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

!Base mos

!Chromatic mosses

(1st descendants)

(1st-order descendants)

!Enharmonic mosses

(2nd descendants)

(2nd-order descendants)

!Subchromatic mosses

(3rd descendants)

(3rd-order descendants)

!''k''th descendant mosses

!''k''th-order descendant mosses

|-

|''mos-name''

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|enharmonic ''mos-name''

|subchromatic ''mos-name''

|(''k''th) ''mos-name'' descendant

|(''k''th-order) ''mos-name'' descendant

|-

|''mos-name''

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|''mosprefix''-monic

|''mosprefix''-subchromatic

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

|(''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 descendants and beyond, as context allows.

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.

{| class="wikitable"

|+Step ratio descriptions

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! colspan="2" |Base mos

! colspan="4" |Chromatic mosses

(1st descendants)

(1st-order descendants)

! colspan="4" |Enharmonic mosses

(2nd descendants)

(2nd-order descendants)

! colspan="4" |Subchromatic mosses

(3rd descendants)

(3rd-order descendants)

|-

!Mos

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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"

|+Descendant mosses of 5L 2s

!Base mos

!1st descendants

!1st-order descendants

!2nd descendants

!2nd-order descendants

!3rd descendants

!3rd-order descendants

!4th descendants

!4th-order descendants

!5th descendants

!5th-order descendants

|-

| rowspan="16" |5L 2s

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|}

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:

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

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

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

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

* There are 2 to the ''k''th power ''k''th descendants, or '''''k''th 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"

|+Descendant mosses of 5L 2s

! colspan="2" |Base mos

! colspan="2" |1st descendants

! colspan="2" |1st-order descendants

! colspan="2" |2nd descendants

! colspan="2" |2nd-order descendants

! colspan="2" |3rd descendants

! colspan="2" |3rd-order descendants

! colspan="2" |4th descendants

! colspan="2" |4th-order descendants

|-

!Mos

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| rowspan="2" |ultrasoft diasubchromatic

|7L 26s

| rowspan="2" |ultrasoft 4th diadescendants

| rowspan="2" |ultrasoft 4th-order diadescendants

|-

|26L 7s

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| rowspan="2" |parasoft diasubchromatic

|26L 19s

| rowspan="2" |parasoft 4th diadescendants

| rowspan="2" |parasoft 4th-order diadescendants

|-

|19L 26s

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| rowspan="2" |quasisoft diasubchromatic

|19L 31s

| rowspan="2" |quasisoft 4th diadescendants

| rowspan="2" |quasisoft 4th-order diadescendants

|-

|31L 19s

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| rowspan="2" |minisoft diasubchromatic

|31L 12s

| rowspan="2" |minisoft 4th diadescendants

| rowspan="2" |minisoft 4th-order diadescendants

|-

|12L 31s

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| rowspan="2" |minihard diasubchromatic

|12L 29s

| rowspan="2" |minihard 4th diadescendants

| rowspan="2" |minihard 4th-order diadescendants

|-

|29L 12s

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| rowspan="2" |quasisoft diasubchromatic

|29L 17s

| rowspan="2" |quasihard 4th diadescendants

| rowspan="2" |quasihard 4th-order diadescendants

|-

|17L 29s

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| rowspan="2" |parahard diasubchromatic

|17L 22s

| rowspan="2" |parahard4th diadescendants

| rowspan="2" |parahard4th-order diadescendants

|-

|22L 17s

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| rowspan="2" |ultrahard diasubchromatic

|22L 5s

| rowspan="2" |ultrahard 4th diadescendants

| rowspan="2" |ultrahard 4th-order diadescendants

|-

|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
 !Base mos
 !Chromatic mosses
-(1st descendants)
+(1st-order descendants)
 !Enharmonic mosses
-(2nd descendants)
+(2nd-order descendants)
 !Subchromatic mosses
-(3rd descendants)
+(3rd-order descendants)
-!''k''th descendant mosses
+!''k''th-order descendant mosses
 |-
 |''mos-name''
@@ Line 31: / Line 31: @@
 |enharmonic ''mos-name''
 |subchromatic ''mos-name''
-|(''k''th) ''mos-name'' descendant
+|(''k''th-order) ''mos-name'' descendant
 |-
 |''mos-name''
@@ Line 37: / Line 37: @@
 |''mosprefix''-monic
 |''mosprefix''-subchromatic
-|(''k''th) ''mosprefix''-descendant
+|(''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 descendants and beyond, as context allows.
+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.
 {| class="wikitable"
 |+Step ratio descriptions
@@ Line 46: / Line 55: @@
 ! colspan="2" |Base mos
 ! colspan="4" |Chromatic mosses
-(1st descendants)
+(1st-order descendants)
 ! colspan="4" |Enharmonic mosses
-(2nd descendants)
+(2nd-order descendants)
 ! colspan="4" |Subchromatic mosses
-(3rd descendants)
+(3rd-order descendants)
 |-
 !Mos
@@ 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"
 |+Descendant mosses of 5L 2s
 !Base mos
-!1st descendants
+!1st-order descendants
-!2nd descendants
+!2nd-order descendants
-!3rd descendants
+!3rd-order descendants
-!4th descendants
+!4th-order descendants
-!5th descendants
+!5th-order descendants
 |-
 | rowspan="16" |5L 2s
@@ 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:
-* There are 16 4th descendants, or '''4th diadescendant''' scales''.''
+* There are 16 4th-order descendants, or '''4th-order diadescendant''' scales''.''
-* There are 32 5th descendants, or '''5th diadescendant''' scales.
+* There are 32 5th-order descendants, or '''5th-order diadescendant''' scales.
-* There are 2 to the ''k''th power ''k''th descendants, or '''''k''th 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"
 |+Descendant mosses of 5L 2s
 ! colspan="2" |Base mos
-! colspan="2" |1st descendants
+! colspan="2" |1st-order descendants
-! colspan="2" |2nd descendants
+! colspan="2" |2nd-order descendants
-! colspan="2" |3rd descendants
+! colspan="2" |3rd-order descendants
-! colspan="2" |4th descendants
+! colspan="2" |4th-order descendants
 |-
 !Mos
@@ Line 237: / Line 247: @@
 | rowspan="2" |ultrasoft diasubchromatic
 |7L 26s
-| rowspan="2" |ultrasoft 4th diadescendants
+| rowspan="2" |ultrasoft 4th-order diadescendants
 |-
 |26L 7s
@@ Line 244: / Line 254: @@
 | rowspan="2" |parasoft diasubchromatic
 |26L 19s
-| rowspan="2" |parasoft 4th diadescendants
+| rowspan="2" |parasoft 4th-order diadescendants
 |-
 |19L 26s
@@ Line 253: / Line 263: @@
 | rowspan="2" |quasisoft diasubchromatic
 |19L 31s
-| rowspan="2" |quasisoft 4th diadescendants
+| rowspan="2" |quasisoft 4th-order diadescendants
 |-
 |31L 19s
@@ Line 260: / Line 270: @@
 | rowspan="2" |minisoft diasubchromatic
 |31L 12s
-| rowspan="2" |minisoft 4th diadescendants
+| rowspan="2" |minisoft 4th-order diadescendants
 |-
 |12L 31s
@@ Line 271: / Line 281: @@
 | rowspan="2" |minihard diasubchromatic
 |12L 29s
-| rowspan="2" |minihard 4th diadescendants
+| rowspan="2" |minihard 4th-order diadescendants
 |-
 |29L 12s
@@ Line 278: / Line 288: @@
 | rowspan="2" |quasisoft diasubchromatic
 |29L 17s
-| rowspan="2" |quasihard 4th diadescendants
+| rowspan="2" |quasihard 4th-order diadescendants
 |-
 |17L 29s
@@ Line 287: / Line 297: @@
 | rowspan="2" |parahard diasubchromatic
 |17L 22s
-| rowspan="2" |parahard4th diadescendants
+| rowspan="2" |parahard4th-order diadescendants
 |-
 |22L 17s
@@ Line 294: / Line 304: @@
 | rowspan="2" |ultrahard diasubchromatic
 |22L 5s
-| rowspan="2" |ultrahard 4th diadescendants
+| rowspan="2" |ultrahard 4th-order diadescendants
 |-
 |5L 22s
 |}
-== Additional temperament-agnostic mos names ==