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

Line 3:

== Proposed terminology ==

* Mosperiod - the period in which the step pattern for a mos repeats. For single-period scales, the mosperiod is the same as the mosoctave, but for multi-period scales, the mosperiod will repeat more than once. ~~Mosperiod intervals are~~ perfect, ~~as are their~~ scale ~~degrees~~.

* Mosperiod - the period in which the step pattern for a mos repeats. For single-period scales, the mosperiod is the same as the mosoctave, but for multi-period scales, the mosperiod will repeat more than once. By default, the term refers to a perfect mosperiod, and the corresponding scale degree is perfect.

* Moscomplement - the octave-complement, or possibly equave-complement, for a mos interval.

* Mosgenerator - the term can be used to refer to a mosstep interval that is the mos's generators. By default, this term should refer to the bright generator, but the terms ''bright mosgenerator'' and ''dark mosgenerator'' can be used for clarification.

* Mosgenerator or mosgen - the term can be used to refer to a mosstep interval that is the mos's generators, in situations where it's easier to say than k-mosstep. By default, this term should refer to the bright generator, but the terms ''bright mosgenerator'' and ''dark mosgenerator'' can be used for clarification.

== Sandboxed section: Naming mos modes ==

Line 12:

This section's running example is 5L 3s, whose brightest mode is LLsLLsLs.

=== ~~Modifications to~~ UDP notation ===

=== Simplified UDP notation ===

Normal UDP notation is described below:

* For single-period mosses, the UDP is notated as ''u''|''d'', where ''u'' is the number of bright generators stacked ''above'' the tonic, ''d'' is the number of bright generators stacked ''below'' the tonic, and "|" is pronounced as "pipe". The full name of a mos's mode is '''xL ys u|d'''.

Line 22:

* The UDP for multi-period mosses may be written as ''u|d''(''p'') rather than ''up|dp''(''p''). This is because the period already appears in both the quantity of bright (''u times p'') and dark (''d times p'') generators, and omitting the ''p'' term makes the notation less redundant. In contexts where it doesn't cause confusion, the notation can be simplified further to ''u|d.''

* The UDP for a mode may be shortened to "u|" under the reasoning of omitting the ''d'' term makes the notation less redundant. For example, "5L 3s 5|", which refers to LsLLsLLs, is read as "5 ell 3 ess 5 pipe".

* The UDP for a mode may be shortened to "u|" under the reasoning that omitting the ''d'' term makes the notation less redundant and can be inferred by the ''u'' term. For example, "5L 3s 5|", which refers to LsLLsLLs, is read as "5 ell 3 ess 5 pipe".

** The shortened notation of "u|" is sufficient in most cases, but in situations where it makes more sense to think in terms of the dark generator, such as with a mos whose dark generator is the bright generator of a related mos, the notation is instead "|d".

In any case, the name of a mos can be substituted for its xL ys form.

This simplified notation will be used throughout, unless otherwise specified. In any case, the name of a mos can be substituted for its xL ys form.

=== Finding mos modes ===

Rotating the sequence of steps - that is, moving the step at the beginning to the end - produces a different mode. This can be repeated until the initial mode that was started with is produced.

This rotation process usually returns the modes in rotational order, not by brightness. To get the modes in order by brightness, ~~first~~ produce every interval for each mode, starting at the mosunison and ending at the mosoctave~~. This produces~~ an [[interval matrix]]. The brightest mode will be the mode that has all of its intervals - excluding the mosunison, mosoctave, and mosperiods if multi-period - in its large size. The 2nd-brightest mode will have one interval in its small size - for multi-period mosses, one interval is in its small size for every instance of the mosperiod - and so on. The darkest mode will have all of its intervals in its small size. A much faster way to do this process is ~~by sorting~~ the modes produced ~~this way~~ in alphabetical order, effectively sorting all modes by decreasing brightness.

This rotation process usually returns the modes in rotational order, not by brightness. To get the modes in order by brightness, produce every interval for each mode - starting at the mosunison and ending at the mosoctave - producing an [[interval matrix]]. The brightest mode will be the mode that has all of its intervals - excluding the mosunison, mosoctave, and mosperiods if multi-period - in its large size. The 2nd-brightest mode will have one interval in its small size - for multi-period mosses, one interval is in its small size for every instance of the mosperiod - and so on. The darkest mode will have all of its intervals in its small size. A much faster way to do this process is to skip making an interval matrix and sort the modes produced by rotation in alphabetical order, effectively sorting all modes by decreasing brightness. In either case, the UDP for the modes sorted by brightness are (n-1)|0, (n-2)|1, and so on to 0|(n-1). The table below shows the modes produced rotationally, and can be sorted by UDP.

~~Using simplified notation as described in the previous section, for a mode with n pitches (or n pitches per period)~~, the UDP for the modes sorted by brightness are (n-1)|0, (n-2)|1, and so on to 0|(n-1)~~, which may be shortened to (n-1)|, (n-2)|, and so on to 0|~~. The table below shows the modes produced rotationally, and can be sorted by UDP.

{| class="wikitable sortable"

|+Modes of 5L 3s, with interval sizes

Line 171:

Line 169:

|-

|LssLssLss

|<nowiki>3L 6s 6|</nowiki>

|<nowiki>3L 6s 2|</nowiki>

|<nowiki>2|0</nowiki>

|0

Line 186:

Line 184:

|-

|sLssLssLs

|<nowiki>3L 6s 3|</nowiki>

|<nowiki>3L 6s 1|</nowiki>

|<nowiki>1|1</nowiki>

|2

Line 215:

Line 213:

|3L+6s (perfect)

|}

==== Alterations to a mode ====

To denote alterations to a mode, we can use any accidental alteration whose meaning is clear. For non-diatonic mosses, the degree modified is indicated using TAMNAMS's 0-indexing convention. For example, LsLsLLLs can be written "5L 3s 5| @4d" (read "5L 3s 5 pipe at-4-degree"), using the @ accidental from [[diamond-mos notation]].

@@ Line 3: / Line 3: @@
 == Proposed terminology ==
-* Mosperiod - the period in which the step pattern for a mos repeats. For single-period scales, the mosperiod is the same as the mosoctave, but for multi-period scales, the mosperiod will repeat more than once. Mosperiod intervals are perfect, as are their scale degrees.
+* Mosperiod - the period in which the step pattern for a mos repeats. For single-period scales, the mosperiod is the same as the mosoctave, but for multi-period scales, the mosperiod will repeat more than once. By default, the term refers to a perfect mosperiod, and the corresponding scale degree is perfect.
 * Moscomplement - the octave-complement, or possibly equave-complement, for a mos interval.
-* Mosgenerator - the term can be used to refer to a mosstep interval that is the mos's generators. By default, this term should refer to the bright generator, but the terms ''bright mosgenerator'' and ''dark mosgenerator'' can be used for clarification.
+* Mosgenerator or mosgen - the term can be used to refer to a mosstep interval that is the mos's generators, in situations where it's easier to say than k-mosstep. By default, this term should refer to the bright generator, but the terms ''bright mosgenerator'' and ''dark mosgenerator'' can be used for clarification.
 == Sandboxed section: Naming mos modes ==
@@ Line 12: / Line 12: @@
 This section's running example is 5L 3s, whose brightest mode is LLsLLsLs.
-=== Modifications to UDP notation ===
+=== Simplified UDP notation ===
 Normal UDP notation is described below:
 * For single-period mosses, the UDP is notated as ''u''|''d'', where ''u'' is the number of bright generators stacked ''above'' the tonic, ''d'' is the number of bright generators stacked ''below'' the tonic, and "|" is pronounced as "pipe". The full name of a mos's mode is '''xL ys u|d'''.
@@ Line 22: / Line 22: @@
 * The UDP for multi-period mosses may be written as ''u|d''(''p'') rather than ''up|dp''(''p''). This is because the period already appears in both the quantity of bright (''u times p'') and dark (''d times p'') generators, and omitting the ''p'' term makes the notation less redundant. In contexts where it doesn't cause confusion, the notation can be simplified further to ''u|d.''
-* The UDP for a mode may be shortened to "u|" under the reasoning of omitting the ''d'' term makes the notation less redundant. For example, "5L 3s 5|", which refers to LsLLsLLs, is read as "5 ell 3 ess 5 pipe".
+* The UDP for a mode may be shortened to "u|" under the reasoning that omitting the ''d'' term makes the notation less redundant and can be inferred by the ''u'' term. For example, "5L 3s 5|", which refers to LsLLsLLs, is read as "5 ell 3 ess 5 pipe".
 ** The shortened notation of "u|" is sufficient in most cases, but in situations where it makes more sense to think in terms of the dark generator, such as with a mos whose dark generator is the bright generator of a related mos, the notation is instead "|d".
-In any case, the name of a mos can be substituted for its xL ys form.
+This simplified notation will be used throughout, unless otherwise specified. In any case, the name of a mos can be substituted for its xL ys form.
 === Finding mos modes ===
 Rotating the sequence of steps - that is, moving the step at the beginning to the end - produces a different mode. This can be repeated until the initial mode that was started with is produced.
-This rotation process usually returns the modes in rotational order, not by brightness. To get the modes in order by brightness, first produce every interval for each mode, starting at the mosunison and ending at the mosoctave. This produces an [[interval matrix]]. The brightest mode will be the mode that has all of its intervals - excluding the mosunison, mosoctave, and mosperiods if multi-period - in its large size. The 2nd-brightest mode will have one interval in its small size - for multi-period mosses, one interval is in its small size for every instance of the mosperiod - and so on. The darkest mode will have all of its intervals in its small size. A much faster way to do this process is by sorting the modes produced this way in alphabetical order, effectively sorting all modes by decreasing brightness.
+This rotation process usually returns the modes in rotational order, not by brightness. To get the modes in order by brightness, produce every interval for each mode - starting at the mosunison and ending at the mosoctave - producing an [[interval matrix]]. The brightest mode will be the mode that has all of its intervals - excluding the mosunison, mosoctave, and mosperiods if multi-period - in its large size. The 2nd-brightest mode will have one interval in its small size - for multi-period mosses, one interval is in its small size for every instance of the mosperiod - and so on. The darkest mode will have all of its intervals in its small size. A much faster way to do this process is to skip making an interval matrix and sort the modes produced by rotation in alphabetical order, effectively sorting all modes by decreasing brightness. In either case, the UDP for the modes sorted by brightness are (n-1)|0, (n-2)|1, and so on to 0|(n-1). The table below shows the modes produced rotationally, and can be sorted by UDP.
-Using simplified notation as described in the previous section, for a mode with n pitches (or n pitches per period), the UDP for the modes sorted by brightness are (n-1)|0, (n-2)|1, and so on to 0|(n-1), which may be shortened to (n-1)|, (n-2)|, and so on to 0|. The table below shows the modes produced rotationally, and can be sorted by UDP.
 {| class="wikitable sortable"
 |+Modes of 5L 3s, with interval sizes
@@ Line 171: / Line 169: @@
 |-
 |LssLssLss
-|<nowiki>3L 6s 6|</nowiki>
+|<nowiki>3L 6s 2|</nowiki>
 |<nowiki>2|0</nowiki>
 |0
@@ Line 186: / Line 184: @@
 |-
 |sLssLssLs
-|<nowiki>3L 6s 3|</nowiki>
+|<nowiki>3L 6s 1|</nowiki>
 |<nowiki>1|1</nowiki>
 |2
@@ Line 215: / Line 213: @@
 |3L+6s (perfect)
 |}
+==== Alterations to a mode ====
 To denote alterations to a mode, we can use any accidental alteration whose meaning is clear. For non-diatonic mosses, the degree modified is indicated using TAMNAMS's 0-indexing convention. For example, LsLsLLLs can be written "5L 3s 5| @4d" (read "5L 3s 5 pipe at-4-degree"), using the @ accidental from [[diamond-mos notation]].