User:Ganaram inukshuk/TAMNAMS: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Ganaram inukshuk (talk | contribs)
autopatrolled
4,810 edits
Ganaram inukshuk (talk | contribs)
autopatrolled
4,810 edits
appendix -> faq
 
(95 intermediate revisions by 2 users not shown)
Line 1: Line 1:
{{Mbox|text=This page is a work-in-progress, '''proposed rewrite''' of the following page: [[TAMNAMS]]}}
{{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.
* 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.


'''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.


''No other changes to lead section''.
This article outlines TAMNAMS conventions as it applies to octave-equivalent moment of symmetry scales, or such scales with tempered octaves.
==Credits==
This page and its associated pages were mainly written by [[User:Godtone]], [[User:SupahstarSaga]], [[User:Inthar]], and [[User:Ganaram inukshuk]].
== Step ratio spectrum==
===Simple step ratios===
TAMNAMS provides names for nine specific simple [[Blackwood's R|step ratios]]. These correspond to the simplest edos that have the mos scale, and can be used in place of their respective step ratio.
{| class="wikitable"
|-
|+Simple step ratio names
|-
!TAMNAMS Name
!Ratio
! Hardness
!Diatonic example
|-
|Equalized
|L:s = 1:1
|1.000
|[[7edo]]
|-
|Supersoft
|L:s = 4:3
|1.333
|[[26edo]]
|-
|Soft (or monosoft)
|L:s = 3:2
|1.500
|[[19edo]]
|-
|Semisoft
|L:s = 5:3
|1.667
|[[31edo]]
|-
| Basic
|L:s = 2:1
|2.000
|[[12edo]]
|-
|Semihard
|L:s = 5:2
|2.500
|[[29edo]]
|-
|Hard (or monohard)
|L:s = 3:1
|3.000
|[[17edo]]
|-
|Superhard
|L:s = 4:1
|4.000
|[[22edo]]
|-
| Collapsed
|L:s = 1:0
|∞ (infinity)
|[[5edo]]
|}For example, the 5L 2s (diatonic) scale of 19edo has a step ratio of 3:2, which is ''soft'', and is thus called ''soft diatonic''. Tunings of a mos with L:s larger than that ratio are ''harder'', and tunings with L:s smaller than that are ''softer''.


== Credits ==
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.
<blockquote>''No changes.''</blockquote>
===Step ratio ranges===
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.


==Step ratio spectrum==
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.
<blockquote>''No changes''.</blockquote>
 
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''.
{| class="wikitable"
|+Step ratio range names
!TAMNAMS Name
!Ratio range
!Hardness
|-
|Hyposoft
|3:2 ≤ L:s ≤ 2:1
|1.500 ≤ L/s ≤ 2.000
|-
|Ultrasoft
|1:1 ≤ L:s ≤ 4:3
|1.000 ≤ L/s ≤ 1.333
|-
|Parasoft
|4:3 ≤ L:s ≤ 3:2
| 1.333 ≤ L/s ≤ 1.500
|-
|Quasisoft
|3:2 ≤ L:s ≤ 5:3
|1.500 ≤ L/s ≤ 1.667
|-
|Minisoft
|5:3 ≤ L:s ≤ 2:1
|1.667 ≤ L/s ≤ 2.000
|-
|Minihard
|2:1 ≤ L:s ≤ 5:2
|2.000 ≤ L/s ≤ 2.500
|-
|Quasihard
|5:2 ≤ L:s ≤ 3:1
|2.500 ≤ L/s ≤ 3.000
|-
|Parahard
|3:1 ≤ L:s ≤ 4:1
|3.000 ≤ L/s ≤ 4.000
|-
|Ultrahard
|4:1 ≤ L:s ≤ 1:0
|4.000 ≤ L/s ≤ ∞
|-
|Hypohard
|2:1 ≤ L:s ≤ 3:1
|2.000 ≤ L/s ≤ 3.000
|}
===Central spectrum===
{| class="wikitable center-all"
|+Central spectrum of step ratio ranges and specific step ratios
|-
! colspan="3" |Step ratio ranges
!Specific step ratios
!Notes
|-
|
|
|
|'''1:1 (equalized)'''
|Trivial/pathological
|-
| rowspan="7" |1:1 to 2:1 (soft-of-basic)
| colspan="2" |1:1 to 4:3 (ultrasoft)
|
|Step ratios especially close to 1:1 may be called pseudoequalized
|-
|
|
|'''4:3 (supersoft)'''
|
|-
| colspan="2" |4:3 to 3:2 (parasoft)
|
|
|-
|
|
|'''3:2 (soft)'''
|Also called monosoft
|-
| rowspan="3" |3:2 to 2:1 (hyposoft)
|3:2 to 5:3 (quasisoft)
|
|
|-
|
|'''5:3 (semisoft)'''
|
|-
|5:3 to 2:1 (minisoft)
|
|
|-
|
|
|
|'''2:1 (basic)'''
|
|-
| rowspan="7" |2:1 to 1:0 (hard-of-basic)
| rowspan="3" |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
|-
| colspan="2" |3:1 to 4:1 (parahard)
|
|
|-
|
|
|'''4:1 (superhard)'''
|
|-
| colspan="2" |4:1 to 1:0 (ultrahard)
|
|Step ratios especially close to 1:0 may be called pseudocollapsed
|-
|
|
|
|'''1:0 (collapsed)'''
|Trivial/pathological
|}
 
=== Expanded spectrum and other terminology ===
For a derivation of these ratio ranges, see <link>.


==Naming mos intervals==
==Naming mos intervals==
<blockquote>''Move neutral/interordinal naming to Extensions section''.</blockquote>
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.
 
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 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:
 
* 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) 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 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'''.
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.
 
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.
 
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>
 
===Alterations by a chroma===
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.
 
* Raising a minor interval by a chroma makes it minor.
* 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.
 
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"
|+Table of alterations, with abbreviations
|-
! rowspan="2" |Chromas
! colspan="2" |Perfectable intervals
! colspan="2" | Non-perfectable intervals
|-
!Interval quality
!Abbrev.
!Interval quality
!Abbrev.
|-
|  +4
|Quadruply-augmented
|A<sup>4</sup> or A^4
|Quadruply-augmented
|A<sup>4</sup> or A^4
|-
|  +3
|Triply-augmented
|AAA, A<sup>3</sup>, or A^3
|Triply-augmented
|AAA, A<sup>3</sup>, or A^3
|-
|  +2
|Doubly-augmented
|AA
|Doubly-augmented
|AA
|-
|  +1
|Augmented
|A
|Augmented
|A
|-
| rowspan="2" |0
| rowspan="2" |Perfect
| rowspan="2" |P
|Major
|M
|-
|Minor
|m
|-
|  -1
|Diminished
|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
|}
 
=== Intervals smaller than a chroma ===
{| class="wikitable"
!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==
<blockquote>''No changes''.</blockquote>
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===
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 analyze a chord as an inversion of another chord (i.e. when the bass is not seen as the root), the following strategies can be used:
#One can write the root degree first: (6s, 0s, 2s, 7s). The first degree is assumed to be the tonic unless the following method is used:
#One can write "T" to the left of the tonic: (0s, 2s, T6s, 7s).
#One can use 0 for the root, using negative numbers for notes below the root. For example, to analyze (0s, 2s, 6s, 7s) on the 7-degree of the LsLLsLLs mode as being rooted on its 6s (thus on the 5-degree of LsLLsLLs), we write 5d(0s, -6s, -4s, 1s). The "5d" here is essential for avoiding confusion with the previous notation.
#If clarity is desired as to what the root position chord is, slash notation can be used as in conventional notation. Thus the above chord can be written 5d(0s 1s 2s 4s)/7d.
==Naming mos modes==
TAMNAMS uses [[Modal UDP notation]] to name modes. For example, the names of modes for 5L 3s are the names of the mos followed by the UDP of that mode.
For modes with altered scale degrees, the abbreviations for the scale degrees are listed after the UDP for the mode.
Notation, such as [[Diamond-mos notation|diamond-mos]], can be used instead of the abbreviation of a mosdegree. For example, LsLsLLLs can be written "5L 3s 5|2 m4md". "5L 3s 5|2 @4d".
{{MOS mode degrees|Scale Signature=5L 3s|MOS Prefix=mos|Mode Names=Default}}
{{MOS mode degrees|Scale Signature=5L 3s|MOS Prefix=mos|MODMOS Step Pattern=LsLsLLLs|Mode Names=Default}}
==Mos pattern names==
==Mos pattern names==
''Proposed section changes:''
''This section contains unapproved namechanges. They are provided for reference/completeness and, unless approved, should not be included in the main-namespace rewrite.''
 
* ''Define the named range as "octave-equivalent mosses with note counts 6-10".''
* ''Make abbreviations be suggestive of the full name wherever possible, and have no more than 4 letters. Prefixes do not need to be suggestive of the full name.''
* ''The names column has one name and one name only. Other names can be added either into the etymology column.''


TAMNAMS uses the following names for mosses with step counts between 6 and 10. These names are optional; interval size names and step ratio names can be combined with conventional ''xL ys'' names.
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.


Some of the names come from older temperament-agnostic mos names, such as names (such as ''mosh'') from [[Graham Breed]]'s [[Graham Breed's MOS naming scheme|mos names]]. These names have been coined so that mosses can be discussed more independently of RTT temperaments. Sometimes the prefix has a different source than the scale name for euphonic reasons.
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.


This list is maintained by [[User:Inthar]] and [[User:Godtone]].
This list is maintained by [[User:Inthar]] and [[User:Godtone]].
{| class="wikitable center-all"
{| class="wikitable center-all"
|+TAMNAMS moss names
|+TAMNAMS mos names
|-
|-
! colspan="5" |6-note mosses
! colspan="5" |6-note mosses
|-
|-
!Pattern!!Name!!Prefix<ref name="prefix">used in interval, degree and mode names, e.g. ''perfect 3-oneirostep, perfect 3-oneirodegree, oneiro-3-up''</ref>!!Abbr.<ref name="abbr">written abbreviations of prefixes, e.g. ''P3oneis, P3oneid, onei-3|4''</ref>!!Etymology
!Pattern!!Name!!Prefix!!Abbr.!!Etymology
|-
|-
|[[1L 5s]]||selenite||sel-||sel||indirect reference to [[luna]] temperament
|[[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>''.
|-
|-
|[[2L 4s]]||malic||mal-||mal||apples have two concave ends, lemons have two pointy ends.
|[[2L 4s]]||malic||mal-||mal||Sister mos of 4L 2s; apples have concave ends, whereas lemons/limes have convex ends.
|-
|-
|[[3L 3s]]||triwood||triwd-||twd||from 3-wood
|[[3L 3s]]||triwood||triwd-||tw||[[Blackwood]][10] and [[whitewood]][14] generalized to 3 periods.
|-
|-
|[[4L 2s]]||citric||citro-||cit||parent mos of lemon and lime
|[[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
|-
|-
!Pattern!!Name!!Prefix<ref name="prefix" />!!Abbr.<ref name="abbr" />!!Etymology
!Pattern!!Name!!Prefix!!Abbr.!!Etymology
|-
|-
|[[1L 6s]]||onyx||on-||on||from a ''lot'' of naming puns
|[[1L 6s]]||onyx|| on-||on|| Sounds like "one-six" depending on one's pronunciation; also called ''anti-archeotonic<ref name="anti-name" />''.
|-
|-
|[[2L 5s]]||antidiatonic||pel-||pel||pel- is from pelog
|[[2L 5s]]||pelotonic||pel-||pel||From pelog; also called ''antidiatonic<ref name="anti-name" />'', a common name.
|-
|-
|[[3L 4s]]||mosh||mosh-||mo||Graham Breed's name; from "mohajira-ish"
|[[3L 4s]]||mosh ||mosh-|| mosh||From "mohajira-ish", a name from [[Graham Breed's MOS naming scheme|Graham Breed's naming scheme]].
|-
|-
|[[4L 3s]]||smitonic||smi-||smi||from "sharp minor third"
|[[4L 3s]]||smitonic||smi-||smi||From "sharp minor third".
|-
|-
|[[5L 2s]]||diatonic||dia-||dia||
|[[5L 2s]]|| diatonic||dia-||dia||
|-
|-
|[[6L 1s]]||archaeotonic||arch-||arch||originally a name for 13edo's 6L 1s; also called ''archeotonic'' as a spelling variation
|[[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
|-
|-
!Pattern!!Name!!Prefix<ref name="prefix" />!!Abbr.<ref name="abbr" />!!Etymology
!Pattern!! Name!!Prefix!!Abbr.!!Etymology
|-
|-
|[[1L 7s]]||spinel||spin-||sp||contains the string "pine", referencing its sister mos
|[[1L 7s]]||spinel||spin-||sp||Contains the string "pine", referencing its sister mos; also called ''antipine<ref name="anti-name" />.''
|-
|-
|[[2L 6s]]||subaric||subar-||sb||largest subset mos of jaric and taric
|[[2L 6s]]||subaric || subar-||sb ||Parent (or subset) mos of 2L 8s and 8L 2s.
|-
|-
|[[3L 5s]]||checkertonic||check-||chk||from the [[Kite Giedraitis's Categorizations of 41edo Scales|Kite guitar checkerboard scale]]
|[[3L 5s]]||checkertonic||check-||chk||From the [[Kite Giedraitis's Categorizations of 41edo Scales|Kite guitar checkerboard scale]].
|-
|-
|[[4L 4s]]||tetrawood||tetrawd-||ttwd||from 4-wood; 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
|[[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 temperaments [[echidna]] and [[hedgehog]]
|[[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
|-
|-
!Pattern!!Name!!Prefix<ref name="prefix" />!!Abbr.<ref name="abbr" />!!Etymology
!Pattern!!Name!!Prefix!!Abbr.!!Etymology
|-
|-
|[[1L 8s]]||agate||ag-||ag||rhymes with "eight", depending on one's pronunciation
|[[1L 8s]]||agate||ag- ||ag||Rhymes with "eight", depending on one's pronunciation; also called ''antisubneutralic<ref name="anti-name" />.''
|-
|-
|[[2L 7s]]||balzano||bal- /bæl/||bal||from Balzano scale in 20edo which is 2L 7s
|[[2L 7s]]||balzano||bal-||bz||Originally a name for 20edo's 2L 7s (and 2L 11) scales; bal- is pronounced /bæl/.
|-
|-
|[[3L 6s]]||tcherepnin||cher-||ch||common name
|[[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-||sq||from "half fourth" and "chthonic"
|[[5L 4s]]||semiquartal||cthon-||ct||From "half fourth"; cthon- is from "chthonic".
|-
|-
|[[6L 3s]]||hyrulic||hyru-||hy||allusion to [[triforce]] temperament
|[[6L 3s]]||hyrulic||hyru-||hy||References [[triforce]] temperament.
|-
|-
|[[7L 2s]]||armotonic||arm-||arm||arm- and armotonic references [[Armodue]]; 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
|-
|-
!Pattern!!Name!!Prefix<ref name="prefix" />!!Abbr.<ref name="abbr" />!!Etymology
!Pattern!!Name!!Prefix!!Abbr.!!Etymology
|-
|-
|[[1L 9s]]||olivnie||oli-||oli||rhymes with "nine", depending on one's pronunciation
|[[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 temperaments [[pajara]], [[injera]] and [[diaschismic]]
|[[2L 8s]]||jaric||jara-||ja||From [[pajara]], [[injera]], and [[diaschismic]] temperaments.
|-
|-
|[[3L 7s]]||sephiratonic||seph-||seph||from [[sephiroth]] temperament
|[[3L 7s]]||sephiroid||seph-|| sp||From [[sephiroth]] temperament.
|-
|-
|[[4L 6s]]||lime||lime-||lim||limes/4L 6s's steps tend to be smaller than lemons/6L 4s's steps
|[[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-||pwd||from 5-wood
|[[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||pronounced /'daɪˌkɔɪd/; from exotemperaments [[Dicot family#Dichotic|dichotic]] and [[dicot]] (dicoid)
|[[7L 3s]]||dicoid||dico-||di ||From [[Dicot family#Dichotic|dichotic]] and [[dicot]] (dicoid) exotemperaments; pronounced /'daɪˌkɔɪd/.
|-
|-
|[[8L 2s]]||taric||tara-||tar||from Hindi ''aṭhārah'' '[[#Taric (8L 2s)|18]]'
|[[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||from [[sinaic]]
|[[9L 1s]]|| sinatonic||sina-||si|| Derived from the generator being within the range of a [[sinaic]].
|}
|}
<references />
<references />
==Naming mos modes==
<blockquote>''No changes''. </blockquote>


==Generalization to non-mos scales==
===Names for smaller mosses===
<blockquote>''No changes''.</blockquote>
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.
{| 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.


== Extensions ==
==Frequently asked questions==
'''Do I need to use this system over temperament names?'''


=== Naming neutral and interordinal intervals ===
'''Why are intervals zero-indexed?'''
For a discussion of semi-moschroma-altered versions of mos intervals, see [[Neutral and interordinal intervals in MOS scales]].


=== Naming mosses outside the named range ===
'''What's the difference between mosdegrees and mosintervals?'''
For a discussion of mos names outside the named range, see [[TAMNAMS Extension|TAMNAMS extension]].


==Appendix==
===Reasoning for step ratio names===
{{Main|TAMNAMS/Appendix#Reasoning for step ratio names}}


=== Reasoning for mos pattern names ===
===Reasoning for mos interval names===
{{Main|TAMNAMS/Appendix#Reasoning for mos interval names}}
===Reasoning for mos pattern names===
{{Main|TAMNAMS/Appendix#Reasoning for mos pattern names}}


: ''Main article: [[TAMNAMS/Appendix#Reasoning for mos pattern names]]''
[[Category:TAMNAMS]]
: ''The following should be added to the above appendix section.''

Latest revision as of 09:39, 9 August 2024

The following is a draft for a proposed rewrite of the following page: TAMNAMS

The primary changes are as follows:

  • Base TAMNAMS applies to mosses with 6-10 notes.
  • Simplify A LOT of wording!

The original page can be compared with this page here.

TAMNAMS (read "tame names"; from Temperament-Agnostic Mos NAMing System), devised by the XA Discord in 2021, is a system of temperament-agnostic names for scales – primarily 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.

This article outlines TAMNAMS conventions as it applies to octave-equivalent moment of symmetry scales, or such scales with tempered octaves.

Credits

This page and its associated pages were mainly written by User:Godtone, User:SupahstarSaga, User:Inthar, and User:Ganaram inukshuk.

Step ratio spectrum

Simple step ratios

TAMNAMS provides names for nine specific simple step ratios. These correspond to the simplest edos that have the mos scale, and can be used in place of their respective step ratio.

Simple step ratio names
TAMNAMS Name Ratio Hardness Diatonic example
Equalized L:s = 1:1 1.000 7edo
Supersoft L:s = 4:3 1.333 26edo
Soft (or monosoft) L:s = 3:2 1.500 19edo
Semisoft L:s = 5:3 1.667 31edo
Basic L:s = 2:1 2.000 12edo
Semihard L:s = 5:2 2.500 29edo
Hard (or monohard) L:s = 3:1 3.000 17edo
Superhard L:s = 4:1 4.000 22edo
Collapsed L:s = 1:0 ∞ (infinity) 5edo

For example, the 5L 2s (diatonic) scale of 19edo has a step ratio of 3:2, which is soft, and is thus called soft diatonic. Tunings of a mos with L:s larger than that ratio are harder, and tunings with L:s smaller than that are softer.

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

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.

Step ratio range names
TAMNAMS Name Ratio range Hardness
Hyposoft 3:2 ≤ L:s ≤ 2:1 1.500 ≤ L/s ≤ 2.000
Ultrasoft 1:1 ≤ L:s ≤ 4:3 1.000 ≤ L/s ≤ 1.333
Parasoft 4:3 ≤ L:s ≤ 3:2 1.333 ≤ L/s ≤ 1.500
Quasisoft 3:2 ≤ L:s ≤ 5:3 1.500 ≤ L/s ≤ 1.667
Minisoft 5:3 ≤ L:s ≤ 2:1 1.667 ≤ L/s ≤ 2.000
Minihard 2:1 ≤ L:s ≤ 5:2 2.000 ≤ L/s ≤ 2.500
Quasihard 5:2 ≤ L:s ≤ 3:1 2.500 ≤ L/s ≤ 3.000
Parahard 3:1 ≤ L:s ≤ 4:1 3.000 ≤ L/s ≤ 4.000
Ultrahard 4:1 ≤ L:s ≤ 1:0 4.000 ≤ L/s ≤ ∞
Hypohard 2:1 ≤ L:s ≤ 3:1 2.000 ≤ L/s ≤ 3.000

Central spectrum

Central spectrum of step ratio ranges and specific step ratios
Step ratio ranges Specific step ratios Notes
1:1 (equalized) Trivial/pathological
1:1 to 2:1 (soft-of-basic) 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)
2:1 to 1:0 (hard-of-basic) 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 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

Expanded spectrum and other terminology

For a derivation of these ratio ranges, see <link>.

Naming mos intervals

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.

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 denote the sizes, or 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:

  • 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) 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 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.

There is one exception to the above rules: the designations of augmented, perfect, and diminished don't apply for the generators for nL ns mosses. Instead, major and minor is used, so as to prevent ambiguity over calling every interval perfect.

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.

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>.

Intervals of 5L 2s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-diastep Perfect 0-diastep P0dias 0 0.0 ¢
1-diastep Minor 1-diastep m1dias s 0.0 ¢ to 171.4 ¢
Major 1-diastep M1dias L 171.4 ¢ to 240.0 ¢
2-diastep Minor 2-diastep m2dias L + s 240.0 ¢ to 342.9 ¢
Major 2-diastep M2dias 2L 342.9 ¢ to 480.0 ¢
3-diastep Perfect 3-diastep P3dias 2L + s 480.0 ¢ to 514.3 ¢
Augmented 3-diastep A3dias 3L 514.3 ¢ to 720.0 ¢
4-diastep Diminished 4-diastep d4dias 2L + 2s 480.0 ¢ to 685.7 ¢
Perfect 4-diastep P4dias 3L + s 685.7 ¢ to 720.0 ¢
5-diastep Minor 5-diastep m5dias 3L + 2s 720.0 ¢ to 857.1 ¢
Major 5-diastep M5dias 4L + s 857.1 ¢ to 960.0 ¢
6-diastep Minor 6-diastep m6dias 4L + 2s 960.0 ¢ to 1028.6 ¢
Major 6-diastep M6dias 5L + s 1028.6 ¢ to 1200.0 ¢
7-diastep Perfect 7-diastep P7dias 5L + 2s 1200.0 ¢
Intervals of 4L 4s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-tetrawdstep Perfect 0-tetrawdstep P0ttws 0 0.0 ¢
1-tetrawdstep Minor 1-tetrawdstep m1ttws s 0.0 ¢ to 150.0 ¢
Major 1-tetrawdstep M1ttws L 150.0 ¢ to 300.0 ¢
2-tetrawdstep Perfect 2-tetrawdstep P2ttws L + s 300.0 ¢
3-tetrawdstep Minor 3-tetrawdstep m3ttws L + 2s 300.0 ¢ to 450.0 ¢
Major 3-tetrawdstep M3ttws 2L + s 450.0 ¢ to 600.0 ¢
4-tetrawdstep Perfect 4-tetrawdstep P4ttws 2L + 2s 600.0 ¢
5-tetrawdstep Minor 5-tetrawdstep m5ttws 2L + 3s 600.0 ¢ to 750.0 ¢
Major 5-tetrawdstep M5ttws 3L + 2s 750.0 ¢ to 900.0 ¢
6-tetrawdstep Perfect 6-tetrawdstep P6ttws 3L + 3s 900.0 ¢
7-tetrawdstep Minor 7-tetrawdstep m7ttws 3L + 4s 900.0 ¢ to 1050.0 ¢
Major 7-tetrawdstep M7ttws 4L + 3s 1050.0 ¢ to 1200.0 ¢
8-tetrawdstep Perfect 8-tetrawdstep P8ttws 4L + 4s 1200.0 ¢

Alterations by a chroma

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.

  • Raising a minor interval by a chroma makes it minor.
  • 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.

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.

Table of alterations, with abbreviations
Chromas Perfectable intervals Non-perfectable intervals
Interval quality Abbrev. Interval quality Abbrev.
+4 Quadruply-augmented A4 or A^4 Quadruply-augmented A4 or A^4
+3 Triply-augmented AAA, A3, or A^3 Triply-augmented AAA, A3, or A^3
+2 Doubly-augmented AA Doubly-augmented AA
+1 Augmented A Augmented A
0 Perfect P Major M
Minor m
-1 Diminished d Diminished d
-2 Doubly-diminished dd Doubly-diminished dd
-3 Triply-diminished ddd, d3, or d^3 Triply-diminished ddd, d3, or d^3
-4 Quadruply-diminished d4 or d^4 Quadruply-diminished d4 or d^4

Intervals smaller than a chroma

Interval name Absolute value of a...
Moschroma (generalized chroma, provided for reference) Large step minus a small step
Mosdiesis (generalized 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

The pitches of a mos are called k-mosdegrees (abbreviated kmd), 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

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 below for the convention we have used to name the mode).

To analyze a chord as an inversion of another chord (i.e. when the bass is not seen as the root), the following strategies can be used:

  1. One can write the root degree first: (6s, 0s, 2s, 7s). The first degree is assumed to be the tonic unless the following method is used:
  2. One can write "T" to the left of the tonic: (0s, 2s, T6s, 7s).
  3. One can use 0 for the root, using negative numbers for notes below the root. For example, to analyze (0s, 2s, 6s, 7s) on the 7-degree of the LsLLsLLs mode as being rooted on its 6s (thus on the 5-degree of LsLLsLLs), we write 5d(0s, -6s, -4s, 1s). The "5d" here is essential for avoiding confusion with the previous notation.
  4. If clarity is desired as to what the root position chord is, slash notation can be used as in conventional notation. Thus the above chord can be written 5d(0s 1s 2s 4s)/7d.

Naming mos modes

TAMNAMS uses Modal UDP notation to name modes. For example, the names of modes for 5L 3s are the names of the mos followed by the UDP of that mode.

For modes with altered scale degrees, the abbreviations for the scale degrees are listed after the UDP for the mode.

Notation, such as diamond-mos, can be used instead of the abbreviation of a mosdegree. For example, LsLsLLLs can be written "5L 3s 5|2 m4md". "5L 3s 5|2 @4d".


Scale degrees of the modes of 5L 3s
UDP Cyclic
order 		Step
pattern 		Scale degree (oneirodegree)
0 1 2 3 4 5 6 7 8
7|0 1 LLsLLsLs Perf. Maj. Maj. Perf. Maj. Aug. Maj. Maj. Perf.
6|1 4 LLsLsLLs Perf. Maj. Maj. Perf. Maj. Perf. Maj. Maj. Perf.
5|2 7 LsLLsLLs Perf. Maj. Min. Perf. Maj. Perf. Maj. Maj. Perf.
4|3 2 LsLLsLsL Perf. Maj. Min. Perf. Maj. Perf. Maj. Min. Perf.
3|4 5 LsLsLLsL Perf. Maj. Min. Perf. Min. Perf. Maj. Min. Perf.
2|5 8 sLLsLLsL Perf. Min. Min. Perf. Min. Perf. Maj. Min. Perf.
1|6 3 sLLsLsLL Perf. Min. Min. Perf. Min. Perf. Min. Min. Perf.
0|7 6 sLsLLsLL Perf. Min. Min. Dim. Min. Perf. Min. Min. Perf.
Scale degrees of the modes of 5L 3s (LsLsLLLs)
UDP and
alterations 		Cyclic
order 		Step
pattern 		Scale degree (oneirodegree)
0 1 2 3 4 5 6 7 8
5|2 m4md
3|4 M7md 		1 LsLsLLLs Perf. Maj. Min. Perf. Min. Perf. Maj. Maj. Perf.
2|5 d3md
0|7 M6md 		2 sLsLLLsL Perf. Min. Min. Dim. Min. Perf. Maj. Min. Perf.
7|0 m2md
5|2 A5md 		3 LsLLLsLs Perf. Maj. Min. Perf. Maj. Aug. Maj. Maj. Perf.
4|3 m1md
2|5 M4md 		4 sLLLsLsL Perf. Min. Min. Perf. Maj. Perf. Maj. Min. Perf.
7|0 A3md 5 LLLsLsLs Perf. Maj. Maj. Aug. Maj. Aug. Maj. Maj. Perf.
6|1 m7md
4|3 M2md 		6 LLsLsLsL Perf. Maj. Maj. Perf. Maj. Perf. Maj. Min. Perf.
3|4 m6md
1|6 M1md 		7 LsLsLsLL Perf. Maj. Min. Perf. Min. Perf. Min. Min. Perf.
0|7 d5md 8 sLsLsLLL Perf. Min. Min. Dim. Min. Dim. Min. Min. Perf.

Mos pattern names

This section contains unapproved namechanges. They are provided for reference/completeness and, unless approved, should not be included in the main-namespace rewrite.

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.

This list is maintained by User:Inthar and User:Godtone.

TAMNAMS mos names
6-note mosses
Pattern Name Prefix Abbr. Etymology
1L 5s selenite sel- sel References luna temperament (selenite is named after the moon); also called antimachinoid[1].
2L 4s malic mal- mal Sister mos of 4L 2s; apples have concave ends, whereas lemons/limes have convex ends.
3L 3s triwood triwd- tw Blackwood[10] and whitewood[14] generalized to 3 periods.
4L 2s citric citro- cit Parent (or subset) mos of 4L 6s and 6L 4s.
5L 1s machinoid mech- mk From machine temperament.
7-note mosses
Pattern Name Prefix Abbr. Etymology
1L 6s onyx on- on Sounds like "one-six" depending on one's pronunciation; also called anti-archeotonic[1].
2L 5s pelotonic pel- pel From pelog; also called antidiatonic[1], a common name.
3L 4s mosh mosh- mosh From "mohajira-ish", a name from Graham Breed's naming scheme.
4L 3s smitonic smi- smi From "sharp minor third".
5L 2s diatonic dia- dia
6L 1s archaeotonic arch- arc Originally a name for 13edo's 6L 1s scale; also called archæotonic/archeotonic[2].
8-note mosses
Pattern Name Prefix Abbr. Etymology
1L 7s spinel spin- sp Contains the string "pine", referencing its sister mos; also called antipine[1].
2L 6s subaric subar- sb Parent (or subset) mos of 2L 8s and 8L 2s.
3L 5s checkertonic check- chk From the Kite guitar checkerboard scale.
4L 4s tetrawood tetrawd- ttw Blackwood[10] and whitewood[14] generalized to 4 periods; also called diminished[3].
5L 3s oneirotonic oneiro- or Originally a name for 13edo's 5L 3s scale; also called oneiro[4].
6L 2s ekic ek- ek From echidna and hedgehog temperaments.
7L 1s pine pine- p From porcupine temperament.
9-note mosses
Pattern Name Prefix Abbr. Etymology
1L 8s agate ag- ag Rhymes with "eight", depending on one's pronunciation; also called antisubneutralic[1].
2L 7s balzano bal- bz Originally a name for 20edo's 2L 7s (and 2L 11) scales; bal- is pronounced /bæl/.
3L 6s tcherepnin cher- ch In reference to Tcherepnin's 9-note scale in 12edo.
4L 5s gramitonic gram- gm From "grave minor third".
5L 4s semiquartal cthon- ct From "half fourth"; cthon- is from "chthonic".
6L 3s hyrulic hyru- hy References triforce temperament.
7L 2s armotonic arm- am From Armodue theory; also called superdiatonic[3].
8L 1s subneutralic blu- bl Derived from the generator being between supraminor and neutral quality; blu- is from bleu temperament.
10-note mosses
Pattern Name Prefix Abbr. Etymology
1L 9s olivnie oli- ol Rhymes with "nine", depending on one's pronunciation; also called antisinatonic[1].
2L 8s jaric jara- ja From pajara, injera, and diaschismic temperaments.
3L 7s sephiroid seph- sp From sephiroth temperament.
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.
6L 4s lemon lem- le From lemba temperament. Also sister mos of 4L 6s.
7L 3s dicoid dico- di From dichotic and dicot (dicoid) exotemperaments; pronounced /'daɪˌkɔɪd/.
8L 2s taric tara- ta Sister mos of 2L 8s; based off of 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.
  1. ↑ 1.0 1.1 1.2 1.3 1.4 1.5 Alternate name based on the name of its sister mos, with anti- prefix added.
  2. ↑ Spelling variant.
  3. ↑ 3.0 3.1 Common name no longer recommend by TAMNAMS due to risk of ambiguity. Provided for reference.
  4. ↑ Shortened form of name.

Names for smaller mosses

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.

2-note mosses
Pattern Name Prefix Abbr. Must be 2/1-equivalent? Etymology
1L 1s trivial triv- tw No The simplest valid mos pattern.
monowood monowd- w Yes Blackwood[10] and whitewood[14] generalized to 1 period.
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.
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.
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

Main article: TAMNAMS/Appendix § Reasoning for step ratio names

Reasoning for mos interval names

Main article: TAMNAMS/Appendix § Reasoning for mos interval names

Reasoning for mos pattern names

Main article: TAMNAMS/Appendix § Reasoning for mos pattern names
Retrieved from "https://en.xen.wiki/index.php?title=User:Ganaram_inukshuk/TAMNAMS&oldid=149830"