TAMNAMS: Difference between revisions

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.

== Credits ==

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

== Step ratio spectrum ==

{{Main| Step ratio }}

=== Simple step ratios ===

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

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! TAMNAMS Name

! Ratio

! Diatonic example

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| Equalized

| L:s = 1:1

| [[7edo]]

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| Supersoft

| L:s = 4:3

| [[26edo]]

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| Soft (or monosoft)

| L:s = 3:2

| [[19edo]]

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| Semisoft

| L:s = 5:3

| [[31edo]]

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| Basic

| L:s = 2:1

| [[12edo]]

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| Semihard

| L:s = 5:2

| [[29edo]]

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| Hard (or monohard)

| L:s = 3:1

| [[17edo]]

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| Superhard

| L:s = 4:1

| [[22edo]]

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| Collapsed

| L:s = 1:0

| [[5edo]]

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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]].)

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One may ask "what about [[hypersoft]] and [[hyperhard]], given you have [[hyposoft]] and [[hypohard]]?" and they would be right: see [[TAMNAMS/Appendix#Extended spectrum]] which details a more complete glossary that this set of terms is a subset of.

=== Central spectrum ===

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

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

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See [[TAMNAMS/Appendix#Extended spectrum]] which details a more complete glossary that this set of terms is a subset of.

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.

*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.

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| '''Perfect 2-mosstep'''

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| Major 3-mosstep

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| rowspan="2" | 4-mosstep

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| P7ms

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TAMNAMS also uses the modifiers of ''augmented'' and ''diminished'' to refer to ''alterations'' of a mos interval, much like with using sharps and flats in standard notation. Mos intervals are altered by raising or lowering it by a ''moschroma'' (or simply ''chroma'', if context allows), a generalized sharp/flat that is the difference between a large step and a small step. Raising a minor mos interval by a chroma makes it major; the reverse is true. Raising a major or perfect mos interval repeatedly makes an augmented, doubly-augmented, and a triply-augmented mos interval. Likewise, lowering a minor or perfect mos interval repeatedly makes a diminished, doubly-diminished, and a triply-diminished mos interval. A unison, period or equave that is itself augmented or diminished may also be referred to a ''mosaugmented'' or ''mosdiminished'' unison, period or equave, respectively. Here, the meaning of unison and octave does not change depending on the mos pattern, but the meanings of augmented and diminished do.

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.

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! Major/minor intervals

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=== Naming neutral and interordinal intervals===

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.

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).

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

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! colspan="6" | 3-note mosses (non-octave<ref name="general" />)

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

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! colspan="6" | 10-note mosses

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<references />

{{see also| TAMNAMS Extension}}

Various users have proposed names for mosses with more than 10 steps, commonly referred to as "TAMNAMS extensions". Chief among these are the following:

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.

{{MOS mode degrees|Scale Signature=5L 3s|MOS Prefix=mos|Mode Names=Default}}

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".

Zero-indexed interval names are also used for arbitrary scales, so we can still call a k-step interval a ''k-step'' and the corresponding degree the ''k-degree''. But instead of ''k-mosstep'' and ''k-mosdegree'', we use ''k-scalestep'' and ''k-scaledegree'' for arbitrary scales.

* 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 ==

=== Reasoning for step ratio names ===

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

=== Reasoning for mos pattern names ===

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

[[Category:Naming]]

[[Category:MOS scale]]