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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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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
|C
|Named analogously to the monolarge family
|D
|E
|F#
|G
|A
|B
|-
|-
|<nowiki>5|1</nowiki>
|3L (3n+1)s
|Ionian
|trilarge family
|C
|Named analogously to the monolarge family
|D
Prevents potential confusion with the name "tetralinear"
|E
|F
|G
|A
|B
|-
|-
|<nowiki>4|2</nowiki>
! colspan="3" |Families with 3 large steps
|Mixolydian
|C
|D
|E
|F
|G
|A
|Bb
|-
|-
|<nowiki>3|3</nowiki>
!Mos
|Dorian
!Name
|C
!Reasoning
|D
|Eb
|F
|G
|A
|Bb
|-
|-
|<nowiki>2|4</nowiki>
|3L (3n+2)s
|Aeolian
|apentilinear family
|C
|Named after anpentic
|D
|Eb
|F
|G
|Ab
|Bb
|-
|-
|<nowiki>1|5</nowiki>
! colspan="3" |Families with 4 large steps
|Phrygian
|C
|Db
|Eb
|F
|G
|Ab
|Bb
|-
|-
|<nowiki>0|6</nowiki>
!Mos
|Locrian
!Name
|C
!Reasoning
|Db
|Eb
|F
|Gb
|Ab
|Bb
|}
{| class="wikitable sortable"
|+
! colspan="14" |Modes of 2L 3s
|-
|-
! rowspan="2" |UDP
|4L (4n+1)s
! rowspan="2" |Mode "names"
|manulinear family
! colspan="5" |Scale degrees (independent of 5L 2s)
|Named after manual
! colspan="7" |Scale degrees (in relation to 5L 2s)
|-
|-
!0d
|4L (4n+3)s
!1d
|smilinear family
!2d
|Named after smitonic
!3d
!4d
!1st
!2nd
!3rd
!4th
!5th
!6th
!7th
|-
|-
|<nowiki>4|0</nowiki>
! colspan="3" |Families with 5 large steps
|Pentatonic Phrygian (default mode for sake of example)
|J
|K
|L
|M
|N
|C
| -
|Eb
|F
| -
|Ab
|Bb
|-
|-
|<nowiki>3|1</nowiki>
!Mos
|Pentatonic Aeolian (minor pentatonic)
!Name
|J
!Reasoning
|K
|L
|M-at
|N
|C
| -
|Eb
|F
|G
| -
|Bb
|-
|-
|<nowiki>2|2</nowiki>
|5L (5n+1)s
|Pentatonic Dorian
|mechlinear family
|J
|Named after machinoid (prefix mech-)
|K-at
|L
|M-at
|N
|C
|D
| -
|F
|G
| -
|Bb
|-
|-
|<nowiki>1|3</nowiki>
|5L (5n+2)s
|Pentatonic Mixolydian
|p-linear family
|J
|Named after p-chromatic rather than diatonic, which has no prefix
|K-at
|L
|M-at
|N-at
|C
|D
| -
|F
|G
|A
| -
|-
|-
|<nowiki>0|4</nowiki>
|5L (5n+3)s
|Pentatonic Ionian (major pentatonic)
|oneirolinear family
|J
|Named after oneirotonic
|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.
 
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.
 
== Proposal: Equave-agnostic mos names (work-in-progress) ==
This is an attempt at naming mosses, much like [[TAMNAMS]] and with [[MOS Naming Scheme|past naming schemes]]. However, whereas most mos naming systems focus on naming mosses in an octave-equivalent context, this system uses names for an equave-agnostic context, which may be useful when talking about non-octave mosses such as tritave-equivalent or fifth-equivalent scales, or talking about nested mos pattern, such as with a [[MOS Cradle|mos cradle]].
 
If anything, this is an exercise in completeness.
 
=== Table and scale tree of mos pattern names ===
{| class="wikitable"
! colspan="7" |2-note mosses (from TAMNAMS)
|-
|-
! colspan="2" |Mos pair
|5L (5n+4)s
!Single-period?
|chtonlinear family
!Names
|Named after semiquartal (prefix chton-)
!Prefix
!Etymology
!Language
|-
|-
| colspan="2" |1L 1s
! colspan="3" |Families with 6 large steps
|Yes
|trivial
|triv-
|Trivial mos, and hence named trivial.
|Latin
|-
|-
! colspan="7" |3-note mosses (from TAMNAMS)
!Mos
!Name
!Reasoning
|-
|-
! colspan="2" |Mos pair
|6L (6n+1)s
!Single-period?
|archeolinear family
!Names
|Named after archeotonic
!Prefix
!Etymology
!Language
|-
|-
|1L 2s
|6L (6n+5)s
|2L 1s
|xeimlinear family
|Yes
|Named after xeimtonic, a former name for 6L 5s
|antrial and trial
|(a)tri-
|Three-note mosses that descend from the trivial mos.
|Greek/Latin
|-
|-
! colspan="7" |4-note mosses (from TAMNAMS)
! colspan="3" |Families with 7 large steps
|-
|-
! colspan="2" |Mos pair
!Mos
!Single-period?
!Name
!Names
!Reasoning
!Prefix
!Etymology
!Language
|-
|-
|1L 3s
|7L (7n+1)s
|3L 1s
|pinelinear family
|Yes
|Named after pine
|antetric and tetric
|(a)tet-
|Four-note mosses that descend from antrial.
|Greek
|-
|-
| colspan="2" |2L 2s
|7L (7n+2)s
|No
|armlinear family
|2-trivial
|Named after superdiatonic (also called armotonic)
|
|Two copies of the trivial mos pattern.
|
|-
|-
! colspan="7" |5-note mosses (from TAMNAMS)
|7L (7n+3)s
|dicolinear family
|Named after dicotonic
|-
|-
! colspan="2" |Mos pair
|7L (7n+4)s
!Single-period?
|prasmilinear family
!Names
|Named after a truncation of a former name for 7L 4s (suprasmitonic)
!Prefix
!Etymology
!Language
|-
|-
|1L 4s
|7L (7n+5)s
|4L 1s
|m-linear family
|Yes
|Named after m-chromaticralic (prefix blu-)
|pedal and manual
|ped- and manu-
|In reference to feet (one big toe and four smaller toes) and hands (four long fingers and one shorter thumb).
|Latin
|-
|-
|2L 3s
! colspan="3" |Families with 8 large steps
|3L 2s
|Yes
|antipentic and pentic
|(a)pent-
|In reference to the pentatonic scale. Note that 2L 3s is pentic, and 3L 2s is anpentic; this is because the pentatonic scale, a subset of the familiar diatonic scale, is of the form 2L 3s.
|Greek
|-
|-
! colspan="7" |6-note mosses
!Mos
!Name
!Reasoning
|-
|-
! colspan="2" |Mos pair
|8L (8n+3)s
!Single-period?
!Names
!Prefix
!Etymology
!Language
|-
|1L 5s
|5L 1s
|Yes
|anhexic and hexic
|(an)hexa-
|From hex-, meaning six; there is only one pair of single-period hexatonic mosses.
|Greek
|-
|2L 4s
|4L 2s
|No
|2-antrial and 2-trial
|
|
|2 copies of the (an)trial mos patterns.
|
|
|-
|-
| colspan="2" |3L 3s
|8L (8n+5)s
|No
|petrlinear family
|3-trivial
|Named after petroid, a former name for 8L 5s
|-
|8L (8n+7)s
|
|
|3 copies of the trivial mos pattern.
|
|
|-
|-
! colspan="7" |7-note mosses
! colspan="3" |Families with 9 large steps
|-
|-
! colspan="2" |Mos pair
!Mos
!Single-period?
!Name
!Names
!Reasoning
!Prefix
!Etymology
!Language
|-
|-
|1L 6s
|9L (9n+1)s
|6L 1s
|sinalinear family
|Yes
|Named after sinatonic
|ansaptic and saptic
|(an)sap-
|These mosses appear further down the mos family tree. Sanskrit is used to differentiate them from the other four mosses.
|Sanskrit
|-
|-
|2L 5s
|9L (9n+2)s
|5L 2s
|
|Yes
|
|anheptic and heptic
|(an)hept-
|In reference to diatonic being a heptatonic scale, perhaps the most well-known heptatonic mos.
|Greek
|-
|3L 4s
|4L 3s
|Yes
|anseptenic and septenic
|(an)sept-
|Latin prefix is used to differentiate these mosses from heptic and anheptic. Septenic has a similar stress pattern as smitonic, coincidentally.
|Latin
|-
! colspan="7" |8-note mosses
|-
! colspan="2" |Mos pair
!Single-period?
!Names
!Prefix
!Etymology
!Language
|-
|1L 7s
|7L 1s
|Yes
|anastaic and astaic
|(an)asta-
|Follows same pattern with heptatonic mosses where 1L ns and nL 1s are named using Sanskrit.
|Sanskrit
|-
|-
|2L 6s
|9L (9n+4)s
|6L 2s
|No
|2-antetric and 2-tetric
|
|
|2 copies of the (an)tetric mos patterns.
|
|
|-
|-
|3L 5s
|9L (9n+5)s
|5L 3s
|Yes
|anoctic and octic
|(an)oct-
|If going by generational depth from 1L 1s, 3L 5s and 5L 3s are the first octatonic scales encountered. (Greek and Latin prefixes for eight are too similar.)
|Greek/Latin
|-
| colspan="2" |4L 4s
|No
|
|
|
|4 copies of the trivial mos pattern.
|
|
|-
|-
! colspan="7" |9-note mosses
|9L (9n+7)s
|-
! colspan="2" |Mos pair
!Single-period?
!Names
!Prefix
!Etymology
!Language
|-
|1L 8s
|8L 1s
|Yes
|annavic and navic
|(an)nav-
|Follows pattern with heptatonic mosses where 1L ns and nL 1s are named using Sanskrit.
|Sanskrit
|-
|2L 7s
|7L 2s
|Yes
|anennaic and ennaic
|(an)enna-
|Follows pattern with heptatonic mosses where the next mos pair after 1L ns and nL 1s are named using Greek.
|Greek
|-
|3L 6s
|6L 3s
|No
|3-antrial and 3-trial
|
|
|3 copies of the (an)trial mos patterns.
|
|
|-
|-
|4L 5s
|9L (9n+8)s
|5L 4s
|Yes
|annovemic and novemic
|(an)nov-
|Follows pattern with heptatonic where the 2nd next mos pair after 1L ns and nL 1s are named using Latin.
|Latin
|-
! colspan="7" |10-note mosses
|-
! colspan="2" |Mos pair
!Single-period?
!Names
!Prefix
!Etymology
!Language
|-
|1L 9s
|9L 1s
|Yes
|andashic and dashic
|(an)dash-
|Follows pattern with heptatonic mosses where 1L ns and nL 1s are named using Sanskrit.
|Sanskrit
|-
|2L 8s
|8L 2s
|No
|2-manual and 2-pedal
|
|
|2 copies of the pedal or manual mos patterns.
|
|
|}
== 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
|-
|-
|3L 7s
| rowspan="2" |5L 2s
|7L 3s
|<nowiki>5|1 (ionian mode)</nowiki>
|Yes
|5U 1D
|andekic and dekic
|(an)dek-
|Follows pattern with heptatonic mosses where the next mos pair after 1L ns and nL 1s are named using Greek.
|Greek
|-
|-
|4L 6s
|<nowiki>3|3 (dorian mode)</nowiki>
|6L 4s
|3U 3D
|No
|2-pentic and 2-anpentic
|
|2 copies of the (an)pentic mos patterns.
|
|-
|-
| colspan="2" |5L 5s
|3L 3s
|No
|<nowiki>3|0(3)</nowiki>
|5-trivial
|3U 0D
|
|5 copies of the trivial mos pattern.
|
|}
|}
=== 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"
{| class="wikitable"
!Mos
|+ Example for 5L 2s (LLsLLLs, mode 5 |Example with standard notation (5L 2s, mode 5|1)
!Name
!Mossteps from root
!Mos
!Substring
!Name
!Mosstep sum
!Mos
!Standard note name
!Name
!Nk note name
!Mos
!Name
!Mos
!Name
!Mos
!Name
!Mos
!Name
!Mos
!Name
!Mos
!Name
|-
|-
| rowspan="16" |1L 1s
|0
| rowspan="16" |''trivial''
|''none''
| rowspan="11" |1L 2s
|0
| rowspan="11" |''antrial''
|C
| rowspan="8" |1L 3s
|N(0)
| rowspan="8" |''antetric''
| rowspan="6" |1L 4s
| rowspan="6" |''pedal''
| rowspan="5" |1L 5s
| rowspan="5" |anhexic
| rowspan="4" |1L 6s
| rowspan="4" |ansaptic
| rowspan="3" |1L 7s
| rowspan="3" |anastaic
| rowspan="2" |1L 8s
| rowspan="2" |annavic
|1L  9s
|andashic
|-
|-
|9L 1s
|1
|dashic
|L
|L
|D
|N(1)
|-
|-
|8L 1s
|2
|navic
|LL
| colspan="2" rowspan="14" |
|2L
|E
|N(2)
|-
|-
|7L 1s
|3
|astaic
|LLs
| colspan="2" rowspan="13" |
|2L+s
|F
|N(3)
|-
|-
|6L 1s
|4
|saptic
|LLsL
| colspan="2" rowspan="12" |
|3L+s
|G
|N(4)
|-
|-
|5L 1s
|5
|hexic
|LLsLL
| colspan="2" rowspan="11" |
|4L+s
|A
|N(5)
|-
|-
| rowspan="2" |4L 1s
|6
| rowspan="2" |''manual''
|LLsLLL
|5L 4s
|5L+s
|novemic
|B
|N(6)
|-
|-
|4L 5s
|7
|annovemic
|LLsLLLs
|5L+2s
|C
|N(7) (same as N(0))
|}
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.
 
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.
 
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
|-
|-
| rowspan="3" |3L 1s
|C
| rowspan="3" |''tetric''
|N(0)
|4L 3s
|0
|septenic
|0
| colspan="2" |
|0
|0
|-
|-
| rowspan="2" |3L 4s
|C#
| rowspan="2" |anseptenic
|N(0)+c
|7L 3s
|L-s
|deckic
|L-s
|1
|1
|-
|-
|3L 7s
|Db
|andeckic
|N(1)-c
|L-(L-s)
|s
|1
|2
|-
|-
| rowspan="5" |2L 1s
|D
| rowspan="5" |''trial''
|N(1)
| rowspan="2" |3L 2s
|L
| rowspan="2" |''antipentic''
|L
|3L 5s
|2
|anoctic
|3
| colspan="2" rowspan="3" |
|-
|-
|5L 3s
|B
|octic
|N(6)
|5L+s
|5L+s
|11
|17
|-
|-
| rowspan="3" |2L 3s
|B#
| rowspan="3" |''pentic''
|N(6)+c
|5L 2s
|5L+s+(L-s)
|heptic
|6L
|12
|18
|-
|-
| rowspan="2" |2L 5s
|Cb
| rowspan="2" |anheptic
|N(7)-c
|7L 2s
|5L+2s-(L-s)
|anennaic
|4L+3s
|11
|18
|-
|-
|2L 7s
|C (one octave up)
|ennaic
|N(7) (same as N(0), as a pitch class)
|5L+2s (reduced to 0 due to modular arithmetic)
|5L+2s (reduced to 0)
|12 (reduced to 0)
|19 (reduced to 0)
|}
|}
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.


=== Reasoning for names ===
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.
Names for these mosses are meant to be as general as possible, following in the spirit of TAMNAMS names for mosses up to 5 notes. In fact, those names are borrowed from TAMNAMS as they already may be used for non-octave periods, and as such, equave-agnostic names are given starting at 6-note mosses, using numerical prefixes that suggest how many steps (or notes) each mos has. Mosses are named in pairs of xL ys and yL xs, where the mos with more small steps than large steps is given the an- prefix, short for anti-.


As there is only one pair of 6-note single-period mosses, 5L 1s and 1L 5s, the pair is named '''hexic'''.
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.


With 7-note mosses, there are three pairs of mosses. The problem is to name mosses with a unique name, which is solved by using numeric prefixes based on different languages, not only Greek or Latin. The pair for 5L 2s and 2L 5s is named '''heptic''', in reference to how 5L 2s (TAMNAMS name of diatonic) is the most well-known heptatonic mos, where hepta- is Greek for seven. Similarly, the pair 4L 3s and 3L 4s is the same number of generations away from the root (1L 1s) as 5L 2s and 2L 5s, and is named '''septenic''', where sept- is Latin for seven. The third pair, 6L 1s and 1L 6s, is farther from the root than the other two mosses, and is named '''saptic''', based off of Sanskrit ṣaṭ-, which also means seven.
=== 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:
From here, mosses of n+1 notes follow this pattern: 1L ns and nL 1s are named after Sanskrit, then the following pair is named after Greek, and then Latin. Multi-period mosses are skipped in this process. With 8-note mosses, there are only two pairs, and are named '''astaic''' (7L 1s and 1L 7s) and '''octic''' (5L 3s and 3L 5s) respectively. As with saptic and heptic, astaic is further from the root than octic. With 9-note mosses, there are three pairs again: '''navic''' (8L 1s and 1L 8s), '''ennaic''' (7L 2s and 2L 7s), and '''novemic''' (4L 5s and 5L 4s). Finally, with 10-note mosses, there are two more pairs: '''dashic''' (9L 1s and 1L 9s) and '''dekic''' (7L 3s and 3L 7s).
 
As with TAMNAMS, only mosses with no more than 10 notes are named.
 
Multi-period mosses are not given their own, unique names. Rather, for a mos xL ys where x and y share a greatest common factor of k, the name reflects some smaller base mos xL ys duplicated k times; for example, 5L 5s is named 5-trivial, and 2L 6s is named 2-antetric.
 
=== Proposal for naming equave-agnostic mosdescendants ===
Mosdescendants are named by adding prefixes to the base names described above, but only to those whose child mosses exceed 10 notes. The proposed prefixes are listed below.
{| class="wikitable"
{| class="wikitable"
|+
|+
!Extension prefix
!If the interval s1 mossteps from the root is...
!Meaning
!And the interval s2 mossteps from there is...
!Reasoning
!Then the overall chord is
!Example
!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)
|-
|-
|eka-
|the large interval
|Child mos
|the small interval
|Sanskrit for one; follows similar logic as eka-elements that Dmitri Mendeleev had named.
|Major asymmetric
|ekaheptic, referring to 7L 5s and 5L 7s
|Major chord (M3+m3)
|-
|-
|dvi-
|the small interval
|Grandchild mos
|the large interval
|Sanskrit for two; follows similar logic as dvi-elements that Dmitri Mendeleev had named.
|Minor asymmetric
|dviheptic, referring to 5A 12B and 7A 12B
|Minor chord (m3+M3)
|-
|-
|meta-
|the small interval
|Any mos any number of generations from a named mos
|the small interval
|The Sanskrit prefix of tri- isn't used to avoid confusion with the tri- prefix used for trial.
|Small symmetric
|metaheptic
|Diminished chord (m3+m3)
|}
|}
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.
== Proposal (wip): strict and weak definitions for a chromatic pair ==
=== Strict definition ===
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.
=== Weak definition ===
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.


== Mosses related to metallic mosses ==
=== Things to consider ===


=== Fibonacci numbers and the golden ratio ===
* 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.
Let F(n) be a recursive function that returns the nth Fibonacci number.
* An albitonic scale's note count should be around 7 notes.


* For the base cases of n = 1 or n = 0:
== Warped scales ==
** If n = 1, then F(1) = 1.
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).
** If n = 0, then F(0) = 0.
* For the recursive case of n > 1:
** If n > 1, then F(n) = F(n-1) + F(n-2)


Mosses whose step ratio approximates the golden ratio will have a step ratio L:s that is F(n):F(n-1), or two consecutive Fibonacci numbers. In relation to a parent mos xL ys with an arbitrarily large step ratio F(n):F(n-1) (where n is arbitrarily large) there is a sequence of mosses of the form (xF(k)+yF(k-1))L (xF(k-1)+yF(k-2))s (where F(k), F(k-1), and F(k-2) are the kth, (k-1)th, and (k-2)th Fibonacci numbers) that descend from xL ys. Due to mos recursion, the mos (xF(n)+yF(n-1))L (xF(n-1)+yF(n-2))s contains xL ys, as well as every mos between xL ys and (xF(n)+yF(n-1))L (xF(n-1)+yF(n-2))s. The table below illustrates these mosses.
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.  


As an example, golden meantone describes the mos 5L 2s whose step ratio approaches the golden ratio. This also describes a series of mos descendants that contain 5L 2s as a subset, which are 7L 5s, 12L 7s, 19L 12s, 31L 19s, 50L 31s, and so on. This is to say that the aforementioned mosses are supported by golden meantone, or rather, approximated by golden meantone if n sufficiently large.
{| class="wikitable"
{| class="wikitable"
|+Golden mos sequence, with golden meantone example
|+Warped 5L 2s
! rowspan="2" |k
! rowspan="2" |Small step changes
! colspan="2" |General form
! colspan="3" |Large step changes
! colspan="3" |Example for 5L 2s (diatonic, golden meantone)
|-
!-1L
!+0L
!+1L
|-
|-
!Mos
!-1s
!Step ratio in relation to parent of xL ys
|
!Mos
|5L 1s
!Step ratio of parent (5L 2s) needed to produce mos with L:s = 2:1
|6L 1s
!Edo
|-
!+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
|-
|-
|0
!+1s
|xL ys
|1L 11s
|L:s (self; L and s are two consecutive Fibonacci numbers)
|12L 1s
|5L 2s
|
|2:1 (self)
|}
|12edo
{| class="wikitable"
|+Warped 4L 4s
! rowspan="2" |Small step changes
! colspan="3" |Large step changes
|-
|-
|1
!-1L
|(x+y)L xs
!+0L
|(L+s):L
!+1L
|7L 5s
|3:2
|19edo
|-
|-
|2
!-1s
|(2x+y)L (x+y)s
|
|(2L+s):(L+s)
|4L 3s
|7L 12s
|5L 3s
|5:3
|31edo
|-
|-
|3
!+0s
|(3x+2y)L (2x+y)s
|3L 4s
|(3L+2s):(2L+s)
|'''4L 4s'''
|19L 12s
|5L 4s
|8:5
|50edo
|-
|-
|n
!+1s
|(xF(n)+yF(n-1))L (xF(n-1)+yF(n-2))s
|3L 5s
|(LF(n)+sF(n-1)):(LF(n-1)+sF(n-2))
|4L 5s
|(5F(n)+2F(n-1))L (5F(n-1)+2F(n-2))s
|
|F(n):F(n-1)
|(2(5F(n)+2F(n-1))+(5F(n-1)+2F(n-2)))-edo
|}
|}


Any arbitrary mos is the start of a '''golden mos sequence''' (the temperament-agnostic equivalent of a golden temperament), even if it coincides with that of another mos.
== EDO/ED classifications ==
 
* 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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