TAMNAMS: Difference between revisions

'''TAMNAMS''' (read as "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.

{{Main| Step ratio }}

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. It has been argued, however, that this is not a particularly important property, both because "improper" MOSSes still admit an ordering if you allow "off-by-one" errors and because larger moses tend to sound more distinct when L/s > 1, which is in some sense the more vast/varied side of the tuning spectrum, because as L/s becomes larger, the scale becomes increasingly close to the [[equalized]] tuning, which is usually radically different from most "proper" tunings while softer tunings don't have much room to be different compared to the basic tuning. (This is explained in more detail in [[TAMNAMS/Appendix#Extending the spectrum's edges]].)

|+ style="font-size: 110%;" | Central spectrum of step ratio ranges and specific step ratios

! Specific step ratios

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

| rowspan="7" | 1:1 to 2:1 (soft-of-basic)

| colspan="2" | 1:1 to 4:3 (ultrasoft)

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| '''4:3 (supersoft)'''

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| colspan="2" | 4:3 to 3:2 (parasoft)

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

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

| 3:2 to 5:3 (quasisoft)

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

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| 5:3 to 2:1 (minisoft)

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| '''2:1 (basic)'''

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| rowspan="7" | 2:1 to 1:0 (hard-of-basic)

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

| 2:1 to 5:2 (minihard)

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| '''5:2 (semihard)'''

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| 5:2 to 3:1 (quasihard)

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| '''3:1 (hard)'''

| colspan="2" | 3:1 to 4:1 (parahard)

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| '''4:1 (superhard)'''

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| colspan="2" | 4:1 to 1:0 (ultrahard)

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| '''1:0 (collapsed)'''

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

*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 bright generator is '''perfect''', and the small size is '''diminished'''.

*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.

|+ style="font-size: 110%;" | Names for mos intervals for 3L 4s

| −3

| −6

| −2

| −5

| −1

| −4

|+ style="font-size: 110%;" | Table of alterations, with abbreviations

| −1 chroma

| −2 chromas

| −3 chromas

|+Mos intervals smaller than a moschroma

|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

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 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.

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 2-step is a neutral third of size 342.9 cents.''

=== Names for mosses with 2-10 steps ===

|+ style="font-size: 110%;" | TAMNAMS moss names

! 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

| [[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

| [[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

| [[1L 7s]] || antipine || apine- || apine || || opposite pattern of pine

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

| [[4L 4s]] || tetrawood (aka diminished<ref name="unofficial">This is a common name but is no longer the recommended TAMNAMS name due to ambiguity; we provide it here for reference.</ref>) || 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

| [[2L 7s]] || balzano || bal- /bæl/ || bal || || from Balzano scale in 20edo which is 2L 7s

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

| [[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]] || armotonic (aka superdiatonic<ref name="unofficial" />) || arm- || arm || || arm-(otonic) references [[Armodue]]

| [[8L 1s]] || subneutralic || blu- || blu || || from the gen's flat 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

| [[1L 9s]] || antisinatonic || asina- || asi || || opposite pattern of sinatonic

| [[2L 8s]] || jaric || jara- || jar || pedal mos w/ 2 periods per octave || from temperaments [[pajara]], [[injera]] and [[diaschismic]]

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

<references />

=== Expansion to mosses with more than 10 steps ===

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.

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".

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".

Analogously to binary scales including mosses, 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).

[[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 ==