User:Ganaram inukshuk/TAMNAMS: Difference between revisions

{{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.

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 [[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]]

|[[26edo]]

|Soft (or monosoft)

|L:s = 3:2

|1.500

|[[19edo]]

|[[31edo]]

| Basic

|L:s = 2:1

|2.000

|[[12edo]]

|L:s = 5:2

|[[29edo]]

|3.000

|[[22edo]]

|[[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.

 

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''.

|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

|5:3 ≤ L:s ≤ 2:1

|1.667 ≤ L/s ≤ 2.000

|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

|}

{| class="wikitable center-all"

|+Central spectrum of step ratio ranges and specific step ratios

! colspan="3" |Step ratio ranges

|

|

|

|'''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)'''

| rowspan="3" |3:2 to 2:1 (hyposoft)

|3:2 to 5:3 (quasisoft)

|

|

|'''5:3 (semisoft)'''

|

|

|

|

|'''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 ===

==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 [[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:

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>.

<td style="vertical-align:top">{{MOS intervals|Scale Signature=5L 2s}}</td><td style="vertical-align:top">{{MOS intervals|Scale Signature=4L 4s}}</td>

===Alterations by a chroma===

* 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

!Abbrev.

| +4

|Quadruply-augmented

|A⁴ or A^4

|Quadruply-augmented

|A⁴ or A^4

| +3

|Triply-augmented

|Doubly-augmented

| +1

|Augmented

|A

|Augmented

|A

| rowspan="2" |0

| rowspan="2" |Perfect

| rowspan="2" |P

|Major

|M

|Minor

| -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

|}

 

{| class="wikitable"

! Absolute value of a...

|Moschroma (generalized [[chroma]], provided for reference)

| 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.

==Naming mos degrees==

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.

===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).

#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.

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|MODMOS Step Pattern=LsLsLLLs|Mode Names=Default}}

''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]].

! colspan="5" |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<ref name="anti-name">Alternate name based on the name of its sister mos, with anti- prefix added.</ref>''.

! colspan="5" |7-note mosses

|[[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".

|[[5L 2s]]|| diatonic||dia-||dia||

|[[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

!Pattern!! Name!!Prefix!!Abbr.!!Etymology

|[[1L 7s]]||spinel||spin-||sp||Contains the string "pine", referencing its sister mos; also called ''antipine<ref name="anti-name" />.''

|-

|[[3L 5s]]||checkertonic||check-||chk||From the [[Kite Giedraitis's Categorizations of 41edo Scales|Kite guitar checkerboard scale]].

|[[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-||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.

|[[7L 1s]]||pine||pine-||p||From [[porcupine]] temperament.

! colspan="5" | 9-note mosses

!Pattern!!Name!!Prefix!!Abbr.!!Etymology

|[[1L 8s]]||agate||ag- ||ag||Rhymes with "eight", depending on one's pronunciation; also called ''antisubneutralic<ref name="anti-name" />.''

|[[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<ref name="unofficial" />.''

|[[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

!Pattern!!Name!!Prefix!!Abbr.!!Etymology

|[[1L 9s]]||olivnie ||oli- ||ol||Rhymes with "nine", depending on one's pronunciation; also called ''antisinatonic<ref name="anti-name" />.''

|[[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 [[Dicot family#Dichotic|dichotic]] and [[dicot]] (dicoid) exotemperaments; pronounced /'daɪˌkɔɪd/.

|[[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]].

|}

 

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.

| rowspan="2" |[[1L 1s]]|| trivial|| triv-||tw

| Blackwood[10] and whitewood[14] generalized to 1 period.

! colspan="6" |3-note mosses

!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

!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.