the root, then the mos degree reached this way is a major k-mosdegree. Much like "k-mossteps" being shortened to "k-steps" if context allows, k-mosdegrees may also be shortened to "k-degrees". The modifiers of major/minor or augmented/perfect/diminished may also be omitted when clear from context.
-==== Naming mos chords ====
-To denote a chord or a mode on a given degree, write the chord or the mode in parentheses after the degree symbol. The most explicit option is to write out the chord in cents, edosteps or mossteps (e.g. in [[13edo]] [[5L 3s]], the 0-369-646 chord can be written 0-4-7\13, P0ms-M2ms-M4ms or 7|0 0-2-4ms) and to write the mode. To save space, you can use whatever names or abbreviations for the chord or mode you have defined for the reader. For example, in the LsLLsLLs mode of 5L 3s, we have m2md(0-369-646), or the chord 0-369-646 on the 2-mosdegree which is a minor 2-mosstep. The LsLLsLLs mode also has m2md(7|), meaning that we have the 7| (LLsLLsLs) mode on the 2-mosdegree which is a minor 2-mosstep in LsLLsLLs (see [[TAMNAMS#Proposal:%20Naming%20mos%20modes|below]] for the convention we have used to name the mode).
 === Naming alterations by a chroma ===
-TAMNAMS also uses the designations of augmented and diminished to refer to alterations of a mos interval, much like with using sharps and flats in standard notation. However, mos intervals are altered by raising or lowering it by a moschroma, 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, and lowering a major mos interval makes it minor. A major or perfect mos interval can be raised by a chroma repeatedly to produce an augmented, doubly-augmented, and (uncommonly) a triply-augmented mos interval. Likewise, a minor or perfect mos interval can be lowered by a chroma repeatedly to produce a diminished, doubly-diminished, and (uncommonly) a triply-diminished mos interval. The names of alterations also apply to mos degrees.
+TAMNAMS also uses the designations of augmented and diminished to refer to alterations of a mos interval, much like with using sharps and flats in standard notation. However, mos intervals are altered by raising or lowering it by a moschroma, 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, and lowering a major mos interval makes it minor. A major or perfect mos interval can be raised by a chroma repeatedly to produce an augmented, doubly-augmented, and (uncommonly) a triply-augmented mos interval. Likewise, a minor or perfect mos interval can be lowered by a chroma repeatedly to produce a diminished, doubly-diminished, and (uncommonly) 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.
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 |-
 !Number of chromas
-!Perfect intervals and degrees
+!Perfect intervals
-!Major/minor intervals and degrees
+!Major/minor intervals
 |-
 |3 chromas
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 * Mosdiesis (a generalized diesis for use with mosses): |L - 2s|
 * Moskleisma (a generalized kleisma for use with mosses): |L - 3s|
+=== Naming mos degrees ===
+Individual mos degrees are based on the labels assigned to intervals using the process for naming mos intervals, including naming alterations. Mos degrees are enumerated starting at the 0-mosdegree, the tonic. For example, if you go up a major k-mosstep up from the root, then the mos degree reached this way is a major k-mosdegree. Much like "k-mossteps" being shortened to "k-steps" if context allows, k-mosdegrees may also be shortened to "k-degrees". The modifiers of major/minor or augmented/perfect/diminished may also be omitted when clear from context.
+==== Naming mos chords ====
+To denote a chord or a mode on a given degree, write the chord or the mode in parentheses after the degree symbol. The most explicit option is to write out the chord in cents, edosteps or mossteps (e.g. in [[13edo]] [[5L 3s]], the 0-369-646 chord can be written 0-4-7\13, P0ms-M2ms-M4ms or 7|0 0-2-4ms) and to write the mode. To save space, you can use whatever names or abbreviations for the chord or mode you have defined for the reader. For example, in the LsLLsLLs mode of 5L 3s, we have m2md(0-369-646), or the chord 0-369-646 on the 2-mosdegree which is a minor 2-mosstep. The LsLLsLLs mode also has m2md(7|), meaning that we have the 7| (LLsLLsLs) mode on the 2-mosdegree which is a minor 2-mosstep in LsLLsLLs (see [[TAMNAMS#Proposal:%20Naming%20mos%20modes|below]] for the convention we have used to name the mode).
 == Other sandboxed rewrites ==