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Rewrote lead section and step ratio spectrum section based on my rewrite page and a remark from the talk page regarding temperament[k] names
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'''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 (designed especially with small octave-equivalent [[mos]]ses in mind), their intervals and their associated generator ranges, taking into account the relative sizes of large and small steps.
'''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.


== Step ratio spectrum ==
== Step ratio spectrum ==
=== Simple step ratios ===
=== Simple step ratios ===
The TAMNAMS system names nine specific simple [[Blackwood's R|L:s ratios]]. These correspond to the simplest edos that have the mos scale.
TAMNAMS names nine specific simple [[Blackwood's R|L:s ratios]]. These correspond to the simplest edos that have the mos scale.


{| class=wikitable
{| class=wikitable
Line 11: Line 13:
! TAMNAMS Name
! TAMNAMS Name
! Ratio
! Ratio
!Hardness
! Diatonic example
! Diatonic example
|-
|-
| Equalized
| Equalized
| L:s = 1:1
| L:s = 1:1
|1.000
| [[7edo]]
| [[7edo]]
|-
|-
| Supersoft
| Supersoft
| L:s = 4:3
| L:s = 4:3
|1.333
| [[26edo]]
| [[26edo]]
|-
|-
| Soft (or monosoft)
| Soft (or monosoft)
| L:s = 3:2
| L:s = 3:2
|1.500
| [[19edo]]
| [[19edo]]
|-
|-
| Semisoft
| Semisoft
| L:s = 5:3
| L:s = 5:3
|1.667
| [[31edo]]
| [[31edo]]
|-
|-
| Basic
| Basic
| L:s = 2:1
| L:s = 2:1
|2.000
| [[12edo]]
| [[12edo]]
|-
|-
| Semihard
| Semihard
| L:s = 5:2
| L:s = 5:2
|2.500
| [[29edo]]
| [[29edo]]
|-
|-
| Hard (or monohard)
| Hard (or monohard)
| L:s = 3:1
| L:s = 3:1
|3.000
| [[17edo]]
| [[17edo]]
|-
|-
| Superhard
| Superhard
| L:s = 4:1
| L:s = 4:1
|4.000
| [[22edo]]
| [[22edo]]
|-
|-
| Collapsed
| Collapsed
| L:s = 1:0
| L:s = 1:0
|∞ (infinity)
| [[5edo]]
| [[5edo]]
|}
|}


For example, the 5L2s (diatonic) scale of 19edo has a step ratio of 3:2, which is ''soft''. We call the 19edo diatonic scale ''soft diatonic''. Tunings of a mos with L:s larger are ''harder'', and tunings with L:s smaller are ''softer''.
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.
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.


=== Step ratio ranges ===
=== Step ratio ranges ===
In between the nine specific ratios there are eight ranges of ratios. Each range has a name. These names are useful for classifying mos tunings which don't match any of the nine simple step ratios. ''Hypohard'' could be used for tunings that are harder than basic but not as hard as the 3:1 tuning; similarly, ''hyposoft'' can be used for the range between soft and basic. Note that the soft-of-basic range is always strictly proper while the hard-of-basic range is often improper but is always proper in the case that there is 1 small step per period in the mos pattern.
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''.
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.
{| class="wikitable"
{| class="wikitable"
|+Intermediate ranges
|+Intermediate ranges
!TAMNAMS Name
!TAMNAMS Name
!Range
!Ratio range
!Hardness
|-
|-
|Hyposoft
|Hyposoft
|3:2 ≤ L:s ≤ 2:1
|3:2 ≤ L:s ≤ 2:1
|1.500 ≤ L/s ≤ 2.000
|-
|-
|Ultrasoft
|Ultrasoft
|1:1 ≤ L:s ≤ 4:3
|1:1 ≤ L:s ≤ 4:3
|1.000 ≤ L/s ≤ 1.333
|-
|-
|Parasoft
|Parasoft
|4:3 ≤ L:s ≤ 3:2
|4:3 ≤ L:s ≤ 3:2
|1.333 ≤ L/s ≤ 1.500
|-
|-
|Quasisoft
|Quasisoft
|3:2 ≤ L:s ≤ 5:3
|3:2 ≤ L:s ≤ 5:3
|1.500 ≤ L/s ≤ 1.667
|-
|-
|Minisoft
|Minisoft
|5:3 ≤ L:s ≤ 2:1
|5:3 ≤ L:s ≤ 2:1
|1.667 ≤ L/s ≤ 2.000
|-
|-
|Minihard
|Minihard
|2:1 ≤ L:s ≤ 5:2
|2:1 ≤ L:s ≤ 5:2
|2.000 ≤ L/s ≤ 2.500
|-
|-
|Quasihard
|Quasihard
|5:2 ≤ L:s ≤ 3:1
|5:2 ≤ L:s ≤ 3:1
|2.500 ≤ L/s ≤ 3.000
|-
|-
|Parahard
|Parahard
|3:1 ≤ L:s ≤ 4:1
|3:1 ≤ L:s ≤ 4:1
|3.000 ≤ L/s ≤ 4.000
|-
|-
|Ultrahard
|Ultrahard
|4:1 ≤ L:s ≤ 1:0
|4:1 ≤ L:s ≤ 1:0
|4.000 ≤ L/s ≤ ∞
|-
|-
|Hypohard
|Hypohard
|2:1 ≤ L:s ≤ 3:1
|2:1 ≤ L:s ≤ 3:1
|2.000 ≤ L/s ≤ 3.000
|}
|}


=== Central spectrum ===
=== Central spectrum ===
'''Equalized''': L/s = 1/1 (trivial/pathological)
{| class="wikitable"
 
|+Central spectrum of step ratio ranges and specific step ratios
::: ('''Ultrasoft''' range here, may also be called ''pseudoequalized'' if especially close to equalized.)
|-
 
! colspan="3" |Step ratio ranges
:: '''Supersoft''': L/s = 4/3
!Specific step ratios
 
!Notes
::: ('''Parasoft''' range here.)
|-
 
|
: '''Soft''': L/s = 3/2
|
 
|
::: (Beginning of '''hyposoft''' range here.)
|'''1:1 (equalized)'''
 
| Trivial/pathological
::: ('''Quasisoft''' range here.)
|-
 
| rowspan="7" |1:1 to 2:1 (soft-of-basic)
:: '''Semisoft''': L/s = 5/3
| colspan="2" | 1:1 to 4:3 (ultrasoft)
 
|
::: ('''Minisoft''' range here.)
|Step ratios especially close to 1:1 may be called pseudoequalized
 
|-
::: (End of '''hyposoft''' range here.)
|
 
|
'''Basic''': L/s = 2/1
|'''4:3 (supersoft)'''
 
|
::: (Beginning of '''hypohard''' range here.)
|-
 
| colspan="2" |4:3 to 3:2 (parasoft)
::: ('''Minihard''' range here.)
|
 
|
:: '''Semihard''': L/s = 5/2
|-
 
|
::: ('''Quasihard''' range here.)
|
 
|'''3:2 (soft)'''
::: (End of '''hypohard''' range here.)
|Also called monosoft
 
|-
: '''Hard''': L/s = 3/1
| rowspan="3" |3:2 to 2:1 (hyposoft)
 
|3:2 to 5:3 (quasisoft)
::: ('''Parahard''' range here.)
|
 
|
:: '''Superhard''': L/s = 4/1
|-
 
|
::: ('''Ultrahard''' range here, may also be called ''pseudocollapsed'' if especially close to collapsed.)
|'''5:3 (semisoft)'''
 
|
'''Collapsed''': L/s = 1/0 = infinity (trivial/pathological)
|-
 
|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
|}
== Naming mos intervals ==
== 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.
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.
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