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This section's running example is 5L 3s, whose brightest mode is LLsLLsLs.
This section's running example is 5L 3s, whose brightest mode is LLsLLsLs.
=== Modifications to UDP notation (wip) ===
TAMNAMS makes the following modifications to regular UDP notation to make notation simpler:
* The UDP for multi-period mosses may be denoted as though one instance of its period is a single-period mos; instead of ''up|dp''(p), it is notated as ''u|d''(p) or, in contexts where it doesn't cause confusion, ''u|d''.
* The UDP for a mode may be shortened to "u|", indicating the mode that is formed by stacking u generators above the tonic and n-1-u generators below the tonic. For example, "5L 3s 5|", which refers to LsLLsLLs, is read as "5 ell 3 ess 5 pipe".
* In contexts where using the dark generator is preferred, such as a mos whose dark generator is the bright generator of a mos related to it, the shortened notation is instead "|d", indicating the mode is formed by stacking generators below the tonic, rather than above. Relative to "u|" notation, which can be thought of as ordering modes by decreasing brightness, "|d" reverses that order. The notation is otherwise identical, but "u|" notation is sufficient in most cases.
For an altered 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]].


=== Finding mos modes ===
=== 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.
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 (0-mosstep) and ending at the mosoctave (8-mosstep). 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. For a mos with n pitches, the brightest mode's UDP is (n-1)|0, then the next brightest is (n-2)|1, and so on until the darkest mode of UDP 0|(n-1) is reached.
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.


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. 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"
{| class="wikitable sortable"
|+Modes of 5L 3s, with interval sizes
|+Modes of 5L 3s, with interval sizes
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|5L+3s (perfect)
|5L+3s (perfect)
|}
|}
Since multi-period mosses repeats every period rather than at every octave, the number of modes corresponds to the number of pitches in the period. As a result, multi-period mosses always have fewer modes. An example is shown for 3L 6s.
Since multi-period mosses repeats every period rather than at every octave, the number of modes corresponds to the number of pitches in the period. As a result, multi-period mosses always have fewer modes. An example is shown for 3L 6s, with modified UDPs as described in the previous section.
{| class="wikitable sortable"
{| class="wikitable sortable"
|+Modes of 3L 6s, with interval sizes
|+Modes of 3L 6s, with interval sizes
!Mode
!Mode
!Mode name
!Mode name
!UDP
!Modified UDP
!Rotational order
!Rotational order
!mosunison
!mosunison
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|LssLssLss
|LssLssLss
|<nowiki>3L 6s 6|</nowiki>
|<nowiki>3L 6s 6|</nowiki>
|<nowiki>6|0(3)</nowiki>
|<nowiki>2|0</nowiki>
|0
|0
|0 (perfect)
|0 (perfect)
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|sLssLssLs
|sLssLssLs
|<nowiki>3L 6s 3|</nowiki>
|<nowiki>3L 6s 3|</nowiki>
|<nowiki>3|3(3)</nowiki>
|<nowiki>1|1</nowiki>
|2
|2
|0 (perfect)
|0 (perfect)
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|ssLssLssL
|ssLssLssL
|<nowiki>3L 6s 0|</nowiki>
|<nowiki>3L 6s 0|</nowiki>
|<nowiki>0|6(3)</nowiki>
|<nowiki>0|2</nowiki>
|1
|1
|0 (perfect)
|0 (perfect)
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|3L+6s (perfect)
|3L+6s (perfect)
|}
|}
=== Modifications to UDP notation (wip) ===
TAMNAMS makes the following modifications to regular UDP notation:
* The UDP for a mode may be shortened to "u|", indicating the mode that is formed by stacking u generators above the tonic and n-1-u generators below the tonic. For example, "5L 3s 5|", which refers to LsLLsLLs, is read as "5 ell 3 ess 5 pipe".
* In contexts where using the dark generator is preferred, such as a mos whose dark generator is the bright generator of a mos related to it, the shortened notation is instead "|d", indicating the mode is formed by stacking generators below the tonic, rather than above. Relative to "u|" notation, which can be thought of as ordering modes by decreasing brightness, "|d" reverses that order. The notation is otherwise identical, but "u|" notation is sufficient in most cases.
* The UDP for multi-period mosses can be denoted as though one instance of its period is a single-period mos; instead of ''up|dp''(p), it is notated as ''u|d''(p) or, in contexts where it doesn't cause confusion, ''u|d''.
For an altered 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]].


=== Named mos modes ===
=== Named mos modes ===
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