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→Sandboxed section: Naming mos modes: Sandoxed rewrite for multi-period mode naming; additional discussion needed on multi-period mosses may be needed
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→Sandboxed section: Naming mos modes: Under the reasoning that UDP is good enough, the proposals for tamnams mode names are listed as modifications to standard UDP; clarified what happens with multi-period mos interval sizes
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== Sandboxed section: Naming mos modes ==
== Sandboxed section: Naming mos modes ==
''Reasoning: what if TAMNAMS had a formal section for naming mos modes, the same with mos names? Due to size, it may make more sense to have the individual mos pages have mos mode names.''
''Reasoning: what if TAMNAMS had a formal section for naming mos modes, the same with mos names?''


The easiest way to name the modes of a mos, without having to memorize any names, is to refer to them by their [[Modal UDP notation|UDP]], notated as ''u''|''p'', 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|p'''. The name of the mos itself may also be used instead of its xL ys form.
The easiest way to name the modes of a mos, without having to memorize any names, is to refer to them by their [[Modal UDP notation|UDP]], notated as ''u''|''p'', 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|p'''. The name of the mos itself may also be used instead of its xL ys form.
For a multi-period mos with p periods, the UDP of is notated as ''up''|''dp''(''p''). Since there are generators being stacked above and below every mosperiod - not just the tonic - there are in total ''u times p'' and ''d times p'' generators being stacked above and below their respective starting pitches. The full name in this case is '''xL ys up|dp(p)'''.


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.


=== 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 we return to the same mode we started with.
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, we can 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 multiples of the period if applicable - in its large size. The next brightest mode will have one interval in its small size, the next-next brightest mode will have two intervals in its small size, and so on. The darkest mode will have all of its intervals in its small size. If the mos has 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 (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.


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.
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.
Line 133: Line 135:
|5L+3s (perfect)
|5L+3s (perfect)
|}
|}
For a multi-period mos with ''p'' periods, a matrix with fewer rows will be produced because the initial mos pattern is reached after ''p'' rotations, which is to say that the mos repeats every ''p'' steps, rather than at every mosoctave. The number of modes produced corresponds to the number of pitches in the period, rather than the mosoctave. The UDP of a multi-period mos is notated as ''up''|''dp''(''p'') instead, to denote that generators are being stacked not just at the root, but also at every multiple of the mosperiod that isn't the mosoctave, hence there are ''u times p'' and ''d times p'' generators being stack above and below their respective starting pitches. As an example, the table below shows the modes 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.
{| class="wikitable sortable"
{| class="wikitable sortable"
|+Modes of 3L 6s, with interval sizes
|+Modes of 3L 6s, with interval sizes
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|}
|}


=== TAMNAMS format for mos modes ===
=== TAMNAMS modifications for UDP notation (wip) ===
When referring to a specific mode for a specific mos, the format is "xL ys u|d". The UDP notation 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 situations where using the dark generator is preferred, such as a mos with a bright generator that is the dark generator of a mos immediately related to it, the shortened notation is instead "|d", indicating the mode is formed by stacking generator below the tonic, rather than above. Given that "u|" effectively enumerates mosses by brightness from most generators stacked above the tonic to least, "|d" basically reverses that order, but the notation is otherwise equivalent. When in doubt, use "u|" or even "u|d".
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]].
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]].


=== Genchain mode names ===
=== Named mos modes ===
If a more memorable name is desired and the mos itself is named, names can be made using [[genchain mode numbering]] on the name of the mos, where the first-brightest mode is called 1st mosname, the second-brightest mode is called 2nd mosname, and so on. The table below shows an example for 7L 1s.
Many people, or groups of people, who have described individual mosses have independently came up with names for the mos's modes. The mosses listed below have named mos modes on their respective pages. (todo: add links)
{| class="wikitable"
 
|+Genchain mode names for 7L 1s
* 5-note mosses: 4L 1s
!Mode
* 7-note mosses: 1L 6s, 2L 5s, 3L 4s, 4L 3s, 5L 2s, and 6L 1s
!UDP
* 8-note mosses: 3L 5s and 5L 3s
!Mode name
* 9-note mosses: 5L 4s and 7L 2s
|-
* 10-note mosses: 3L 7s
|LLLLLLLs
 
|<nowiki>7|0</nowiki>
For mossess that no such mode names but a less mathematical name is desired, [[genchain mode numbering]] may be used, producing 1st xL ys, 2nd xL ys, and so on.
|1st pine
 
|-
== Sandboxed rewrite: Naming mos intervals and mos degrees ==
|LLLLLLsL
Already deployed on main TAMNAMS page: [[TAMNAMS#Naming mos intervals]]
|<nowiki>6|1</nowiki>
 
|2nd pine
=== Complements of intervals ===
|-
The ''octave complement'' (or ''moscomplement'', or ''complement'') of a mos interval follows the same logic as the [[octave complement]] in regular music theory: in general, for a mos with n pitches, a k-mosstep in its large form has a complement of an (n-k)-mosstep in its small form, and the two intervals are complements of one another. If a mos interval is altered by raising it by some number of chromas, its complement will be lowered by the same number of chromas.
|LLLLLsLL
|<nowiki>5|2</nowiki>
|3rd pine
|-
|LLLLsLLL
|<nowiki>4|3</nowiki>
|4th pine
|-
|LLLsLLLL
|<nowiki>3|4</nowiki>
|5th pine
|-
|LLsLLLLL
|<nowiki>2|5</nowiki>
|6th pine
|-
|LsLLLLLL
|<nowiki>1|6</nowiki>
|7th pine
|-
|sLLLLLLL
|<nowiki>0|7</nowiki>
|8th pine
|}


=== Named mos modes ===
Alternatively, if a specific mos interval is thought of as a quantity of large and small steps, then its complement is the number of steps needed to produce the mos pattern of xL ys itself.
Many people, or groups of people, who have described individual mosses have independently came up with names for the mos's modes. The following tables shows all of the mosses that have names as well as the step pattern and UDP, as well as the names' origin. Some modes may have more than one name.
{| class="wikitable"
{| class="wikitable"
! colspan="3" |1L 6s modes
|+Moscomplements of 3L 4s
Mode names borrowed from sister mos
! colspan="2" |Interval
! colspan="3" |2L 5s modes
! colspan="2" |Complement
Modes named under armodue theory
! colspan="3" |3L 4s modes
Modes named by Andrew Heathwaite
! colspan="3" |4L 3s modes
Modes named by Alexander Ianu
! colspan="3" |5L 2s modes
Modes named under normal music theory
! colspan="3" |6L 1s modes
Modes named by Cryptic Ruse
|-
|-
!Mode
!Name
!UDP
!Size
!Mode name
!Name
!Mode
!Size
!UDP
!Mode name
!Mode
!UDP
!Mode name
!Mode
!UDP
!Mode name
!Mode
!UDP
!Mode name
!Mode
!UDP
!Mode name
|-
|-
|Lssssss
|Perfect 0-mosstep (mosunison)
|<nowiki>6|0</nowiki>
|'''0'''
|anti-zokalarian
|Perfect 7-mosstep (mosoctave)
|LssLsss
|'''3L+4s'''
|<nowiki>6|0</nowiki>
|antilociran
|LsLsLss
|<nowiki>6|0</nowiki>
|dil
|LLsLsLs
|<nowiki>6|0</nowiki>
|nerevarine
|LLLsLLs
|<nowiki>6|0</nowiki>
|lydian
|LLLLLLs
|<nowiki>6|0</nowiki>
|ryonian
|-
|-
|sLsssss
|Major 1-mosstep
|<nowiki>5|1</nowiki>
|'''L'''
|antitamashian
|Minor 6-mosstep
|LsssLss
|'''2L+4s'''
|<nowiki>5|1</nowiki>
|antiphrygian
|LsLssLs
|<nowiki>5|1</nowiki>
|gil
|LsLLsLs
|<nowiki>5|1</nowiki>
|vivecan
|LLsLLLs
|<nowiki>5|1</nowiki>
|ionian
|LLLLLsL
|<nowiki>5|1</nowiki>
|karakalian
|-
|-
|ssLssss
|Perfect 2-mosstep
|<nowiki>4|2</nowiki>
|'''L+s'''
|anti-oukranian
|Diminished 5-mosstep
|sLssLss
|'''2L+3s'''
|<nowiki>4|2</nowiki>
|anti-aeolian
|LssLsLs
|<nowiki>4|2</nowiki>
|kleeth
|LsLsLLs
|<nowiki>4|2</nowiki>
|lorkhanic
|LLsLLsL
|<nowiki>4|2</nowiki>
|mixolydian
|LLLLsLL
|<nowiki>4|2</nowiki>
|lobonian
|-
|-
|sssLsss
|Major 3-mosstep
|<nowiki>3|3</nowiki>
|'''2L+s'''
|antihorthathian
|Minor 4-mosstep
|sLsssLs
|'''1L+3s'''
|<nowiki>3|3</nowiki>
|antidorian
|sLsLsLs
|<nowiki>3|3</nowiki>
|bish
|LsLsLsL
|<nowiki>3|3</nowiki>
|sothic
|LsLLLsL
|<nowiki>3|3</nowiki>
|dorian
|LLLsLLL
|<nowiki>3|3</nowiki>
|horthathian
|-
|-
|ssssLss
|Major 4-mosstep
|<nowiki>2|4</nowiki>
|'''2L+2s'''
|antilobonian
|Minor 3-mosstep
|ssLssLs
|'''1L+2s'''
|<nowiki>2|4</nowiki>
|antimixolydian
|sLsLssL
|<nowiki>2|4</nowiki>
|fish
|sLLsLsL
|<nowiki>2|4</nowiki>
|kagrenacan
|LsLLsLL
|<nowiki>2|4</nowiki>
|aeolian
|LLsLLLL
|<nowiki>2|4</nowiki>
|oukranian
|-
|-
|sssssLs
|Augmented 5-mosstep
|<nowiki>1|5</nowiki>
|'''3L+2s'''
|antikarakalian
|Perfect 2-mosstep
|ssLsssL
|'''2s'''
|<nowiki>1|5</nowiki>
|anti-ionian
|sLssLsL
|<nowiki>1|5</nowiki>
|jwl
|sLsLLsL
|<nowiki>1|5</nowiki>
|almalexian
|sLLLsLL
|<nowiki>1|5</nowiki>
|phrygian
|LsLLLLL
|<nowiki>1|5</nowiki>
|tamashian
|-
|-
|ssssssL
|Major 6-mosstep
|<nowiki>0|6</nowiki>
|'''3L+3s'''
|antiryonian
|Minor 1-mosstep
|sssLssL
|'''s'''
|<nowiki>0|6</nowiki>
|antilydian
|ssLsLsL
|<nowiki>0|6</nowiki>
|led
|sLsLsLL
|<nowiki>0|6</nowiki>
|dagothic
|sLLsLLL
|<nowiki>0|6</nowiki>
|locrian
|sLLLLLL
|<nowiki>0|6</nowiki>
|zo-kalarian
|}
{| class="wikitable"
! colspan="3" |3L 5s modes
Mode names borrowed from sister mos
! colspan="3" |5L 3s modes
Modes named by Cryptic Ruse
|-
|-
!Mode
|Perfect 7-mosstep (mosoctave)
!UDP
|'''3L+4s'''
!Mode name
|Perfect 0-mosstep (mosunison)
!Mode
|'''0'''
!UDP
!Mode name
|-
|LsLssLss
|<nowiki>7|0</nowiki>
|antisarnathian, antisarnian
|LLsLLsLs
|<nowiki>7|0</nowiki>
|dylathian, dylian
|-
|LssLsLss
|<nowiki>6|1</nowiki>
|antihlanithian, antihlanian
|LLsLsLLs
|<nowiki>6|1</nowiki>
|ilarnekian
|-
|LssLssLs
|<nowiki>5|2</nowiki>
|antikadathian, antikadian
|LsLLsLLs
|<nowiki>5|2</nowiki>
|celephaisian
|-
|sLsLssLs
|<nowiki>4|3</nowiki>
|antimnarian
|LsLLsLsL
|<nowiki>4|3</nowiki>
|ultharian
|-
|sLssLsLs
|<nowiki>3|4</nowiki>
|anti-ultharian
|LsLsLLsL
|<nowiki>3|4</nowiki>
|mnarian
|-
|sLssLssL
|<nowiki>2|5</nowiki>
|anticelephaisian
|sLLsLLsL
|<nowiki>2|5</nowiki>
|kadathian, kadian
|-
|ssLsLssL
|<nowiki>1|6</nowiki>
|anti-ilarnekian
|sLLsLsLL
|<nowiki>1|6</nowiki>
|hlanithian, hlanian
|-
|ssLssLsL
|<nowiki>0|7</nowiki>
|antidylathian, antidylian
|sLsLLsLL
|<nowiki>0|7</nowiki>
|sarnathian, sarnian
|}
|}
{| class="wikitable"
! colspan="3" |7L 2s modes
Modes named under armodue theory
|-
!Mode
!UDP
!Mode name
|-
|LLLLsLLLs
|<nowiki>8|0</nowiki>
|superlydian
|-
|LLLsLLLLs
|<nowiki>7|1</nowiki>
|super-ionian
|-
|LLLsLLLsL
|<nowiki>6|2</nowiki>
|supermixolydian
|-
|LLsLLLLsL
|<nowiki>5|3</nowiki>
|supercorinthian
|-
|LLsLLLsLL
|<nowiki>4|4</nowiki>
|super-olympian
|-
|LsLLLLsLL
|<nowiki>3|5</nowiki>
|superdorian
|-
|LsLLLsLLL
|<nowiki>2|6</nowiki>
|super-aeolian
|-
|sLLLLsLLL
|<nowiki>1|7</nowiki>
|superphrygian
|-
|sLLLsLLLL
|<nowiki>0|8</nowiki>
|superlocrian
|}
{| class="wikitable"
! colspan="3" |3L 7s modes
Modes named by Peter Kosmorsky
|-
!Mode
!UDP
!Mode name
|-
|LssLssLsss
|<nowiki>9|0</nowiki>
|malkuth
|-
|LssLsssLss
|<nowiki>8|1</nowiki>
|yesod
|-
|LsssLssLss
|<nowiki>7|2</nowiki>
|hod
|-
|sLssLssLss
|<nowiki>6|3</nowiki>
|netzach
|-
|sLssLsssLs
|<nowiki>5|4</nowiki>
|tiferet
|-
|sLsssLssLs
|<nowiki>4|5</nowiki>
|genvurah
|-
|ssLssLssLs
|<nowiki>3|6</nowiki>
|chesed
|-
|ssLssLsssL
|<nowiki>2|7</nowiki>
|binah
|-
|ssLsssLssL
|<nowiki>1|8</nowiki>
|chokmah
|-
|sssLssLssL
|<nowiki>0|9</nowiki>
|keter
|}
== Sandboxed rewrite: Naming mos intervals and mos degrees ==
Already deployed on main TAMNAMS page: [[TAMNAMS#Naming mos intervals]]


== Other sandboxed rewrites ==
== Other sandboxed rewrites ==
Retrieved from "https://en.xen.wiki/w/User:Ganaram_inukshuk/Notes/TAMNAMS"