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{{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.
{{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.
* Extension/generalizations are moved to (sub)pages.}}'''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.
* Extension/generalizations are moved to (sub)pages.
* 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.
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.
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== Step ratio spectrum==
== Step ratio spectrum==
===Simple step ratios===
===Simple step ratios===
TAMNAMS provides names for nine specific simple [[Blackwood's R|L:s ratios]]. These correspond to the simplest edos that have the mos scale, and can be usedd in place of their respective step ratio.
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.
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===Specific mos intervals===
===Specific mos intervals===
Specific mos intervals denote the specific sizes 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 a large and small size.
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 designations of ''major'', ''minor'', ''augmented'', ''perfect'', and ''diminished'' are applied in the following manner:


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.
* Multiples of the period such as the root and octave are '''perfect''', as they only have one size each.
 
* The generators use the terms '''augmented''', '''perfect''', and '''diminished'''. Note that there are two generators (bright and dark), where their perfect varieties are used to generate the scale. Thus:
The modifiers of ''major'', ''minor'', ''augmented'', ''perfect'', and ''diminished'' (abbreviated as M, m, A, P, and d respectively) are given as such:
** The large size of the bright generator is '''perfect''', and the small size is '''diminished'''.
*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'''.
**The large size of the dark generator is '''augmented''', and the small size is '''perfect'''.
**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 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.
The designations for these intervals repeat for intervals that exceed the octave; in other words, an interval that is raised by an octave will be the same interval quality that it was before raising.
{| class="wikitable"
 
|+Names for mos intervals for 3L 4s
Additionally, the designations of augmented, perfect, and diminished don't apply for the generators for mosses of the form ''n''L ''n''s; instead, major and minor is used. This is to prevent ambiguity over calling every interval perfect.
!Interval classes
 
!Specific intervals
==== Examples ====
!Interval size
Examples using 5L 2s and 4L 4s are provided below. Note that 5L 2s interval names are identical to that of standard music theory, apart from the 0-indexed interval names. For a detailed derivation of these intervals, see the appendix.{{MOS intervals|Scale Signature=5L 2s}}{{MOS intervals|Scale Signature=4L 4s}}
! Abbreviation
 
!Gens up
|-
|0-mosstep (unison)
|Perfect unison
|0
|P0ms
|0
|-
| rowspan="2" |1-mosstep
|Minor mosstep (or small mosstep)
|s
|m1ms
| -3
|-
|Major mosstep (or large mosstep)
|L
|M1ms
|4
|-
| rowspan="2" |'''2-mosstep'''
|Diminished 2-mosstep
|2s
|d2ms
|  -6
|-
|'''Perfect 2-mosstep'''
|L+s
|P2ms
| 1
|-
| 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
|2L+2s
|M4ms
|2
|-
| rowspan="2" |'''5-mosstep'''
|'''Perfect 5-mosstep'''
|2L+3s
|P5ms
| -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
|}
===Alterations by a chroma===
===Alterations by a chroma===
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.
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.
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