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Proposed terms: mega-edo explicitly refers to divisions in the millions; deka-, hecto-, and kilo-edo for divisions in the tens, hundreds, and thousands
 
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== Extending TAMNAMS names (archived) ==
== TAMNAMS-related notes ==
This is an attempt to describe various mosses that I feel are worth describing, based on experimenting with these scales or for completion. This contains unofficial scale names that try to be as close to existing names as possible and are not meant to be official or standard. The following table shows single-period mosses sorted by generation rather than note count. As of August 2022, much of this section is rendered unnecessary due to [[TAMNAMS#Mos pattern names|TAMNAMS names]] being reorganized and many scales being renamed, hence this section is kept for archival purposes.
See [[User:Ganaram inukshuk/Notes/TAMNAMS]].
 
Extended names are denoted with an asterisk. Named 1L ns (monolarge) scales are denoted using italics and are based on its sister scale with the anti- prefix added.
{| class="wikitable mw-collapsible"
! colspan="12" |Mos Family Tree (single-period only), with TAMNAMS Names and extended names
|-
! colspan="2" |Progenitor scale
! colspan="2" |1st-order child mosses
! colspan="2" |2nd-order child mosses
! colspan="2" |3rd-order child mosses
! colspan="2" |4th-order child mosses
! colspan="2" |5th-order child mosses
|-
!Steps
!Scale name
!Steps
!Scale name
!Steps
!Scale name
!Steps
!Scale name
!Steps
!Scale name
!Steps
!Scale name
|-
| rowspan="63" |1L 1s
| rowspan="63" |''prototonic*''
(currently monowood and trivial)
| rowspan="31" |1L 2s
| rowspan="31" |''antideuteric*''
(currently antrial)
| rowspan="15" |1L 3s
| rowspan="15" |''antitetric*''
(currently antetric)
| rowspan="7" |1L 4s
| rowspan="7" |''antimanic''
(currently pedal)
| rowspan="3" |1L 5s
| rowspan="3" |''antimachinoid*''
(currently antimachinoid)
|1L 6s
|''anti-archeotonic''
(currently onyx)
|-
|
|
|-
|6L 1s
|archeotonic
|-
|
|
|
|
|-
| rowspan="3" |5L 1s
| rowspan="3" |machinoid
|5L 6s
|
|-
|
|
|-
|6L 5s
|
|-
|
|
|
|
|
|
|-
| rowspan="7" |4L 1s
| rowspan="7" |manual
(formerly manic)
| rowspan="3" |4L 5s
| rowspan="3" |gramitonic
(formerly orwelloid)
|4L 9s
|
|-
|
|
|-
|9L 4s
|
|-
|
|
|
|
|-
| rowspan="3" |5L 4s
| rowspan="3" |semiquartal
|5L 9s
|
|-
|
|
|-
|9L 5s
|
|-
|
|
|
|
|
|
|
|
|-
| rowspan="15" |3L 1s
| rowspan="15" |tetric
| rowspan="7" |3L 4s
| rowspan="7" |mosh
| rowspan="3" |3L 7s
| rowspan="3" |sephiroid
|3L 10s
|
|-
|
|
|-
|10L 3s
|
|-
|
|
|
|
|-
| rowspan="3" |7L 3s
| rowspan="3" |dicoid
(formerly dicotonic)
|7L 10s
|
|-
|
|
|-
|10L 7s
|
|-
|
|
|
|
|
|
|-
| rowspan="7" |4L 3s
| rowspan="7" |smitonic
| rowspan="3" |4L 7s
| rowspan="3" |(formerly kleistonic)
|4L 11s
|
|-
|
|
|-
|11L 4s
|
|-
|
|
|
|
|-
| rowspan="3" |7L 4s
| rowspan="3" |(formerly suprasmitonic)
|7L 11s
|
|-
|
|
|-
|11L 7s
|
|-
|
|
|
|
|
|
|
|
|
|
|-
| rowspan="31" |2L 1s
| rowspan="31" |deuteric*
(currently trial)
| rowspan="15" |2L 3s
| rowspan="15" |pentic
| rowspan="7" |2L 5s
| rowspan="7" |antidiatonic
| rowspan="3" |2L 7s
| rowspan="3" |balzano
(formerly joanatonic)
|2L 9s
|
|-
|
|
|-
|9L 2s
|
|-
|
|
|
|
|-
| rowspan="3" |7L 2s
| rowspan="3" |superdiatonic
|7L 9s
|
|-
|
|
|-
|9L 7s
|
|-
|
|
|
|
|
|
|-
| rowspan="7" |5L 2s
| rowspan="7" |diatonic
| rowspan="3" |5L 7s
| rowspan="3" |(formerly p-chromatic)
|5L 12s
|s-enharmonic*
|-
|
|
|-
|12L 5s
|p-enharmonic*
|-
|
|
|
|
|-
| rowspan="3" |7L 5s
| rowspan="3" |(formerly m-chromatic)
|7L 12s
|f-enharmonic*
|-
|
|
|-
|12L 7s
|m-enharmonic*
|-
|
|
|
|
|
|
|
|
|-
| rowspan="15" |3L 2s
| rowspan="15" |antipentic
| rowspan="7" |3L 5s
| rowspan="7" |checkertonic
(formerly sensoid)
| rowspan="3" |3L 8s
| rowspan="3" |
|3L 11s
|
|-
|
|
|-
|11L 3s
|
|-
|
|
|
|
|-
| rowspan="3" |8L 3s
| rowspan="3" |
|8L 11s
|
|-
|
|
|-
|11L 8s
|
|-
|
|
|
|
|
|
|-
| rowspan="7" |5L 3s
| rowspan="7" |oneirotonic
| rowspan="3" |5L 8s
| rowspan="3" |
|5L 13s
|
|-
|
|
|-
|13L 5s
|
|-
|
|
|
|
|-
| rowspan="3" |8L 5s
| rowspan="3" |
|8L 13s
|
|-
|
|
|-
|13L 8
|}
 
=== 1L 1s, 1L 2s, and 2L 1s, and their child mosses (archived) ===
As of August 14, 2022, all of these scales have been named. These descriptions are kept for archival purposes.
{| class="wikitable"
! colspan="4" |Parent scale
! colspan="4" |1st-order child scales
! colspan="4" |2nd-order child scales
|-
!Steps
!Originally proposed name
!Current name
!Notes
!Steps
!Originally proposed name
!Current name
!Notes
!Steps
!Originally proposed name
!Current name
!Notes
|-
| rowspan="7" |1L 1s
| rowspan="7" |prototonic, protic, or monowood
| rowspan="7" |monowood and trivial
| rowspan="7" |The progenitor scale of all single-period mosses.
Despite being a monolarge scale, it's also its own sister and is named regardless.
 
The current name "monowood" comes from nL ns scales (such as pentawood for 5L 5s), and is used as a base for such scales. The name trivial comes from the fact that this is a trivial (octave-equivalent) scale, consisting of only its generators.
| rowspan="3" |1L 2s
| rowspan="3" |antideuterotonic or antideuteric
| rowspan="3" | antrial
| rowspan="3" |One of the child scales of 1L 1s.
Being a monolarge scale, tetric (3L 1s) may be more worth considering as a parent scale.
|1L 3s
|antitetric
| antetric
|Monolarge scale. Similarly to 3L 1s with 1L 2s, 4L 1s may be worth considering as a parent scale.
|-
|
|
|
|
|-
|3L 1s
|tetric
|tetric
|Parent scale to orwelloid (now gramitonic) and semiquartal, the name tetric is assigned similarly to pentic being the parent of diatonic and antidiatonic.
|-
|
|
|
|
|
|
|
|
|-
| rowspan="3" |2L 1s
| rowspan="3" |deuterotonic or deuteric
| rowspan="3" |trial
| rowspan="3" |One of the child scales of 1L 1s.
|2L 3s
| -
|pentic
|Already established name.
|-
|
|
|
|
|-
|3L 2s
| -
|antipentic
|Already established name.
|}
 
=== 5L 7s, 7L 5s, and their child mosses (archived) ===
5L 2s has two children: 5L 7s and 7L 5s, or formerly p- and m-chromatic respectively. This section describes a scheme for naming the daughter and granddaughter scales for 5L 2s, which can be generalized to any parent mos; see [[User:Frostburn/TAMNAMS Extension]] or the following section for more information.
{| class="wikitable"
! colspan="3" |Parent scale
! colspan="3" |1st-order child scales
! colspan="3" |2nd-order child scales
|-
!Steps
!Name
!Notes
!Steps
!Name
!Notes
!Steps
!Name
!Notes
|-
| rowspan="7" |5L 2s
| rowspan="7" |diatonic
| rowspan="7" |Already established name.
| rowspan="3" |5L 7s
| rowspan="3" |p-chromatic
| rowspan="7" |Names are based on former names of these mosses: p-chromatic and m-chromatic.
If the distinction between p- and m- isn't needed, both scales may collectively be referred to as "chromatic".
|5L 12s
|s-enharmonic
| rowspan="7" |Names are based on discussions with xen discord members on attempting to name daughter and granddaughter scales in a systematic way.
If the distinction between s-, p-, f-, and m- isn't needed, all four scales may collectively be referred to as "enharmonic".
|-
|
|
|-
|12L 5s
|p-enharmonic
|-
|
|
|
|
|-
| rowspan="3" |7L 5s
| rowspan="3" |m-chromatic
|7L 12s
|f-enharmonic
|-
|
|
|-
|12L 7s
|m-enharmonic
|}
 
=== Describing moschromatic and mosenharmonic scales ===
This is a system for describing scales beyond the set of named TAMNAMS scales. Although this is already described by [[User:Frostburn]], this is how I would word it.
 
Although naming scales beyond the current cap of 10 notes is antithetical to the purpose of TAMNAMS, a general description can still be made without establishing concrete names, while using names for already named scales. Any mos will have 2 child scales, collectively referred to as moschromatic. Those child scales scales will have 2 child scales of their own, or 4 grandchild scales, collectively referred to as mosenharmonic. For describing the scales of a named mos, the prefix of mos- is removed and replaced with the mos's prefix instead; for example, the child and grandchild scales for the mos 5L 3s (oneirotonic, prefix oneiro-) are oneirochromatic and oneiroenharmonic respectively. Note that the absence of a prefix will specifically describe the chromatic and enharmonic scales of 5L 2s. If talking about a specific scale, p-, m-, s-, or f- can be added based on the step ratio of the parent mos.
 
{| class="wikitable"
! colspan="2" |Parent scale
! colspan="3" |Moschromatic scales
! colspan="3" |Mosenharmonic scales
|-
!Steps
!Step ratio range
(hardest to softest)
!Steps
!Specific name
!Step ratio range
(hardest to softest)
!Steps
!Specific name
!Step ratio range
(hardest to softest)
|-
| rowspan="7" |xL ys
| rowspan="7" |1:0 to 1:1
| rowspan="3" |xL (x+y)s
| rowspan="3" |p-moschromatic
| rowspan="3" |1:0 to 2:1
|xL (2x+y)s
|s-mosenharmonic
|1:0 to 3:1
|-
|
|
|
|-
|(2x+y)L xs
|p-mosenharmonic
|3:1 to 2:1
|-
|
|
|
|
|
|
|-
| rowspan="3" |(x+y)L xs
| rowspan="3" |m-moschromatic
| rowspan="3" |2:1 to 1:1
|(x+y)L (2x+y)s
|f-mosenharmonic
|3:2 to 1:1
|-
|
|
|
|-
|(2x+y)L (x+y)s
|m-mosenharmonic
|2:1 to 3:2
|}
 
== Changes to TAMNAMS names ==
This section describes changes to existing TAMNAMS names that I would make.
{| class="wikitable"
|+
!Mos
!Current name
!Proposed name
!Reasoning
|-
|1L 5s
|antimachinoid
|selenic
|An indirect reference to luna temperament; "selene" is Greek for "moon". This drops the anti- prefix.
|-
|2L 5s
|antidiatonic
|pelic
| rowspan="2" |From "pelog" and "armodue". The proposed names are to make both scales more distinct from diatonic. This drops the anti- and super- prefixes.
|-
|7L 2s
|superdiatonic
|armic
|}


== Mode matrix, interval matrix, and degree matrix ==
== Mode matrix, interval matrix, and degree matrix ==
Line 1,842: Line 1,289:
This also describes a property of the generating intervals: they appear in one specific size in all but one mode; for 5L 2s's perfect 4th, it appears as the smaller size except in the lydian mode where it appears as an augmented 4th, and for the perfect 5th, it appears as the larger size except in the locrian mode where it's a diminished 5th.
This also describes a property of the generating intervals: they appear in one specific size in all but one mode; for 5L 2s's perfect 4th, it appears as the smaller size except in the lydian mode where it appears as an augmented 4th, and for the perfect 5th, it appears as the larger size except in the locrian mode where it's a diminished 5th.


== Interpreting UDP as two mode enumeration methods ==
== Proposal: Equave-agnostic mos names (work-in-progress) ==
[[Modal UDP notation|UDP notation]] is one of many mode notation systems that primarily focuses on how to organize the modes of a mos by modal brightness. This notation necessarily requires the notation to distinguish between the chroma-positive and chroma-negative generators of a mos. One issue with this focus on only its chroma-positive generator is that the generators may "flip". As an example, 5L 2s is said to have a perfect 5th as its generator, but although 2L 3s (the pentatonic scale) is said to have a perfect 4th as its chroma-positive generator, it's common to think of its generator as a perfect 5th regardless.
See [[User:Ganaram inukshuk/TAMNAMS Extension]]
{| class="wikitable sortable"
 
! colspan="9" |Modes of 5L 2s
== Other mos naming schemes ==
 
===Names by large step count===
Rather than name mosses related by the number of large steps they have, where the mosses are of the form xL (nx + y)s and relate back to a mos xL ys (n=0), these mosses can be described as members of a family. An example of such a family is the mos sequence 5L 2s, 5L 7s, 5L 12s, 5L 17s, etc, where each successive mos has 5 more small steps than the last. By extension, the mos 7L 5s (the sister of 5L 7s) is not seen as a member of this linear family even though it's part of the diatonic family as a whole, but rather as the start of its own linear family; put another way, the mosses 5L 2s, 5L 7s, 5L 12s, 5L 17s, etc are a subfamily within the larger diatonic family.
 
Mosses in a linear family are based on repeated applications of the replacement ruleset L->Ls and s->s on the initial mos, and reaching the nth member of a linear family requires the initial mos have a hard or pseudocollapsed step ratio. The child mos (x+y)L xs is the start of its own linear family, which relates back to the initial mos xL ys if the initial mos has a step ratio that is soft or pseudoequalized.
 
Names for these families describe a subset of a mos descendant family, and most mos families go by the name of ''(mos name)'' ''linear family'' or ''(mos-prefix)linear family''.
{| class="wikitable"
|+Names of single-period mos linear families (work-in-progress)
! colspan="3" |Trivial families (names not based on "linear")
|-
|-
! rowspan="2" |UDP
! Mos
! rowspan="2" |Mode names
!Name
! colspan="7" |Scale degrees (starting at C)
!Reasoning
|-
|-
!1st
|1L (n+1)s
!2nd
|monolarge family
!3rd
|Represents an entire family of mosses formerly unnamed by TAMNAMS
!4th
The name "monolarge" is chosen as it succinctly describes the only possible 1L family
!5th
!6th
!7th
|-
|-
|<nowiki>6|0</nowiki>
|2L (2n+1)s
|Lydian
|bilarge family
|Named analogously to the monolarge family
|-
|3L (3n+1)s
|trilarge family
|Named analogously to the monolarge family
Prevents potential confusion with the name "tetralinear"
|-
! colspan="3" |Families with 3 large steps
|-
!Mos
!Name
!Reasoning
|-
|3L (3n+2)s
|apentilinear family
|Named after anpentic
|-
! colspan="3" |Families with 4 large steps
|-
!Mos
!Name
!Reasoning
|-
|4L (4n+1)s
|manulinear family
|Named after manual
|-
|4L (4n+3)s
|smilinear family
|Named after smitonic
|-
! colspan="3" |Families with 5 large steps
|-
!Mos
!Name
!Reasoning
|-
|5L (5n+1)s
|mechlinear family
|Named after machinoid (prefix mech-)
|-
|5L (5n+2)s
|p-linear family
|Named after p-chromatic rather than diatonic, which has no prefix
|-
|5L (5n+3)s
|oneirolinear family
|Named after oneirotonic
|-
|5L (5n+4)s
|chtonlinear family
|Named after semiquartal (prefix chton-)
|-
! colspan="3" |Families with 6 large steps
|-
!Mos
!Name
!Reasoning
|-
|6L (6n+1)s
|archeolinear family
|Named after archeotonic
|-
|6L (6n+5)s
|xeimlinear family
|Named after xeimtonic, a former name for 6L 5s
|-
! colspan="3" |Families with 7 large steps
|-
!Mos
!Name
!Reasoning
|-
|7L (7n+1)s
|pinelinear family
|Named after pine
|-
|7L (7n+2)s
|armlinear family
|Named after superdiatonic (also called armotonic)
|-
|7L (7n+3)s
|dicolinear family
|Named after dicotonic
|-
|7L (7n+4)s
|prasmilinear family
|Named after a truncation of a former name for 7L 4s (suprasmitonic)
|-
|7L (7n+5)s
|m-linear family
|Named after m-chromaticralic (prefix blu-)
|-
! colspan="3" |Families with 8 large steps
|-
!Mos
!Name
!Reasoning
|-
|8L (8n+3)s
|
|
|-
|8L (8n+5)s
|petrlinear family
|Named after petroid, a former name for 8L 5s
|-
|8L (8n+7)s
|
|
|-
! colspan="3" |Families with 9 large steps
|-
!Mos
!Name
!Reasoning
|-
|9L (9n+1)s
|sinalinear family
|Named after sinatonic
|-
|9L (9n+2)s
|
|
|-
|9L (9n+4)s
|
|
|-
|9L (9n+5)s
|
|
|-
|9L (9n+7)s
|
|
|-
|9L (9n+8)s
|
|
|}
== Miscellaneous notation ==
=== Alternative UDP notation for filenames ===
UDP notation is currently notated as u|d for single-period mosses, and up|dp(p) for multi-period mosses. An alternative notation, intended for use for filenames since "|" cannot be used as part of a filename, is uU dD, or upU dpD.
{| class="wikitable"
|+Examples
!Example mos
!Standard UDP notation
!Alternate notation
|-
| rowspan="2" |5L 2s
|<nowiki>5|1 (ionian mode)</nowiki>
|5U 1D
|-
|<nowiki>3|3 (dorian mode)</nowiki>
|3U 3D
|-
|3L 3s
|<nowiki>3|0(3)</nowiki>
|3U 0D
|}
 
=== N(k) note name notation (work-in-progress) ===
Rather than using alphabetical names, notes of the form N(k) are used. These are used to indicate position on a staff, where N(0) is the root. These names serve as an alternative to using different notations for different scales, but may be interpreted as blanks for one to fill in with different, more specific notation. If k is unbounded, then this notation denotes position on a staff. However, k may be bounded within the range [0, n), where n is the note count, to indicate pitch classes.
 
For a given mos xL ys, note names are based on a mode u|p; the choice of mode is up to the user. Starting at the root of N(0), successive pitch classes are named N(1), N(2), and so on. If note names are given and assuming N(0) is the root, then N(k) can be thought of as a function that returns an unaltered note name corresponding to the k-mosdegree of a mos xL ys in the mode u|p. In standard notation, N(0) is C, N(1), is D, and so on. Since this is cyclical, N(7) and N(0) are both the same value of C.
 
If two pitches, reached by going up or down some quantity of mossteps, have the same remainder when divided by xL+ys (which is the same as octave-reducing), then they are in the same pitch class.
{| class="wikitable"
|+ Example for 5L 2s (LLsLLLs, mode 5 |Example with standard notation (5L 2s, mode 5|1)
!Mossteps from root
!Substring
!Mosstep sum
!Standard note name
!Nk note name
|-
|0
|''none''
|0
|C
|C
|N(0)
|-
|1
|L
|L
|D
|D
|N(1)
|-
|2
|LL
|2L
|E
|E
|F#
|N(2)
|G
|A
|B
|-
|-
|<nowiki>5|1</nowiki>
|3
|Ionian
|LLs
|C
|2L+s
|D
|E
|F
|F
|N(3)
|-
|4
|LLsL
|3L+s
|G
|G
|N(4)
|-
|5
|LLsLL
|4L+s
|A
|A
|N(5)
|-
|6
|LLsLLL
|5L+s
|B
|B
|N(6)
|-
|-
|<nowiki>4|2</nowiki>
|7
|Mixolydian
|LLsLLLs
|5L+2s
|C
|C
|D
|N(7) (same as N(0))
|E
|}
|F
Chromas are denoted using the letter c, and are expressed as a multiple of c being added (or subtracted) from a note N(k). Half-accidentals are denoted as fractions (such as c/2) or decimals (such as 0.5c). Dieses, if present, are expressed similarly using the letter d. If this notation denotes position on a staff, then chromas and dieses don't change position on a staff, but modify the pitch at that position. If this notation is treated as placeholders for more specific notation, then adding or subtracting c represents the use of sharp or flat (or equivalent) accidentals.
|G
 
|A
Since chromas and dieses can be expressed in terms of L and s – where a chroma is L - s and a diesis is the absolute value of L - 2s – modifying a note by a chroma or diesis can equivalently expressed as going up (or down) some interval iL+js. If, for a given step ratio L:s, two pitch classes Np and Nq are modified by different amounts of chromas uc and vc to produce pitch classes N(p)+uc and N(q)+vc, if dividing both by xL+ys produces the same remainder, then the two pitches are enharmonic equivalents.
|Bb
 
As an example, the table below denotes diatonic (5L 2s) pitch classes as sums of L's and s's, and shows how different step ratios produce different enharmonic equivalences; namely, in 12edo, C# and Db are equivalent, but in 19edo, C# and Db are not equivalent but B# and Cb are equivalent.
{| class="wikitable"
|+Examples with standard diatonic notation
!Note name
!N(k) note name with chroma
!Mosstep sum
!Like terms combined
!If L:s = 2:1
!If L:s = 3:2
|-
|-
|<nowiki>3|3</nowiki>
|Dorian
|C
|C
|N(0)
|0
|0
|0
|0
|-
|C#
|N(0)+c
|L-s
|L-s
|1
|1
|-
|Db
|N(1)-c
|L-(L-s)
|s
|1
|2
|-
|D
|D
|Eb
|N(1)
|F
|L
|G
|L
|A
|2
|Bb
|3
|-
|B
|N(6)
|5L+s
|5L+s
|11
|17
|-
|-
|<nowiki>2|4</nowiki>
|B#
|Aeolian
|N(6)+c
|C
|5L+s+(L-s)
|D
|6L
|Eb
|12
|F
|18
|G
|Ab
|Bb
|-
|-
|<nowiki>1|5</nowiki>
|Cb
|Phrygian
|N(7)-c
|C
|5L+2s-(L-s)
|Db
|4L+3s
|Eb
|11
|F
|18
|G
|Ab
|Bb
|-
|-
|<nowiki>0|6</nowiki>
|C (one octave up)
|Locrian
|N(7) (same as N(0), as a pitch class)
|C
|5L+2s (reduced to 0 due to modular arithmetic)
|Db
|5L+2s (reduced to 0)
|Eb
|12 (reduced to 0)
|F
|19 (reduced to 0)
|Gb
|Ab
|Bb
|}
|}
{| class="wikitable sortable"
N(k) notation can also be used to build a genchain that is agnostic of the size (in cents) of the generator and equave. For example, the genchain for standard notation can be written as N(0), N(4), N(8), N(12), N(16), N(20), N(24)+c, N(28)+c for the ascending chain. The descending chain can be written as N(0), N(3), N(6)-c, N(9)-c, N(12)-c, N(15)-c, N(18)-c, N(21)-c, or as N(0), N(-4), N(-8)-c, N(-12)-c, N(-16)-c, N(-20)-c, N(-24)-c, N(-28)-c. The value k isn't entered into the function, but rather its remainder when divided by the number of steps in the mos (modulo 7, for the case of standard notation), so N(8) is equivalent to N(1) for example.
 
Since the gamut on C is based on the ionian mode, or produced using 5 generators going up and 1 going down, the first note after N(20) has a chroma added, producing N(24)+c. Simply put, the first 5 notes after the root have zero chromas added, the next 6 after that have 1 chroma added, the next 6 have 2 chromas added, and so on. For the descending chain, accidentals are subtracted after the first note, and every 6 notes thereafter has one more chroma subtracted.
 
Ups and downs may also be represented, using the variable u. Up-C-sharp, or ^C#, is written as N(0)+c+u, where u is an edostep.
 
=== Chord notation using mossteps ===
For a chord built using stacked mossteps s1 and s2, the chord is referred to as an s1+s2 chord. The rules for classifying the shape of the chord are as follows:
{| class="wikitable"
|+
|+
! colspan="14" |Modes of 2L 3s
!If the interval s1 mossteps from the root is...
!And the interval s2 mossteps from there is...
!Then the overall chord is
!Which, if s1 and s2 are diatonic or diatonic-like 3rds, is a(n)...
|-
|the large interval (eg, major)
|the large interval (eg, minor)
|Large symmetric
|Augmented chord (M3+M3)
|-
|-
! rowspan="2" |UDP
|the large interval
! rowspan="2" |Mode "names"
|the small interval
! colspan="5" |Scale degrees (independent of 5L 2s)
|Major asymmetric
! colspan="7" |Scale degrees (in relation to 5L 2s)
|Major chord (M3+m3)
|-
|-
!0d
|the small interval
!1d
|the large interval
!2d
|Minor asymmetric
!3d
|Minor chord (m3+M3)
!4d
!1st
!2nd
!3rd
!4th
!5th
!6th
!7th
|-
|-
|<nowiki>4|0</nowiki>
|the small interval
|Pentatonic Phrygian (default mode for sake of example)
|the small interval
|J
|Small symmetric
|K
|Diminished chord (m3+m3)
|L
|}
|M
If the quantities of mossteps s1 and s2 are different, then the symmetric chrods are quasisymmetric instead. The interval sizes don't need to be major or minor, either; they can also be augmented, perfect, or diminished if it's a generator.
|N
 
|C
== Proposal (wip): strict and weak definitions for a chromatic pair ==
| -
 
|Eb
=== Strict definition ===
|F
A '''chromatic pair''' is a pair of mosses zL ws and xL ys within some temperament, such that x = z + w and y = z, where zL ws is a '''haplotonic''' '''scale''' and xL ys is an '''albitonic''' '''scale'''. The large steps of the albitonic scale are such that haplotonic scale can be found within the large steps, forming a '''chromatic scale''' of either xL (x+y)s or (x+y)L xs, or more generally, xA (x+y)B.
| -
 
|Ab
=== Weak definition ===
|Bb
A chromatic pair, under the weak definition, is a pair of mosses zL ws and xL ys, such that x = nz + w and y = z. The strict definition is such that n = 1. However, rather than the mosses zL ys and xL ys that form the chromatic scale of xA (x+y)B, it's the mosses zL ((n-1)z+w)s and xL ys that form the chromatic scale.
 
=== Things to consider ===
 
* A haplotonic scale's note count should be 4 or 5 notes, corresponding to the note counts of the grandchild mosses of 1L 1s: 2L 3s, 3L 2s, 1L 3s, and 3L 1s.
* An albitonic scale's note count should be around 7 notes.
 
== Warped scales ==
A somewhat generalized notion of warping, described by the addition, removal, or substitution of a single step. The most common scales of 12edo are used as examples: 5L 2s, the whole-tone scale (effectively 6edo), the chromatic scale (effectively 12edo), and the diminished scale (4L 4s, hardness of 2).
 
The simplest ways to warp a scale are through the addition of a step and the removal of a step. Substitution of a step, where one step is changed for a step of a different size, can be thought of removing a step of one size and adding a step of a different size.
 
{| class="wikitable"
|+Warped 5L 2s
! rowspan="2" |Small step changes
! colspan="3" |Large step changes
|-
!-1L
!+0L
!+1L
|-
!-1s
|
|5L 1s
|6L 1s
|-
!+0s
|5L 1s
|'''5L 2s'''
|6L 2s
|-
!+1s
|4L 3s
|5L 3s
|
|}
{| class="wikitable"
|+Warped 6edo
(equal-tempered whole-tone scale)
! rowspan="2" |Small step changes
! colspan="3" |Large step changes
|-
!-1L
!+0L
!+1L
|-
!-1s
|
|
|1L 5s
|-
!+0s
|
|'''6edo'''
|1L 6s
|-
!+1s
|5L 1s
|6L 1s
|
|}
{| class="wikitable"
|+Warped 12edo
(equal-tempered chromatic scale)
! rowspan="2" |Small step changes
! colspan="3" |Large step changes
|-
!-1L
!+0L
!+1L
|-
!-1s
|
|
|1L 11s
|-
!+0s
|
|'''12edo'''
|1L 12s
|-
!+1s
|1L 11s
|12L 1s
|
|}
{| class="wikitable"
|+Warped 4L 4s
! rowspan="2" |Small step changes
! colspan="3" |Large step changes
|-
|-
|<nowiki>3|1</nowiki>
!-1L
|Pentatonic Aeolian (minor pentatonic)
!+0L
|J
!+1L
|K
|L
|M-at
|N
|C
| -
|Eb
|F
|G
| -
|Bb
|-
|-
|<nowiki>2|2</nowiki>
!-1s
|Pentatonic Dorian
|
|J
|4L 3s
|K-at
|5L 3s
|L
|M-at
|N
|C
|D
| -
|F
|G
| -
|Bb
|-
|-
|<nowiki>1|3</nowiki>
!+0s
|Pentatonic Mixolydian
|3L 4s
|J
|'''4L 4s'''
|K-at
|5L 4s
|L
|M-at
|N-at
|C
|D
| -
|F
|G
|A
| -
|-
|-
|<nowiki>0|4</nowiki>
!+1s
|Pentatonic Ionian (major pentatonic)
|3L 5s
|J
|4L 5s
|K-at
|L-at
|M-at
|
|
|C
|D
|E
| -
|G
|A
|
|}
|}
Note: the recommended TAMNAMS symbol to denote a downchroma (@) is replaced with the word "at" to prevent the note names from being parsed as email addresses.
This ironically means that major pentatonic is the darkest mode of 2L 3s, though this irony comes from specifying which generator is which.
UDP notation denotes how a scale is produced in terms of how many chroma-positive generators going up (u) and down (d) are needed, notated as "u|d". This can also be interpreted as how many chroma-negative generators are needed going down (d') and up (u'), where the notation is otherwise identical (since d' = u and u' = d). As of writing, TAMNAMS has a proposed mode-naming scheme that drops the number of generators going down, where modes are notated as "u|" instead. An equivalent system that favors a chroma-negative generator can thereby be notated as "|d". In relation to UDP, this is basically the notation of "u|d" separated into two: "u|" and "|d".


In the case of the modes of 2L 3s, even though the perfect 4th is the chroma-positive generator, enumerating modes either using standard UDP notation ("u|d") or the proposed TAMNAMS mode-naming scheme ("u|") and sorting by brightness results in mode 0|4 as being the "last" mode, whereas notating modes as "|d" notates mode 0|4 as the first mode.
== EDO/ED classifications ==


This notion of favoring a generator can also extend to mosses that come after a specific mos, such as the chromatic mosses of 5L 7s and 7L 5s for 5L 2s, where the chroma-positive generators (relative to 5L 2s) are the perfect 5th and perfect 4th respectively, though it may be possible to think of the generator of either mos as being the perfect 5th regardless.
* Deka-edo (deka-division): an equal division of the octave (or equave) where the number of divisions is in the tens.
* Hecto-edo (hecto-division): an equal division of the octave (or equave) where the number of divisions is in the hundreds.
* Kilo-edo (kilo-division): an equal division of the octave (or equave) where the number of divisions is in the thousands.
* Mega-edo (mega-division): an equal division of the octave (or equave) where the number of divisions is in the millions.
** This term already exists to refer to a large edo, but how large is subjective. Since the terms deka-, hecto-, and kilo-edo (and deka-, hecto-, and kilo-division) explicitly refer to specific powers of 10 (specifically, tens, hundreds, and thousands), so should mega-edo and mega-division to refer to divisions in the millions.
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