User:Ganaram inukshuk/TAMNAMS: Difference between revisions

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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 In both cases, the mos structure is no longer valid.

===Step ratio ranges===

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.

In between the nine specific ratios there are eight named intermediate ranges of step ratios. These terms are used 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''.

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"

|+Step ratio range names

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==Naming mos intervals==

Mos intervals, the difference between scale ~~degrees~~, are named after the number of steps (large or small) they subtend. An interval that spans ''k'' mossteps is called a ''k-mosstep interval'', or simply a ''k-mosstep'' (abbreviated ''kms''). This can be further shortened to ''k-step'' if context allows.

Mos intervals, the difference between any two tones in the scale, are named after the number of steps (large or small) they subtend. An interval that spans ''k'' mossteps is called a ''k-mosstep interval'', or simply a ''k-mosstep'' (abbreviated ''kms''). This can be further shortened to ''k-step'' if context allows.

Generic mos intervals only denote how many mossteps an interval subtends. Mossteps are zero-indexed, counting the number of steps subtended rather than the number of scale degrees, meaning that the unison is called a ''0-mosstep'', since a unison has zero steps. A mosstep that reaches the octave can simply be called the ''octave''.

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* Raising or lowering a perfect interval makes it augmented or diminished, respectively.

Repetition of "A" or "d" is used to denote repeatedly augmented/diminished intervals, and is sufficient in most cases. It's typically uncommon to alter an interval more than three times, and superscript numbers or alternate notation is advised for such cases. The table below shows how ~~these would~~ be notated.

Repetition of "A" or "d" is used to denote repeatedly augmented/diminished intervals, and is sufficient in most cases. It's typically uncommon to alter an interval more than three times, and superscript numbers or alternate notation is advised for such cases. The table below shows how such intervals can be notated.

{| class="wikitable"

|+Table of alterations, with abbreviations

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|Quadruply-diminished (d<sup>4</sup> or d^4)

|}

===~~Naming neutral and interordinal~~ intervals~~===~~

===Other intervals and other terminology===

~~For a discussion of semi-moschroma-altered versions of mos intervals, see [[Neutral~~ and ~~interordinal k-mossteps]].~~

Intervals that have a perfect variety (the unison, period, and generators) are called ''perfectable intervals'', whereas intervals that do not have a perfect variety are called ''non-perfectable intervals''.

~~===Other~~ terminology===

~~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~~.

==Naming mos degrees==

~~Individual mos degrees, (that is, specific notes~~ of a mos ~~scale,) or~~ '''k-mosdegrees''' (abbreviated ''k''md), follow the same rules as that with mosstep intervals. 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.

The pitches of a mos are called '''k-mosdegrees''' (abbreviated ''k''md), and follow the same rules as that with mosstep intervals. 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.

===Naming mos chords===

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).

@@ Line 68: / Line 68: @@
 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.
 ===Step ratio ranges===
-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.
+In between the nine specific ratios there are eight named intermediate ranges of step ratios. These terms are used 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''.
-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"
 |+Step ratio range names
@@ Line 213: / Line 213: @@
 ==Naming mos intervals==
-Mos intervals, the difference between scale degrees, are named after the number of steps (large or small) they subtend. An interval that spans ''k'' mossteps is called a ''k-mosstep interval'', or simply a ''k-mosstep'' (abbreviated ''kms''). This can be further shortened to ''k-step'' if context allows.
+Mos intervals, the difference between any two tones in the scale, are named after the number of steps (large or small) they subtend. An interval that spans ''k'' mossteps is called a ''k-mosstep interval'', or simply a ''k-mosstep'' (abbreviated ''kms''). This can be further shortened to ''k-step'' if context allows.
 Generic mos intervals only denote how many mossteps an interval subtends. Mossteps are zero-indexed, counting the number of steps subtended rather than the number of scale degrees, meaning that the unison is called a ''0-mosstep'', since a unison has zero steps. A mosstep that reaches the octave can simply be called the ''octave''.
@@ Line 247: / Line 247: @@
 * Raising or lowering a perfect interval makes it augmented or diminished, respectively.
-Repetition of "A" or "d" is used to denote repeatedly augmented/diminished intervals, and is sufficient in most cases. It's typically uncommon to alter an interval more than three times, and superscript numbers or alternate notation is advised for such cases. The table below shows how these would be notated.
+Repetition of "A" or "d" is used to denote repeatedly augmented/diminished intervals, and is sufficient in most cases. It's typically uncommon to alter an interval more than three times, and superscript numbers or alternate notation is advised for such cases. The table below shows how such intervals can be notated.
 {| class="wikitable"
 |+Table of alterations, with abbreviations
@@ Line 293: / Line 293: @@
 |Quadruply-diminished (d<sup>4</sup> or d^4)
 |}
-===Naming neutral and interordinal intervals===
+===Other intervals and other terminology===
-For a discussion of semi-moschroma-altered versions of mos intervals, see [[Neutral and interordinal k-mossteps]].
+Intervals that have a perfect variety (the unison, period, and generators) are called ''perfectable intervals'', whereas intervals that do not have a perfect variety are called ''non-perfectable intervals''.
-===Other terminology===
-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.
 ==Naming mos degrees==
-Individual mos degrees, (that is, specific notes of a mos scale,) or '''k-mosdegrees''' (abbreviated ''k''md), follow the same rules as that with mosstep intervals. 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.
+The pitches of a mos are called '''k-mosdegrees''' (abbreviated ''k''md), and follow the same rules as that with mosstep intervals. 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.
 ===Naming mos chords===
 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).