User:Ganaram inukshuk/TAMEX: Difference between revisions

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~~Work~~-in-progress

{{Mbox|text=This article is a work-in-progress, '''proposed rewrite''' of the following page: [[TAMNAMS Extension]] and [[User:Ganaram inukshuk/TAMNAMS Extension]]}}

:''This page assumes the reader is familiar with [[TAMNAMS]] mos names, mos prefixes, and step ratios.''

'''TAMEX''' (from '''''T'''emperament'''-A'''gnostic '''M'''oment-of-Symmetry Scale '''Ex'''tension Description System''), originally devised by [[User:Frostburn|Frostburn]] and [[User:Ganaram inukshuk|Ganaram inukshuk]] as two separate naming schemes, is an extension to the mos pattern names provided by TAMNAMS. This scheme is a means of describing how ~~descendant scales~~ (namely, chromatic and enharmonic mosses) ~~with more than 10 steps~~ relate ~~back~~ to smaller mosses and, to a lesser extent, what step ~~ratios of the original mos is needed to produce~~ that descendant mos. Additionally, it is a means of generalizing the notion of a [[chromatic scale]] to nondiatonic mosses.

'''TAMEX''' (from '''''T'''emperament'''-A'''gnostic '''M'''oment-of-Symmetry Scale '''Ex'''tension Description System''), originally devised by [[User:Frostburn|Frostburn]] and [[User:Ganaram inukshuk|Ganaram inukshuk]] as two separate naming schemes, is an extension to the mos pattern names provided by TAMNAMS. This scheme is a means of describing how mosses with more than 10 steps (namely, chromatic and enharmonic mosses) relate to smaller, TAMNAMS-named mosses and, to a lesser extent, what step ratio produces that descendant mos. Additionally, it is a means of generalizing the notion of a [[chromatic scale]] to nondiatonic mosses.

Despite looking like a naming system, what TAMEX provides are ''descriptions'' of descendant mosses that relate to a single, TAMNAMS-named mos. Hence, "names" for mosses are ~~meant to be as~~ general as ~~possible and~~ can refer to ~~more than one mos~~.

Despite looking like a naming system, what TAMEX provides are ''descriptions'' of descendant mosses that relate to a single, TAMNAMS-named mos. Hence, "names" for mosses under this system are more general than typical mos names, as these phrases can refer to multiple mosses.

== Description scheme for TAMNAMS-named mosses ==

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* The grandchild scale of a mos is an ''enharmonic'' mos.

* The great-grandchild scale of a ''subchromatic'' mos.

* ~~In general~~, ~~a mos that is a~~ ''k''~~th descendant~~ of a named mos ~~is a ''~~k''th descendant.

* For great-great-grandchild mosses and beyond, the term ''descendant'' is used. Optionally, the number of generations between a named mos and descendant mos can be provided to produce the term k''th-order descendant.''

Descriptions can take on one of two forms: a description as two words, or a single word bearing the mos's prefix. Which one to be used is up the user and whichever form is best ~~depending on context. In the case of ''k''th descendants, the ordinal value ''k''th can be omitted to refer to any or all descendant mosses,~~ depending on context.

Descriptions can take on one of two forms: a description as two words, or a single word bearing the mos's prefix. Which one to be used is up the user and whichever form is best depending on context.

{| class="wikitable"

|+Base descriptions

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|(''k''th-order) ''mosprefix''-descendant

|}

=== Calculating the number of generations for ''k''th-order descendants ===

For a mos ''x''L ''y''s, where ''x''+''y'' is greater than 10:

# Let ''z'' and ''w'' be the number of large and small steps of the parent mos to be found. Assign to ''z'' and ''w'' the values ''x'' and ''y'' respectively. Let ''k'' = 0, where ''k'' is the number of generations away from ''z''L ''w''s.

# Let ''m1'' be equal to max(''z'', ''w'') and ''m2'' be equal to min(''z'', ''w'').

# Assign the value ''m2'' to ''z'' and value ''m1''-''m2'' to ''w''. Increment ''n'' by 1.

# If the sum of ''z'' and ''w'' is no more than 10, then the parent mos is ''z''L ''w''s, where ''x''L ''y''s is a ''k''th-order descendant of ''z''L ''w''s. If not, repeat the process starting at step 2.

=== Step ratio descriptions ===

Optionally, the names for a step ratio range, describing the step ratio of the root mos, can be added before these descriptions, either as a single word or prefix. Any step ratio range can be used for 4th-order descendants and beyond, as context allows.

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| rowspan="4" |(x+y)L xs

| rowspan="4" |1:1 to 2:1

| rowspan="4" |soft

| rowspan="4" |soft-of-basic

| rowspan="4" |s-

| rowspan="2" |(x+y)L (2x+y)s

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| rowspan="4" |xL (x+y)s

| rowspan="4" |2:1 to 1:0

| rowspan="4" |hard

| rowspan="4" |hard-of-basic

| rowspan="4" |h-

| rowspan="2" |(2x+y)L xs

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|}

=== ~~Example: descendants~~ of 5L 2s ===

== Examples ==

=== Descendants of 5L 2s ===

The descendants of 5L 2s can be organized as a scale tree, as shown.

{| class="wikitable"

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Line 209:

|}

With 5L 2s as the root mos:

* There are 2 chromatic ~~descendants~~, or '''diachromatic''' scales: 7L 5s and 5L 7s

* There are 2 1st-order descendants, chromatic scales, or specifically '''diachromatic''' scales: 7L 5s and 5L 7s

* There are 4 enharmonic ~~descendants~~, or '''diamonic''' scales: 7L 12s, 12L 7s, 12L 5s, and 5L 12s

* There are 4 2nd-order descendants, enharmonic scales, or specifically '''diamonic''' scales: 7L 12s, 12L 7s, 12L 5s, and 5L 12s

* There are 8 subchromatic ~~descendants~~, or '''diasubchromatic''' scales: 7L 19s, 19L 7s, 19L 12s, 12L 19s, 12L 17, 17L 12s, 17L 5s, and 5L 17s.

* There are 8 3rd-order descendants, subchromatic scales, or specifically '''diasubchromatic''' scales: 7L 19s, 19L 7s, 19L 12s, 12L 19s, 12L 17, 17L 12s, 17L 5s, and 5L 17s.

Each successive generation has twice as many mosses than the last, but all mosses within the same generation all share the same name:

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* There are 16 4th-order descendants, or '''4th-order diadescendant''' scales''.''

* There are 32 5th-order descendants, or '''5th-order diadescendant''' scales.

* There are 2 to the ''k''th power ''k''th-order descendants, or '''''k''th-order diadescendant''' scales.

* There are 2<sup>k</sup> (2 to the ''k''th power) ''k''th-order descendants, or '''''k''th-order diadescendant''' scales.

Step ratios ranges can be added to these descriptions, as shown.

{| class="wikitable"

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|5L 22s

|}

~~== Additional temperament-agnostic mos names ==~~

@@ Line 1: / Line 1: @@
-Work-in-progress
+{{Mbox|text=This article is a work-in-progress, '''proposed rewrite''' of the following page: [[TAMNAMS Extension]] and [[User:Ganaram inukshuk/TAMNAMS Extension]]}}
 :''This page assumes the reader is familiar with [[TAMNAMS]] mos names, mos prefixes, and step ratios.''
-'''TAMEX''' (from '''''T'''emperament'''-A'''gnostic '''M'''oment-of-Symmetry Scale '''Ex'''tension Description System''), originally devised by [[User:Frostburn|Frostburn]] and [[User:Ganaram inukshuk|Ganaram inukshuk]] as two separate naming schemes, is an extension to the mos pattern names provided by TAMNAMS. This scheme is a means of describing how descendant scales (namely, chromatic and enharmonic mosses) with more than 10 steps relate back to smaller mosses and, to a lesser extent, what step ratios of the original mos is needed to produce that descendant mos. Additionally, it is a means of generalizing the notion of a [[chromatic scale]] to nondiatonic mosses.
+'''TAMEX''' (from '''''T'''emperament'''-A'''gnostic '''M'''oment-of-Symmetry Scale '''Ex'''tension Description System''), originally devised by [[User:Frostburn|Frostburn]] and [[User:Ganaram inukshuk|Ganaram inukshuk]] as two separate naming schemes, is an extension to the mos pattern names provided by TAMNAMS. This scheme is a means of describing how mosses with more than 10 steps (namely, chromatic and enharmonic mosses) relate to smaller, TAMNAMS-named mosses and, to a lesser extent, what step ratio produces that descendant mos. Additionally, it is a means of generalizing the notion of a [[chromatic scale]] to nondiatonic mosses.
-Despite looking like a naming system, what TAMEX provides are ''descriptions'' of descendant mosses that relate to a single, TAMNAMS-named mos. Hence, "names" for mosses are meant to be as general as possible and can refer to more than one mos.
+Despite looking like a naming system, what TAMEX provides are ''descriptions'' of descendant mosses that relate to a single, TAMNAMS-named mos. Hence, "names" for mosses under this system are more general than typical mos names, as these phrases can refer to multiple mosses.
 == Description scheme for TAMNAMS-named mosses ==
@@ Line 13: / Line 13: @@
 * The grandchild scale of a mos is an ''enharmonic'' mos.
 * The great-grandchild scale of a ''subchromatic'' mos.
-* In general, a mos that is a ''k''th descendant of a named mos is a ''k''th descendant.
+* For great-great-grandchild mosses and beyond, the term ''descendant'' is used. Optionally, the number of generations between a named mos and descendant mos can be provided to produce the term k''th-order descendant.''
-Descriptions can take on one of two forms: a description as two words, or a single word bearing the mos's prefix. Which one to be used is up the user and whichever form is best depending on context. In the case of ''k''th descendants, the ordinal value ''k''th can be omitted to refer to any or all descendant mosses, depending on context.
+Descriptions can take on one of two forms: a description as two words, or a single word bearing the mos's prefix. Which one to be used is up the user and whichever form is best depending on context.
 {| class="wikitable"
 |+Base descriptions
@@ Line 39: / Line 39: @@
 |(''k''th-order) ''mosprefix''-descendant
 |}
+=== Calculating the number of generations for ''k''th-order descendants ===
+For a mos ''x''L ''y''s, where ''x''+''y'' is greater than 10:
+# Let ''z'' and ''w'' be the number of large and small steps of the parent mos to be found. Assign to ''z'' and ''w'' the values ''x'' and ''y'' respectively. Let ''k'' = 0, where ''k'' is the number of generations away from ''z''L ''w''s.
+# Let ''m1'' be equal to max(''z'', ''w'') and ''m2'' be equal to min(''z'', ''w'').
+# Assign the value ''m2'' to ''z'' and value ''m1''-''m2'' to ''w''. Increment ''n'' by 1.
+# If the sum of ''z'' and ''w'' is no more than 10, then the parent mos is ''z''L ''w''s, where ''x''L ''y''s is a ''k''th-order descendant of ''z''L ''w''s. If not, repeat the process starting at step 2.
 === Step ratio descriptions ===
 Optionally, the names for a step ratio range, describing the step ratio of the root mos, can be added before these descriptions, either as a single word or prefix. Any step ratio range can be used for 4th-order descendants and beyond, as context allows.
@@ Line 71: / Line 80: @@
 | rowspan="4" |(x+y)L xs
 | rowspan="4" |1:1 to 2:1
-| rowspan="4" |soft
+| rowspan="4" |soft-of-basic
 | rowspan="4" |s-
 | rowspan="2" |(x+y)L (2x+y)s
@@ Line 103: / Line 112: @@
 | rowspan="4" |xL (x+y)s
 | rowspan="4" |2:1 to 1:0
-| rowspan="4" |hard
+| rowspan="4" |hard-of-basic
 | rowspan="4" |h-
 | rowspan="2" |(2x+y)L xs
@@ Line 134: / Line 143: @@
 |}
-=== Example: descendants of 5L 2s ===
+== Examples ==
+=== Descendants of 5L 2s ===
 The descendants of 5L 2s can be organized as a scale tree, as shown.
 {| class="wikitable"
@@ Line 199: / Line 209: @@
 |}
 With 5L 2s as the root mos:
-* There are 2 chromatic descendants, or '''diachromatic''' scales: 7L 5s and 5L 7s
+* There are 2 1st-order descendants, chromatic scales, or specifically '''diachromatic''' scales: 7L 5s and 5L 7s
-* There are 4 enharmonic descendants, or '''diamonic''' scales: 7L 12s, 12L 7s, 12L 5s, and 5L 12s
+* There are 4 2nd-order descendants, enharmonic scales, or specifically '''diamonic''' scales: 7L 12s, 12L 7s, 12L 5s, and 5L 12s
-* There are 8 subchromatic descendants, or '''diasubchromatic''' scales: 7L 19s, 19L 7s, 19L 12s, 12L 19s, 12L 17, 17L 12s, 17L 5s, and 5L 17s.
+* There are 8 3rd-order descendants, subchromatic scales, or specifically '''diasubchromatic''' scales: 7L 19s, 19L 7s, 19L 12s, 12L 19s, 12L 17, 17L 12s, 17L 5s, and 5L 17s.
 Each successive generation has twice as many mosses than the last, but all mosses within the same generation all share the same name:
@@ Line 207: / Line 217: @@
 * There are 16 4th-order descendants, or '''4th-order diadescendant''' scales''.''
 * There are 32 5th-order descendants, or '''5th-order diadescendant''' scales.
-* There are 2 to the ''k''th power ''k''th-order descendants, or '''''k''th-order diadescendant''' scales.
+* There are 2<sup>k</sup> (2 to the ''k''th power) ''k''th-order descendants, or '''''k''th-order diadescendant''' scales.
 Step ratios ranges can be added to these descriptions, as shown.
 {| class="wikitable"
@@ Line 298: / Line 308: @@
 |5L 22s
 |}
-== Additional temperament-agnostic mos names ==