User:Ganaram inukshuk/TAMNAMS: Difference between revisions

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

TAMNAMS names nine specific simple [[Blackwood's R|L:s ratios]]. These correspond to the simplest edos that have the mos scale.

{| class="wikitable"

|+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''.

 

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.

 

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.

|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

|

|

|

|'''3:2 (soft)'''

| 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)

|

|

|

|

|

|'''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

==Naming mos intervals==

Mos intervals are denoted as a ''quantity'' of '''mossteps''', large or small. An interval that is k mossteps wide is referred to as a ''k-mosstep interval'' or simply ''k-mosstep'' (abbreviated as ''k''ms). A mos's intervals are a 0-mosstep or [[1/1|''unison'']], followed by a 1-mosstep, then a 2-mosstep, and so on, until an n-mosstep interval equal to the ''period'' is reached, where n is thus the number of pitches in the mos per period. If a positive integer multiple of the period equals an octave (or some close approximation thereof), that interval can be referred to plainly as an octave if one prefers, but ''mosoctave'' should not be used unless there is exactly 7 notes per octave. The prefix of mos- in the term mosstep may be replaced with the mos's prefix, specified in the section mos pattern names.

In contexts where it doesn't cause ambiguity, the term ''k-mosstep'' can be shortened to ''k-step'', which allows for generalizing terminology described here to non-mos scales. Additionally, for [[non-octave]] scales that assume some generalisation of [[octave equivalence]], the term ''octave'' is replaced with the term ''equave''. Note this also means that if an n-mosstep interval is an octave, this can be referred to as the ''mosequave'' unambiguously and unconfusingly, regardless of what positive integer ''n'' is.

The phrase ''k-mosstep'' by itself does not specify the exact size of an interval. To refer to specific intervals, the familiar modifiers of ''major'', ''minor'', ''augmented'', ''diminished'' and ''perfect'' are used. As mosses have [[maximum variety]] 2, every interval (except for the [[1/1|unison]] and multiples of the [[period]] which is usually the [[2/1|octave]]) will be in no more than two sizes.

The modifiers of ''major'', ''minor'', ''augmented'', ''perfect'', and ''diminished'' (abbreviated as M, m, A, P, and d respectively) are given as such:

*Integer multiples of the period, such as the unison and (often but not always) the octave, are '''perfect''' because they only have one size each.

*The generating intervals, or generators, are referred to as '''perfect'''. Note that a mos actually has two generators - a bright and dark generator - and both generators have two sizes each, specifically, the only time the less common size appears is at the end of the generator chain. For our running example of 3L 4s, the generators are a 2-mosstep and 5-mosstep (the following subsection explains how to find these). Referring to a mos's generating intervals usually implies its perfect form (a.k.a the common form); specifically:

** 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 k-mossteps where k is greater than the number of pitches in the mos, those intervals have the same modifiers as an octave-reduced interval. Similarly, multiples of the octave are perfect, as are generators raised by some multiple of the octave.

For multi-period mosses, note that both the bright and dark generators appear in every period, not just every octave, as what it means for a mos to be multi-period is that there is multiple periods per octave so that some number of periods is (intended to be interpreted to) equal the octave. Therefore, generators that are raised or lowered by some integer multiple of the mos's period are also '''perfect'''. There is an important exception in interval naming for ''n''L ''n''s mosses, in which the generators are '''major''' and '''minor''' (for the bright and dark generator respectively) rather than augmented, perfect and diminished, and all other intervals (the octave, unison and multiples of the period) are perfect as would be expected. This is to prevent ambiguity over calling every interval present perfect.

{| class="wikitable"

|+Names for mos intervals for 3L 4s

!Specific intervals

!Interval size

!Abbreviation

!Gens up

| rowspan="2" |1-mosstep

| Minor mosstep (or small mosstep)

|s

|m1ms

| -3

|Major mosstep (or large mosstep)

|L

| M1ms

|4

| rowspan="2" |'''2-mosstep'''

| rowspan="2" | 3-mosstep

| Minor 3-mosstep

| 1L+2s

|m3ms

| -2

|Major 3-mosstep

| 2L+s

|M3ms

|5

| rowspan="2" |4-mosstep

|Minor 4-mosstep

|1L+3s

|m4ms

| -5

|Major 4-mosstep

| -1

|Augmented 5-mosstep

|3L+2s

| A5ms

| 6

| rowspan="2" |6-mosstep

| Minor 6-mosstep

|2L+4s

|m6ms

| -4

| Major 6-mosstep

|3L+3s

|M6ms

|3

| 7-mosstep (octave)

|Perfect octave

|3L+4s

| P7ms

|0

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.

|+Table of alterations, with abbreviations

| +3 chromas

| Triply-augmented (AAA, A³, or A^3)

| +2 chromas

|Doubly-augmented (AA)

| Doubly-augmented (AA)

| +1 chroma

|Augmented (A)

|Augmented (A)

| rowspan="2" | 0 chromas (unaltered)

| rowspan="2" |Perfect (P)

|Minor (m)

| -1 chroma

| Diminished (d)

|Diminished (d)

| -2 chromas

|Doubly-diminished (dd)

| Doubly-diminished (dd)

| -3 chromas

|Triply-diminished (ddd, d³, or d^3)

|Triply-diminished (ddd, d³, or d^3)

|}Other intervals include the following:

*A generalized [[Diesis (scale theory)|diesis]], or ''mosdiesis'': |L - 2s|

**''m-moskleisma'': |mosdiesis - s|

**''p-moskleisma'': |mosdiesis - (L-s)|

For a discussion of semi-moschroma-altered versions of mos intervals, see [[Neutral and interordinal k-mossteps]].

===Other terminology===

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.

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.

===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.

==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 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.

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>''.

|[[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-||mech||From [[machine]] temperament.

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

|[[1L 6s]]||onyx||on-||on||Sounds like "one-six" depending on one's pronunciation; also called ''anti-archeotonic<ref name="anti-name" />''.

|[[2L 5s]]||pelotonic||pel-||pel ||From pelog; also called ''antidiatonic<ref name="anti-name" />'', a common name.

|[[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-||arch||Originally a name for 13edo's 6L 1s scale; also called ''archæotonic/archeotonic<ref name="spelling">Spelling variant.</ref>''.

!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" />.''

|[[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]].

|[[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>.

|[[6L 2s]]||ekic||ek-||ek || From [[echidna]] and [[hedgehog]] temperaments.

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

!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-||bal||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" />''.

|[[4L 5s]]||gramitonic||gram-||gram||From "grave minor third".

|[[5L 4s]]||semiquartal||cthon-||cth||From "half fourth"; cthon- is from "chthonic".

|[[6L 3s]]||hyrulic||hyru-|| hy||References [[triforce]] temperament.

|[[7L 2s]]||armotonic||arm-||arm||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.

!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" />.''

|[[2L 8s]]||jaric||jara-||jar||From [[pajara]], [[injera]], and [[diaschismic]] temperaments.

|[[3L 7s]]||sephiroid||seph-||seph||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.

|[[5L 5s]]||pentawood||pentawd- || pw||Blackwood[10] and whitewood[14] generalized to 5 periods.

|[[6L 4s]]||lemon||lem-||lem||From [[lemba]] temperament.

|[[7L 3s]]||dicoid ||dico-|| dico||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.

|[[9L 1s]]|| sinatonic||sina- ||si||Derived from the generator being within the range of a [[sinaic]].