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Mos mode names
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This is a subpage for [[TAMNAMS]]-related notes, containing various proposals of varying degrees of usefulness and other useful things. This also contains rewrites of sections of the main TAMNAMS page that aren't quite ready to be deployed.
This is a subpage for [[TAMNAMS]]-related notes, containing various proposals of varying degrees of usefulness and other useful things. This also contains rewrites of sections of the main TAMNAMS page that aren't quite ready to be deployed.


== Sandboxed rewrite: Naming mos intervals and mos degrees ==
== Sandboxed section: Naming mos modes ==
Already deployed on main TAMNAMS page: [[TAMNAMS#Naming mos intervals]]
''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.''


== Other sandboxed rewrites ==
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


=== Reasoning for names ===
=== TAMNAMS format for mos modes ===
See: [[TAMNAMS#Reasoning for the names]]
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".


The goal of TAMNAMS mos names is to choose memorable but aesthetically neutral names.
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]].


==== Names for small mosses ====
=== Genchain mode names ===
All names for single-period mosses (mosses of the form xL ys where x and y are coprime) with no more than 5 notes require that some small integer multiple of the period is equal to an octave or a tempered octave, under the reasoning that these mosses are common and broad enough that they may be of interest in non-octave contexts. As such, the names for these mosses are chosen to be extremely general to avoid bias and to avoid being too flavorful, and to allow these names to be reused for such non-octave contexts.
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.
 
{| class="wikitable"
The names of monowood and biwood, for 1L 1s and 2L 2s respectively, requires that an equivalence interval be an octave, whereas the name trivial, also referring to 1L 1s, is equave-agnostic and may be used for non-octave contexts.
|+Genchain mode names for 7L 1s
 
!Mode
==== Names for multi-period mosses ====
!UDP
Multi-period mosses (mosses of the form xL ys where x and y have a greatest common factor of 2 or greater) are given unique names that do not depend on the name of a smaller, octave-specific mos. The inclusion of such mos names was for completeness, which prompted reconsiderations on how these mosses were named. These mosses were formerly named using names that were octave-specific, producing former names such as "antidimanic" and "dipentic".
!Mode name
 
|-
==== Names based on a temperament ====
|LLLLLLLs
All names ending in -oid refer to an exotemperament which, when including extreme tunings, covers the entire range of the corresponding octave-period mos, such that many edos with simple step ratios for that mos will correspond to valid tunings, if not by patent val, then with a small number of warts.
|<nowiki>7|0</nowiki>
 
|1st pine
Former names like "orwelloid" and "sensoid" were abandoned because the names were too temperament-specific in the sense that even considering extreme tunings didn't cover the whole range of the mos. The remaining temperament-based names have been abstracted or altered heavily, namely "pine", "hyrulic", "jaric", "ekic" and "lemon".
|-
 
|LLLLLLsL
==== Names for 1L ns mosses ====
|<nowiki>6|1</nowiki>
Mosses of the form 1L ns were originally left unnamed as the range for their generator was too broad and such mosses were considered better analyzed as subsets of its (n+1)L 1s mos. An example of this is 1L 6s and 7L 1s, a pair of mosses that are commonly associated with porcupine temperament.
|2nd pine
 
|-
Although the tuning range is very unhelpful for knowing what such mosses will sound like, it is nonetheless useful for describing structure in situations where one does not want to use the mathematical name of 1L ns, especially given that in such situations the tuning will likely be specified somewhere already, hence the inclusion of these mos names.
|LLLLLsLL
 
|<nowiki>5|2</nowiki>
This inclusion also affected the names of multi-period mosses. Jaric and taric specifically were chosen over bipedal and bimanual because of this, and to a lesser extent, lemon and lime were chosen over antibipentic and bipentic respectively (with their parent mos of 4L 2s named citric for consistency).
|3rd pine
 
==== The anti- prefix vs the an- prefix for naming 1L ns mosses ====
The distinction between using the prefixes "anti-" vs "an-" for reversing the number of large vs. small steps is not as trivial as it may sound.
 
In the case of mosses with six or more notes, as the period is always an octave, there is a very large tuning range for the 1L ns mosses (hence their original omission), but the "anti-" prefix shows that what is significant is that it has the opposite structure to the corresponding nL 1s mos while pointing out the resulting ambiguity of range.
 
In the case of mosses with five or fewer notes, as the period is not known and therefore could be very small, this is not as much of a concern as fuller specification is likely required anyway, especially in the case of larger periods, so the name should not be tediously long as the name refers to a very simple mos pattern, and for related reasons, the name shouldn't give as much of a sense of one 'orientation' of the structure being more 'primary' than the other, while with mosses with more than five notes, this suggestion of sense is very much intended, because it will almost always make more sense to talk about the (n+1)L 1s child mos of whatever 1L ns mos you want to speak of.
 
==== Names for mosses with more than 10 notes ====
The scope of TAMNAMS name is to give mosses with small note count a notable name. To keep the number of names controlled, only mosses with no more than 10 notes are named. As a result, the names of mosses with 11 and 12 notes were abandoned, notably the names kleistonic, suprasmitonic, m-chromatic, and p-chromatic.
 
== Step ratio spectrum visualization ==
I wanted to make a table that better visualizes the step ratio ranges as described by TAMNAMS.
 
=== Central spectrum ===
{| class="wikitable"
! colspan="6" |Central spectrum of step ratios
|-
|-
! colspan="4" |Intermediate ranges
|LLLLsLLL
!Specific step ratios
|<nowiki>4|3</nowiki>
!Notes
|4th pine
|-
|-
|
|LLLsLLLL
|
|<nowiki>3|4</nowiki>
|
|5th pine
|
|'''1:1 (equalized)'''
|Trivial/pathological
|-
|-
| rowspan="15" |1:1 to 1:0
|LLsLLLLL
| rowspan="7" |1:1 to 2:1
|<nowiki>2|5</nowiki>
| rowspan="3" |1:1 to 3:2
|6th pine
|1:1 to 4:3 (ultrasoft)
|
|Step ratios especially close to 1:1 may be called pseudoequalized
|-
|-
|
|LsLLLLLL
|'''4:3 (supersoft)'''
|<nowiki>1|6</nowiki>
|
|7th pine
|-
|-
|4:3 to 3:2 (parasoft)
|sLLLLLLL
|
|<nowiki>0|7</nowiki>
|
|8th pine
|}
 
=== Named mos modes ===
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"
! colspan="3" |2L 3s modes
Mode names are modified from 5L 2s
! colspan="3" |4L 1s modes
Mode names by CellularAutomaton
|-
|-
|
!Mode
|
!UDP
|'''3:2 (soft)'''
!Mode name
|Also called monosoft
!Mode
!UDP
!Mode name
|-
|-
| rowspan="3" |3:2 to 2:1 (hyposoft)
|LsLss
|3:2 to 5:3 (quasisoft)
|<nowiki>4|0</nowiki>
|
|phrygipentic
|
|LLLLs
|<nowiki>4|0</nowiki>
|minimal
|-
|-
|
|LssLs
|'''5:3 (semisoft)'''
|<nowiki>3|1</nowiki>
|
|aeolipentic
|LLLsL
|<nowiki>3|1</nowiki>
|medicinal
|-
|-
|5:3 to 2:1 (minisoft)
|sLsLs
|
|<nowiki>2|2</nowiki>
|
|doripentic
|LLsLL
|<nowiki>2|2</nowiki>
|medial
|-
|-
|
|sLssL
|
|<nowiki>1|3</nowiki>
|
|mixopentic
|'''2:1 (basic)'''
|LsLLL
|Also called quintessential
|<nowiki>1|3</nowiki>
|indical
|-
|-
| rowspan="7" |2:1 to 1:0
|ssLsL
| rowspan="3" |2:1 to 3:1 (hypohard)
|<nowiki>0|4</nowiki>
|2:1 to 5:2 (minihard)
|ionipentic
|
|sLLLL
|
|<nowiki>0|4</nowiki>
|pollical
|}
{| class="wikitable"
! colspan="3" |1L 6s modes
Mode names borrowed from sister mos
! colspan="3" |2L 5s modes
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
|'''5:2 (semihard)'''
!UDP
|
!Mode name
!Mode
!UDP
!Mode name
!Mode
!UDP
!Mode name
!Mode
!UDP
!Mode name
!Mode
!UDP
!Mode name
!Mode
!UDP
!Mode name
|-
|Lssssss
|<nowiki>6|0</nowiki>
|anti-zokalarian
|LssLsss
|<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
|-
|-
|5:2 to 3:1 (quasihard)
|sLsssss
|
|<nowiki>5|1</nowiki>
|
|antitamashian
|LsssLss
|<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
|
|<nowiki>4|2</nowiki>
|'''3:1 (hard)'''
|anti-oukranian
|Also called monohard
|sLssLss
|<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
|-
|-
| rowspan="3" |3:1 to 1:0
|sssLsss
|3:1 to 4:1 (parahard)
|<nowiki>3|3</nowiki>
|
|antihorthathian
|
|sLsssLs
|<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
|'''4:1 (superhard)'''
|<nowiki>2|4</nowiki>
|
|antilobonian
|ssLssLs
|<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
|-
|-
|4:1 to 1:0 (ultrahard)
|sssssLs
|
|<nowiki>1|5</nowiki>
|Step ratios especially close to 1:0 may be called pseudocollapsed
|antikarakalian
|ssLsssL
|<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
|
|<nowiki>0|6</nowiki>
|
|antiryonian
|
|sssLssL
|'''1:0 (collapsed)'''
|<nowiki>0|6</nowiki>
|Trivial/pathological
|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
|}
|}
=== Extended spectrum ===
{| class="wikitable"
{| class="wikitable"
! colspan="8" |Extended spectrum of step ratios
! colspan="3" |3L 5s modes
Mode names borrowed from sister mos
! colspan="3" |5L 3s modes
Modes named by Cryptic Ruse
|-
|-
! colspan="4" |Central ranges
!Mode
! colspan="2" |Extended ranges
!UDP
!Specific step ratios
!Mode name
!Notes
!Mode
!UDP
!Mode name
|-
|-
|
|LsLssLss
|
|<nowiki>7|0</nowiki>
|
|antisarnathian, antisarnian
|
|LLsLLsLs
| colspan="2" |
|<nowiki>7|0</nowiki>
|'''1:1 (equalized)'''
|dylathian, dylian
|Trivial/pathological
|-
|-
| rowspan="21" |1:1 to 1:0
|LssLsLss
| rowspan="9" |1:1 to 2:1
|<nowiki>6|1</nowiki>
| rowspan="5" |1:1 to 3:2
|antihlanithian, antihlanian
| rowspan="3" |1:1 to 4:3 (ultrasoft)
|LLsLsLLs
| colspan="2" |1:1 to 6:5 (pseudoequalized)
|<nowiki>6|1</nowiki>
|
|ilarnekian
|
|-
|-
| colspan="2" |
|LssLssLs
|'''6:5 (semiequalized)'''
|<nowiki>5|2</nowiki>
|
|antikadathian, antikadian
|LsLLsLLs
|<nowiki>5|2</nowiki>
|celephaisian
|-
|-
| colspan="2" |6:5 to 4:3 (ultrasoft)
|sLsLssLs
|
|<nowiki>4|3</nowiki>
|
|antimnarian
|LsLLsLsL
|<nowiki>4|3</nowiki>
|ultharian
|-
|-
|
|sLssLsLs
| colspan="2" |
|<nowiki>3|4</nowiki>
|'''4:3 (supersoft)'''
|anti-ultharian
| rowspan="13" |Nonextreme range, as detailed by central spectrum
|LsLsLLsL
|<nowiki>3|4</nowiki>
|mnarian
|-
|-
|4:3 to 3:2 (parasoft)
|sLssLssL
| colspan="2" |4:3 to 3:2 (parasoft)
|<nowiki>2|5</nowiki>
|
|anticelephaisian
|sLLsLLsL
|<nowiki>2|5</nowiki>
|kadathian, kadian
|-
|-
|
|ssLsLssL
|
|<nowiki>1|6</nowiki>
| colspan="2" |
|anti-ilarnekian
|'''3:2 (soft)'''
|sLLsLsLL
|<nowiki>1|6</nowiki>
|hlanithian, hlanian
|-
|-
| rowspan="3" |3:2 to 2:1 (hyposoft)
|ssLssLsL
|3:2 to 5:3 (quasisoft)
|<nowiki>0|7</nowiki>
| colspan="2" |3:2 to 5:3 (quasisoft)
|antidylathian, antidylian
|
|sLsLLsLL
|<nowiki>0|7</nowiki>
|sarnathian, sarnian
|}
{| class="wikitable"
! colspan="3" |5L 4s modes
Modes named by inthar
! colspan="3" |7L 2s modes
Modes named under armodue theory
|-
|-
|
!Mode
| colspan="2" |
!UDP
|'''5:3 (semisoft)'''
!Mode name (inthar)
!Mode
!UDP
!Mode name
|-
|-
|5:3 to 2:1 (minisoft)
|LLsLsLsLs
| colspan="2" |5:3 to 2:1 (minisoft)
|<nowiki>8|0</nowiki>
|
|cristatan
|LLLLsLLLs
|<nowiki>8|0</nowiki>
|superlydian
|-
|-
|
|LsLLsLsLs
|
|<nowiki>7|1</nowiki>
|
|pican
| colspan="2" |
|LLLsLLLLs
|'''2:1 (basic)'''
|<nowiki>7|1</nowiki>
|super-ionian
|-
|-
| rowspan="11" |2:1 to 1:0
|LsLsLLsLs
| rowspan="3" |2:1 to 3:1 (hypohard)
|<nowiki>6|2</nowiki>
|2:1 to 5:2 (minihard)
|stellerian
| colspan="2" |2:1 to 5:2 (minihard)
|LLLsLLLsL
|
|<nowiki>6|2</nowiki>
|supermixolydian
|-
|-
|
|LsLsLsLLs
| colspan="2" |
|<nowiki>5|3</nowiki>
|'''5:2 (semihard)'''
|cornician
|LLsLLLLsL
|<nowiki>5|3</nowiki>
|supercorinthian
|-
|-
|5:2 to 3:1 (quasihard)
|LsLsLsLsL
| colspan="2" |5:2 to 3:1 (quasihard)
|<nowiki>4|4</nowiki>
|
|nucufraga
|LLsLLLsLL
|<nowiki>4|4</nowiki>
|super-olympian
|-
|-
|
|sLLsLsLsL
|
|<nowiki>3|5</nowiki>
| colspan="2" |
|coracian
|'''3:1 (hard)'''
|LsLLLLsLL
|<nowiki>3|5</nowiki>
|superdorian
|-
|-
| rowspan="7" |3:1 to 1:0
|sLsLLsLsL
|3:1 to 4:1 (parahard)
|<nowiki>2|6</nowiki>
| colspan="2" |3:1 to 4:1 (parahard)
|frudilegian
|
|LsLLLsLLL
|<nowiki>2|6</nowiki>
|super-aeolian
|-
|-
|
|sLsLsLLsL
| colspan="2" |
|<nowiki>1|7</nowiki>
|'''4:1 (superhard)'''
|coloean
|sLLLLsLLL
|<nowiki>1|7</nowiki>
|superphrygian
|-
|sLsLsLsLL
|<nowiki>0|8</nowiki>
|pyrrhocoracian, pyrrhian
|sLLLsLLLL
|<nowiki>0|8</nowiki>
|superlocrian
|}
{| class="wikitable"
! colspan="3" |3L 7s modes
Modes named by Peter Kosmorsky
|-
!Mode
!UDP
!Mode name
|-
|-
| rowspan="5" |4:1 to 1:0 (ultrahard)
|LssLssLsss
| rowspan="3" |4:1 to 10:1 (ultrahard)
|<nowiki>9|0</nowiki>
|4:1 to 6:1 (hyperhard)
|malkuth
|
|
|-
|-
|
|LssLsssLss
|'''6:1 (extrahard)'''
|<nowiki>8|1</nowiki>
|
|yesod
|-
|-
|6:1 to 10:1 (clustered)
|LsssLssLss
|
|<nowiki>7|2</nowiki>
|
|hod
|-
|-
| colspan="2" |
|sLssLssLss
|'''10:1 (semicollapsed)'''
|<nowiki>6|3</nowiki>
|
|netzach
|-
|-
| colspan="2" |10:1 to 1:0 (pseudocollapsed)
|sLssLsssLs
|
|<nowiki>5|4</nowiki>
|
|tiferet
|-
|-
|
|sLsssLssLs
|
|<nowiki>4|5</nowiki>
|
|genvurah
|
|-
| colspan="2" |
|ssLssLssLs
|'''1:0 (collapsed)'''
|<nowiki>3|6</nowiki>
|Trivial/pathological
|chesed
|-
|ssLssLsssL
|<nowiki>2|7</nowiki>
|binah
|-
|ssLsssLssL
|<nowiki>1|8</nowiki>
|chokmah
|-
|sssLssLssL
|<nowiki>0|9</nowiki>
|keter
|}
|}


== Original table of extended TAMNAMS names (archived) ==
== Sandboxed rewrite: Naming mos intervals and mos degrees ==
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%20pattern%20names|TAMNAMS names]] being reorganized and many scales being renamed, hence this section is kept for archival purposes.
Already deployed on main TAMNAMS page: [[TAMNAMS#Naming mos intervals]]
 
== Other sandboxed rewrites ==
 
=== Reasoning for names ===
See: [[TAMNAMS#Reasoning for the names]]
 
The goal of TAMNAMS mos names is to choose memorable but aesthetically neutral names.


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.
==== Names for small mosses ====
{| class="wikitable mw-collapsible"
All names for single-period mosses (mosses of the form xL ys where x and y are coprime) with no more than 5 notes require that some small integer multiple of the period is equal to an octave or a tempered octave, under the reasoning that these mosses are common and broad enough that they may be of interest in non-octave contexts. As such, the names for these mosses are chosen to be extremely general to avoid bias and to avoid being too flavorful, and to allow these names to be reused for such non-octave contexts.
! colspan="12" |Mos Family Tree (single-period only), with TAMNAMS Names and extended names
 
|-
The names of monowood and biwood, for 1L 1s and 2L 2s respectively, requires that an equivalence interval be an octave, whereas the name trivial, also referring to 1L 1s, is equave-agnostic and may be used for non-octave contexts.
! colspan="2" |Progenitor scale
 
! colspan="2" |1st-order child mosses
==== Names for multi-period mosses ====
! colspan="2" |2nd-order child mosses
Multi-period mosses (mosses of the form xL ys where x and y have a greatest common factor of 2 or greater) are given unique names that do not depend on the name of a smaller, octave-specific mos. The inclusion of such mos names was for completeness, which prompted reconsiderations on how these mosses were named. These mosses were formerly named using names that were octave-specific, producing former names such as "antidimanic" and "dipentic".
! colspan="2" |3rd-order child mosses
 
! colspan="2" |4th-order child mosses
==== Names based on a temperament ====
! colspan="2" |5th-order child mosses
All names ending in -oid refer to an exotemperament which, when including extreme tunings, covers the entire range of the corresponding octave-period mos, such that many edos with simple step ratios for that mos will correspond to valid tunings, if not by patent val, then with a small number of warts.
|-
 
!Steps
Former names like "orwelloid" and "sensoid" were abandoned because the names were too temperament-specific in the sense that even considering extreme tunings didn't cover the whole range of the mos. The remaining temperament-based names have been abstracted or altered heavily, namely "pine", "hyrulic", "jaric", "ekic" and "lemon".
!Scale name
 
!Steps
==== Names for 1L ns mosses ====
!Scale name
Mosses of the form 1L ns were originally left unnamed as the range for their generator was too broad and such mosses were considered better analyzed as subsets of its (n+1)L 1s mos. An example of this is 1L 6s and 7L 1s, a pair of mosses that are commonly associated with porcupine temperament.
!Steps
 
!Scale name
Although the tuning range is very unhelpful for knowing what such mosses will sound like, it is nonetheless useful for describing structure in situations where one does not want to use the mathematical name of 1L ns, especially given that in such situations the tuning will likely be specified somewhere already, hence the inclusion of these mos names.
!Steps
 
!Scale name
This inclusion also affected the names of multi-period mosses. Jaric and taric specifically were chosen over bipedal and bimanual because of this, and to a lesser extent, lemon and lime were chosen over antibipentic and bipentic respectively (with their parent mos of 4L 2s named citric for consistency).
!Steps
 
!Scale name
==== The anti- prefix vs the an- prefix for naming 1L ns mosses ====
!Steps
The distinction between using the prefixes "anti-" vs "an-" for reversing the number of large vs. small steps is not as trivial as it may sound.
!Scale name
 
|-
In the case of mosses with six or more notes, as the period is always an octave, there is a very large tuning range for the 1L ns mosses (hence their original omission), but the "anti-" prefix shows that what is significant is that it has the opposite structure to the corresponding nL 1s mos while pointing out the resulting ambiguity of range.
| rowspan="63" |1L 1s
 
| rowspan="63" |''prototonic*''
In the case of mosses with five or fewer notes, as the period is not known and therefore could be very small, this is not as much of a concern as fuller specification is likely required anyway, especially in the case of larger periods, so the name should not be tediously long as the name refers to a very simple mos pattern, and for related reasons, the name shouldn't give as much of a sense of one 'orientation' of the structure being more 'primary' than the other, while with mosses with more than five notes, this suggestion of sense is very much intended, because it will almost always make more sense to talk about the (n+1)L 1s child mos of whatever 1L ns mos you want to speak of.
(currently monowood and trivial)
 
| rowspan="31" |1L 2s
==== Names for mosses with more than 10 notes ====
| rowspan="31" |''antideuteric*''
The scope of TAMNAMS name is to give mosses with small note count a notable name. To keep the number of names controlled, only mosses with no more than 10 notes are named. As a result, the names of mosses with 11 and 12 notes were abandoned, notably the names kleistonic, suprasmitonic, m-chromatic, and p-chromatic.
(currently antrial)
 
| rowspan="15" |1L 3s
== Step ratio spectrum visualization ==
| rowspan="15" |''antitetric*''
I wanted to make a table that better visualizes the step ratio ranges as described by TAMNAMS.
(currently antetric)
 
| rowspan="7" |1L 4s
=== Central spectrum ===
| rowspan="7" |''antimanic''
{| class="wikitable"
(currently pedal)
! colspan="6" |Central spectrum of step ratios
| rowspan="3" |1L 5s
|-
| rowspan="3" |''antimachinoid*''
! colspan="4" |Intermediate ranges
(currently antimachinoid)
!Specific step ratios
|1L 6s
!Notes
|''anti-archeotonic''
(currently onyx)
|-
|-
|
|
|
|
|-
|6L 1s
|archeotonic
|-
|
|
|
|
|'''1:1 (equalized)'''
|Trivial/pathological
|-
| rowspan="15" |1:1 to 1:0
| rowspan="7" |1:1 to 2:1
| rowspan="3" |1:1 to 3:2
|1:1 to 4:3 (ultrasoft)
|
|
|Step ratios especially close to 1:1 may be called pseudoequalized
|-
|
|'''4:3 (supersoft)'''
|
|
|-
|-
| rowspan="3" |5L 1s
|4:3 to 3:2 (parasoft)
| rowspan="3" |machinoid
|
|5L 6s
|
|
|-
|-
|
|
|
|
|'''3:2 (soft)'''
|Also called monosoft
|-
|-
|6L 5s
| rowspan="3" |3:2 to 2:1 (hyposoft)
|3:2 to 5:3 (quasisoft)
|
|
|
|-
|-
|
|
|'''5:3 (semisoft)'''
|
|
|-
|5:3 to 2:1 (minisoft)
|
|
|
|
|-
|
|
|
|
|-
| rowspan="7" |4L 1s
| rowspan="7" |manual
(formerly manic)
| rowspan="3" |4L 5s
| rowspan="3" |gramitonic
(formerly orwelloid)
|4L 9s
|
|
|'''2:1 (basic)'''
|Also called quintessential
|-
|-
| rowspan="7" |2:1 to 1:0
| rowspan="3" |2:1 to 3:1 (hypohard)
|2:1 to 5:2 (minihard)
|
|
|
|
|-
|-
|9L 4s
|
|'''5:2 (semihard)'''
|
|
|-
|-
|5:2 to 3:1 (quasihard)
|
|
|
|
|-
|
|
|
|
|'''3:1 (hard)'''
|Also called monohard
|-
|-
| rowspan="3" |5L 4s
| rowspan="3" |3:1 to 1:0
| rowspan="3" |semiquartal
|3:1 to 4:1 (parahard)
|5L 9s
|
|
|
|-
|-
|
|
|'''4:1 (superhard)'''
|
|
|-
|-
|9L 5s
|4:1 to 1:0 (ultrahard)
|
|
|Step ratios especially close to 1:0 may be called pseudocollapsed
|-
|-
|
|
Line 373: Line 595:
|
|
|
|
|
|'''1:0 (collapsed)'''
|
|Trivial/pathological
|
|}
|
 
=== Extended spectrum ===
{| class="wikitable"
! colspan="8" |Extended spectrum of step ratios
|-
|-
| rowspan="15" |3L 1s
! colspan="4" |Central ranges
| rowspan="15" |tetric
! colspan="2" |Extended ranges
| rowspan="7" |3L 4s
!Specific step ratios
| rowspan="7" |mosh
!Notes
| rowspan="3" |3L 7s
|-
| rowspan="3" |sephiroid
|
|3L 10s
|
|
|
|
| colspan="2" |
|'''1:1 (equalized)'''
|Trivial/pathological
|-
|-
| rowspan="21" |1:1 to 1:0
| rowspan="9" |1:1 to 2:1
| rowspan="5" |1:1 to 3:2
| rowspan="3" |1:1 to 4:3 (ultrasoft)
| colspan="2" |1:1 to 6:5 (pseudoequalized)
|
|
|
|
|-
|-
|10L 3s
| colspan="2" |
|'''6:5 (semiequalized)'''
|
|
|-
|-
| colspan="2" |6:5 to 4:3 (ultrasoft)
|
|
|
|
|-
|
|
|
| colspan="2" |
|'''4:3 (supersoft)'''
| rowspan="13" |Nonextreme range, as detailed by central spectrum
|-
|-
| rowspan="3" |7L 3s
|4:3 to 3:2 (parasoft)
| rowspan="3" |dicoid
| colspan="2" |4:3 to 3:2 (parasoft)
(formerly dicotonic)
|7L 10s
|
|
|-
|-
|
|
|
|
| colspan="2" |
|'''3:2 (soft)'''
|-
|-
|10L 7s
| rowspan="3" |3:2 to 2:1 (hyposoft)
|3:2 to 5:3 (quasisoft)
| colspan="2" |3:2 to 5:3 (quasisoft)
|
|
|-
|-
|
|
| colspan="2" |
|'''5:3 (semisoft)'''
|-
|5:3 to 2:1 (minisoft)
| colspan="2" |5:3 to 2:1 (minisoft)
|
|
|-
|
|
|
|
|
|
| colspan="2" |
|'''2:1 (basic)'''
|-
| rowspan="11" |2:1 to 1:0
| rowspan="3" |2:1 to 3:1 (hypohard)
|2:1 to 5:2 (minihard)
| colspan="2" |2:1 to 5:2 (minihard)
|
|
|-
|-
| rowspan="7" |4L 3s
|
| rowspan="7" |smitonic
| colspan="2" |
| rowspan="3" |4L 7s
|'''5:2 (semihard)'''
| rowspan="3" |(formerly kleistonic)
|-
|4L 11s
|5:2 to 3:1 (quasihard)
| colspan="2" |5:2 to 3:1 (quasihard)
|
|
|-
|-
|
|
|
|
| colspan="2" |
|'''3:1 (hard)'''
|-
|-
|11L 4s
| rowspan="7" |3:1 to 1:0
|3:1 to 4:1 (parahard)
| colspan="2" |3:1 to 4:1 (parahard)
|
|
|-
|-
|
|
| colspan="2" |
|'''4:1 (superhard)'''
|-
| rowspan="5" |4:1 to 1:0 (ultrahard)
| rowspan="3" |4:1 to 10:1 (ultrahard)
|4:1 to 6:1 (hyperhard)
|
|
|
|
|-
|
|
|-
|'''6:1 (extrahard)'''
| rowspan="3" |7L 4s
| rowspan="3" |(formerly suprasmitonic)
|7L 11s
|
|
|-
|-
|6:1 to 10:1 (clustered)
|
|
|
|
|-
|-
|11L 7s
| colspan="2" |
|'''10:1 (semicollapsed)'''
|
|
|-
|-
| colspan="2" |10:1 to 1:0 (pseudocollapsed)
|
|
|
|
|-
|
|
|
|
|
|
|
|
|
| colspan="2" |
|
|'''1:0 (collapsed)'''
|
|Trivial/pathological
|
|}
 
== Original table of extended TAMNAMS names (archived) ==
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%20pattern%20names|TAMNAMS names]] being reorganized and many scales being renamed, hence this section is kept for archival purposes.
 
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
|-
|-
| rowspan="31" |2L 1s
! colspan="2" |Progenitor scale
| rowspan="31" |deuteric*
! colspan="2" |1st-order child mosses
(currently trial)
! colspan="2" |2nd-order child mosses
| rowspan="15" |2L 3s
! colspan="2" |3rd-order child mosses
| rowspan="15" |pentic
! colspan="2" |4th-order child mosses
| rowspan="7" |2L 5s
! colspan="2" |5th-order child mosses
| rowspan="7" |antidiatonic
| rowspan="3" |2L 7s
| rowspan="3" |balzano
(formerly joanatonic)
|2L 9s
|
|-
|-
|
!Steps
|
!Scale name
|-
!Steps
|9L 2s
!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
|-
|-
|
|
Line 481: Line 781:
|
|
|-
|-
| rowspan="3" |7L 2s
| rowspan="3" |5L 1s
| rowspan="3" |superdiatonic
| rowspan="3" |machinoid
|7L 9s
|5L 6s
|
|
|-
|-
Line 489: Line 789:
|
|
|-
|-
|9L 7s
|6L 5s
|
|
|-
|-
Line 499: Line 799:
|
|
|-
|-
| rowspan="7" |5L 2s
| rowspan="7" |4L 1s
| rowspan="7" |diatonic
| rowspan="7" |manual
| rowspan="3" |5L 7s
(formerly manic)
| rowspan="3" |(formerly p-chromatic)
| rowspan="3" |4L 5s
|5L 12s
| rowspan="3" |gramitonic
|s-enharmonic*
(formerly orwelloid)
|4L 9s
|
|-
|-
|
|
|
|
|-
|-
|12L 5s
|9L 4s
|p-enharmonic*
|
|-
|-
|
|
Line 517: Line 819:
|
|
|-
|-
| rowspan="3" |7L 5s
| rowspan="3" |5L 4s
| rowspan="3" |(formerly m-chromatic)
| rowspan="3" |semiquartal
|7L 12s
|5L 9s
|f-enharmonic*
|
|-
|-
|
|
|
|
|-
|-
|12L 7s
|9L 5s
|m-enharmonic*
|
|-
|-
|
|
Line 537: Line 839:
|
|
|-
|-
| rowspan="15" |3L 2s
| rowspan="15" |3L 1s
| rowspan="15" |antipentic
| rowspan="15" |tetric
| rowspan="7" |3L 5s
| rowspan="7" |3L 4s
| rowspan="7" |checkertonic
| rowspan="7" |mosh
(formerly sensoid)
| rowspan="3" |3L 7s
| rowspan="3" |3L 8s
| rowspan="3" |sephiroid
| rowspan="3" |
|3L 10s
|3L 11s
|
|
|-
|-
Line 550: Line 851:
|
|
|-
|-
|11L 3s
|10L 3s
|
|
|-
|-
Line 558: Line 859:
|
|
|-
|-
| rowspan="3" |8L 3s
| rowspan="3" |7L 3s
| rowspan="3" |
| rowspan="3" |dicoid
|8L 11s
(formerly dicotonic)
|7L 10s
|
|
|-
|-
Line 566: Line 868:
|
|
|-
|-
|11L 8s
|10L 7s
|
|
|-
|-
Line 576: Line 878:
|
|
|-
|-
| rowspan="7" |5L 3s
| rowspan="7" |4L 3s
| rowspan="7" |oneirotonic
| rowspan="7" |smitonic
| rowspan="3" |5L 8s
| rowspan="3" |4L 7s
| rowspan="3" |
| rowspan="3" |(formerly kleistonic)
|5L 13s
|4L 11s
|
|
|-
|-
Line 586: Line 888:
|
|
|-
|-
|13L 5s
|11L 4s
|
|
|-
|-
Line 594: Line 896:
|
|
|-
|-
| rowspan="3" |8L 5s
| rowspan="3" |7L 4s
| rowspan="3" |
| rowspan="3" |(formerly suprasmitonic)
|8L 13s
|7L 11s
|
|
|-
|-
Line 602: Line 904:
|
|
|-
|-
|13L 8
|11L 7s
|}
|
 
=== Extended mos pattern names (fewer than 5 steps, 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.
|-
|-
|
|
Line 646: Line 911:
|
|
|
|
|-
|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.
|-
|
|
|
|
Line 658: Line 917:
|
|
|
|
|-
| 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
|
|-
|
|
|
|
|-
|-
| rowspan="3" |2L 1s
|9L 2s
| rowspan="3" |deuterotonic or deuteric
|
| rowspan="3" |trial
| rowspan="3" |One of the child scales of 1L 1s.
|2L 3s
| -
|pentic
|Already established name.
|-
|-
|
|
Line 675: Line 942:
|
|
|-
|-
|3L 2s
| rowspan="3" |7L 2s
| -
| rowspan="3" |superdiatonic
|antipentic
|7L 9s
|Already established name.
|
|}
|-
 
|
== Proposal: Naming mosses with more than 10 steps (work-in-progress) ==
|
This is a system for describing scales beyond the set of named TAMNAMS scales. Both [[User:Frostburn]] ([[User:Frostburn/TAMNAMS Extension]]) and I have similar systems, with the main difference here being that mosses are technically not limited to being only three generations away.
|-
 
|9L 7s
=== Naming mosdescendants up to 3 generations ===
|
Although naming scales beyond the current cap of 10 notes is antithetical to the purpose of TAMNAMS, names for mosses greater than 10 notes can be made systematically using existing names. The rules are described as such:
|-
 
|
* If the scale is the child of a named parent scale, then the scale is '''moschromatic'''.
|
* If the scale is the grandchild of a named parent scale, then the scale is '''mosenharmonic.'''
|
* If the scale is the great-grandchild of a named parent scale, then the scale is '''mosschismic'''. (tentative name; [[Schismatic family|schismic]] refers to a family of temperaments; open to better name suggestions)
|
* If the scale is more than 3 generations from a named parent scale, or if referring to a scale regardless of number of generations from the parent, then the scale is a '''mosdescendant''' scale.
|
 
|
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, grandchild, and great-grandchild scales for the mos 5L 3s (oneirotonic, prefix oneiro-) are oneirochromatic, oneiroenharmonic, and oneiroschismic respectively, and the entire family of mosses related to oneirotonic are oneirodescendants.
|-
 
| rowspan="7" |5L 2s
Additionally, the lack of a prefix will specifically describe the descendant scales of 5L 2s: chromatic, enharmonic, and schismic. Descendants of 5L 2s are referred to as "diatonic descendants" rather than "descendants".
| rowspan="7" |diatonic
 
| rowspan="3" |5L 7s
Single-letter prefixes for these names are optional, as the single-letter prefixes are meant for specificity. With no prefix specified, moschromatic refers to one of two child scales, mosenharmonic refers to one of four grandchild scales, and mosschismic refers to one of eight great-grandchild scales. The table below shows those prefixes and the mosdescendants for which they apply, as well as the step ratio of the parent mos needed to reach these scales.
| rowspan="3" |(formerly p-chromatic)
{| class="wikitable"
|5L 12s
|+Mosdescendant scales sorted by step ratio
|s-enharmonic*
! colspan="3" |Parent scale
! colspan="4" |Moschromatic (child) scales
! colspan="4" |Mosenharmonic (grandchild) scales
! colspan="4" |Mosschismic (great-grandchild) scales
|-
|-
! rowspan="2" |Steps
|
! colspan="2" |Step ratio
|
! rowspan="2" |Steps
|-
! rowspan="2" |Specific name
|12L 5s
! colspan="2" |Step ratio of parent
|p-enharmonic*
! rowspan="2" |Steps
! rowspan="2" |Specific name
! colspan="2" |Step ratio of grandparent
! rowspan="2" |Steps
! rowspan="2" |Specific name
! colspan="2" |Step ratio of great-grandparent
|-
|-
!General range
|
!Step ratio for 2:1
|
!General range
|
!For L:s = 2:1
|
!General range
!For L:s = 2:1
!General range
!For L:s = 2:1
|-
|-
| rowspan="8" |xL ys
| rowspan="3" |7L 5s
| rowspan="8" |1:1 to 1:0
| rowspan="3" |(formerly m-chromatic)
| rowspan="8" |2:1 (basic)
|7L 12s
| rowspan="4" |(x+y)L xs
|f-enharmonic*
| rowspan="4" |m-moschromatic
| rowspan="4" |1:1 to 2:1
| rowspan="4" |3:2 (soft)
| rowspan="2" |(x+y)L (2x+y)s
| rowspan="2" |f-mosenharmonic
| rowspan="2" |1:1 to 3:2
| rowspan="2" |4:3 (supersoft)
|(x+y)L (3x+2y)s
|f-mosschismic
|1:1 to 4:3 (ultrasoft)
|5:4
|-
|-
|(3x+2y)L (x+y)s
|
|a-mosschismic
|
|4:3 to 3:2 (parasoft)
|7:5
|-
|-
| rowspan="2" |(2x+y)L (x+y)s
|12L 7s
| rowspan="2" |m-mosenharmonic
|m-enharmonic*
| rowspan="2" |3:2 to 2:1 (hyposoft)
| rowspan="2" |5:3 (semisoft)
|(3x+2y)L (2x+y)s
|u-mosschismic
|3:2 to 5:3 (quasisoft)
|8:5
|-
|-
|(2x+y)L (3x+2y)s
|
|m-mosschismic
|
|5:3 to 2:1 (minisoft)
|
|7:4
|
|
|
|
|
|-
|-
| rowspan="4" |xL (x+y)s
| rowspan="15" |3L 2s
| rowspan="4" |p-moschromatic
| rowspan="15" |antipentic
| rowspan="4" |2:1 to 1:0
| rowspan="7" |3L 5s
| rowspan="4" |3:1 (hard)
| rowspan="7" |checkertonic
| rowspan="2" |(2x+y)L xs
(formerly sensoid)
| rowspan="2" |p-mosenharmonic
| rowspan="3" |3L 8s
| rowspan="2" |2:1 to 3:1 (hypohard)
| rowspan="3" |
| rowspan="2" |5:2 (semihard)
|3L 11s
|(2x+y)L (3x+y)s
|
|p-mosschismic
|-
|2:1 to 5:2 (minihard)
|
|7:3
|
|-
|-
|(3x+y)L (2x+y)s
|11L 3s
|q-mosschismic
|
|5:2 to 3:1 (quasihard)
|8:3
|-
|-
| rowspan="2" |xL (2x+y)s
|
| rowspan="2" |s-mosenharmonic
|
| rowspan="2" |3:1 to 1:0
|
| rowspan="2" |4:1 (superhard)
|
|(3x+y)L xs
|r-mosschismic
|3:1 to 4:1 (parahard)
|7:2
|-
|-
|xL (3x+y)s
| rowspan="3" |8L 3s
|s-mosschismic
| rowspan="3" |
|4:1 to 1:0 (ultrahard)
|8L 11s
|5:1
|
|}
{| class="wikitable"
|+Simplified table, without step ratios, sorted by position on mos family tree
!Parent scale
! colspan="2" |Moschromatic scales
! colspan="2" |Mosenharmonic scales
! colspan="2" |Mosschismic scales
|-
|-
!Steps
|
!Steps
|
!Specific name
!Steps
!Specific name
!Steps
!Specific name
|-
|-
| rowspan="8" |xL ys
|11L 8s
| rowspan="4" |xL (x+y)s
|
| rowspan="4" |p-moschromatic
| rowspan="2" |xL (2x+y)s
| rowspan="2" |s-mosenharmonic
|xL (3x+y)s
|s-mosschismic
|-
|-
|(3x+y)L xs
|
|r-mosschismic
|
|
|
|
|
|-
|-
| rowspan="2" |(2x+y)L xs
| rowspan="7" |5L 3s
| rowspan="2" |p-mosenharmonic
| rowspan="7" |oneirotonic
|(2x+y)L (3x+y)s
| rowspan="3" |5L 8s
|p-mosschismic
| rowspan="3" |
|5L 13s
|
|-
|-
|(3x+y)L (2x+y)s
|
|q-mosschismic
|
|-
|-
| rowspan="4" |(x+y)L xs
|13L 5s
| rowspan="4" |m-moschromatic
|
| rowspan="2" |(x+y)L (2x+y)s
| rowspan="2" |f-mosenharmonic
|(x+y)L (3x+2y)s
|f-mosschismic
|-
|-
|(3x+2y)L (x+y)s
|
|a-mosschismic
|
|
|
|-
| rowspan="3" |8L 5s
| rowspan="3" |
|8L 13s
|
|-
|-
| rowspan="2" |(2x+y)L (x+y)s
|
| rowspan="2" |m-mosenharmonic
|
|(2x+y)L (3x+2y)s
|m-mosschismic
|-
|-
|(3x+2y)L (2x+y)s
|13L 8
|u-mosschismic
|}
|}


=== Mosdescendants for single-period mosses ===
=== Extended mos pattern names (fewer than 5 steps, archived) ===
Although it's possible for any mos to have mosdescendants named as described above, it's recommended that mosdescendant scale names should apply to mosses whose immediate child mosses exceed 10 steps. The following tables show which mosses, marked in '''bold''', mosdescendant names can apply.
As of August 14, 2022, all of these scales have been named. These descriptions are kept for archival purposes.
{| class="wikitable"
{| class="wikitable"
|+Single-period mosses for which mosdescendant names apply
! colspan="4" |Parent scale
!Mos
! colspan="4" |1st-order child scales
!Name
! colspan="4" |2nd-order child scales
!Mos
!Name
!Mos
!Name
!Mos
!Name
!Mos
!Name
!Mos
!Name
!Mos
!Name
!Mos
!Name
!Mos
!Name
|-
|-
| rowspan="16" |1L 1s
!Steps
| rowspan="16" |trivial
!Originally proposed name
| rowspan="11" |1L 2s
!Current name
| rowspan="11" |antrial
!Notes
| rowspan="8" |1L 3s
!Steps
| rowspan="8" |antetric
!Originally proposed name
| rowspan="6" |1L 4s
!Current name
| rowspan="6" |pedal
!Notes
| rowspan="5" |1L 5s
!Steps
| rowspan="5" |antimachinoid
!Originally proposed name
| rowspan="4" |1L 6s
!Current name
| rowspan="4" |onyx
!Notes
| rowspan="3" |1L 7s
| rowspan="3" |antipine
| rowspan="2" |1L 8s
| rowspan="2" |antisubneutralic
|1L 9s
|'''antisinatonic (asina-)'''
|-
|-
|9L 1s
| rowspan="7" |1L 1s
|'''sinatonic (sina-)'''
| rowspan="7" |prototonic, protic, or monowood
|-
| rowspan="7" |monowood and trivial
|8L 1s
| rowspan="7" |The progenitor scale of all single-period mosses.
|'''subneutralic (blu-)'''
Despite being a monolarge scale, it's also its own sister and is named regardless.
| colspan="2" rowspan="14" |
 
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.
|-
|-
|7L 1s
|
|'''pine (pine-)'''
|
| colspan="2" rowspan="13" |
|
|
|-
|-
|6L 1s
|3L 1s
|'''arch(a)eotonic (arch-)'''
|tetric
| colspan="2" rowspan="12" |
|tetric
|Parent scale to orwelloid (now gramitonic) and semiquartal, the name tetric is assigned similarly to pentic being the parent of diatonic and antidiatonic.
|-
|-
|5L 1s
|
|'''machinoid (mech-)'''
|
| colspan="2" rowspan="11" |
|
|
|
|
|
|
|-
|-
| rowspan="2" |4L 1s
| rowspan="3" |2L 1s
| rowspan="2" |manual
| rowspan="3" |deuterotonic or deuteric
|5L 4s
| rowspan="3" |trial
|'''semiquartal (chton-)'''
| rowspan="3" |One of the child scales of 1L 1s.
|2L 3s
| -
|pentic
|Already established name.
|-
|-
|4L 5s
|
|'''gramitonic (gram-)'''
|
|
|
|-
|-
| rowspan="3" |3L 1s
|3L 2s
| rowspan="3" |tetric
| -
|4L 3s
|antipentic
|'''smitonic (smi-)'''
|Already established name.
| colspan="2" |
|}
 
== Proposal: Naming mosses with more than 10 steps (work-in-progress) ==
This is a system for describing scales beyond the set of named TAMNAMS scales. Both [[User:Frostburn]] ([[User:Frostburn/TAMNAMS Extension]]) and I have similar systems, with the main difference here being that mosses are technically not limited to being only three generations away.
 
=== Naming mosdescendants up to 3 generations ===
Although naming scales beyond the current cap of 10 notes is antithetical to the purpose of TAMNAMS, names for mosses greater than 10 notes can be made systematically using existing names. The rules are described as such:
 
* If the scale is the child of a named parent scale, then the scale is '''moschromatic'''.
* If the scale is the grandchild of a named parent scale, then the scale is '''mosenharmonic.'''
* If the scale is the great-grandchild of a named parent scale, then the scale is '''mosschismic'''. (tentative name; [[Schismatic family|schismic]] refers to a family of temperaments; open to better name suggestions)
* If the scale is more than 3 generations from a named parent scale, or if referring to a scale regardless of number of generations from the parent, then the scale is a '''mosdescendant''' scale.
 
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, grandchild, and great-grandchild scales for the mos 5L 3s (oneirotonic, prefix oneiro-) are oneirochromatic, oneiroenharmonic, and oneiroschismic respectively, and the entire family of mosses related to oneirotonic are oneirodescendants.
 
Additionally, the lack of a prefix will specifically describe the descendant scales of 5L 2s: chromatic, enharmonic, and schismic. Descendants of 5L 2s are referred to as "diatonic descendants" rather than "descendants".
 
Single-letter prefixes for these names are optional, as the single-letter prefixes are meant for specificity. With no prefix specified, moschromatic refers to one of two child scales, mosenharmonic refers to one of four grandchild scales, and mosschismic refers to one of eight great-grandchild scales. The table below shows those prefixes and the mosdescendants for which they apply, as well as the step ratio of the parent mos needed to reach these scales.
{| class="wikitable"
|+Mosdescendant scales sorted by step ratio
! colspan="3" |Parent scale
! colspan="4" |Moschromatic (child) scales
! colspan="4" |Mosenharmonic (grandchild) scales
! colspan="4" |Mosschismic (great-grandchild) scales
|-
|-
| rowspan="2" |3L 4s
! rowspan="2" |Steps
| rowspan="2" |mosh
! colspan="2" |Step ratio
|7L 3s
! rowspan="2" |Steps
|'''dicoid/zaltertic (dico-/zal-)'''
! rowspan="2" |Specific name
! colspan="2" |Step ratio of parent
! rowspan="2" |Steps
! rowspan="2" |Specific name
! colspan="2" |Step ratio of grandparent
! rowspan="2" |Steps
! rowspan="2" |Specific name
! colspan="2" |Step ratio of great-grandparent
|-
|-
|3L 7s
!General range
|'''sephiroid (seph-)'''
!Step ratio for 2:1
!General range
!For L:s = 2:1
!General range
!For L:s = 2:1
!General range
!For L:s = 2:1
|-
|-
| rowspan="5" |2L 1s
| rowspan="8" |xL ys
| rowspan="5" |trial
| rowspan="8" |1:1 to 1:0
| rowspan="2" |3L 2s
| rowspan="8" |2:1 (basic)
| rowspan="2" |antipentic
| rowspan="4" |(x+y)L xs
|3L 5s
| rowspan="4" |m-moschromatic
|'''checkertonic (check-)'''
| rowspan="4" |1:1 to 2:1
| colspan="2" rowspan="3" |
| rowspan="4" |3:2 (soft)
| rowspan="2" |(x+y)L (2x+y)s
| rowspan="2" |f-mosenharmonic
| rowspan="2" |1:1 to 3:2
| rowspan="2" |4:3 (supersoft)
|(x+y)L (3x+2y)s
|f-mosschismic
|1:1 to 4:3 (ultrasoft)
|5:4
|-
|-
|5L 3s
|(3x+2y)L (x+y)s
|'''oneirotonic (oneiro-)'''
|a-mosschismic
|4:3 to 3:2 (parasoft)
|7:5
|-
|-
| rowspan="3" |2L 3s
| rowspan="2" |(2x+y)L (x+y)s
| rowspan="3" |pentic
| rowspan="2" |m-mosenharmonic
|5L 2s
| rowspan="2" |3:2 to 2:1 (hyposoft)
|'''diatonic ''(no prefix)'''''
| rowspan="2" |5:3 (semisoft)
|(3x+2y)L (2x+y)s
|u-mosschismic
|3:2 to 5:3 (quasisoft)
|8:5
|-
|-
| rowspan="2" |2L 5s
|(2x+y)L (3x+2y)s
| rowspan="2" |antidiatonic
|m-mosschismic
|7L 2s
|5:3 to 2:1 (minisoft)
|'''superdiatonic (arm-)'''
|7:4
|-
|-
|2L 7s
| rowspan="4" |xL (x+y)s
|'''balzano (bal-)'''
| rowspan="4" |p-moschromatic
|}
| rowspan="4" |2:1 to 1:0
 
| rowspan="4" |3:1 (hard)
=== Mosdescendants for multi-period mosses ===
| rowspan="2" |(2x+y)L xs
TAMNAMS has names for 2-period mosses up to 10 notes, and as such, mosdescendant names apply to mosses whose children have more than 10 notes: '''jaric''', '''taric''', '''ekic''', '''lemon''', and '''lime'''. Likewise, there are 3-period scales up to 9 notes, so mosdescendant names apply to '''tcherepnin''' and '''hyrulic''', the only 3-period mosses named under TAMNAMS, apart from triwood.
| rowspan="2" |p-mosenharmonic
{| class="wikitable"
| rowspan="2" |2:1 to 3:1 (hypohard)
|+2 and 3-period mosses for which mosdescendant names apply
| rowspan="2" |5:2 (semihard)
! colspan="8" |2-period mosses
|(2x+y)L (3x+y)s
|p-mosschismic
|2:1 to 5:2 (minihard)
|7:3
|-
|-
!Mos
|(3x+y)L (2x+y)s
!Name
|q-mosschismic
!Mos
|5:2 to 3:1 (quasihard)
!Name
|8:3
!Mos
!Name
!Mos
!Name
|-
|-
| rowspan="5" |[[2L 2s]]
| rowspan="2" |xL (2x+y)s
| rowspan="5" |biwood
| rowspan="2" |s-mosenharmonic
| rowspan="3" |[[2L 4s]]
| rowspan="2" |3:1 to 1:0
| rowspan="3" |malic
| rowspan="2" |4:1 (superhard)
| rowspan="2" |[[2L 6s]]
|(3x+y)L xs
| rowspan="2" |subaric
|r-mosschismic
|[[2L 8s]]
|3:1 to 4:1 (parahard)
|'''jaric (jara-)'''
|7:2
|-
|-
|[[8L 2s]]
|xL (3x+y)s
|'''taric (tara-)'''
|s-mosschismic
|4:1 to 1:0 (ultrahard)
|5:1
|}
{| class="wikitable"
|+Simplified table, without step ratios, sorted by position on mos family tree
!Parent scale
! colspan="2" |Moschromatic scales
! colspan="2" |Mosenharmonic scales
! colspan="2" |Mosschismic scales
|-
|-
|[[6L 2s]]
!Steps
|'''ekic (ek-)'''
!Steps
| colspan="2" rowspan="3" |
!Specific name
!Steps
!Specific name
!Steps
!Specific name
|-
|-
| rowspan="2" |[[4L 2s]]
| rowspan="8" |xL ys
| rowspan="2" |citric
| rowspan="4" |xL (x+y)s
|[[6L 4s]]
| rowspan="4" |p-moschromatic
|'''lemon (lem-)'''
| rowspan="2" |xL (2x+y)s
| rowspan="2" |s-mosenharmonic
|xL (3x+y)s
|s-mosschismic
|-
|-
|[[4L 6s]]
|(3x+y)L xs
|'''lime (lime-)'''
|r-mosschismic
|-
|-
! colspan="8" |3-period mosses
| rowspan="2" |(2x+y)L xs
| rowspan="2" |p-mosenharmonic
|(2x+y)L (3x+y)s
|p-mosschismic
|-
|-
!Mos
|(3x+y)L (2x+y)s
!Name
|q-mosschismic
!Mos
!Name
| colspan="4" rowspan="3" |
|-
|-
| rowspan="2" |[[3L 3s]]
| rowspan="4" |(x+y)L xs
| rowspan="2" |triwood
| rowspan="4" |m-moschromatic
|[[3L 6s]]
| rowspan="2" |(x+y)L (2x+y)s
|'''tcherepnin (cher-)'''
| rowspan="2" |f-mosenharmonic
|(x+y)L (3x+2y)s
|f-mosschismic
|-
|(3x+2y)L (x+y)s
|a-mosschismic
|-
| rowspan="2" |(2x+y)L (x+y)s
| rowspan="2" |m-mosenharmonic
|(2x+y)L (3x+2y)s
|m-mosschismic
|-
|-
|[[6L 3s]]
|(3x+2y)L (2x+y)s
|'''hyrulic (hyru-)'''
|u-mosschismic
|}
|}
Starting at 4 periods, mosdescendant names apply only to n-wood scales (tetrawood, pentawood, etc), where the names of mosdescendants are based on names for single-period mosses up to 5 notes rather than based on moschromatic, mosenharmonic, and mosschismic, and thereby limited to mosdescendants with 5n notes; any descendants after that are referred as to '''n-wood descendants'''.


Since the names for single-period mosses up to 5 notes may also be used for non-octave periods, these names are used for multi-period mosses, producing '''n-antrial''', '''n-trial''', '''n-antetric''', '''n-tetric''', '''n-antipentic''', '''n-pentic''', '''n-pedal''', and '''n-manual'''. Note that there are only two named 3rd-generation mosses from nL ns rather than the usual eight; the missing six names (what would be n-smitonic, n-mosh, n-checkertonic, n-oneiorotonic, n-diatonic, and n-antidiatonic) are unsuitable for use for multi-period mos names as these names must refer to an octave period.
=== Mosdescendants for single-period mosses ===
 
Although it's possible for any mos to have mosdescendants named as described above, it's recommended that mosdescendant scale names should apply to mosses whose immediate child mosses exceed 10 steps. The following tables show which mosses, marked in '''bold''', mosdescendant names can apply.
The table outlines possible names for n-wood descendants for tetrawood, pentawood, and, in the general case, n-wood. Numeric prefixes may be used for these names, rather than n-.
{| class="wikitable"
{| class="wikitable"
|+Possible mosdescendant names for mosses with 4 periods or more
|+Single-period mosses for which mosdescendant names apply
|-
!Mos
! colspan="9" |4-period mosses
!Name
|-
!Mos
!Name
!Mos
!Name
!Mos
!Name
!Mos
!Name
!Mos
!Mos
!Name
!Name
Line 1,026: Line 1,328:
!Mos
!Mos
!Name
!Name
!Other notes
|-
|-
| rowspan="5" |[[4L 4s]]
| rowspan="16" |1L 1s
| rowspan="5" |'''tetrawood'''
| rowspan="16" |trivial
| rowspan="3" |[[4L 8s]]
| rowspan="11" |1L 2s
| rowspan="3" |quadantrial
| rowspan="11" |antrial
| rowspan="2" |[[4L 12s]]
| rowspan="8" |1L 3s
| rowspan="2" |quadantetric
| rowspan="8" |antetric
|[[4L 16s]]
| rowspan="6" |1L 4s
|tetrapedal
| rowspan="6" |pedal
| rowspan="5" |Some names have Latin prefixes for ease of spelling.
| rowspan="5" |1L 5s
| rowspan="5" |antimachinoid
| rowspan="4" |1L 6s
| rowspan="4" |onyx
| rowspan="3" |1L 7s
| rowspan="3" |antipine
| rowspan="2" |1L 8s
| rowspan="2" |antisubneutralic
|1L 9s
|'''antisinatonic (asina-)'''
|-
|-
|[[16L 4s]]
|9L 1s
|tetramanual
|'''sinatonic (sina-)'''
|-
|-
|[[12L 4s]]
|8L 1s
|quadtetric
|'''subneutralic (blu-)'''
| colspan="2" rowspan="3" |
| colspan="2" rowspan="14" |
|-
|-
| rowspan="2" |[[8L 4s]]
|7L 1s
| rowspan="2" |quadtrial
|'''pine (pine-)'''
|[[12L 8s]]
| colspan="2" rowspan="13" |
|tetrantipentic
|-
|-
|[[8L 12s]]
|6L 1s
|tetrapentic
|'''arch(a)eotonic (arch-)'''
| colspan="2" rowspan="12" |
|-
|5L 1s
|'''machinoid (mech-)'''
| colspan="2" rowspan="11" |
|-
|-
! colspan="9" |5-period mosses
| rowspan="2" |4L 1s
| rowspan="2" |manual
|5L 4s
|'''semiquartal (chton-)'''
|-
|-
!Mos
|4L 5s
!Name
|'''gramitonic (gram-)'''
!Mos
!Name
!Mos
!Name
!Mos
!Name
!Other notes
|-
|-
| rowspan="5" |[[5L 5s]]
| rowspan="3" |3L 1s
| rowspan="5" |'''pentawood'''
| rowspan="3" |tetric
| rowspan="3" |[[5L 10s]]
|4L 3s
| rowspan="3" |quinantrial
|'''smitonic (smi-)'''
| rowspan="2" |[[5L 15s]]
| colspan="2" |
| rowspan="2" |quinantetric
|-
|[[5L 20s]]
| rowspan="2" |3L 4s
|pentapedal
| rowspan="2" |mosh
| rowspan="5" |Some names have Latin prefixes for ease of spelling.
|7L 3s
|'''dicoid/zaltertic (dico-/zal-)'''
|-
|-
|[[20L 5s]]
|3L 7s
|pentamanual
|'''sephiroid (seph-)'''
|-
|-
|[[15L 5s]]
| rowspan="5" |2L 1s
|quintetric
| rowspan="5" |trial
| rowspan="2" |3L 2s
| rowspan="2" |antipentic
|3L 5s
|'''checkertonic (check-)'''
| colspan="2" rowspan="3" |
| colspan="2" rowspan="3" |
|-
|-
| rowspan="2" |[[10L 5s]]
|5L 3s
| rowspan="2" |quintrial
|'''oneirotonic (oneiro-)'''
|[[15L 10s]]
|-
|quinantipentic
| rowspan="3" |2L 3s
| rowspan="3" |pentic
|5L 2s
|'''diatonic ''(no prefix)'''''
|-
|-
|[[10L 15s]]
| rowspan="2" |2L 5s
|quinpentic
| rowspan="2" |antidiatonic
|7L 2s
|'''superdiatonic (arm-)'''
|-
|-
! colspan="9" |n-period mosses
|2L 7s
|'''balzano (bal-)'''
|}
 
=== Mosdescendants for multi-period mosses ===
TAMNAMS has names for 2-period mosses up to 10 notes, and as such, mosdescendant names apply to mosses whose children have more than 10 notes: '''jaric''', '''taric''', '''ekic''', '''lemon''', and '''lime'''. Likewise, there are 3-period scales up to 9 notes, so mosdescendant names apply to '''tcherepnin''' and '''hyrulic''', the only 3-period mosses named under TAMNAMS, apart from triwood.
{| class="wikitable"
|+2 and 3-period mosses for which mosdescendant names apply
! colspan="8" |2-period mosses
|-
|-
!Mos
!Mos
Line 1,100: Line 1,428:
!Mos
!Mos
!Name
!Name
!Other notes
|-
|-
| rowspan="5" |nL ns
| rowspan="5" |[[2L 2s]]
| rowspan="5" |'''n-wood'''
| rowspan="5" |biwood
| rowspan="3" |nL 2ns
| rowspan="3" |[[2L 4s]]
| rowspan="3" |n-antrial
| rowspan="3" |malic
| rowspan="2" |nL 3ns
| rowspan="2" |[[2L 6s]]
| rowspan="2" |n-antetric
| rowspan="2" |subaric
|nL 4ns
|[[2L 8s]]
|n-pedal
|'''jaric (jara-)'''
| rowspan="5" |A numeric prefix may be used instead, such as hexawood instead of 6-wood.
When in doubt, prefix names for n-period mosses with n-.
|-
|-
|4nL ns
|[[8L 2s]]
|n-manual
|'''taric (tara-)'''
|-
|-
|3nL ns
|[[6L 2s]]
|n-tetric
|'''ekic (ek-)'''
| colspan="2" rowspan="3" |
| colspan="2" rowspan="3" |
|-
|-
| rowspan="2" |2nL ns
| rowspan="2" |[[4L 2s]]
| rowspan="2" |n-trial
| rowspan="2" |citric
|3nL 2ns
|[[6L 4s]]
|n-anpentic
|'''lemon (lem-)'''
|-
|[[4L 6s]]
|'''lime (lime-)'''
|-
! colspan="8" |3-period mosses
|-
!Mos
!Name
!Mos
!Name
| colspan="4" rowspan="3" |
|-
| rowspan="2" |[[3L 3s]]
| rowspan="2" |triwood
|[[3L 6s]]
|'''tcherepnin (cher-)'''
|-
|-
|2nL 3ns
|[[6L 3s]]
|n-pentic
|'''hyrulic (hyru-)'''
|}
|}
Starting at 4 periods, mosdescendant names apply only to n-wood scales (tetrawood, pentawood, etc), where the names of mosdescendants are based on names for single-period mosses up to 5 notes rather than based on moschromatic, mosenharmonic, and mosschismic, and thereby limited to mosdescendants with 5n notes; any descendants after that are referred as to '''n-wood descendants'''.


=== Naming mosdescendants beyond 3 generations ===
Since the names for single-period mosses up to 5 notes may also be used for non-octave periods, these names are used for multi-period mosses, producing '''n-antrial''', '''n-trial''', '''n-antetric''', '''n-tetric''', '''n-antipentic''', '''n-pentic''', '''n-pedal''', and '''n-manual'''. Note that there are only two named 3rd-generation mosses from nL ns rather than the usual eight; the missing six names (what would be n-smitonic, n-mosh, n-checkertonic, n-oneiorotonic, n-diatonic, and n-antidiatonic) are unsuitable for use for multi-period mos names as these names must refer to an octave period.
Each generation has twice as many mosdescendants as the last, so rather than try to name every possible descendant, mosdescendants more than 3 generations from a given parent mos may be referred to how many generations away it is. Mosschismic scales are 3rd mosdescendants, so after that are 4th-mosdescendants, 5th-mosdescendants, and so on. The algorithms below shows how to find how many generations away a mos xL ys is from another scale.


* For mosses with up to 3 periods: finding a parent mos zL ws for the mosdescendant xL ys, where x, y, z, and w share a greatest common factor that is no greater than 3:
The table outlines possible names for n-wood descendants for tetrawood, pentawood, and, in the general case, n-wood. Numeric prefixes may be used for these names, rather than n-.
*# Let z and w be the number of large and small steps of the parent mos to be found. Assign to z and w the values x and y respectively. Let g = 0, where g is the number of generations away from zL ws.
{| class="wikitable"
*# Let m1 be equal to max(z, w) and m2 be equal to min(z, w).
|+Possible mosdescendant names for mosses with 4 periods or more
*# Assign to z the value m2 and w the value m1-m2. Increment g by 1.
*# If the sum of z and w is no more than 10, then the parent mos is zL ws and has a TAMNAMS name. If not, repeat the process starting at step 2.
* For mosses with 4 periods or more: finding how many generations away a mosdescendant xL ys is from its n-wood scale, where x and y have a greatest common factor of n that is 4 or greater:
*# Let z and w be assigned the values x and y respectively. Let g = 0, where g is the number of generations away from nL ns.
*# Let m1 be equal to max(z, w) and m2 be equal to min(z, w).
*# Assign to z the value m2 and w the value m1-m2. Increment g by 1.
*# If the sum of z and w is exactly 2n, then the mos nL ns is g generations away from xL ys. If not, repeat the process starting at step 2.
 
=== Naming mosdescendants for linearly growing scales (work-in-progress) ===
Some noteworthy mosdescendants may be more than 3 generations away, but may have the same number of large steps as a named parent mos. In such cases, the number of notes with each successive mosdescendant grows linearly, and these mosses may be assigned a letter to refer to a specific mosdescendant. Currently, this applies to mosdescendants whose parent mos has a step ratio that is along the extreme edges of the step ratio spectrum, around pseudoequalized and pseudocollapsed, producing '''nth s-mosdescendants''' and '''nth f-mosdescendants'''. The mos family tree better shows which mosses grow linearly, shown in bold, as the upper child of each node is always xL (x+y)s, which becomes of xL (nx+y)s over n generations.
{| class="wikitable"
|+Mosdescendants sorted by position on the mos family tree
!Parent scale
! colspan="2" |Moschromatic scales
(1st mosdescendants)
! colspan="2" |Mosenharmonic scales
(2nd mosdescendants)
! colspan="2" |Mosschismic scales
(3rd mosdescendants)
! colspan="2" |4th-mosdescendant scales
(selected mosdescendants)
! colspan="2" |5th-mosdescendant scales
(selected mosdescendants)
! colspan="2" |nth-mosdescendant scales
(selected mosdescendants)
|-
|-
!Steps
! colspan="9" |4-period mosses
!Steps
!Specific name
!Steps
!Specific name
!Steps
!Specific name
!Steps
!Specific name
!Steps
!Specific name
!Steps
!Specific name
|-
|-
| rowspan="8" |xL ys
!Mos
| rowspan="4" |'''xL (x+y)s'''
!Name
| rowspan="4" |'''p-moschromatic'''
!Mos
| rowspan="2" |'''xL (2x+y)s'''
!Name
| rowspan="2" |'''s-mosenharmonic'''
!Mos
|'''xL (3x+y)s'''
!Name
|'''s-mosschismic'''
!Mos
|'''xL (4x+y)s'''
!Name
|'''4th s-mosdescendant'''
!Other notes
|'''xL (5x+y)s'''
|-
|'''5th s-mosdescendant'''
| rowspan="5" |[[4L 4s]]
|'''xL (nx+y)s'''
| rowspan="5" |'''tetrawood'''
|'''nth s-mosdescendant'''
| rowspan="3" |[[4L 8s]]
| rowspan="3" |quadantrial
| rowspan="2" |[[4L 12s]]
| rowspan="2" |quadantetric
|[[4L 16s]]
|tetrapedal
| rowspan="5" |Some names have Latin prefixes for ease of spelling.
|-
|-
|(3x+y)L xs
|[[16L 4s]]
|r-mosschismic
|tetramanual
|
|
|
|
|
|
|-
|-
| rowspan="2" |(2x+y)L xs
|[[12L 4s]]
| rowspan="2" |p-mosenharmonic
|quadtetric
|(2x+y)L (3x+y)s
| colspan="2" rowspan="3" |
|p-mosschismic
|-
|(2x+y)L (5x+2y)s
| rowspan="2" |[[8L 4s]]
|4th p-mosdescendant
| rowspan="2" |quadtrial
|(2x+y)L (7x+3y)s
|[[12L 8s]]
|5th p-mosdescendant
|tetrantipentic
|
|
|-
|-
|(3x+y)L (2x+y)s
|[[8L 12s]]
|q-mosschismic
|tetrapentic
|
|
|
|
|
|
|-
|-
| rowspan="4" |(x+y)L xs
! colspan="9" |5-period mosses
| rowspan="4" |m-moschromatic
| rowspan="2" |'''(x+y)L (2x+y)s'''
| rowspan="2" |'''f-mosenharmonic'''
|'''(x+y)L (3x+2y)s'''
|'''f-mosschismic'''
|'''(x+y)L (4x+3y)s'''
|'''4th f-mosdescendant'''
|'''(x+y)L (5x+4y)s'''
|'''5th f-mosdescendant'''
|'''(x+y)L (nx+(n-1)y)s'''
|'''nth f-mosdescendant'''
|-
|-
|(3x+2y)L (x+y)s
!Mos
|a-mosschismic
!Name
|
!Mos
|
!Name
|
!Mos
|
!Name
|
!Mos
|
!Name
!Other notes
|-
|-
| rowspan="2" |(2x+y)L (x+y)s
| rowspan="5" |[[5L 5s]]
| rowspan="2" |m-mosenharmonic
| rowspan="5" |'''pentawood'''
|(2x+y)L (3x+2y)s
| rowspan="3" |[[5L 10s]]
|m-mosschismic
| rowspan="3" |quinantrial
|(2x+y)L (5x+3y)s
| rowspan="2" |[[5L 15s]]
|4th m-mosdescendant
| rowspan="2" |quinantetric
|(2x+y)L (7x+4y)s
|[[5L 20s]]
|5th m-mosdescendant
|pentapedal
|
| rowspan="5" |Some names have Latin prefixes for ease of spelling.
|
|-
|[[20L 5s]]
|pentamanual
|-
|[[15L 5s]]
|quintetric
| colspan="2" rowspan="3" |
|-
|-
|(3x+2y)L (2x+y)s
| rowspan="2" |[[10L 5s]]
|u-mosschismic
| rowspan="2" |quintrial
|
|[[15L 10s]]
|
|quinantipentic
|
|
|
|
|}
{| class="wikitable"
|+Mosdescendants sorted by step ratio
!Parent scale
! colspan="2" |Moschromatic scales
(1st mosdescendants)
! colspan="2" |Mosenharmonic scales
(2nd mosdescendants)
! colspan="2" |Mosschismic scales
(3rd mosdescendants)
! colspan="3" |nth-mosdescendant scales
|-
|-
!Steps
|[[10L 15s]]
!Steps
|quinpentic
!Specific name
!Steps
!Specific name
!Steps
!Specific name
!Steps
!Specific name
!Step ratio of parent
|-
|-
| rowspan="10" |xL ys
! colspan="9" |n-period mosses
| rowspan="5" |(x+y)L xs
| rowspan="5" |m-moschromatic
| rowspan="3" |(x+y)L (2x+y)s
| rowspan="3" |f-mosenharmonic
| rowspan="2" |(x+y)L (3x+2y)s
| rowspan="2" |f-mosschismic
|(x+y)L (nx+(n-1)y)s
|nth f-mosdescendant
|Softer than 5:4
|-
|-
| rowspan="8" |
!Mos
| rowspan="8" |
!Name
| rowspan="8" |
!Mos
!Name
!Mos
!Name
!Mos
!Name
!Other notes
|-
|-
|(3x+2y)L (x+y)s
| rowspan="5" |nL ns
|a-mosschismic
| rowspan="5" |'''n-wood'''
|-
| rowspan="3" |nL 2ns
| rowspan="2" |(2x+y)L (x+y)s
| rowspan="3" |n-antrial
| rowspan="2" |m-mosenharmonic
| rowspan="2" |nL 3ns
|(3x+2y)L (2x+y)s
| rowspan="2" |n-antetric
|u-mosschismic
|nL 4ns
|n-pedal
| rowspan="5" |A numeric prefix may be used instead, such as hexawood instead of 6-wood.
When in doubt, prefix names for n-period mosses with n-.
|-
|-
|(2x+y)L (3x+2y)s
|4nL ns
|m-mosschismic
|n-manual
|-
|-
| rowspan="5" |xL (x+y)s
|3nL ns
| rowspan="5" |p-moschromatic
|n-tetric
| rowspan="2" |(2x+y)L xs
| colspan="2" rowspan="3" |
| rowspan="2" |p-mosenharmonic
|(2x+y)L (3x+y)s
|p-mosschismic
|-
|-
|(3x+y)L (2x+y)s
| rowspan="2" |2nL ns
|q-mosschismic
| rowspan="2" |n-trial
|3nL 2ns
|n-anpentic
|-
|-
| rowspan="3" |xL (2x+y)s
|2nL 3ns
| rowspan="3" |s-mosenharmonic
|n-pentic
|(3x+y)L xs
|r-mosschismic
|-
| rowspan="2" |xL (3x+y)s
| rowspan="2" |s-mosschismic
|-
|xL (nx+y)s
|nth s-mosdescendant
|Harder than 5:1
|}
|}


=== Reasoning for names ===
=== Naming mosdescendants beyond 3 generations ===
The names for moschromatic scales are based on former names for the child scales for diatonic (5L 2s): p-chromatic (5L 7s) and m-chromatic (7L 5s). This was generalized to "chromatic" and "moschromatic", with the prefixes m- and p- for specificity. The names for mosenharmonic scales are based on discussions with xen Discord members for systematically naming the daughter and granddaughter scales of a mos, producing "enharmonic" and "mosenharmonic" with the prefixes f-, m-, p-, and s- for specificity.
Each generation has twice as many mosdescendants as the last, so rather than try to name every possible descendant, mosdescendants more than 3 generations from a given parent mos may be referred to how many generations away it is. Mosschismic scales are 3rd mosdescendants, so after that are 4th-mosdescendants, 5th-mosdescendants, and so on. The algorithms below shows how to find how many generations away a mos xL ys is from another scale.


Names for mosdescendants are thereby based on replacing the mos- prefix with that for a mos's TAMNAMS name. This effectively brings back the names of m-chromatic and p-chromatic, as TAMNAMS specifically names mosses up to 10 notes. This also names other mosses whose names were lost entirely, mainly kleistonic (4L 7s, now p-smichromatic) and suprasmitonic (7L 4s, now m-smichromatic), two names that were dropped because these mosses had more than 10 notes.
* For mosses with up to 3 periods: finding a parent mos zL ws for the mosdescendant xL ys, where x, y, z, and w share a greatest common factor that is no greater than 3:
*# Let z and w be the number of large and small steps of the parent mos to be found. Assign to z and w the values x and y respectively. Let g = 0, where g is the number of generations away from zL ws.
*# Let m1 be equal to max(z, w) and m2 be equal to min(z, w).
*# Assign to z the value m2 and w the value m1-m2. Increment g by 1.
*# If the sum of z and w is no more than 10, then the parent mos is zL ws and has a TAMNAMS name. If not, repeat the process starting at step 2.
* For mosses with 4 periods or more: finding how many generations away a mosdescendant xL ys is from its n-wood scale, where x and y have a greatest common factor of n that is 4 or greater:
*# Let z and w be assigned the values x and y respectively. Let g = 0, where g is the number of generations away from nL ns.
*# Let m1 be equal to max(z, w) and m2 be equal to min(z, w).
*# Assign to z the value m2 and w the value m1-m2. Increment g by 1.
*# If the sum of z and w is exactly 2n, then the mos nL ns is g generations away from xL ys. If not, repeat the process starting at step 2.


The reason why mosdescendants for mosses with 4 periods or greater are not based on their corresponding n-wood scale is because these mosses do not have any child mosses with 10 notes or fewer, and therefore have no named child mosses from which to build mosdescendant names. Rather, names for these mosdescendants are based on period-agnostic names (antrial, trial, antetric, tetric, etc) to reflect that these are scales based on duplicating a base mos multiple times within an octave.
=== Naming mosdescendants for linearly growing scales (work-in-progress) ===
 
Some noteworthy mosdescendants may be more than 3 generations away, but may have the same number of large steps as a named parent mos. In such cases, the number of notes with each successive mosdescendant grows linearly, and these mosses may be assigned a letter to refer to a specific mosdescendant. Currently, this applies to mosdescendants whose parent mos has a step ratio that is along the extreme edges of the step ratio spectrum, around pseudoequalized and pseudocollapsed, producing '''nth s-mosdescendants''' and '''nth f-mosdescendants'''. The mos family tree better shows which mosses grow linearly, shown in bold, as the upper child of each node is always xL (x+y)s, which becomes of xL (nx+y)s over n generations.
The addition of mosschismic scales for great-grandchild scales was done for completeness, with the prefixes f-, a-, u-, m-, p- q-, r-, and s- for specificity (names not finalized). Note that mosschismic scales borrows the prefixes as mosenharmonic scales, which itself borrows those for mosenharmonic scales. The table below shows what prefixes are used for which generation of mosdescendants, with an added mnemonic for memorization.
{| class="wikitable"
{| class="wikitable"
|+Table of mosdescendent prefixes and meanings
|+Mosdescendants sorted by position on the mos family tree
!Prefix
!Parent scale
!For moschromatic scales
! colspan="2" |Moschromatic scales
!For mosenharmonic scales
(1st mosdescendants)
!For mosschismic scales
! colspan="2" |Mosenharmonic scales
!Mnemonic
(2nd mosdescendants)
! colspan="2" |Mosschismic scales
(3rd mosdescendants)
! colspan="2" |4th-mosdescendant scales
(selected mosdescendants)
! colspan="2" |5th-mosdescendant scales
(selected mosdescendants)
! colspan="2" |nth-mosdescendant scales
(selected mosdescendants)
|-
|-
|f-
!Steps
|n/a
!Steps
|F for '''f'''lat; f-mosenharmonic scales have a grandparent whose pitches are flatter compared to basic (L:s = 2:1).
!Specific name
|F for '''f'''lat.
!Steps
| rowspan="4" |FAUM sounds like foam, which sounds '''soft'''.
!Specific name
F-, a-, u-, and m-mosschismic scales generally have a great-grandparent with a '''soft''' step ratio.
!Steps
!Specific name
!Steps
!Specific name
!Steps
!Specific name
!Steps
!Specific name
|-
|-
|a-
| rowspan="8" |xL ys
|n/a
| rowspan="4" |'''xL (x+y)s'''
|n/a
| rowspan="4" |'''p-moschromatic'''
|A from p'''a'''rasoft, as "P" is taken.
| rowspan="2" |'''xL (2x+y)s'''
|-
| rowspan="2" |'''s-mosenharmonic'''
|u-
|'''xL (3x+y)s'''
|n/a
|'''s-mosschismic'''
|n/a
|'''xL (4x+y)s'''
|U from q'''u'''asisoft, as "Q" is taken.
|'''4th s-mosdescendant'''
|'''xL (5x+y)s'''
|'''5th s-mosdescendant'''
|'''xL (nx+y)s'''
|'''nth s-mosdescendant'''
|-
|-
|m-
|(3x+y)L xs
|M for '''m'''aybe/'''m'''ellow; based on old name for 7L 5s
|r-mosschismic
| rowspan="2" |M- and p-mosenharmonic scales have a grandparent whose step ratio is close to the "'''m'''id'''p'''oint" of L:s = 2:1.
|
| rowspan="2" |M and P for '''m'''id'''p'''oint.
|
|
|
|
|
|-
|-
|p-
| rowspan="2" |(2x+y)L xs
|P for '''p'''ure/shar'''p'''; based on old name for 5L 7s
| rowspan="2" |p-mosenharmonic
| rowspan="4" |PQRS are four consecutive letters in the alphabet. It's '''hard''' to pronounce because there are no vowels.
|(2x+y)L (3x+y)s
P-, q-, r-, and s-mosschismic scales generally have a great-grandparent with a '''hard''' step ratio.
|p-mosschismic
|-
|(2x+y)L (5x+2y)s
|q-
|4th p-mosdescendant
|n/a
|(2x+y)L (7x+3y)s
|n/a
|5th p-mosdescendant
|Q and R are the only two letters between P and S. Q may stand for '''q'''uasihard.
|
|
|-
|-
|r-
|(3x+y)L (2x+y)s
|n/a
|q-mosschismic
|n/a
|
|Q and R are the only two letters between P and S. R may stand for pa'''r'''ahard.
|
|
|
|
|
|-
|-
|s-
| rowspan="4" |(x+y)L xs
|n/a
| rowspan="4" |m-moschromatic
|S for '''s'''harp; s-mosenharmonic scales have a grandparent whose pitches are sharper compared to basic (L:s = 2:1).
| rowspan="2" |'''(x+y)L (2x+y)s'''
|"S" for '''s'''harp.
| rowspan="2" |'''f-mosenharmonic'''
|}
|'''(x+y)L (3x+2y)s'''
 
|'''f-mosschismic'''
=== Examples ===
|'''(x+y)L (4x+3y)s'''
{| class="wikitable"
|'''4th f-mosdescendant'''
|+Names for descendant scales of 5L 2s (diatonic)
|'''(x+y)L (5x+4y)s'''
! colspan="2" |Diatonic scale
|'''5th f-mosdescendant'''
! colspan="2" |Chromatic scales
|'''(x+y)L (nx+(n-1)y)s'''
! colspan="2" |Enharmonic scales
|'''nth f-mosdescendant'''
! colspan="2" |Schismic scales
!4th diatonic descendants
|-
|-
!Steps
|(3x+2y)L (x+y)s
!Name
|a-mosschismic
!Steps
|
!Name
|
!Steps
|
!Name
|
!Steps
|
!Name
|
!Steps
|-
|-
| rowspan="8" |[[5L 2s]]
| rowspan="2" |(2x+y)L (x+y)s
| rowspan="8" |diatonic
| rowspan="2" |m-mosenharmonic
| rowspan="4" |[[7L 5s]]
|(2x+y)L (3x+2y)s
| rowspan="4" |m-chromatic
|m-mosschismic
| rowspan="2" |[[7L 12s]]
|(2x+y)L (5x+3y)s
| rowspan="2" |f-enharmonic
|4th m-mosdescendant
|[[7L 19s]]
|(2x+y)L (7x+4y)s
|f-schismic
|5th m-mosdescendant
|7A 26B
|
|
|-
|-
|[[19L 7s]]
|(3x+2y)L (2x+y)s
|a-schismic
|u-mosschismic
|19A 26B
|
|
|
|
|
|
|}
{| class="wikitable"
|+Mosdescendants sorted by step ratio
!Parent scale
! colspan="2" |Moschromatic scales
(1st mosdescendants)
! colspan="2" |Mosenharmonic scales
(2nd mosdescendants)
! colspan="2" |Mosschismic scales
(3rd mosdescendants)
! colspan="3" |nth-mosdescendant scales
|-
|-
| rowspan="2" |[[12L 7s]]
!Steps
| rowspan="2" |m-enharmonic
!Steps
|[[19L 12s]]
!Specific name
|u-schismic
!Steps
|19A 31B
!Specific name
!Steps
!Specific name
!Steps
!Specific name
!Step ratio of parent
|-
|-
|[[12L 19s]]
| rowspan="10" |xL ys
|m-schismic
| rowspan="5" |(x+y)L xs
|12A 31B
| rowspan="5" |m-moschromatic
| rowspan="3" |(x+y)L (2x+y)s
| rowspan="3" |f-mosenharmonic
| rowspan="2" |(x+y)L (3x+2y)s
| rowspan="2" |f-mosschismic
|(x+y)L (nx+(n-1)y)s
|nth f-mosdescendant
|Softer than 5:4
|-
|-
| rowspan="4" |[[5L 7s]]
| rowspan="8" |
| rowspan="4" |p-chromatic
| rowspan="8" |
| rowspan="2" |[[12L 5s]]
| rowspan="8" |
| rowspan="2" |p-enharmonic
|[[12L 17s]]
|p-schismic
|12A 29B
|-
|-
|[[17L 12s]]
|(3x+2y)L (x+y)s
|q-schismic
|a-mosschismic
|17A 29B
|-
|-
| rowspan="2" |[[5L 12s]]
| rowspan="2" |(2x+y)L (x+y)s
| rowspan="2" |s-enharmonic
| rowspan="2" |m-mosenharmonic
|[[17L 5s]]
|(3x+2y)L (2x+y)s
|r-schismic
|u-mosschismic
|17A 22B
|-
|-
|[[5L 17s]]
|(2x+y)L (3x+2y)s
|s-schismic
|m-mosschismic
|5A 22B
|}
{| class="wikitable"
|+Names for descendant scales for 5L 3s (oneirotonic)
! colspan="2" |Oneirotonic scale
! colspan="2" |Oneirochromatic scales
! colspan="2" |Oneiroenharmonic scales
! colspan="2" |Oneiroschismic scales
!4th oneirodescendants
|-
|-
!Steps
| rowspan="5" |xL (x+y)s
!Name
| rowspan="5" |p-moschromatic
!Steps
| rowspan="2" |(2x+y)L xs
!Name
| rowspan="2" |p-mosenharmonic
!Steps
|(2x+y)L (3x+y)s
!Name
|p-mosschismic
!Steps
!Name
!Steps
|-
|-
| rowspan="8" |[[8L 5s]]
|(3x+y)L (2x+y)s
| rowspan="8" |oneirotonic
|q-mosschismic
| rowspan="4" |[[8L 5s]]
| rowspan="4" |m-oneirochromatic
| rowspan="2" |[[8L 13s]]
| rowspan="2" |f-oneiroenharmonic
|[[8L 21s]]
|f-oneiroschismic
|8A 29B
|-
|-
|[[21L 8s]]
| rowspan="3" |xL (2x+y)s
|a-oneiroschismic
| rowspan="3" |s-mosenharmonic
|21A 29B
|(3x+y)L xs
|r-mosschismic
|-
|-
| rowspan="2" |[[13L 8s]]
| rowspan="2" |xL (3x+y)s
| rowspan="2" |m-oneiroenharmonic
| rowspan="2" |s-mosschismic
|[[21L 13s]]
|u-oneiroschismic
|21A 34B
|-
|-
|[[13L 21s]]
|xL (nx+y)s
|m-oneiroschismic
|nth s-mosdescendant
|13A 34B
|Harder than 5:1
|-
|}
| rowspan="4" |[[5L 8s]]
 
| rowspan="4" |p-oneirochromatic
=== Reasoning for names ===
| rowspan="2" |[[13L 5s]]
The names for moschromatic scales are based on former names for the child scales for diatonic (5L 2s): p-chromatic (5L 7s) and m-chromatic (7L 5s). This was generalized to "chromatic" and "moschromatic", with the prefixes m- and p- for specificity. The names for mosenharmonic scales are based on discussions with xen Discord members for systematically naming the daughter and granddaughter scales of a mos, producing "enharmonic" and "mosenharmonic" with the prefixes f-, m-, p-, and s- for specificity.
| rowspan="2" |p-oneiroenharmonic
 
|[[13L 18s]]
Names for mosdescendants are thereby based on replacing the mos- prefix with that for a mos's TAMNAMS name. This effectively brings back the names of m-chromatic and p-chromatic, as TAMNAMS specifically names mosses up to 10 notes. This also names other mosses whose names were lost entirely, mainly kleistonic (4L 7s, now p-smichromatic) and suprasmitonic (7L 4s, now m-smichromatic), two names that were dropped because these mosses had more than 10 notes.
|p-oneiroschismic
 
|13A 31B
The reason why mosdescendants for mosses with 4 periods or greater are not based on their corresponding n-wood scale is because these mosses do not have any child mosses with 10 notes or fewer, and therefore have no named child mosses from which to build mosdescendant names. Rather, names for these mosdescendants are based on period-agnostic names (antrial, trial, antetric, tetric, etc) to reflect that these are scales based on duplicating a base mos multiple times within an octave.
 
The addition of mosschismic scales for great-grandchild scales was done for completeness, with the prefixes f-, a-, u-, m-, p- q-, r-, and s- for specificity (names not finalized). Note that mosschismic scales borrows the prefixes as mosenharmonic scales, which itself borrows those for mosenharmonic scales. The table below shows what prefixes are used for which generation of mosdescendants, with an added mnemonic for memorization.
{| class="wikitable"
|+Table of mosdescendent prefixes and meanings
!Prefix
!For moschromatic scales
!For mosenharmonic scales
!For mosschismic scales
!Mnemonic
|-
|-
|[[18L 13s]]
|f-
|q-oneiroschismic
|n/a
|18A 31B
|F for '''f'''lat; f-mosenharmonic scales have a grandparent whose pitches are flatter compared to basic (L:s = 2:1).
|F for '''f'''lat.
| rowspan="4" |FAUM sounds like foam, which sounds '''soft'''.
F-, a-, u-, and m-mosschismic scales generally have a great-grandparent with a '''soft''' step ratio.
|-
|-
| rowspan="2" |[[5L 13s]]
|a-
| rowspan="2" |s-oneiroenharmonic
|n/a
|[[18L 5s]]
|n/a
|r-oneiroschismic
|A from p'''a'''rasoft, as "P" is taken.
|18A 23B
|-
|-
|[[5L 18s]]
|u-
|s-oneiroschismic
|n/a
|5A 23B
|n/a
|}
|U from q'''u'''asisoft, as "Q" is taken.
 
|-
=== Notes and issues ===
|m-
* Interestingly, there is evidence that another Xen Discord user ([[user:Flirora]]) suggested the same naming system described here up to 3 generations, with only slight differences with 3rd-generation names. As I was part of a discussion on limiting TAMNAMS names to 10-note mosses, which facilitated naming mosdescendants up to two generations (mosenharmonic scales), rather than this earlier suggestion, it's possible that the same proposal for mosenharmonic scales may have been independently developed twice.
|M for '''m'''aybe/'''m'''ellow; based on old name for 7L 5s
* Some names with this system are not finalized, particularly the term "mosschismic" and some of the single-letter prefixes.
| rowspan="2" |M- and p-mosenharmonic scales have a grandparent whose step ratio is close to the "'''m'''id'''p'''oint" of L:s = 2:1.
** Better names than "mosschismic" include "mossubharmonic" (adapted from the above suggestion which had "prefix-sub-prefix-enharmonic") and "mossubchromatic", possibly shortened to "mossubchromic" (adapted from "subchromatic", as seen in [[Diatonic, Chromatic, Enharmonic, Subchromatic|this page]]).
| rowspan="2" |M and P for '''m'''id'''p'''oint.
** An issue with using letter-based prefixes is that many of them are based on temperaments. A temperament-agnostic interpretation will be needed if these letters are to be generalized outside of the diatonic family.
** Yet another issue is that the pattern of f-, m-, p-, and s-, all based on temperaments, does not continue with 3rd-generation mosses in that f- and s- are no longer at the extremes and p- is no longer at the midpoint (see table below). Either 3rd-generation mosses need a different set of prefixes, or a different set of prefixes are needed throughout.
** In the spirit of TAMNAMS being temperament-agnostic, a proper solution may be to not use and shoehorn temperament-suggestive prefixes, but rather use the names for step ratios. This lines up with Frostburn's proposal, but applies to the first three generations, not just the third. (Frostburn's proposed abbreviations may also work.) Under this system, all prefixes can work for all three generations, so soft-chromatic, hyposoft-chromatic, and minisoft-chromatic is allowed, just as soft-subchromatic, hyposoft-subchromatic, and minisoft-subchromatic. The absence of prefixes is also allowed.
*** Hard and soft are preferred over sharp and flat, as those describe accidentals specific to diatonic notation. TAMNAMS and diamond-mos notation has generalized sharps and flats, called amps/ams and ats.
{| class="wikitable"
! rowspan="2" |Diatonic scale
! colspan="2" |Child scales
! colspan="2" |Grandchild scales
! colspan="3" |Great-grandchild scales
|-
|-
!Steps
|p-
!Notable temperament(s)
|P for '''p'''ure/shar'''p'''; based on old name for 5L 7s
!Steps
| rowspan="4" |PQRS are four consecutive letters in the alphabet. It's '''hard''' to pronounce because there are no vowels.
!Notable temperament(s)
P-, q-, r-, and s-mosschismic scales generally have a great-grandparent with a '''hard''' step ratio.
!Steps
!Notable temperament(s)
!Would-be prefix
|-
|-
| rowspan="8" |[[5L 2s]]
|q-
| rowspan="4" |[[7L 5s]]
|n/a
| rowspan="4" |meantone
|n/a
| rowspan="2" |[[7L 12s]]
|Q and R are the only two letters between P and S. Q may stand for '''q'''uasihard.
| rowspan="2" |flattone
|[[7L 19s]]
|tridecimal
|t-
|-
|-
|[[19L 7s]]
|r-
|'''flattone'''
|n/a
|f-
|n/a
|Q and R are the only two letters between P and S. R may stand for pa'''r'''ahard.
|-
|-
| rowspan="2" |[[12L 7s]]
|s-
| rowspan="2" |meantone
|n/a
|[[19L 12s]]
|S for '''s'''harp; s-mosenharmonic scales have a grandparent whose pitches are sharper compared to basic (L:s = 2:1).
|'''meanpop'''
|"S" for '''s'''harp.
|m-
|}
 
=== Examples ===
{| class="wikitable"
|+Names for descendant scales of 5L 2s (diatonic)
! colspan="2" |Diatonic scale
! colspan="2" |Chromatic scales
! colspan="2" |Enharmonic scales
! colspan="2" |Schismic scales
!4th diatonic descendants
|-
|-
|[[12L 19s]]
!Steps
|huygens
!Name
|h-
!Steps
!Name
!Steps
!Name
!Steps
!Name
!Steps
|-
| rowspan="8" |[[5L 2s]]
| rowspan="8" |diatonic
| rowspan="4" |[[7L 5s]]
| rowspan="4" |m-chromatic
| rowspan="2" |[[7L 12s]]
| rowspan="2" |f-enharmonic
|[[7L 19s]]
|f-schismic
|7A 26B
|-
|[[19L 7s]]
|a-schismic
|19A 26B
|-
| rowspan="2" |[[12L 7s]]
| rowspan="2" |m-enharmonic
|[[19L 12s]]
|u-schismic
|19A 31B
|-
|[[12L 19s]]
|m-schismic
|12A 31B
|-
|-
| rowspan="4" |[[5L 7s]]
| rowspan="4" |[[5L 7s]]
| rowspan="4" |pythagorean
| rowspan="4" |p-chromatic
| rowspan="2" |[[12L 5s]]
| rowspan="2" |[[12L 5s]]
| rowspan="2" |pythagorean
| rowspan="2" |p-enharmonic
|[[12L 17s]]
|[[12L 17s]]
|'''pythagorean'''
|p-schismic
|p-
|12A 29B
|-
|-
|[[17L 12s]]
|[[17L 12s]]
|gentle
|q-schismic
|g-
|17A 29B
|-
|-
| rowspan="2" |[[5L 12s]]
| rowspan="2" |[[5L 12s]]
| rowspan="2" |superpyth
| rowspan="2" |s-enharmonic
|[[17L 5s]]
|[[17L 5s]]
|'''superpyth'''
|r-schismic
|s-
|17A 22B
|-
|-
|[[5L 17s]]
|[[5L 17s]]
|ultrapyth
|s-schismic
|u-
|5A 22B
|}
|}
{| class="wikitable"
{| class="wikitable"
! rowspan="2" |Diatonic scale
|+Names for descendant scales for 5L 3s (oneirotonic)
! colspan="3" |Child scales
! colspan="2" |Oneirotonic scale
! colspan="3" |Grandchild scales
! colspan="2" |Oneirochromatic scales
! colspan="3" |Great-grandchild scales
! colspan="2" |Oneiroenharmonic scales
! colspan="2" |Oneiroschismic scales
!4th oneirodescendants
|-
|-
!Steps
!Steps
!Name based on step ratio
!Name
!Possible abbrev.
!Steps
!Steps
!Name based on step ratio
!Name
!Possible abbrev.
!Steps
!Name
!Steps
!Name
!Steps
!Steps
!Name based on step ratio
!Possible abbrev.
|-
|-
| rowspan="15" |[[5L 2s]]
| rowspan="8" |[[8L 5s]]
| rowspan="7" |[[7L 5s]]
| rowspan="8" |oneirotonic
| rowspan="7" |soft-chromatic
| rowspan="4" |[[8L 5s]]
| rowspan="7" |s-chromatic
| rowspan="4" |m-oneirochromatic
| rowspan="3" |[[7L 12s]]
| rowspan="2" |[[8L 13s]]
| rowspan="3" |soft-enharmonic
| rowspan="2" |f-oneiroenharmonic
| rowspan="3" |s-enharmonic
|[[8L 21s]]
|[[7L 19s]]
|f-oneiroschismic
|ultrasoft-subchromatic
|8A 29B
|us-subchromatic
|-
|-
|26edo
|[[21L 8s]]
|
|a-oneiroschismic
|
|21A 29B
|-
|-
|[[19L 7s]]
| rowspan="2" |[[13L 8s]]
|parasoft-subchromatic
| rowspan="2" |m-oneiroenharmonic
|ps-subchromatic
|[[21L 13s]]
|u-oneiroschismic
|21A 34B
|-
|-
|19edo
|[[13L 21s]]
|
|m-oneiroschismic
|
|13A 34B
|
|
|
|-
|-
| rowspan="3" |[[12L 7s]]
| rowspan="4" |[[5L 8s]]
| rowspan="3" |hyposoft-enharmonic
| rowspan="4" |p-oneirochromatic
| rowspan="3" |hs-enharmonic
| rowspan="2" |[[13L 5s]]
|[[19L 12s]]
| rowspan="2" |p-oneiroenharmonic
|quasisoft-subchromatic
|[[13L 18s]]
|qs-subchromatic
|p-oneiroschismic
|13A 31B
|-
|-
|50edo
|[[18L 13s]]
|
|q-oneiroschismic
|
|18A 31B
|-
|-
|[[12L 19s]]
| rowspan="2" |[[5L 13s]]
|minisoft-subchromatic
| rowspan="2" |s-oneiroenharmonic
|ms-subchromatic
|[[18L 5s]]
|r-oneiroschismic
|18A 23B
|-
|-
|12edo
|[[5L 18s]]
|equalized-chromatic
|s-oneiroschismic
|e-chromatic
|5A 23B
|
|}
|
 
|
=== Notes and issues ===
|
* Interestingly, there is evidence that another Xen Discord user ([[user:Flirora]]) suggested the same naming system described here up to 3 generations, with only slight differences with 3rd-generation names. As I was part of a discussion on limiting TAMNAMS names to 10-note mosses, which facilitated naming mosdescendants up to two generations (mosenharmonic scales), rather than this earlier suggestion, it's possible that the same proposal for mosenharmonic scales may have been independently developed twice.
|
* Some names with this system are not finalized, particularly the term "mosschismic" and some of the single-letter prefixes.
|
** Better names than "mosschismic" include "mossubharmonic" (adapted from the above suggestion which had "prefix-sub-prefix-enharmonic") and "mossubchromatic", possibly shortened to "mossubchromic" (adapted from "subchromatic", as seen in [[Diatonic, Chromatic, Enharmonic, Subchromatic|this page]]).
** An issue with using letter-based prefixes is that many of them are based on temperaments. A temperament-agnostic interpretation will be needed if these letters are to be generalized outside of the diatonic family.
** Yet another issue is that the pattern of f-, m-, p-, and s-, all based on temperaments, does not continue with 3rd-generation mosses in that f- and s- are no longer at the extremes and p- is no longer at the midpoint (see table below). Either 3rd-generation mosses need a different set of prefixes, or a different set of prefixes are needed throughout.
** In the spirit of TAMNAMS being temperament-agnostic, a proper solution may be to not use and shoehorn temperament-suggestive prefixes, but rather use the names for step ratios. This lines up with Frostburn's proposal, but applies to the first three generations, not just the third. (Frostburn's proposed abbreviations may also work.) Under this system, all prefixes can work for all three generations, so soft-chromatic, hyposoft-chromatic, and minisoft-chromatic is allowed, just as soft-subchromatic, hyposoft-subchromatic, and minisoft-subchromatic. The absence of prefixes is also allowed.
*** Hard and soft are preferred over sharp and flat, as those describe accidentals specific to diatonic notation. TAMNAMS and diamond-mos notation has generalized sharps and flats, called amps/ams and ats.
{| class="wikitable"
! rowspan="2" |Diatonic scale
! colspan="2" |Child scales
! colspan="2" |Grandchild scales
! colspan="3" |Great-grandchild scales
|-
|-
| rowspan="7" |[[5L 7s]]
!Steps
| rowspan="7" |hard-chromatic
!Notable temperament(s)
| rowspan="7" |h-chromatic
!Steps
| rowspan="3" |[[12L 5s]]
!Notable temperament(s)
| rowspan="3" |hypohard-enharmonic
!Steps
| rowspan="3" |hh-enharmonic
!Notable temperament(s)
|[[12L 17s]]
!Would-be prefix
|minihard-subchromatic
|mh-subchromatic
|-
|-
|31edo
| rowspan="8" |[[5L 2s]]
|
| rowspan="4" |[[7L 5s]]
|
| rowspan="4" |meantone
| rowspan="2" |[[7L 12s]]
| rowspan="2" |flattone
|[[7L 19s]]
|tridecimal
|t-
|-
|-
|[[17L 12s]]
|[[19L 7s]]
|quasihard-subchromatic
|'''flattone'''
|qh-subchromatic
|f-
|-
|-
|17edo
| rowspan="2" |[[12L 7s]]
|
| rowspan="2" |meantone
|
|[[19L 12s]]
|
|'''meanpop'''
|
|m-
|
|-
|[[12L 19s]]
|huygens
|h-
|-
|-
| rowspan="3" |[[5L 12s]]
| rowspan="4" |[[5L 7s]]
| rowspan="3" |hard-enharmonic
| rowspan="4" |pythagorean
| rowspan="3" |h-enharonic
| rowspan="2" |[[12L 5s]]
|[[17L 5s]]
| rowspan="2" |pythagorean
|parahard-subchromatic
|[[12L 17s]]
|ph-subchromatic
|'''pythagorean'''
|p-
|-
|-
|39edo
|[[17L 12s]]
|
|gentle
|
|g-
|-
|-
|[[5L 17s]]
| rowspan="2" |[[5L 12s]]
|ultrahard-subchromatic
| rowspan="2" |superpyth
|uh-subchromatic
|[[17L 5s]]
|'''superpyth'''
|s-
|-
|[[5L 17s]]
|ultrapyth
|u-
|}
|}
== Proposal: Naming mos modes ==
=== Current proposal, with proposed amendment for emphasis on dark generator ===
There is currently a proposed system for naming mos modes as follows: '''xL ys u|''', where x is the number of large steps, y is the number of small steps, u corresponds to the the mode's UDP (the u in u|d), and | is pronounced as "pipe". As an example, the modes of 4L 1s (manual) can be named as the following:
{| class="wikitable"
{| class="wikitable"
|+Modes of manual (4L 1s)
! rowspan="2" |Diatonic scale
!Mode
! colspan="3" |Child scales
!UDP
! colspan="3" |Grandchild scales
!TAMNAMS name
! colspan="3" |Great-grandchild scales
|-
|-
|LLLLs
!Steps
|<nowiki>4|0</nowiki>
!Name based on step ratio
|<nowiki>4L 1s 4|</nowiki>
!Possible abbrev.
!Steps
!Name based on step ratio
!Possible abbrev.
!Steps
!Name based on step ratio
!Possible abbrev.
|-
|-
|LLLsL
| rowspan="15" |[[5L 2s]]
|<nowiki>3|1</nowiki>
| rowspan="7" |[[7L 5s]]
|<nowiki>4L 1s 3|</nowiki>
| rowspan="7" |soft-chromatic
| rowspan="7" |s-chromatic
| rowspan="3" |[[7L 12s]]
| rowspan="3" |soft-enharmonic
| rowspan="3" |s-enharmonic
|[[7L 19s]]
|ultrasoft-subchromatic
|us-subchromatic
|-
|-
|LLsLL
|26edo
|<nowiki>2|2</nowiki>
|
|<nowiki>4L 1s 2|</nowiki>
|
|-
|-
|LsLLL
|[[19L 7s]]
|<nowiki>1|3</nowiki>
|parasoft-subchromatic
|<nowiki>4L 1s 1|</nowiki>
|ps-subchromatic
|-
|-
|sLLLL
|19edo
|<nowiki>0|4</nowiki>
|
|<nowiki>4L 1s 0|</nowiki>
|
|}
|
In situations where it's more intuitive to think in terms of the dark generator instead of the bright generator, the format is instead '''xL ys |d''', where d corresponds to the mode's UDP (the d in u|d). An example of this can be seen in the classic pentatonic scale (2L 3s), where even though the bright generator corresponds to diatonic's perfect 4th (which is actually diatonic's dark generator), it's common to think of these modes in terms of diatonic's bright generator (even though it's the dark generator of 2L 3s). This is because the bright and dark generators "flip" between 2L 3s to 5L 2s. (In general, generators flip when a mos xL ys has a child of (x+y)L xs, but don't flip if the child is xL (x+y)s, and in general, looking at modes in terms of the dark generator reverses the order of modes compared with the bright generator.)
|
{| class="wikitable"
|
|+Modes of pentic (2L 3s)
!Mode
!UDP
!TAMNAMS name
|-
|-
|sLsLL
| rowspan="3" |[[12L 7s]]
|<nowiki>0|4</nowiki>
| rowspan="3" |hyposoft-enharmonic
|<nowiki>2L 3s |4</nowiki>
| rowspan="3" |hs-enharmonic
|[[19L 12s]]
|quasisoft-subchromatic
|qs-subchromatic
|-
|-
|sLLsL
|50edo
|<nowiki>1|3</nowiki>
|
|<nowiki>2L 3s |3</nowiki>
|
|-
|-
|LsLsL
|[[12L 19s]]
|<nowiki>2|2</nowiki>
|minisoft-subchromatic
|<nowiki>2L 3s |2</nowiki>
|ms-subchromatic
|-
|-
|LsLLs
|12edo
|<nowiki>3|1</nowiki>
|equalized-chromatic
|<nowiki>2L 3s |1</nowiki>
|e-chromatic
|
|
|
|
|
|
|-
|-
|LLsLs
| rowspan="7" |[[5L 7s]]
|<nowiki>4|0</nowiki>
| rowspan="7" |hard-chromatic
|<nowiki>2L 3s |0</nowiki>
| rowspan="7" |h-chromatic
|}
| rowspan="3" |[[12L 5s]]
 
| rowspan="3" |hypohard-enharmonic
=== Mode names based on mosnames ===
| rowspan="3" |hh-enharmonic
If a more memorable name is desired but there are no assigned names for the mos's modes, interim 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. Note that these names can only be made if there is a TAMNAMS name for a mos. Excluding current proposals to extend TAMNAMS names beyond the 10-note limit, this means most mos mode names will typically be formatted as '''xL ys u|'''.
|[[12L 17s]]
{| class="wikitable"
|minihard-subchromatic
|+Modes of pine (7L 1s)
|mh-subchromatic
!Mode
|-
!UDP
|31edo
!Mode name
|
|
|-
|[[17L 12s]]
|quasihard-subchromatic
|qh-subchromatic
|-
|17edo
|
|
|
|
|
|-
|-
|LLLLLLLs
| rowspan="3" |[[5L 12s]]
|<nowiki>7|0</nowiki>
| rowspan="3" |hard-enharmonic
|1st pine
| rowspan="3" |h-enharonic
|[[17L 5s]]
|parahard-subchromatic
|ph-subchromatic
|-
|-
|LLLLLLsL
|39edo
|<nowiki>6|1</nowiki>
|
|2nd pine
|
|-
|-
|LLLLLsLL
|[[5L 17s]]
|<nowiki>5|2</nowiki>
|ultrahard-subchromatic
|3rd pine
|uh-subchromatic
|-
|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
|}
{| class="wikitable"
|+Modes of tcherepnin (3L 6s)
!Mode
!UDP
!Mode name
|-
|LssLssLss
|<nowiki>6|0(3)</nowiki>
|1st tcherepnin
|-
|sLssLssLs
|<nowiki>3|3(3)</nowiki>
|2nd tcherepnin
|-
|ssLssLssL
|<nowiki>0|6(3)</nowiki>
|3rd tcherepnin
|}
|}
== Suggested changes for mos pattern names (work-in-progress) ==
== Suggested changes for mos pattern names (work-in-progress) ==
This section describes changes to existing [[TAMNAMS]] names that I would make. Reasons:
This section describes changes to existing [[TAMNAMS]] names that I would make. Reasons:
Retrieved from "https://en.xen.wiki/w/User:Ganaram_inukshuk/Notes/TAMNAMS"