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 name and describe moment-of-symmetry scales, or mosses, that is agnostic 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), and to describe the step pattern regardless of step ratio or temperament, the name ''diatonic'' is given for the step pattern ''5L 2s'' itself.

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

 

|-

|-

| [[7edo]]

|1.333

| [[26edo]]

| [[19edo]]

| [[31edo]]

| [[12edo]]

|2.500

| Hard (or monohard)

|3.000

|4.000

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. An equalized mos has L equal to s, so the mos pattern is no longer apparent. A collapsed mos has s = 0, merging adjacent tones s apart into a single tone. In both cases, the mos structure is no longer valid.

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.

|+Intermediate ranges

|2.000 ≤ L/s ≤ 3.000

{| class="wikitable"

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

! colspan="3" |Step ratio ranges

!Specific step ratios

!Notes

|

|

|

|'''1:1 (equalized)'''

| 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)'''

|Also called quintessential

| 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

This section's running example will be 3L 4s.

Note that a unison is a 0-mosstep, rather than a mos1st; likewise, the term 1-mosstep is used rather than a mos2nd. One might be tempted to generalize diatonic 1-indexed ordinal names: ''In 31edo's ultrasoft [[mosh]] scale, the perfect mosthird (aka Pmosh3rd) is a neutral third and the major mosfifth (aka Lmosh5th) is a perfect fifth.'' The way intervals are named above (and in 12edo theory) has a problem. An interval that's n steps wide is named ''(n+1)th''. This means that adding two intervals is more complicated than it should be. Stacking two fifths makes a ninth, when naively it would make a tenth. We're used to this for the diatonic scale, but when dealing with unfamiliar scale structures, it can be very confusing.

To overcome this, TAMNAMS uses a 0-indexed name system for non-diatonic mos intervals, which makes the arithmetic needed to understand mos intervals much smoother. Going up a 0-mosstep means to go up zero steps, and stacking two 4-mossteps produces an 8-mosstep, rather than stacking two mos5ths to produce a mos9th. The use of ordinal indexing is generally discouraged when referring to non-diatonic mos intervals.

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 are [[Distributional evenness|distributionally even]], every interval (except for the [[1/1|unison]] and [[2/1|octave]]) will be in no more than two sizes.

|+Specific interval sizes for 3L 4s

! rowspan="2" | Interval

! colspan="2" |Large size (LsLsLss)

! colspan="2" |Small size (ssLsLsL)

! Interval

! Specific mos interval

!Gens up

|0-mosstep (unison)

|Perfect unison

|P0ms

| rowspan="2" |1-mosstep

|Minor mosstep (or small mosstep)

|s

|Major mosstep (or large mosstep)

|M1ms

|L

|4

| rowspan="2" |2-mosstep

|Diminished 2-mosstep

|d2ms

|2s

| -6

| Perfect 2-mosstep

|L+s

|1

| rowspan="2" |3-mosstep

|Minor 3-mosstep

|1L+2s

| -2

|Major 3-mosstep

|2L+s

|5

| rowspan="2" |4-mosstep

|Minor 4-mosstep

|1L+3s

| -5

|2L+2s

|2

| rowspan="2" | 5-mosstep

|Perfect 5-mosstep

| 2L+3s

| -1

|Augmented 5-mosstep

|3L+2s

|6

| rowspan="2" |6-mosstep

|Minor 6-mosstep

|2L+4s

| -4

|Major 6-mosstep

|3L+3s

|3

|7-mosstep (octave)

|3L+4s

|0

|+Table of alterations, with abbreviations

!Number of chromas

!Perfect intervals

!Major/minor intervals

|Triply-augmented (AAA, A³, or A^3)

|Triply-augmented (AAA, A³, or A^3)

|Doubly-augmented (AA)

|Doubly-augmented (AA)

|Augmented (A)

|Augmented (A)

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

| rowspan="2" |Perfect (P)

|Major (M)

|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:

=== Naming neutral and interordinal intervals ===

Individual mos degrees, 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. 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-mosdegrees'' may also be shortened to ''k-degrees'' 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.

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 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.

== Mos pattern names ==

TAMNAMS uses the following names for selected small mosses. These names are optional; interval size names and step ratio names can be combined with conventional ''xL ys'' names. For example: ''21edo is the soft [[5L 3s]] tuning and its major mosthird is a neutral third of size 342.9 cents.''

1L ns names are named with the an- prefix if they are generalised names and anti- prefix if the name for the corresponding nL1s scale assumed a period of an octave.

|+ TAMNAMS moss names

!colspan=6| 2-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> !! Allows non-octave tunings?<ref name="general">whether the name can be used for mosses with no octaves; lightly tempered octaves are allowed;<br/>names for mosses with more than 5 notes do not admit nonoctave tunings because the names are specific to the corresponding valid tuning range</ref> !! Etymology

| [[2L 2s]] || biwood || biwd- || bw  || No; two periods must be an octave || from 2-wood

| [[3L 1s]] || tetric || tetra- || tt || Yes; can have any period || from tetra- for 4

!colspan=6| 5-note mosses (non-octave<ref name=general/>)

! Pattern !! Name !! Prefix<ref name=prefix/> !! Abbr.<ref name=abbr/> !! (Non-octave periods allowed)<ref name=general/> !! Etymology

| [[1L 4s]] || pedal || ped- || ped || || one big toe and four small toes

| [[2L 3s]] || pentic || pent- || pt || || common pentatonic; from penta- for 5

| [[3L 2s]] || antipentic || apent- || apt || || opposite pattern of common pentatonic mos

| [[4L 1s]] || manual || manu- || manu || || one thumb and four longer fingers

!colspan=6| 6-note mosses

! Pattern !! Name !! Prefix<ref name=prefix/> !! Abbr.<ref name=abbr/> !! See notes on tuning<ref name=general/> !! Etymology

| [[1L 5s]] || antimachinoid || amech- || amech || || opposite pattern of machinoid

| [[2L 4s]] || malic || mal- || mal || antrial mos w/ 2 periods per octave || apples have two concave ends, lemons have two pointy ends.

| [[3L 3s]] || triwood || triwd- || trw || trivial mos w/ 3 periods per octave || from 3-wood

| [[4L 2s]] || citric || citro- || cit || trial mos w/ 2 periods per octave || parent mos of lemon and lime

| [[5L 1s]] || machinoid || mech- || mech || || from [[machine]] temperament

!colspan=6| 7-note mosses

! Pattern !! Name !! Prefix<ref name=prefix/> !! Abbr.<ref name=abbr/> !! See notes on tuning<ref name=general/> !! Etymology

| [[1L 6s]] || onyx || on- || on || || from a ''lot'' of naming puns

| [[2L 5s]] || antidiatonic || pel- || pel || || pel- is from pelog

| [[3L 4s]] || mosh || mosh- || mosh || || Graham Breed's name; from "mohajira-ish"

| [[4L 3s]] || smitonic || smi- || smi || || from "sharp minor third"

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

| [[6L 1s]] || arch(a)eotonic || arch- || arch || || originally a name for 13edo's 6L 1s

!colspan=6| 8-note mosses

! Pattern !! Name !! Prefix<ref name=prefix/> !! Abbr.<ref name=abbr/> !! See notes on tuning<ref name=general/> !! Etymology

| [[2L 6s]] || subaric || subar- || subar || antetric mos w/ 2 periods per octave || largest subset mos of jaric and taric

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

| [[4L 4s]] || tetrawood; diminished || tetrawd- || ttw || trivial mos w/ 4 periods per octave || from 4-wood

| [[5L 3s]] || oneirotonic || oneiro- || onei || || originally a name for 13edo's 5L 3s

| [[6L 2s]] || ekic || ek- || ek || tetric mos w/ 2 periods per octave || from temperaments [[echidna]] and [[hedgehog]]

| [[7L 1s]] || pine || pine- || pine || || from [[porcupine]] temperament

!colspan=6| 9-note mosses

! Pattern !! Name !! Prefix<ref name=prefix/> !! Abbr.<ref name=abbr/> !! See notes on tuning<ref name=general/> !! Etymology

| [[1L 8s]] || antisubneutralic || ablu- || ablu || || opposite pattern of subneutralic

| [[3L 6s]] || tcherepnin || cher- || ch || antrial mos w/ 3 periods per octave || common name

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

| [[5L 4s]] || semiquartal || cthon- || cth || || from "half fourth" and "chthonic"

| [[6L 3s]] || hyrulic || hyru- || hyru || trial mos w/ 3 periods per octave || allusion to [[triforce]] temperament

| [[7L 2s]] || superdiatonic; armotonic || arm- || arm || || superdiatonic is a common name; arm- and armotonic references [[Armodue]]

| [[8L 1s]] || subneutralic || blu- || blu || || derived from the generator being between supraminor and neutral quality. blu- is from [[bleu]] temperament

!colspan=6| 10-note mosses

! Pattern !! Name !! Prefix<ref name=prefix/> !! Abbr.<ref name=abbr/> !! See notes on tuning<ref name=general/> !! Etymology

| [[9L 1s]] || sinatonic || sina- || si || || from [[sinaic]]

<references/>For the reasoning for these names, see [[TAMNAMS/Appendix|TAMNAMS/Appendix#Reasoning for mos pattern names]].

TAMNAMS uses [[UDP]] to name modes (i.e. the format pu|pd (p) for mosses with period 1/p of the equave, where u is the number of bright generators up and d is the number of bright generators down). For non-diatonic mosses, the diamond mos accidentals can be used to alter modes, and the degree modified is indicated using TAMNAMS's 0-indexing convention. For example, LsLsLLLs can be written "5L 3s 5|2 @4d".

 

For a mos pattern given a name in TAMNAMS, there is also the option of using the prefix for the pattern instead of saying "xL ys": the 5L 3s mode LsLLsLLs can be written "onei-5|2".

== Proposal: Extensions for Descendent MOSes ==

{{see also| TAMNAMS Extension}}

{{see also| User:Frostburn/TAMNAMS Extension}}

There is currently a proposal for a series of systematic extensions to this system for naming MOSes descended from the main ones listed here, as well as a few others.  These extensions are currently being worked on mainly by [[User:Frostburn|Frostburn]].

== Non-mos scales ==

=== Proposal: Naming 3-step-size scales' step ratios ===

Analogously to 2-step-size scales including mosses, scales 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''.

* 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''.

* 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''.

=== 3-step scale pattern names ===

=== Naming MV3 intervals ===

[[MV3]] scales, such as [[diasem]], have at most 3 sizes for each interval class. For every interval class that occurs in exactly 3 sizes, we use ''large'', ''medium'' and ''small k-step''. For every interval class that occurs in 2 sizes, we use ''large k-step'' and ''small k-step''.  If an interval class only has one size, then we call it ''perfect k-step''.

== Appendix ==

{{See also|TAMNAMS/Appendix}}

[[Category:MOS scale]]