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{{User:Ganaram inukshuk/Template:Rewrite draft|TAMNAMS|compare=https://en.xen.wiki/w/Special:ComparePages?page1=TAMNAMS&rev1=&page2=User%3AGanaram+inukshuk%2FTAMNAMS&rev2=&action=&diffonly=&unhide=|changes=* Base TAMNAMS applies to mosses with 6-10 notes.
{{User:Ganaram inukshuk/Template:Rewrite draft|TAMNAMS|compare=https://en.xen.wiki/w/Special:ComparePages?page1=TAMNAMS&rev1=&page2=User%3AGanaram+inukshuk%2FTAMNAMS&rev2=&action=&diffonly=&unhide=|changes=* Base TAMNAMS applies to mosses with 6-10 notes.
* Extension/generalizations are moved to (sub)pages.
* Simplify A LOT of wording!}}'''TAMNAMS''' (read "tame names"; from '''''T'''emperament-'''A'''gnostic '''M'''os '''NAM'''ing '''S'''ystem''), devised by the XA Discord in 2021, is a system of temperament-agnostic names for scales – primarily [[Octave equivalence|octave-equivalent]] [[moment of symmetry]] scales – as well as their their intervals, their associated generator ranges, and the ratios describing the proportions of large and small steps.
* Simplify A LOT of wording!}}'''TAMNAMS''' (read "tame names"; from '''''T'''emperament-'''A'''gnostic '''M'''os '''NAM'''ing '''S'''ystem''), devised by the XA Discord in 2021, is a system of temperament-agnostic names for scales – primarily [[Octave equivalence|octave-equivalent]] [[moment of symmetry]] scales – as well as their their intervals, their associated generator ranges, and the ratios describing the proportions of large and small steps.


The goal of TAMNAMS is to allow musicians and theorists to discuss moment-of-symmetry scales, or mosses, independent of the language of [[regular temperament theory]]. For example, the names ''flattone[7]'', ''meantone[7]'', ''pythagorean[7]'', and ''superpyth[7]'' all describe the same step pattern of 5L 2s, with different proportions of large and small steps. Under TAMNAMS parlance, these names can be described broadly as ''soft 5L 2s'' (for flattone and meantone) and ''hard 5L 2s'' (for pythagorean and superpyth). For discussions of the step pattern itself, the name ''5L 2s'' or, in this example, ''diatonic'', is used.
The goal of TAMNAMS is to allow musicians and theorists to discuss moment-of-symmetry scales, or mosses, independent of the language of [[regular temperament theory]]. For example, the names ''flattone[7]'', ''meantone[7]'', ''pythagorean[7]'', and ''superpyth[7]'' all describe the same step pattern of 5L 2s, with different proportions of large and small steps. Under TAMNAMS parlance, these names can be described broadly as ''soft 5L 2s'' (for flattone and meantone) and ''hard 5L 2s'' (for pythagorean and superpyth). For discussions of the step pattern itself, the name ''5L 2s'' or, in this example, ''diatonic'', is used.


This article outlines TAMNAMS as it applies to octave-equivalent moment of symmetry scales, or such scales with tempered octaves.
This article outlines TAMNAMS conventions as it applies to octave-equivalent moment of symmetry scales, or such scales with tempered octaves.
==Credits==
==Credits==
This page and its associated pages were mainly written by [[User:Godtone]], [[User:SupahstarSaga]], [[User:Inthar]], and [[User:Ganaram inukshuk]].
This page and its associated pages were mainly written by [[User:Godtone]], [[User:SupahstarSaga]], [[User:Inthar]], and [[User:Ganaram inukshuk]].
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The two extremes, equalized and collapsed, are degenerate cases and define the boundaries for valid tuning ranges. An equalized mos has large and small steps be the same size (L=s), so the mos pattern is no longer apparent. A collapsed mos has small steps shrunken down to zero (s=0), merging adjacent tones s apart into a single tone. In both cases, the mos structure is no longer valid.
The two extremes, equalized and collapsed, are degenerate cases and define the boundaries for valid tuning ranges. An equalized mos has large and small steps be the same size (L=s), so the mos pattern is no longer apparent. A collapsed mos has small steps shrunken down to zero (s=0), merging adjacent tones s apart into a single tone. In both cases, the mos structure is no longer valid.
===Step ratio ranges===
===Step ratio ranges===
In between the nine specific ratios there are eight named intermediate ranges of step ratios. These names are useful for classifying mos tunings which don't match any of the nine simple step ratios. There are also two additional terms for broader ranges: the term ''hyposoft'' describes step ratios that are ''soft-of-basic'' but not as soft as 3:2; similarly, the term ''hypohard'' describes step ratios that are ''hard-of-basic'' but not as hard as 3:1.
In between the nine specific ratios there are eight named intermediate ranges of step ratios. These terms are used for classifying mos tunings which don't match any of the nine simple step ratios.
 
There are also two additional terms for broader ranges: the term ''hyposoft'' describes step ratios that are ''soft-of-basic'' but not as soft as 3:2; similarly, the term ''hypohard'' describes step ratios that are ''hard-of-basic'' but not as hard as 3:1.


By default, all ranges include their endpoints. For example, a hard tuning is considered a quasihard tuning. To exclude endpoints, the modifier ''strict'' can be used, for example ''strict hyposoft''.
By default, all ranges include their endpoints. For example, a hard tuning is considered a quasihard tuning. To exclude endpoints, the modifier ''strict'' can be used, for example ''strict hyposoft''.
Note that mosses with soft-of-basic step ratios always exhibit [[Rothenberg propriety]], or are ''proper'', whereas mosses with hard-of-basic step ratios do not, or are ''not proper'', with one exception: mosses with only one small step per period are always proper, regardless of the step ratio.
{| class="wikitable"
{| class="wikitable"
|+Step ratio range names
|+Step ratio range names
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=== Expanded spectrum and other terminology ===
=== Expanded spectrum and other terminology ===
For a derivation of these ratio ranges, see <link>.


==Naming mos intervals==
==Naming mos intervals==
Mos intervals are generally named after the number of steps (large or small) they subtend.
Mos intervals, the gap between any two tones in the scale, are named after the number of steps (large or small) between. An interval that spans ''k'' mossteps is called a ''k-mosstep interval'', or simply a ''k-mosstep'' (abbreviated ''kms''). This can be further shortened to ''k-step'' if context allows.
 
The term "mosstep" can be further shortened to "step" if context allows.


=== Generic mos intervals ===
Mossteps are zero-indexed, counting the number of steps subtended rather than the number of scale degrees, meaning that the unison is called a ''0-mosstep'', since a unison has zero steps. A mosstep that reaches the octave can simply be called the ''octave''.
Generic mos intervals only denote how many mossteps an interval subtends.


===Specific mos intervals===
Generic mos intervals only denote how many mossteps an interval subtends. Specific mos intervals denote the sizes, or [[Interval variety|varieties]], an interval has. Per the definition of a moment of symmetry scale (that is, [[maximum variety]] 2), every interval, except for the root and multiples of the period, has two sizes: large and small. The terms ''major'', ''minor'', ''augmented'', ''perfect'', and ''diminished'' are added before the phrase ''k-mosstep'' using the following rules:
Specific mos intervals denote the sizes, or [[Interval variety|varieties]], an interval has. Per the definition of a moment of symmetry scale (that is, [[maximum variety]] 2), every interval, except for the root and multiples of the period has two sizes: large and small. The designations of ''major'', ''minor'', ''augmented'', ''perfect'', and ''diminished'' are applied in the following manner:


* Multiples of the period such as the root and octave are '''perfect''', as they only have one size each.
* Multiples of the period such as the root and octave are '''perfect''', as they only have one size each.
* The generators use the terms '''augmented''', '''perfect''', and '''diminished'''. Note that there are two generators (bright and dark), where their perfect varieties are used to generate the scale. Thus:
* The generators use the terms augmented, perfect, and diminished. Note that there are two generators (bright and dark) whose perfect varieties can be used to create the scale. Thus:
** The large size of the bright generator is '''perfect''', and the small size is '''diminished'''.
** The large size of the bright generator is '''perfect''', and the small size is '''diminished'''.
**The large size of the dark generator is '''augmented''', and the small size is '''perfect'''.
**The large size of the dark generator is '''augmented''', and the small size is '''perfect'''.
*For all other intervals, the large size is '''major''' and the small size is '''minor'''.
*For all other intervals, the large size is '''major''' and the small size is '''minor'''.
There is one exception to the above rules: the designations of augmented, perfect, and diminished don't apply for the generators for ''n''L ''n''s mosses. Instead, major and minor is used, so as to prevent ambiguity over calling every interval perfect.


The designations for these intervals repeat for intervals that exceed the octave; in other words, an interval that is raised by an octave will be the same interval quality that it was before raising.
Mosstep intervals can exceed the octave as they do in standard music theory (eg, a diatonic 9th is a diatonic 2nd raised one octave). For a single-period mos, any interval that is raised by an octave will be the same interval quality that it was before raising. Likewise, for a multi-period mos, any interval raised by the period, where the period is some fraction of the octave, will be the same interval quality that it was before raising.


Additionally, the designations of augmented, perfect, and diminished don't apply for the generators for mosses of the form ''n''L ''n''s; instead, major and minor is used. This is to prevent ambiguity over calling every interval perfect.
Examples using 5L 2s and 4L 4s interval names are provided below. Note that 5L 2s interval names are identical to that of standard music theory, apart from the 0-indexed interval names. To differentiate intervals of a specific mos, the mos's corresponding prefix can be used in place of "mos-", outlined <link>. For a detailed derivation of these intervals, see <link>.
<table>
<tr>
<td style="vertical-align:top">{{MOS intervals|Scale Signature=5L 2s}}</td><td style="vertical-align:top">{{MOS intervals|Scale Signature=4L 4s}}</td>
</tr>
</table>


==== Examples ====
===Alterations by a chroma===
Examples using 5L 2s and 4L 4s are provided below. Note that 5L 2s interval names are identical to that of standard music theory, apart from the 0-indexed interval names. For a detailed derivation of these intervals, see the appendix.{{MOS intervals|Scale Signature=5L 2s}}{{MOS intervals|Scale Signature=4L 4s}}
The terms ''augmented'' and ''diminished'' are also used to describe intervals that are further lowered or raised by an interval called a ''moschroma'' (or simply ''chroma'' if context allows), a generalized sharp or flat. The rules for alteration are the same as with conventional music theory.


===Alterations by a chroma===
* Raising a minor interval by a chroma makes it minor.
TAMNAMS also uses the modifiers of ''augmented'' and ''diminished'' to refer to ''alterations'' of a mos interval, much like with using sharps and flats in standard notation. Mos intervals are altered by raising or lowering it by a ''moschroma'' (or simply ''chroma'', if context allows), a generalized sharp/flat that is the difference between a large step and a small step. Raising a minor mos interval by a chroma makes it major; the reverse is true. Raising a major or perfect mos interval repeatedly makes an augmented, doubly-augmented, and a triply-augmented mos interval. Likewise, lowering a minor or perfect mos interval repeatedly makes a diminished, doubly-diminished, and a triply-diminished mos interval. A unison, period or equave that is itself augmented or diminished may also be referred to a ''mosaugmented'' or ''mosdiminished'' unison, period or equave, respectively. Here, the meaning of unison and octave does not change depending on the mos pattern, but the meanings of augmented and diminished do.
* Lowering a major interval by a chroma makes it major.
* Raising a major interval by a chroma makes it augmented.
* Lowering a minor interval by a chroma makes it diminished.
* Raising an augmented interval by a chroma makes it doubly augmented.
* Lowering a diminished interval by a chroma makes it doubly diminished.
* Raising or lowering a perfect interval makes it augmented or diminished, respectively.


Repetition of "A" or "d" is used to denote repeatedly augmented/diminished mos intervals, and is sufficient in most cases. It's typically uncommon to alter an interval more than three times, such as with a quadruply-augmented and quadruply-diminished interval; in such cases, it's preferable to use a shorthand such as A^n and d^n, or to use alternate notation or terminology.
The terms augmented and diminished can be abbreviated using the letters ''A'' (capitalized A) and ''d'' (lowercase d). Repetition of "A" or "d" is used to denote repeatedly augmented/diminished intervals, and is sufficient in most cases. It's typically uncommon to alter an interval more than three times, and superscript numbers or alternate notation is advised for such cases. The table below shows how such intervals can be notated.
{| class="wikitable"
{| class="wikitable"
|+Table of alterations, with abbreviations
|+Table of alterations, with abbreviations
|-
|-
!Number of chromas
! rowspan="2" |Chromas
!Perfect intervals
! colspan="2" |Perfectable intervals
! Major/minor intervals
! colspan="2" | Non-perfectable intervals
|-
|-
| +3 chromas
!Interval quality
|Triply-augmented (AAA, A³, or A^3)
!Abbrev.
|Triply-augmented (AAA, A³, or A^3)
!Interval quality
!Abbrev.
|-
|-
| +2 chromas
| +4
|Doubly-augmented (AA)
|Quadruply-augmented
|Doubly-augmented (AA)
|A<sup>4</sup> or A^4
|Quadruply-augmented
|A<sup>4</sup> or A^4
|-
|-
| +1 chroma
| +3
|Augmented (A)
|Triply-augmented
|Augmented (A)
|AAA, A<sup>3</sup>, or A^3
|Triply-augmented
|AAA, A<sup>3</sup>, or A^3
|-
|-
| rowspan="2" |0 chromas (unaltered)
| +2
| rowspan="2" |Perfect (P)
|Doubly-augmented
|Major (M)
|AA
|Doubly-augmented
|AA
|-
|-
|Minor (m)
| +1
|Augmented
|A
|Augmented
|A
|-
|-
| -1 chroma
| rowspan="2" |0
|Diminished (d)
| rowspan="2" |Perfect
|Diminished (d)
| rowspan="2" |P
|Major
|M
|-
|-
| -2 chromas
|Minor
|Doubly-diminished (dd)
|m
|Doubly-diminished (dd)
|-
|-
| -3 chromas
| -1
|Triply-diminished (ddd, d³, or d^3)
|Diminished
|Triply-diminished (ddd, d³, or d^3)
|d
|Diminished
|d
|-
|  -2
|Doubly-diminished
|dd
|Doubly-diminished
|dd
|-
|  -3
|Triply-diminished
|ddd, d<sup>3</sup>, or d^3
|Triply-diminished
|ddd, d<sup>3</sup>, or d^3
|-
|  -4
|Quadruply-diminished
|d<sup>4</sup> or d^4
|Quadruply-diminished
|d<sup>4</sup> or d^4
|}
|}
===Naming neutral and interordinal intervals===
 
For a discussion of semi-moschroma-altered versions of mos intervals, see [[Neutral and interordinal k-mossteps]].
=== Intervals smaller than a chroma ===
===Other terminology===
{| class="wikitable"
The tonic (unison), the period, the generator and the period-complement of the generator make up all the intervals in any given mos scale that might be labelled "perfect". With the exception of the tonic and the period, they may also be "imperfect". Therefore, the degrees of a mos scale which come in a "perfect" variety are called ''perfectable'' degrees and the degrees of a mos scale which do not come in a "perfect" variety are called ''non-perfectable'' degrees.
!Interval name
! Absolute value of a...
|-
|Moschroma (generalized [[chroma]], provided for reference)
|Large step minus a small step
|-
| Mosdiesis (generalized [[Diesis (scale theory)|diesis]])
|Large step minus two small steps
|-
| Moskleisma (generalized [[kleisma]])
|Mosdiesis minus a moschroma
|-
| Mosgothma (generalized gothma)
|Mosdiesis minus a small step
|}
===Other terminology and intervals===
Intervals that have a perfect variety (the unison, period intervals, and generators) are called ''perfectable intervals'', whereas intervals that do not have a perfect variety are called ''non-perfectable intervals''. Intervals corresponding to the generators may be called ''imperfect intervals'' since, unlike the period and unison, they have two varieties instead of one.
 
A discussion of neutral and interordinal intervals, which fall between major and minor, can be found at <link>.
 
==Naming mos degrees==
==Naming mos degrees==
Individual mos degrees, (that is, specific notes of a mos scale,) or '''k-mosdegrees''' (abbreviated ''k''md), are based on the modifiers given to intervals using the process for naming mos intervals and alterations. Mosdegrees are 0-indexed and are enumerated starting at the 0-mosdegree, the tonic/root of the scale. For example, if you go up a major k-mosstep up from the root, then the mos degree reached this way is a major k-mosdegree. Much like mossteps, the prefix of mos- may also be replaced with the mos's prefix. If context allows, ''k-mosdegree'' may also be shortened to ''k-degree'' to allow generalization to non-mos scales. When the modifiers major/minor or augmented/perfect/diminished are omitted, they are assumed to be the unmodified degrees of the current mode.
The pitches of a mos are called '''k-mosdegrees''' (abbreviated ''k''md), and follow the same rules as that with mosstep intervals. Mosdegrees are 0-indexed and are enumerated starting at the 0-mosdegree, representing the root or tonic of the scale. For example, if you go up a major k-mosstep up from the root, then the mos degree reached this way is a major k-mosdegree.
 
The phrase ''k-mosdegree'' may also be shortened to ''k-degree'', if context allows. When the modifiers major, minor, augmented, perfect, and diminished are omitted, they are assumed to be the unmodified degrees of a particular mode.
===Naming mos chords===
===Naming mos chords===
To denote a chord or a mode on a given degree, write the notes of the chord separated by spaces or commas, or the mode, in parentheses after the degree symbol. The most explicit option is to write out the chord in cents, edosteps or mossteps (e.g. in [[13edo]] [[5L 3s]], the (0 369 646) chord can be written (0 4 7)\13, (P0ms M2ms M4ms) or 7|0 (0 2 4ms) and to write the mode. To save space, you can use whatever names or abbreviations for the chord or mode you have defined for the reader. For example, in the LsLLsLLs mode of 5L 3s, we have m2md(0 369 646), or the chord (0 369 646) on the 2-mosdegree which is a minor 2-mosstep. The LsLLsLLs mode also has m2md(7|0), meaning that we have the 7| (LLsLLsLs) mode on the 2-mosdegree which is a minor 2-mosstep in LsLLsLLs (see [[TAMNAMS#Proposal:%20Naming%20mos%20modes|below]] for the convention we have used to name the mode).
To denote a chord or a mode on a given degree, write the notes of the chord separated by spaces or commas, or the mode, in parentheses after the degree symbol. The most explicit option is to write out the chord in cents, edosteps or mossteps (e.g. in [[13edo]] [[5L 3s]], the (0 369 646) chord can be written (0 4 7)\13, (P0ms M2ms M4ms) or 7|0 (0 2 4ms) and to write the mode. To save space, you can use whatever names or abbreviations for the chord or mode you have defined for the reader. For example, in the LsLLsLLs mode of 5L 3s, we have m2md(0 369 646), or the chord (0 369 646) on the 2-mosdegree which is a minor 2-mosstep. The LsLLsLLs mode also has m2md(7|0), meaning that we have the 7| (LLsLLsLs) mode on the 2-mosdegree which is a minor 2-mosstep in LsLLsLLs (see [[TAMNAMS#Proposal:%20Naming%20mos%20modes|below]] for the convention we have used to name the mode).
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''This section contains unapproved namechanges. They are provided for reference/completeness and, unless approved, should not be included in the main-namespace rewrite.''
''This section contains unapproved namechanges. They are provided for reference/completeness and, unless approved, should not be included in the main-namespace rewrite.''


TAMNAMS uses the following names for octave-equivalent (or tempered-octave) mosses with step counts between 6 and 10, called the ''named range''. These names are optional, and conventional ''xL ys'' names can be used instead in discussions regarding mosses, its intervals, scale degrees, and modes.
TAMNAMS primarily uses the following names for octave-equivalent (or tempered-octave) mosses with step counts between 6 and 10. These names are optional, and conventional ''xL ys'' names can be used instead in discussions regarding mosses, its intervals, scale degrees, and modes.


Prefixes and abbreviations for each name are also provided, and can used in place of the prefix ''mos-'' and its abbreviation of ''m-'', as seen in mos-related terms, such as ''mosstep'' and ''mosdegree'', and their abbreviations of ''ms'' and ''md'', respectively. For example, discussion of the intervals and scale degrees of ''oneirotonic'' uses the terms ''oneirosteps'' and ''oneirodegrees'', abbreviated as ''oneis'' and ''oneid'', respectively.
Prefixes and abbreviations for each name are also provided, and can used in place of the prefix ''mos-'' and its abbreviation of ''m-'', as seen in mos-related terms, such as ''mosstep'' and ''mosdegree'', and their abbreviations of ''ms'' and ''md'', respectively. For example, discussion of the intervals and scale degrees of ''oneirotonic'' uses the terms ''oneirosteps'' and ''oneirodegrees'', abbreviated as ''oneis'' and ''oneid'', respectively.
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|-
|-
|[[1L 5s]]|| selenite||sel-||sel||References [[luna]] temperament (selenite is named after the moon); also called ''antimachinoid<ref name="anti-name">Alternate name based on the name of its sister mos, with anti- prefix added.</ref>''.
|[[1L 5s]]|| selenite||sel-||sel||References [[luna]] temperament (selenite is named after the moon); also called ''antimachinoid<ref name="anti-name">Alternate name based on the name of its sister mos, with anti- prefix added.</ref>''.
(Provided for lack of a better name)
|-
|-
|[[2L 4s]]||malic||mal-||mal||Sister mos of 4L 2s; apples have concave ends, whereas lemons/limes have convex ends.
|[[2L 4s]]||malic||mal-||mal||Sister mos of 4L 2s; apples have concave ends, whereas lemons/limes have convex ends.
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|[[4L 2s]]||citric||citro-||cit||Parent (or subset) mos of 4L 6s and 6L 4s.
|[[4L 2s]]||citric||citro-||cit||Parent (or subset) mos of 4L 6s and 6L 4s.
|-
|-
|[[5L 1s]]||machinoid||mech-||mech||From [[machine]] temperament.
|[[5L 1s]]||machinoid||mech-||mk||From [[machine]] temperament.
|-
|-
! colspan="5" |7-note mosses
! colspan="5" |7-note mosses
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|[[5L 2s]]|| diatonic||dia-||dia||
|[[5L 2s]]|| diatonic||dia-||dia||
|-
|-
|[[6L 1s]]||archaeotonic ||arch- || arch||Originally a name for 13edo's 6L 1s scale; also called ''archæotonic/archeotonic<ref name="spelling">Spelling variant.</ref>''.
|[[6L 1s]]||archaeotonic ||arch- || arc||Originally a name for 13edo's 6L 1s scale; also called ''archæotonic/archeotonic<ref name="spelling">Spelling variant.</ref>''.
|-
|-
! colspan="5" |8-note mosses
! colspan="5" |8-note mosses
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|[[4L 4s]]|| tetrawood||tetrawd- ||ttw||Blackwood[10] and whitewood[14] generalized to 4 periods; also called ''diminished<ref name="unofficial">Common name no longer recommend by TAMNAMS due to risk of ambiguity. Provided for reference.</ref>.''
|[[4L 4s]]|| tetrawood||tetrawd- ||ttw||Blackwood[10] and whitewood[14] generalized to 4 periods; also called ''diminished<ref name="unofficial">Common name no longer recommend by TAMNAMS due to risk of ambiguity. Provided for reference.</ref>.''
|-
|-
|[[5L 3s]]||oneirotonic ||oneiro-||onei|| Originally a name for 13edo's 5L 3s scale; also called ''oneiro''<ref>Shortened form of name.</ref>.
|[[5L 3s]]||oneirotonic ||oneiro-||or|| Originally a name for 13edo's 5L 3s scale; also called ''oneiro''<ref>Shortened form of name.</ref>.
|-
|-
|[[6L 2s]]||ekic||ek- ||ek||From [[echidna]] and [[hedgehog]] temperaments.
|[[6L 2s]]||ekic||ek- ||ek||From [[echidna]] and [[hedgehog]] temperaments.
|-
|-
|[[7L 1s]]||pine||pine-||pine||From [[porcupine]] temperament.
|[[7L 1s]]||pine||pine-||p||From [[porcupine]] temperament.
|-
|-
! colspan="5" | 9-note mosses
! colspan="5" | 9-note mosses
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|[[1L 8s]]||agate||ag- ||ag||Rhymes with "eight", depending on one's pronunciation; also called ''antisubneutralic<ref name="anti-name" />.''
|[[1L 8s]]||agate||ag- ||ag||Rhymes with "eight", depending on one's pronunciation; also called ''antisubneutralic<ref name="anti-name" />.''
|-
|-
|[[2L 7s]]||balzano||bal-||bal||Originally a name for 20edo's 2L 7s (and 2L 11) scales; bal- is pronounced /bæl/.
|[[2L 7s]]||balzano||bal-||bz||Originally a name for 20edo's 2L 7s (and 2L 11) scales; bal- is pronounced /bæl/.
|-
|-
|[[3L 6s]]||tcheretonic||cher-||ch|| In reference to Tcherepnin's 9-note scale in 12edo. Also called ''cheretonic<ref name="spelling" />''.
|[[3L 6s]]||tcherepnin||cher-||ch|| In reference to Tcherepnin's 9-note scale in 12edo.
|-
|-
|[[4L 5s]]|| gramitonic||gram-||gram||From "grave minor third".
|[[4L 5s]]|| gramitonic||gram-||gm||From "grave minor third".
|-
|-
|[[5L 4s]]||semiquartal||cthon-||cth||From "half fourth"; cthon- is from "chthonic".
|[[5L 4s]]||semiquartal||cthon-||ct||From "half fourth"; cthon- is from "chthonic".
|-
|-
|[[6L 3s]]||hyrulic||hyru-||hy||References [[triforce]] temperament.
|[[6L 3s]]||hyrulic||hyru-||hy||References [[triforce]] temperament.
|-
|-
|[[7L 2s]]||armotonic||arm-||arm||From [[Armodue]] theory; also called ''superdiatonic<ref name="unofficial" />.''
|[[7L 2s]]||armotonic||arm-||am||From [[Armodue]] theory; also called ''superdiatonic<ref name="unofficial" />.''
|-
|-
|[[8L 1s]]||subneutralic||blu-|| blu||Derived from the generator being between supraminor and neutral quality; blu- is from [[bleu]] temperament.
|[[8L 1s]]||subneutralic||blu-|| bl||Derived from the generator being between supraminor and neutral quality; blu- is from [[bleu]] temperament.
|-
|-
! colspan="5" |10-note mosses
! colspan="5" |10-note mosses
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!Pattern!!Name!!Prefix!!Abbr.!!Etymology
!Pattern!!Name!!Prefix!!Abbr.!!Etymology
|-
|-
|[[1L 9s]]||olivnie ||oli- ||oli||Rhymes with "nine", depending on one's pronunciation; also called ''antisinatonic<ref name="anti-name" />.''
|[[1L 9s]]||olivnie ||oli- ||ol||Rhymes with "nine", depending on one's pronunciation; also called ''antisinatonic<ref name="anti-name" />.''
|-
|-
|[[2L 8s]]||jaric||jara-||jar||From [[pajara]], [[injera]], and [[diaschismic]] temperaments.
|[[2L 8s]]||jaric||jara-||ja||From [[pajara]], [[injera]], and [[diaschismic]] temperaments.
|-
|-
|[[3L 7s]]||sephiroid||seph-|| seph||From [[sephiroth]] temperament.
|[[3L 7s]]||sephiroid||seph-|| sp||From [[sephiroth]] temperament.
|-
|-
|[[4L 6s]]||lime ||lime-||lim||Sister mos of 6L 4s; limes are smaller than lemons, as are 4L 6s's step sizes compared to 6L 4s.
|[[4L 6s]]||lime ||lime-||lm||Sister mos of 6L 4s; limes are smaller than lemons, as are 4L 6s's step sizes compared to 6L 4s.
|-
|-
|[[5L 5s]]||pentawood||pentawd-||pw||Blackwood[10] and whitewood[14] generalized to 5 periods.
|[[5L 5s]]||pentawood||pentawd-||pw||Blackwood[10] and whitewood[14] generalized to 5 periods.
|-
|-
|[[6L 4s]]||lemon||lem- ||lem||From [[lemba]] temperament.
|[[6L 4s]]||lemon||lem- ||le||From [[lemba]] temperament. Also sister mos of 4L 6s.
|-
|-
|[[7L 3s]]||dicoid||dico-||dico ||From [[Dicot family#Dichotic|dichotic]] and [[dicot]] (dicoid) exotemperaments; pronounced /'daɪˌkɔɪd/.
|[[7L 3s]]||dicoid||dico-||di ||From [[Dicot family#Dichotic|dichotic]] and [[dicot]] (dicoid) exotemperaments; pronounced /'daɪˌkɔɪd/.
|-
|-
|[[8L 2s]]||taric||tara-||tar||Sister mos of 2L 8s; based off of [[wikipedia:Hindustani_numerals|Hindi]] word for 18 (aṭhārah), since 18edo contains basic 8L 2s.
|[[8L 2s]]||taric||tara-||ta||Sister mos of 2L 8s; based off of [[wikipedia:Hindustani_numerals|Hindi]] word for 18 (aṭhārah), since 18edo contains basic 8L 2s.
|-
|-
|[[9L 1s]]|| sinatonic||sina-||si|| Derived from the generator being within the range of a [[sinaic]].
|[[9L 1s]]|| sinatonic||sina-||si|| Derived from the generator being within the range of a [[sinaic]].
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<references />
<references />


===Extending the named range===
===Names for smaller mosses===
For a discussion of names for mosses with fewer than 6 steps, see <link>. For a discussion of names for mosses with more than 10 steps, see <link>.
In addition to the names listed above are names for smaller mosses, provided for completeness. These names, with the exception of ''monowood'' and ''biwood'', are meant to be as general as possible so as to avoid flavor and to allow for valid reuse for non-octave mosses.
==Appendix==
{| class="wikitable center-all"
! colspan="6" |2-note mosses
|-
!Pattern!!Name!!Prefix!!Abbr.
!Must be 2/1-equivalent?!!Etymology
|-
| rowspan="2" |[[1L 1s]]|| trivial|| triv-||tw
|No||The simplest valid mos pattern.
|-
|monowood
| monowd-
| w
|Yes
| Blackwood[10] and whitewood[14] generalized to 1 period.
|-
! colspan="6" |3-note mosses
|-
!Pattern!!Name!! Prefix!!Abbr.
!Must be 2/1-equivalent?!! Etymology
|-
|[[1L 2s]]||antrial|| atri-||at
|No ||Opposite pattern of 2L 1s, with broader range. Shortening of ''anti-trial''.
|-
|[[2L 1s]]||trial||tri-||t
|No ||From tri- for 3.
|-
! colspan="6" |4-note mosses
|-
!Pattern!! Name!!Prefix!! Abbr.
!Must be 2/1-equivalent?!!Etymology
|-
|[[1L 3s]]|| antetric|| atetra-||att
|No ||Opposite pattern of 3L 1s, with broader range. Shortening of ''anti-tetric''.
|-
|[[2L 2s]]||biwood||biwd-||bw
|Yes||Blackwood[10] and whitewood[14] generalized to 2 periods.
|-
|[[3L 1s]]||tetric|| tetra- ||tt
|No ||From tetra- for 4.
|-
! colspan="6" | 5-note mosses
|-
!Pattern!!Name!!Prefix !! Abbr.
!Must be 2/1-equivalent?!!Etymology
|-
|[[1L 4s]]||pedal||ped-||pd
|No ||From Latin ''ped'', for ''foot''; one big toe and four small toes.
|-
|[[2L 3s]]||pentic||pent- ||pt
|No||Common pentatonic; from penta- for 5.
|-
|[[3L 2s]]||antipentic || apent-||apt
| No||Opposite pattern of 2L 3s.
|-
|[[4L 1s]]||manual ||manu-|| mn
|No||From Latin ''manus'', for ''hand''; one thumb and four longer fingers.
|}
=== Names for larger mosses ===
For a discussion of names for mosses with more than 10 steps, see <link>.
 
== Generalizations to non-mos scales ==
 
=== Non-octave mosses ===
The terminology for intervals and scale degrees can be applied to scales with arbitrary equivalence intervals, replacing the term ''octave'' with the term ''equave''.
 
The mos names provided for step counts 6-10 ''do not apply'' for non-octave mos patterns, unless the equave in question is seen as a tempered octave.
 
=== Intervals for MV3 scales ===
Scales with maximum-variety 3, such as diasem, have at most 3 varieties for each interval class, called ''large k-step'', ''medium k-step'', and ''small k-step''. Interval classes with only two varieties are given the phrases ''large k-step'' and ''small k-step'', and interval classes with only one variety are given the phrase ''perfect k-step''.
 
=== Step ratios for ternary scales ===
Ternary scales, i.e. those with three step sizes L > M > S, including [[MV3]] scales, can also be defined by their L:M:S ratios. Here TAMNAMS names the L/M ratio and then the M/S ratio as if these were mos step ratios: for example, [[21edo]] [[diasem]] (5L 2M 2s, LMLSLMLSL or its inverse) has a step ratio of L:M:S = 3:2:1, so we name it ''soft-basic diasem''. If the ratios are the same, repetition may optionally be omitted, so that [[26edo]] diasem, 4:2:1, may optionally be called "basic diasem" instead of "basic-basic diasem". Not to be confused with step ratios where one ratio is unspecified; for that, use:
 
* x:y:z (where x:y is known but y:z is not) is called ''(hardness term for x/y)-any''. x:x:1 is called ''equalized-any'' or ''LM-equalized'' (where x >= 1 represents a free variable).
* x:y:z (where y:z is known but x:y is not) is called ''any-(hardness term for y/z)''. x:1:1 is called ''any-equalized'' or ''MS-equalized'' (where x >= 1 represents a free variable).
* x:y:z (where x:z is known but x:y and y:z are not) is called ''outer-(hardness term for x/z)-any''. x:1:x is called ''outer-equalized-any'' or ''LS-equalized''. (where x >= 0 represents a free variable).
 
=== Arbitrary scales ===
Zero-indexed interval and degrees can be used for arbitrary scales. However, instead of using the terms ''k-mosstep'' and ''k-mosdegree'', the terms ''k-scalestep'' and ''k-scaledegree'' are used. As with octave-equivalent mosses, these terms can be further shortened to ''k-step'' and ''k-degree'', if context allows.
 
==Frequently asked questions==
'''Do I need to use this system over temperament names?'''
 
'''Why are intervals zero-indexed?'''
 
'''What's the difference between mosdegrees and mosintervals?'''
 
===Reasoning for step ratio names===
===Reasoning for step ratio names===
{{Main|TAMNAMS/Appendix#Reasoning for step ratio names}}
{{Main|TAMNAMS/Appendix#Reasoning for step ratio names}}
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