User:Ganaram inukshuk/TAMEX: Difference between revisions

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 Work-in-progress
 :''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'''tended Naming 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 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 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.
-== Types of mos descendants ==
+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.
+== Description scheme for TAMNAMS-named mosses ==
+=== Base descriptions ===
+To describe mosses that have more than 10 notes, descriptions are based on how they're related to another, named mos, based on how many generations apart the two are:
+* The immediate child of a mos is a ''chromatic'' mos.
+* 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.
+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.
+{| class="wikitable"
+|+Base descriptions
+!Parent mos
+!Chromatic mosses
+(1st descendants)
+!Enharmonic mosses
+(2nd descendants)
+!Subchromatic mosses
+(3rd descendants)
+!''k''th descendant mosses
+|-
+|''mos-name''
+|chromatic ''mos-name''
+|enharmonic ''mos-name''
+|subchromatic ''mos-name''
+|(''k''th) ''mos-name'' descendant
+|-
+|''mos-name''
+|''mosprefix''-chromatic
+|''mosprefix''-monic
+|''mosprefix''-subchromatic
+|(''k''th) ''mosprefix''-descendant
+|}
 Using [[5L 2s]] (diatonic) as an example, a tree of mosses can be produced as a scale tree.
 {| class="wikitable"
@@ Line 11: / Line 46: @@
 !3rd descendants
 !4th descendants
+!5th descendants
 |-
 | rowspan="16" |5L 2s
@@ Line 17: / Line 53: @@
 | rowspan="2" |7L 19s
 |7L 26s
+|7L 29s
 |-
 |26L 7s
+| rowspan="6" |. . .
 |-
 | rowspan="2" |19L 7s
@@ Line 35: / Line 73: @@
 |-
 |12L 31s
+|12L 43s
 |-
 | rowspan="8" |5L 7s
@@ Line 40: / Line 79: @@
 | rowspan="2" |12L 17s
 |12L 29s
+|12L 41s
 |-
 |29L 12s
+| rowspan="6" |. . .
 |-
 | rowspan="2" |17L 12s
@@ Line 58: / Line 99: @@
 |-
 |5L 22s
+|5L 29s
 |}
+With 5L 2s as the root mos:
+* There are 2 chromatic descendants, or '''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 8 subchromatic descendants, or '''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 32 5th descendants, or '''5th diadescendant''' scales.
+* There are 2 to the ''k''th power ''k''th descendants, or '''''k''th diadescendant''' scales.
+=== Step ratio descriptions ===
+Optionally, the names for a step ratio range can be added before these descriptions, describing the step ratio of the root mos. Step ratios only apply to the 1st, 2nd, and 3rd descendants.
+{| class="wikitable"
+|-
+! colspan="2" |Root
+! colspan="4" |Chromatic mosses
+(1st descendants)
+! colspan="4" |Enharmonic mosses
+(2nd descendants)
+! colspan="4" |Subchromatic mosses
+(3rd descendants)
+|-
+!Mos
+!L:s range
+!Mos
+!L:s range
+!Range name
+!Prefix
+!Mos
+!L:s range
+!Range name
+!Prefix
+!Mos
+!L:s range
+!Range name
+!Prefix
+|-
+| rowspan="8" |xL ys
+| rowspan="8" |1:1 to 1:0
+| rowspan="4" |(x+y)L xs
+| rowspan="4" |1:1 to 2:1
+| rowspan="4" |soft-of-basic
+| rowspan="4" |s-
+| rowspan="2" |(x+y)L (2x+y)s
+| rowspan="2" |1:1 to 3:2
+| rowspan="2" |soft
+| rowspan="2" |s-
+|(x+y)L (3x+2y)s
+|1:1 to 4:3
+|ultrasoft
+|us-
+|-
+|(3x+2y)L (x+y)s
+|4:3 to 3:2
+|parasoft
+|ps-
+|-
+| rowspan="2" |(2x+y)L (x+y)s
+| rowspan="2" |3:2 to 2:1
+| rowspan="2" |hyposoft
+| rowspan="2" |hs-
+|(3x+2y)L (2x+y)s
+|3:2 to 5:3
+|quasisoft
+|qs-
+|-
+|(2x+y)L (3x+2y)s
+|5:3 to 2:1
+|minisoft
+|ms-
+|-
+| rowspan="4" |xL (x+y)s
+| rowspan="4" |2:1 to 1:0
+| rowspan="4" |hard-of-basic
+| rowspan="4" |h-
+| rowspan="2" |(2x+y)L xs
+| rowspan="2" |2:1 to 3:1
+| rowspan="2" |hypoard
+| rowspan="2" |hh-
+|(2x+y)L (3x+y)s
+|2:1 to 5:2
+|minihard
+|mh-
+|-
+|(3x+y)L (2x+y)s
+|5:2 to 3:1
+|quasihard
+|qh-
+|-
+| rowspan="2" |xL (2x+y)s
+| rowspan="2" |3:1 to 1:0
+| rowspan="2" |hard
+| rowspan="2" |h-
+|(3x+y)L xs
+|3:1 to 4:1
+|parahard
+|ph-
+|-
+|xL (3x+y)s
+|4:1 to 1:0
+|ultrahard
+|uh-
+|}
 == Naming scheme ==
 == Specific names ==