User:Ganaram inukshuk/TAMNAMS: Difference between revisions

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==Naming mos intervals==

Mos intervals are ~~generally~~ named after the number of steps (large or small) they subtend.

Mos intervals 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.

~~The term "~~mosstep~~" can be further shortened to "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 is simply called the ''octave''.

~~=== Generic mos intervals ===~~

Specific mos intervals denote the sizes, or [[Interval variety|varieties]], an interval can be. 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 terms ''major'', ''minor'', ''augmented'', ''perfect'', and ''diminished'' are added before the phrase ''k-mosstep'' using the following rules:

~~Generic mos intervals only denote how many mossteps an interval subtends.~~

~~===Specific mos intervals===~~

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~~:

* Multiples of the period such as the root and octave are '''perfect''', as they only have one size each.

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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.

~~==== Examples ====~~

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.

<table>

<tr>

<td style="vertical-align:top">{{MOS intervals|Scale Signature=5L 2s}}</td>

<td style="vertical-align:top">{{MOS intervals|Scale Signature=5L 2s}}</td><td></td><td style="vertical-align:top">{{MOS intervals|Scale Signature=4L 4s}}</td>

<td style="vertical-align:top">{{MOS intervals|Scale Signature=4L 4s}}</td>

</tr>

</table>

===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.

The terms ''augmented'' and ''diminished'' are also used to describe intervals that are further lowered or raised by a ''chroma'', a generalized sharp or flat. The rules for alteration are as follows:

* Raising a minor interval by a chroma makes it minor. Lowering a major interval by a chroma makes it major. Thus, a chroma is the difference between a large and small step.

* Raising a major interval by a chroma makes it augmented.

* Lowering a minor interval by a chroma makes it diminished.

* Raising an augmented interval by a chroma makes it doubly augmented.

* Lowering a diminished interval by a chroma makes it doubly diminished.

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~~.

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. The table below shows how these would be notated.

{| class="wikitable"

|+Table of alterations, with abbreviations

|-

!Number of chromas

!~~Perfect~~ intervals

!Perfectable intervals

! Major/minor intervals

|-

| +3 chromas

| +4 chromas

|Triply-augmented (AAA, A³, or A^3)

|Quadruply-augmented (A4 or A^4)

|Triply-augmented (AAA, A³, or A^3)

|Quadruply-augmented (A4 or A^4)

|-

| +3 chromas

|Triply-augmented (AAA, A3, or A^3)

|-

| +2 chromas

|Doubly-augmented (AA)

|-

| +1 chroma

|Augmented (A)

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|Minor (m)

|-

| -1 chroma

|Diminished (d)

|-

| -2 chromas

|Doubly-diminished (dd)

|-

| -3 chromas

|Triply-diminished (ddd, d³, or d^3)

|Triply-diminished (ddd, d3, or d^3)

|Triply-diminished (ddd, d³, or d^3)

|Triply-diminished (ddd, d3, or d^3)

|-

| -4 chromas

|Quadruply-diminished (d4 or d^4)

|}

===Naming neutral and interordinal intervals===

@@ Line 213: / Line 213: @@
 ==Naming mos intervals==
-Mos intervals are generally named after the number of steps (large or small) they subtend.
+Mos intervals 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.
-The term "mosstep" can be further shortened to "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 is simply called the ''octave''.
-=== Generic mos intervals ===
+Specific mos intervals denote the sizes, or [[Interval variety|varieties]], an interval can be. 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 terms ''major'', ''minor'', ''augmented'', ''perfect'', and ''diminished'' are added before the phrase ''k-mosstep'' using the following rules:
-Generic mos intervals only denote how many mossteps an interval subtends.
-===Specific mos intervals===
-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:
 * Multiples of the period such as the root and octave are '''perfect''', as they only have one size each.
@@ Line 233: / Line 229: @@
 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.
-==== Examples ====
 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.
 <table>
 <tr>
-<td style="vertical-align:top">{{MOS intervals|Scale Signature=5L 2s}}</td>
+<td style="vertical-align:top">{{MOS intervals|Scale Signature=5L 2s}}</td><td></td><td style="vertical-align:top">{{MOS intervals|Scale Signature=4L 4s}}</td>
-<td style="vertical-align:top">{{MOS intervals|Scale Signature=4L 4s}}</td>
 </tr>
 </table>
 ===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.
+The terms ''augmented'' and ''diminished'' are also used to describe intervals that are further lowered or raised by a ''chroma'', a generalized sharp or flat. The rules for alteration are as follows:
+* Raising a minor interval by a chroma makes it minor. Lowering a major interval by a chroma makes it major. Thus, a chroma is the difference between a large and small step.
+* Raising a major interval by a chroma makes it augmented.
+* Lowering a minor interval by a chroma makes it diminished.
+* Raising an augmented interval by a chroma makes it doubly augmented.
+* Lowering a diminished interval by a chroma makes it doubly diminished.
-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.
+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. The table below shows how these would be notated.
 {| class="wikitable"
 |+Table of alterations, with abbreviations
 |-
 !Number of chromas
-!Perfect intervals
+!Perfectable intervals
 ! Major/minor intervals
 |-
-| +3 chromas
+| +4 chromas
-|Triply-augmented (AAA, A³, or A^3)
+|Quadruply-augmented (A<sup>4</sup> or A^4)
-|Triply-augmented (AAA, A³, or A^3)
+|Quadruply-augmented (A<sup>4</sup> or A^4)
+|-
+|  +3 chromas
+|Triply-augmented (AAA, A<sup>3</sup>, or A^3)
+|Triply-augmented (AAA, A<sup>3</sup>, or A^3)
 |-
-| +2 chromas
+|  +2 chromas
 |Doubly-augmented (AA)
 |Doubly-augmented (AA)
 |-
-| +1 chroma
+|  +1 chroma
 |Augmented (A)
 |Augmented (A)
@@ Line 271: / Line 275: @@
 |Minor (m)
 |-
-| -1 chroma
+|  -1 chroma
 |Diminished (d)
 |Diminished (d)
 |-
-| -2 chromas
+|  -2 chromas
 |Doubly-diminished (dd)
 |Doubly-diminished (dd)
 |-
 | -3 chromas
-|Triply-diminished (ddd, d³, or d^3)
+|Triply-diminished (ddd, d<sup>3</sup>, or d^3)
-|Triply-diminished (ddd, d³, or d^3)
+|Triply-diminished (ddd, d<sup>3</sup>, or d^3)
+|-
+|  -4 chromas
+|Quadruply-diminished (d<sup>4</sup> or d^4)
+|Quadruply-diminished (d<sup>4</sup> or d^4)
 |}
 ===Naming neutral and interordinal intervals===