User:Ganaram inukshuk/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.

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

== Step ratio spectrum==

|+Step ratio names

|-

!Ratio

! Hardness

|Equalized

|L:s = 1:1

|[[7edo]]

|-

|-

|Semisoft

|1.667

|[[31edo]]

|-

|L:s = 2:1

|2.000

|[[22edo]]

|-

|L:s = 1:0

|[[5edo]]

|}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 and define the boundaries for valid tuning ranges. An equalized mos has large and small steps be the same size (L=s), so the mos pattern is no longer apparent. A collapsed mos has small steps shrunken down to zero (s=0), merging adjacent tones s apart into a single tone. In both cases, the mos structure is no longer valid.

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.

|Parasoft

|4:3 ≤ L:s ≤ 3:2

|-

|Quasisoft

|Minihard

|2:1 ≤ L:s ≤ 5:2

|-

|Quasihard

|-

|Ultrahard

|4.000 ≤ L/s ≤ ∞

|-

*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.

!Specific intervals

!Interval size

!Gens up

|-

|0-mosstep (unison)

|0

|P0ms

|-

| rowspan="2" |1-mosstep

|s

|m1ms

|Major mosstep (or large mosstep)

|L

|4

|-

| rowspan="2" |'''2-mosstep'''

|Diminished 2-mosstep

|d2ms

|-

|'''Perfect 2-mosstep'''

|L+s

|-

|m3ms

| -2

|-

|Major 3-mosstep

|M3ms

|5

|Major 4-mosstep

|2L+2s

|2

|-

| rowspan="2" |'''5-mosstep'''

|'''Perfect 5-mosstep'''

|P5ms

| -1

|-

|Augmented 5-mosstep

|-

| rowspan="2" |6-mosstep

| -4

|-

|3L+3s

|M6ms

|3

|-

|Perfect octave

|3L+4s

|0

|}

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.

|-

!Number of chromas

|-

| +3 chromas

|Triply-augmented (AAA, A³, or A^3)

|-

|Doubly-augmented (AA)

|-

| +1 chroma

|Augmented (A)

|-

| rowspan="2" |Perfect (P)

|Major (M)

|-

| -1 chroma

|Diminished (d)

|-

| -2 chromas

|Doubly-diminished (dd)

|-

| -3 chromas

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".

''This section contains unapproved namechanges. They are provided for reference/completeness and, unless approved, should not be included in the main-namespace rewrite.''

! colspan="5" |6-note mosses

|-

|-

(Provided for lack of a better name)

|-

|[[2L 4s]]||malic||mal-||mal||Sister mos of 4L 2s; apples have concave ends, whereas lemons/limes have convex ends.

|-

|-

|[[4L 2s]]||citric||citro-||cit||Parent (or subset) mos of 4L 6s and 6L 4s.

|-

|-

|-

|-

|-

|-

|-

|-

|-

|-

! colspan="5" |8-note mosses

|-

|-

|[[1L 7s]]||spinel||spin-||sp||Contains the string "pine", referencing its sister mos; also called ''antipine<ref name="anti-name" />.''

|-

|-

|-

|-

|-

|-

|-

|-

|-

|-

|[[2L 7s]]||balzano||bal-||bal||Originally a name for 20edo's 2L 7s (and 2L 11) scales; bal- is pronounced /bæl/.

|-

|-

|-

|[[5L 4s]]||semiquartal||cthon-||cth||From "half fourth"; cthon- is from "chthonic".

|-

|-

|[[7L 2s]]||armotonic||arm-||arm||From [[Armodue]] theory; also called ''superdiatonic<ref name="unofficial" />.''

|-

|-

! colspan="5" |10-note mosses

!Pattern!!Name!!Prefix!!Abbr.!!Etymology

|-

|-

|[[2L 8s]]||jaric||jara-||jar||From [[pajara]], [[injera]], and [[diaschismic]] temperaments.

|-

|-

|-

|-

|-

|-

|-

|}

<references />

===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''.

===Reasoning for step ratio names===

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