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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".
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".


==== Mos names based on a temperament ====
==== Names based on a temperament ====
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.
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.


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".
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".


==== Inclusion of 1L ns mosses ====
==== Names for 1L ns mosses ====
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. A great example of this is 1L 6s and 7L 1s, a pair of mosses that correspond with porcupine temperament.
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.


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.
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.


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 (and for consistency with that their parent MOSS, 4L2s, is named citric).
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).


==== Mos names with the anti- or an- prefix ====
==== 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 also 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.
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.


==== The 10-note limit ====
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.
TAMNAMS only names mosses up to 10 notes. As a result, the names of mosses with 11 and 12 notes were abandoned, such as kleistonic, suprasmitonic, m-chromatic, and p-chromatic.
 
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 ==
== Step ratio spectrum visualization ==

Revision as of 01:53, 29 November 2022

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

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.

Names for small mosses

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.

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.

Names for multi-period 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".

Names based on a temperament

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.

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".

Names for 1L ns mosses

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.

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.

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).

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

Central spectrum of step ratios
Intermediate ranges Specific step ratios Notes
1:1 (equalized) Trivial/pathological
1:1 to 1:0 1:1 to 2:1 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)
4:3 to 3:2 (parasoft)
3:2 (soft) Also called monosoft
3:2 to 2:1 (hyposoft) 3:2 to 5:3 (quasisoft)
5:3 (semisoft)
5:3 to 2:1 (minisoft)
2:1 (basic) Also called quintessential
2:1 to 1:0 2:1 to 3:1 (hypohard) 2:1 to 5:2 (minihard)
5:2 (semihard)
5:2 to 3:1 (quasihard)
3:1 (hard) Also called monohard
3:1 to 1:0 3:1 to 4:1 (parahard)
4:1 (superhard)
4:1 to 1:0 (ultrahard) Step ratios especially close to 1:0 may be called pseudocollapsed
1:0 (collapsed) Trivial/pathological

Extended spectrum

Extended spectrum of step ratios
Central ranges Extended ranges Specific step ratios Notes
1:1 (equalized)
1:1 to 1:0 1:1 to 2:1 1:1 to 3:2 1:1 to 4:3 (ultrasoft) 1:1 to 6:5 (pseudoequalized)
6:5 (semiequalized)
6:5 to 4:3 (ultrasoft)
4:3 (supersoft) Nonextreme range, as detailed by central spectrum
4:3 to 3:2 (parasoft) 4:3 to 3:2 (parasoft)
3:2 (soft)
3:2 to 2:1 (hyposoft) 3:2 to 5:3 (quasisoft) 3:2 to 5:3 (quasisoft)
5:3 (semisoft)
5:3 to 2:1 (minisoft) 5:3 to 2:1 (minisoft)
2:1 (basic)
2:1 to 1:0 2:1 to 3:1 (hypohard) 2:1 to 5:2 (minihard) 2:1 to 5:2 (minihard)
5:2 (semihard)
5:2 to 3:1 (quasihard) 5:2 to 3:1 (quasihard)
3:1 (hard)
3:1 to 1:0 3:1 to 4:1 (parahard) 3:1 to 4:1 (parahard)
4:1 (superhard)
4:1 to 1:0 (ultrahard) 4:1 to 10:1 (ultrahard) 4:1 to 6:1 (hyperhard)
6:1 (extrahard)
6:1 to 10:1 (clustered)
10:1 (pseudocollapsed)
10:1 to 1:0 (pseudocollapsed)
1:0 (collapsed)

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 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.

Mos Family Tree (single-period only), with TAMNAMS Names and extended names
Progenitor scale 1st-order child mosses 2nd-order child mosses 3rd-order child mosses 4th-order child mosses 5th-order child mosses
Steps Scale name Steps Scale name Steps Scale name Steps Scale name Steps Scale name Steps Scale name
1L 1s prototonic*

(currently monowood and trivial)

1L 2s antideuteric*

(currently antrial)

1L 3s antitetric*

(currently antetric)

1L 4s antimanic

(currently pedal)

1L 5s antimachinoid*

(currently antimachinoid)

1L 6s anti-archeotonic

(currently onyx)

6L 1s archeotonic
5L 1s machinoid 5L 6s
6L 5s
4L 1s manual

(formerly manic)

4L 5s gramitonic

(formerly orwelloid)

4L 9s
9L 4s
5L 4s semiquartal 5L 9s
9L 5s
3L 1s tetric 3L 4s mosh 3L 7s sephiroid 3L 10s
10L 3s
7L 3s dicoid

(formerly dicotonic)

7L 10s
10L 7s
4L 3s smitonic 4L 7s (formerly kleistonic) 4L 11s
11L 4s
7L 4s (formerly suprasmitonic) 7L 11s
11L 7s
2L 1s deuteric*

(currently trial)

2L 3s pentic 2L 5s antidiatonic 2L 7s balzano

(formerly joanatonic)

2L 9s
9L 2s
7L 2s superdiatonic 7L 9s
9L 7s
5L 2s diatonic 5L 7s (formerly p-chromatic) 5L 12s s-enharmonic*
12L 5s p-enharmonic*
7L 5s (formerly m-chromatic) 7L 12s f-enharmonic*
12L 7s m-enharmonic*
3L 2s antipentic 3L 5s checkertonic

(formerly sensoid)

3L 8s 3L 11s
11L 3s
8L 3s 8L 11s
11L 8s
5L 3s oneirotonic 5L 8s 5L 13s
13L 5s
8L 5s 8L 13s
13L 8

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.

Parent scale 1st-order child scales 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
1L 1s prototonic, protic, or monowood monowood and trivial 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.

1L 2s antideuterotonic or antideuteric antrial One of the child scales of 1L 1s.

Being a monolarge scale, tetric (3L 1s) may be more worth considering as a parent scale.

1L 3s antitetric antetric Monolarge scale. Similarly to 3L 1s with 1L 2s, 4L 1s may be worth considering as a parent scale.
3L 1s tetric tetric Parent scale to orwelloid (now gramitonic) and semiquartal, the name tetric is assigned similarly to pentic being the parent of diatonic and antidiatonic.
2L 1s deuterotonic or deuteric trial One of the child scales of 1L 1s. 2L 3s - pentic Already established name.
3L 2s - antipentic Already established name.

Proposal: Naming mosses with more than 10 steps

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.

Notes:

  • 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 suggestion described above) and "mossubchromatic", possibly shortened to "mossubchromic" (adapted from "subchromatic", as suggested in this page).
    • Another issue with the single-letter prefixes described here is that they are technically based off of a temperament. A temperament-agnostic interpretation will be needed if these letters are to be generalized outside of the diatonic family.

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; 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.

Mosdescendant scales sorted by step ratio
Parent scale Moschromatic (child) scales Mosenharmonic (grandchild) scales Mosschismic (great-grandchild) scales
Steps Step ratio Steps Specific name Step ratio of parent Steps Specific name Step ratio of grandparent Steps Specific name 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
xL ys 1:1 to 1:0 2:1 (basic) (x+y)L xs m-moschromatic 1:1 to 2:1 3:2 (soft) (x+y)L (2x+y)s f-mosenharmonic 1:1 to 3:2 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
(2x+y)L (x+y)s m-mosenharmonic 3:2 to 2:1 (hyposoft) 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
xL (x+y)s p-moschromatic 2:1 to 1:0 3:1 (hard) (2x+y)L xs p-mosenharmonic 2:1 to 3:1 (hypohard) 5:2 (semihard) (2x+y)L (3x+y)s p-mosschismic 2:1 to 5:2 (minihard) 7:3
(3x+y)L (2x+y)s q-mosschismic 5:2 to 3:1 (quasihard) 8:3
xL (2x+y)s s-mosenharmonic 3:1 to 1:0 4:1 (superhard) (3x+y)L xs r-mosschismic 3:1 to 4:1 (parahard) 7:2
xL (3x+y)s s-mosschismic 4:1 to 1:0 (ultrahard) 5:1
Simplified table, without step ratios, sorted by position on mos family tree
Parent scale Moschromatic scales Mosenharmonic scales Mosschismic scales
Steps Steps Specific name Steps Specific name Steps Specific name
xL ys xL (x+y)s p-moschromatic xL (2x+y)s s-mosenharmonic xL (3x+y)s s-mosschismic
(3x+y)L xs r-mosschismic
(2x+y)L xs p-mosenharmonic (2x+y)L (3x+y)s p-mosschismic
(3x+y)L (2x+y)s q-mosschismic
(x+y)L xs m-moschromatic (x+y)L (2x+y)s f-mosenharmonic (x+y)L (3x+2y)s f-mosschismic
(3x+2y)L (x+y)s a-mosschismic
(2x+y)L (x+y)s m-mosenharmonic (2x+y)L (3x+2y)s m-mosschismic
(3x+2y)L (2x+y)s u-mosschismic

Mosdescendants for single-period mosses

Although it's possible for any mos to have mosdescendants named as described above, for neatness, mosdescendant scale names should apply only to mosses whose immediate child mosses exceed 10 steps. The following tables show which mosses, marked in bold, mosdescendant names can apply.

Single-period mosses for which mosdescendant names apply
Mos Name Mos Name Mos Name Mos Name Mos Name Mos Name Mos Name Mos Name Mos Name
1L 1s trivial 1L 2s antrial 1L 3s antetric 1L 4s pedal 1L 5s antimachinoid 1L 6s onyx 1L 7s antipine 1L 8s antisubneutralic 1L 9s antisinatonic (asina-)
9L 1s sinatonic (sina-)
8L 1s subneutralic (blu-)
7L 1s pine (pine-)
6L 1s arch(a)eotonic (arch-)
5L 1s machinoid (mech-)
4L 1s manual 5L 4s semiquartal (chton-)
4L 5s gramitonic (gram-)
3L 1s tetric 4L 3s smitonic (smi-)
3L 4s mosh 7L 3s dicoid/zaltertic (dico-/zal-)
3L 7s sephiroid (seph-)
2L 1s trial 3L 2s antipentic 3L 5s checkertonic (check-)
5L 3s oneirotonic (oneiro-)
2L 3s pentic 5L 2s diatonic (no prefix)
2L 5s antidiatonic 7L 2s superdiatonic (arm-)
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.

2 and 3-period mosses for which mosdescendant names apply
2-period mosses
Mos Name Mos Name Mos Name Mos Name
2L 2s biwood 2L 4s malic 2L 6s subaric 2L 8s jaric (jara-)
8L 2s taric (tara-)
6L 2s ekic (ek-)
4L 2s citric 6L 4s lemon (lem-)
4L 6s lime (lime-)
3-period mosses
Mos Name Mos Name
3L 3s triwood 3L 6s tcherepnin (cher-)
6L 3s 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.

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.

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-.

Possible mosdescendant names for mosses with 4 periods or more
4-period mosses
Mos Name Mos Name Mos Name Mos Name Other notes
4L 4s tetrawood 4L 8s quadantrial 4L 12s quadantetric 4L 16s tetrapedal Some names have Latin prefixes for ease of spelling.
16L 4s tetramanual
12L 4s quadtetric
8L 4s quadtrial 12L 8s tetrantipentic
8L 12s tetrapentic
5-period mosses
Mos Name Mos Name Mos Name Mos Name Other notes
5L 5s pentawood 5L 10s quinantrial 5L 15s quinantetric 5L 20s pentapedal Some names have Latin prefixes for ease of spelling.
20L 5s pentamanual
15L 5s quintetric
10L 5s quintrial 15L 10s quinantipentic
10L 15s quinpentic
n-period mosses
Mos Name Mos Name Mos Name Mos Name Other notes
nL ns n-wood nL 2ns n-antrial nL 3ns n-antetric nL 4ns n-pedal 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 n-manual
3nL ns n-tetric
2nL ns n-trial 3nL 2ns n-anpentic
2nL 3ns n-pentic

Naming mosdescendants beyond 3 generations

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:
    1. 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.
    2. Let m1 be equal to max(z, w) and m2 be equal to min(z, w).
    3. Assign to z the value m2 and w the value m1-m2. Increment g by 1.
    4. 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:
    1. 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.
    2. Let m1 be equal to max(z, w) and m2 be equal to min(z, w).
    3. Assign to z the value m2 and w the value m1-m2. Increment g by 1.
    4. 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.

Mosdescendants sorted by position on the mos family tree
Parent scale Moschromatic scales

(1st mosdescendants)

Mosenharmonic scales

(2nd mosdescendants)

Mosschismic scales

(3rd mosdescendants)

4th-mosdescendant scales

(selected mosdescendants)

5th-mosdescendant scales

(selected mosdescendants)

nth-mosdescendant scales

(selected mosdescendants)

Steps Steps Specific name Steps Specific name Steps Specific name Steps Specific name Steps Specific name Steps Specific name
xL ys xL (x+y)s p-moschromatic xL (2x+y)s s-mosenharmonic xL (3x+y)s s-mosschismic xL (4x+y)s 4th s-mosdescendant xL (5x+y)s 5th s-mosdescendant xL (nx+y)s nth s-mosdescendant
(3x+y)L xs r-mosschismic
(2x+y)L xs p-mosenharmonic (2x+y)L (3x+y)s p-mosschismic (2x+y)L (5x+2y)s 4th p-mosdescendant (2x+y)L (7x+3y)s 5th p-mosdescendant
(3x+y)L (2x+y)s q-mosschismic
(x+y)L xs m-moschromatic (x+y)L (2x+y)s 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 a-mosschismic
(2x+y)L (x+y)s m-mosenharmonic (2x+y)L (3x+2y)s m-mosschismic (2x+y)L (5x+3y)s 4th m-mosdescendant (2x+y)L (7x+4y)s 5th m-mosdescendant
(3x+2y)L (2x+y)s u-mosschismic
Mosdescendants sorted by step ratio
Parent scale Moschromatic scales

(1st mosdescendants)

Mosenharmonic scales

(2nd mosdescendants)

Mosschismic scales

(3rd mosdescendants)

nth-mosdescendant scales
Steps Steps Specific name Steps Specific name Steps Specific name Steps Specific name Step ratio of parent
xL ys (x+y)L xs m-moschromatic (x+y)L (2x+y)s f-mosenharmonic (x+y)L (3x+2y)s f-mosschismic (x+y)L (nx+(n-1)y)s nth f-mosdescendant Softer than 5:4
(3x+2y)L (x+y)s a-mosschismic
(2x+y)L (x+y)s m-mosenharmonic (3x+2y)L (2x+y)s u-mosschismic
(2x+y)L (3x+2y)s m-mosschismic
xL (x+y)s p-moschromatic (2x+y)L xs p-mosenharmonic (2x+y)L (3x+y)s p-mosschismic
(3x+y)L (2x+y)s q-mosschismic
xL (2x+y)s s-mosenharmonic (3x+y)L xs r-mosschismic
xL (3x+y)s s-mosschismic
xL (nx+y)s nth s-mosdescendant Harder than 5:1

Reasoning for names

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.

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.

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.

Table of mosdescendent prefixes and meanings
Prefix For moschromatic scales For mosenharmonic scales For mosschismic scales Mnemonic
f- n/a F for flat; f-mosenharmonic scales have a grandparent whose pitches are flatter compared to basic (L:s = 2:1). F for flat. FAUM sounds like foam, which sounds soft.

F-, a-, u-, and m-mosschismic scales generally have a great-grandparent with a soft step ratio.

a- n/a n/a A from parasoft, as "P" is taken.
u- n/a n/a U from quasisoft, as "Q" is taken.
m- M for maybe/mellow; based on old name for 7L 5s M- and p-mosenharmonic scales have a grandparent whose step ratio is close to the "midpoint" of L:s = 2:1. M and P for midpoint.
p- P for pure/sharp; based on old name for 5L 7s PQRS are four consecutive letters in the alphabet. It's hard to pronounce because there are no vowels.

P-, q-, r-, and s-mosschismic scales generally have a great-grandparent with a hard step ratio.

q- n/a n/a Q and R are the only two letters between P and S. Q may stand for quasihard.
r- n/a n/a Q and R are the only two letters between P and S. R may stand for parahard.
s- n/a S for sharp; s-mosenharmonic scales have a grandparent whose pitches are sharper compared to basic (L:s = 2:1). "S" for sharp.

Examples

Names for descendant scales of 5L 2s (diatonic)
Diatonic scale Chromatic scales Enharmonic scales Schismic scales 4th diatonic descendants
Steps Name Steps Name Steps Name Steps Name Steps
5L 2s diatonic 7L 5s m-chromatic 7L 12s f-enharmonic 7L 19s f-schismic 7A 26B
19L 7s a-schismic 19A 26B
12L 7s m-enharmonic 19L 12s u-schismic 19A 31B
12L 19s m-schismic 12A 31B
5L 7s p-chromatic 12L 5s p-enharmonic 12L 17s p-schismic 12A 29B
17L 12s q-schismic 17A 29B
5L 12s s-enharmonic 17L 5s r-schismic 17A 22B
5L 17s s-schismic 5A 22B
Names for descendant scales for 5L 3s (oneirotonic)
Oneirotonic scale Oneirochromatic scales Oneiroenharmonic scales Oneiroschismic scales 4th oneirodescendants
Steps Name Steps Name Steps Name Steps Name Steps
8L 5s oneirotonic 8L 5s m-oneirochromatic 8L 13s f-oneiroenharmonic 8L 21s f-oneiroschismic 8A 29B
21L 8s a-oneiroschismic 21A 29B
13L 8s m-oneiroenharmonic 21L 13s u-oneiroschismic 21A 34B
13L 21s m-oneiroschismic 13A 34B
5L 8s p-oneirochromatic 13L 5s p-oneiroenharmonic 13L 18s p-oneiroschismic 13A 31B
18L 13s q-oneiroschismic 18A 31B
5L 13s s-oneiroenharmonic 18L 5s r-oneiroschismic 18A 23B
5L 18s s-oneiroschismic 5A 23B

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:

Modes of manual (4L 1s)
Mode UDP TAMNAMS name
LLLLs 4|0 4L 1s 4|
LLLsL 3|1 4L 1s 3|
LLsLL 2|2 4L 1s 2|
LsLLL 1|3 4L 1s 1|
sLLLL 0|4 4L 1s 0|

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.)

Modes of pentic (2L 3s)
Mode UDP TAMNAMS name
sLsLL 0|4 2L 3s |4
sLLsL 1|3 2L 3s |3
LsLsL 2|2 2L 3s |2
LsLLs 3|1 2L 3s |1
LLsLs 4|0 2L 3s |0

Mode names based on mosnames

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|.

Modes of pine (7L 1s)
Mode UDP Mode name
LLLLLLLs 7|0 1st pine
LLLLLLsL 6|1 2nd pine
LLLLLsLL 5|2 3rd pine
LLLLsLLL 4|3 4th pine
LLLsLLLL 3|4 5th pine
LLsLLLLL 2|5 6th pine
LsLLLLLL 1|6 7th pine
sLLLLLLL 0|7 8th pine
Modes of tcherepnin (3L 6s)
Mode UDP Mode name
LssLssLss 6|0(3) 1st tcherepnin
sLssLssLs 3|3(3) 2nd tcherepnin
ssLssLssL 0|6(3) 3rd tcherepnin

Suggested changes for mos pattern names (work-in-progress)

This section describes changes to existing TAMNAMS names that I would make. Reasons:

  • Some names are still based on a temperament (mainly the -oid names), so those are either replaced with a new name or at least altered so the references are more indirect.
  • There were Discord users with whom I shared a similar sentiment regarding the names of certain scales, mainly the mosses with the anti- prefix and the scales antidiatonic and superdiatonic.
  • Some names are too long (in my opinion).

The choice of names are not perfect and some may have issues. Some names have multiple suggestions. This section is meant to start a discussion on alternate names.

Table of proposed namechanges
Changes to names to reduce or remove references to temperaments
Mos Current name Suggested name(s) Reasoning Possible issues
Name Prefix Abbrev. Name Prefix Abbrev.
5L 1s machinoid mech- mech mechatonic unchagned unchagned A more indirect reference to machine temperament. Still references machine temperament. May also reference mechanism temperament.
3L 7s sephiroid seph- seph sephirotonic or sephiratonic unchagned unchagned Rather than alluding to sephiroth temperament, the name should allude to Peter Kosmorsky's Tractatum de Modi Sephiratorum (A Treatise on the Modes of the Sephirates), whose name ultimately comes from the sefirot. The document describes several edos that are said to contain the "modi sephiratorum" (sephirate modes). Therefore, instead of the name "sephiroid", suggesting that the mos pattern resembles the modi sephiratorum, the mos pattern is the modi sephiratorum, hence the mosname "sephirotonic". May still reference sephiroth temperament. For a more indirect reference, an alternate transliteration of סְפִירוֹת (sefirot) may be used instead.

New name is longer than the old name.

7L 3s dicoid and zaltertic dico- and zal- dico and zal zaltertic zal- zal As of writing, there are two names. I would favor zaltertic over dicoid in that it removes a name that suggests a temperament. Central zalzalian thirds (another name for neutral thirds) are not the scale's bright generator, but are produced by the scale.
Changes to names that bear the anti- prefix
Mos Current name Suggested name(s) Reasoning Possible issues
Name Prefix Abbrev. Name Prefix Abbrev.
1L 5s antimachinoid amech- amech selenic sel- sel An indirect reference to luna temperament; "selene" is Greek for "moon".
1L 7s antipine apine- apine alpine alp- or unchanged alp or unchanged Looks like "anpine" (a shortened form of "antipine", following the logic of the "an-" prefix), but accidentally corrected into "alpine". Somewhat preserves meaning of the anti-/an- prefix. Pun. Too minor of a modification.
1L 8s antisubneutralic ablu- ablu mineric /mɪnˈeɹɪk/ mine- (with a silent e) minc A portmanteau of miracle and negri temperaments. Shorter name. This drops the anti- prefix. References two different temperaments.
1L 9s antisinatonic asina- asi parivalic par- pariv A portmanteau of passion, ripple, and valentine. Shorter name. References three different temperaments.
Changes to names that bear other prefixes
Mos Current name Suggested name(s) Reasoning Possible issues
Name Prefix Abbrev. Name Prefix Abbrev.
2L 5s antidiatonic pel- pel pelotonic unchagned unchagned From "pelog" and "armodue". The proposed names are to make both scales more distinct from diatonic. These names must be changed together. The connection to diatonic may be beneficial to some musicians. Additionally, the mode names commonly used for both mosses are those from diatonic (lydian, ionian, etc) with the anti- and super- prefixes added.

New names reference pelog tuning and armodue theory.

7L 2s superdiatonic arm- arm armotonic unchagned unchagned
8L 1s subneutralic blu- blu azurtonic azu- or unchanged azu or unchanged An indirect reference to bleu temperament; azure is a specific shade of blue. Simplified name. Also, the sub- prefix may falsely suggest another scale called "(prefix)neutralic", similar to how subaric (2L 6s) is the parent to both jaric (2L 8s) and taric (8L 2s). New name is referencing a temperament, albeit indirectly. The sub- prefix reasoning may be a stretch, since subaric, jaric, and taric are the only mosses related this way.
2L 6s subaric subar- subar baric bar- bar Rhymes perfectly with jaric and taric. May also mean "basic -aric", as this mos with a basic step ratio (L:s=2:1) cannot produce jaric or taric. Too minor of a modification. The use of "bar" as a mosprefix or mosabbreviation may be problematic ("bar" may also mean "measure" in sheet music).

Other aesthetic name changes (work-in-progress)

These are additional changes that I feel are less likely to be implemented, but made to convey additional meaning through a name's suffixes; if anything, these changes are merely for the aesthetic. These changes are built upon proposed name changes from the previous section.

Rules for mos names (single-period only)
Rule Names affected Exceptions
All mosses with 5 steps or fewer end with -al.
  • antetric -> antetral
  • tetric -> tetral
  • monowood (referring to 1L 1s with an octave period)
  • pentic and antipentic (pentic is a shortened form of "pentatonic")
All other mosses not of the form 1L ns end with -toinc, excluding those named under the previous rule.
  • machinoid -> mechatonic
  • antidiatonic and superdiatonic -> pelotonic and armotonic
  • sephiroid -> sephirotonic
  • subneutralic -> azurtonic
 The following names are too memorable to change:
  • mosh
  • semiquartal
  • zaltertic
  • balzano
  • pine
All mosses of the form 1L ns mosses end with -ic, excluding those named under the previous rule.
  • antimachinoid -> selenic
  • antipne -> alpine
  • antisubneutralic -> mineric
  • antisinatonic -> parivalic
  • onyx (almost sounds like on-ic)
  • alpine
Table of (single-period) mosses with all proposed name changes
Mos Name Mos Name Mos Name Mos Name Mos Name Mos Name Mos Name Mos Name Mos Name
1L 1s trivial 1L 2s antrial 1L 3s antetral 1L 4s pedal 1L 5s selenic 1L 6s onyx 1L 7s alpine 1L 8s mineric 1L 9s parivalic
9L 1s sinatonic
8L 1s azurtonic
7L 1s pine
6L 1s arch(a)eotonic
5L 1s mechatonic
4L 1s manual 5L 4s semiquartal
4L 5s gramitonic
3L 1s tetral 4L 3s smitonic
3L 4s mosh 7L 3s zaltertic
3L 7s sephirotonic
2L 1s trial 3L 2s antipentic 3L 5s checkertonic
5L 3s oneirotonic
2L 3s pentic 5L 2s diatonic
2L 5s pelotonic 7L 2s armotonic
2L 7s balzano
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