User:Ganaram inukshuk/TAMNAMS Extension: Difference between revisions

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== Relating a mos and its descendants ==

~~Particularly in the absence of any names, larger~~ mosses can be described by how they related back to a more familiar mos and vice-versa. In general, all mosses with ''n'' periods relate back to a root mos of ''n''L ''n''s. For TAMNAMS-named mosses, any octave-equivalent mos with more than 10 steps and no more than 5 periods is related to some TAMNAMS-named mos.

Larger mosses can be described by how they related back to a more familiar mos and vice-versa. In general, all mosses with ''n'' periods relate back to a root mos of ''n''L ''n''s. For TAMNAMS-named mosses, any octave-equivalent mos with more than 10 steps and no more than 5 periods is related to some TAMNAMS-named mos.

In either case, any mos can be related to its descendants by treating it as the root of its own scale tree. ~~For~~ a mos ~~of the form~~ ''x''L ''y''s, ~~its~~ descendants (children, grandchildren, great-grandchildren, ~~etc)~~ contain the following pattern of step counts.

In either case, any mos can be related to its descendants by treating it as the root of its own scale tree. Particularly in the absence of any names, mosses can be ''described'' as being some descendant of a related ancestor mos ''x''L ''y''s. Such mosses, called ''mos descendants'' – or ''children'', ''grandchildren'', and ''great-grandchildren'', for the first three generations of descendants – contain the following pattern of step counts.

{| class="wikitable"

! colspan="2" |Parent

Line 25:

!Small steps

|-

| rowspan="8" |x

| rowspan="8" |''x''

| rowspan="8" |y

| rowspan="8" |''y''

| rowspan="4" |x+y

| rowspan="4" |''x''+''y''

| rowspan="4" |x

| rowspan="4" |''x''

| rowspan="2" |x+y

| rowspan="2" |''x''+''y''

| rowspan="2" |2x+y

| rowspan="2" |2''x''+''y''

|x+y

|''x''+''y''

|3x+2y

|3''x''+2''y''

|-

|3x+2y

|3''x''+2''y''

|x+y

|''x''+''y''

|-

| rowspan="2" |2x+y

| rowspan="2" |2''x''+''y''

| rowspan="2" |x+y

| rowspan="2" |''x''+''y''

|3x+2y

|3''x''+2''y''

|2x+y

|2''x''+''y''

|-

|2x+y

|2''x''+''y''

|3x+2y

|3''x''+2''y''

|-

| rowspan="4" |x

| rowspan="4" |''x''

| rowspan="4" |x+y

| rowspan="4" |''x''+''y''

| rowspan="2" |2x+y

| rowspan="2" |2''x''+''y''

| rowspan="2" |x

| rowspan="2" |''x''

|2x+y

|2''x''+''y''

|3x+y

|3''x''+''y''

|-

|3x+y

|3''x''+''y''

|2x+y

|2''x''+''y''

|-

| rowspan="2" |x

| rowspan="2" |''x''

| rowspan="2" |2x+y

| rowspan="2" |2''x''+''y''

|3x+y

|3''x''+''y''

|x

|''x''

|-

|x

|''x''

|3x+y

|3''x''+''y''

|}

For example, the first three generations of ''diatonic descendants'' can be described as:

=== Finding ~~a named~~ ancestor ~~for~~ a descendant mos ===

* ''Children of 5L 2s'': 7L 5s and 5L 7s

For a mos ''x''L ''y''s, perform the following algorithm to find a familiar ~~descendant~~ with target note count ''n'' or less:

* ''Grandchildren of 5L 2s'': 5L 12s, 12L 5s, 12L 7s, and 7L 12s

* ''Great-grandchildren of 5L 2s'': 5L 17s, 17L 5s, 17L 12s, 12L 17s, 12L 19s, 19L 12s, 12L 7s, and 7L 19s

=== Finding the ancestor of a descendant mos ''x''L ''y''s ===

For a mos ''x''L ''y''s, perform the following algorithm to find a familiar ancestor with target note count ''n'' or less:

#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 ''m1'' be assigned the value of max(''z'', ''w'') and ''m2'' the value of min(''z'', ''w'').

#Let ''m1'' be assigned the value of max(''z'', ''w'') and ''m2'' the value of min(''z'', ''w'').

#Assign to ''z'' the value ''m2'' and ''w'' the value ''m1''-''m2''.

#Assign to ''z'' the value ''m2'' and ''w'' the value ''m1''-''m2''.

#If ''z''+''w'' is less than or equal to ''n'', then the parent mos is ''z''L ''w''s. If not, repeat the process starting at step 2.

#If ''z''+''w'' is less than or equal to ''n'', then the ancestor mos is ''z''L ''w''s. If not, repeat the process starting at step 2.

=== Finding an ancestor's step ratio that produces a descandant mos ''x''L ''y''s ===

For a mos xL ys, perform the following algorithm to find the step ratio for a descendant mos zL ws with target note count n or less:

#Let ''z'' and ''w'' be the number of large and small steps of the parent mos to be found. Let ''U'' and ''V'' be two chunks, vectors containing the amounts of L's and s's from xL ys that make up the ancestor mos's large and small steps.

##Assign to ''z'' and ''w'' the values ''x'' and ''y'' respectively.

##Assign to ''U'' the vector { ''uL'', ''us'' } = { 1, 0 } and V to the vector { ''vL'', ''vs'' } = { 0, 1 }.

#Let ''m1'' be assigned the value of max(''z'', ''w'') and ''m2'' the value of min(''z'', ''w'').

##If w > z, then add ''V'' to ''U''. Otherwise, assign to a temporary vector ''Utemp'' the value of ''U'', add ''V'' to ''U'', and assign to ''V'' the value of ''Utemp''.

#Assign to ''z'' the value ''m2'' and ''w'' the value ''m1''-''m2''.

#If ''z''+''w'' is less than or equal to ''n'', then the ancestor mos is ''z''L ''w''s. The step ratio range for the ''z''L ''w''s is (''uL''+ ''us''):(''vL''+ ''vLs'') to ''uL'':''vs''. If ''z''+''w'' is not less than or equal to ''n'', repeat the process starting at step 2.

== Names for mosses with more than 10 notes ==

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Line 377:

|}

== Names for equave-agnostic mosses ==

Equave-agnostic names (proposed by Ganaram) are an extension to the equave-agnostic names provide by TAMNAMS. They are based on Greek, Latin, and Sanskrit numeral prefixes. Names for multi-period equave-agnostic mosses are not provided, as they would be repetitions of a smaller step pattern.

{| class="wikitable center-all"

~~! colspan="5" |TAMNAMS-named mosses~~

|-

~~!Pattern~~

~~!Name~~

~~!Prefix~~

~~!Abbrev.~~

~~!Reasoning~~

|-

~~|1L 1s~~

~~|trivial~~

~~|triv~~

~~|trv~~

~~|Trivial mos pattern, simplest possible mos pattern~~

|-

~~|1L 2s~~

~~|antrial~~

|

|-

~~|2L 1s~~

~~|trial~~

|

|-

~~|1L 3s~~

~~|antetric~~

|

|-

~~|3L 1s~~

~~|tetric~~

|

|-

~~|1L 4s~~

~~|pedal~~

|

|-

~~|2L 3s~~

~~|pentic~~

|

|-

~~|3L 2s~~

~~|anpentic~~

|

|-

~~|4L 1s~~

~~|manual~~

|

|-

! colspan="5" |6-note mosses

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Line 554:

== Appendix ==

The motivation behind these names is from a desire to expand TAMNAMS-like names past the current note limit of 10 steps and, to a lesser extent, preserve former TAMNAMS names given to such mosses.

The names for mos descendants are given the general terms of ''child'', ''grandchild'', ''great-grandchild'', and so on. Formerly, names based on the terms ''chromatic'' and ''enharmonic'' were prescribed, much in the spirit of ''m-chromatic'' and ''p-chromatic''. These terms, accompanied by single-letter prefixes, such as ''m-'' and ''p-'', and others, were used as bases for the descendants of any mos. However, these names were abandoned since the concept of ''chromatic'' did not generalize well outside the context of chromatic pairs, and the single-letter prefixes were considered temperament-suggestive.

More unique names have been prescribed by others, but have limited use or acceptance by the xen community as a whole.

The names ''m-chromatic'' and ''p-chromatic'', as they apply to 7L 5s and 5L 7s, are left unchanged, but can alternatively be described generally as ''child scales of diatonic'', or specifically, the ''child scale of soft diatonic'' and ''child scale of hard diatonic'' respectively.

@@ Line 7: / Line 7: @@
 == Relating a mos and its descendants ==
-Particularly in the absence of any names, larger mosses can be described by how they related back to a more familiar mos and vice-versa. In general, all mosses with ''n'' periods relate back to a root mos of ''n''L ''n''s. For TAMNAMS-named mosses, any octave-equivalent mos with more than 10 steps and no more than 5 periods is related to some TAMNAMS-named mos.
+Larger mosses can be described by how they related back to a more familiar mos and vice-versa. In general, all mosses with ''n'' periods relate back to a root mos of ''n''L ''n''s. For TAMNAMS-named mosses, any octave-equivalent mos with more than 10 steps and no more than 5 periods is related to some TAMNAMS-named mos.
-In either case, any mos can be related to its descendants by treating it as the root of its own scale tree. For a mos of the form ''x''L ''y''s, its descendants (children, grandchildren, great-grandchildren, etc) contain the following pattern of step counts.
+In either case, any mos can be related to its descendants by treating it as the root of its own scale tree. Particularly in the absence of any names, mosses can be ''described'' as being some descendant of a related ancestor mos ''x''L ''y''s. Such mosses, called ''mos descendants'' – or ''children'', ''grandchildren'', and ''great-grandchildren'', for the first three generations of descendants – contain the following pattern of step counts.
 {| class="wikitable"
 ! colspan="2" |Parent
@@ Line 25: / Line 25: @@
 !Small steps
 |-
-| rowspan="8" |x
+| rowspan="8" |''x''
-| rowspan="8" |y
+| rowspan="8" |''y''
-| rowspan="4" |x+y
+| rowspan="4" |''x''+''y''
-| rowspan="4" |x
+| rowspan="4" |''x''
-| rowspan="2" |x+y
+| rowspan="2" |''x''+''y''
-| rowspan="2" |2x+y
+| rowspan="2" |2''x''+''y''
-|x+y
+|''x''+''y''
-|3x+2y
+|3''x''+2''y''
 |-
-|3x+2y
+|3''x''+2''y''
-|x+y
+|''x''+''y''
 |-
-| rowspan="2" |2x+y
+| rowspan="2" |2''x''+''y''
-| rowspan="2" |x+y
+| rowspan="2" |''x''+''y''
-|3x+2y
+|3''x''+2''y''
-|2x+y
+|2''x''+''y''
 |-
-|2x+y
+|2''x''+''y''
-|3x+2y
+|3''x''+2''y''
 |-
-| rowspan="4" |x
+| rowspan="4" |''x''
-| rowspan="4" |x+y
+| rowspan="4" |''x''+''y''
-| rowspan="2" |2x+y
+| rowspan="2" |2''x''+''y''
-| rowspan="2" |x
+| rowspan="2" |''x''
-|2x+y
+|2''x''+''y''
-|3x+y
+|3''x''+''y''
 |-
-|3x+y
+|3''x''+''y''
-|2x+y
+|2''x''+''y''
 |-
-| rowspan="2" |x
+| rowspan="2" |''x''
-| rowspan="2" |2x+y
+| rowspan="2" |2''x''+''y''
-|3x+y
+|3''x''+''y''
-|x
+|''x''
 |-
-|x
+|''x''
-|3x+y
+|3''x''+''y''
 |}
+For example, the first three generations of ''diatonic descendants'' can be described as:
-=== Finding a named ancestor for a descendant mos ===
+* ''Children of 5L 2s'': 7L 5s and 5L 7s
-For a mos ''x''L ''y''s, perform the following algorithm to find a familiar descendant with target note count ''n'' or less:
+* ''Grandchildren of 5L 2s'': 5L 12s, 12L 5s, 12L 7s, and 7L 12s
+* ''Great-grandchildren of 5L 2s'': 5L 17s, 17L 5s, 17L 12s, 12L 17s, 12L 19s, 19L 12s, 12L 7s, and 7L 19s
+=== Finding the ancestor of a descendant mos ''x''L ''y''s ===
+For a mos ''x''L ''y''s, perform the following algorithm to find a familiar ancestor with target note count ''n'' or less:
 #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 ''m1'' be assigned the value of max(''z'', ''w'') and ''m2'' the value of min(''z'', ''w'').
+#Let ''m<sub>1</sub>'' be assigned the value of max(''z'', ''w'') and ''m<sub>2</sub>'' the value of min(''z'', ''w'').
-#Assign to ''z'' the value ''m2'' and ''w'' the value ''m1''-''m2''.
+#Assign to ''z'' the value ''m<sub>2</sub>'' and ''w'' the value ''m<sub>1</sub>''-''m<sub>2</sub>''.
-#If ''z''+''w'' is less than or equal to ''n'', then the parent mos is ''z''L ''w''s. If not, repeat the process starting at step 2.
+#If ''z''+''w'' is less than or equal to ''n'', then the ancestor mos is ''z''L ''w''s. If not, repeat the process starting at step 2.
+=== Finding an ancestor's step ratio that produces a descandant mos ''x''L ''y''s ===
+For a mos xL ys, perform the following algorithm to find the step ratio for a descendant mos zL ws with target note count n or less:
+#Let ''z'' and ''w'' be the number of large and small steps of the parent mos to be found. Let ''U'' and ''V'' be two chunks, vectors containing the amounts of L's and s's from xL ys that make up the ancestor mos's large and small steps.
+##Assign to ''z'' and ''w'' the values ''x'' and ''y'' respectively.
+##Assign to ''U'' the vector { ''u<sub>L</sub>'', ''u<sub>s</sub>'' } = { 1, 0 } and V to the vector { ''v<sub>L</sub>'', ''v<sub>s</sub>'' } = { 0, 1 }.
+#Let ''m<sub>1</sub>'' be assigned the value of max(''z'', ''w'') and ''m<sub>2</sub>'' the value of min(''z'', ''w'').
+##If w > z, then add ''V'' to ''U''. Otherwise, assign to a temporary vector ''U<sub>temp</sub>'' the value of ''U'', add ''V'' to ''U'', and assign to ''V'' the value of ''U<sub>temp</sub>''.
+#Assign to ''z'' the value ''m<sub>2</sub>'' and ''w'' the value ''m<sub>1</sub>''-''m<sub>2</sub>''.
+#If ''z''+''w'' is less than or equal to ''n'', then the ancestor mos is ''z''L ''w''s. The step ratio range for the ''z''L ''w''s is (''u<sub>L</sub>''+ ''u<sub>s</sub>''):(''v<sub>L</sub>''+ ''v<sub>Ls</sub>'') to ''u<sub>L</sub>'':''v<sub>s</sub>''. If ''z''+''w'' is not less than or equal to ''n'', repeat the process starting at step 2.
 == Names for mosses with more than 10 notes ==
@@ Line 361: / Line 377: @@
 |}
 == Names for equave-agnostic mosses ==
+Equave-agnostic names (proposed by Ganaram) are an extension to the equave-agnostic names provide by TAMNAMS. They are based on Greek, Latin, and Sanskrit numeral prefixes. Names for multi-period equave-agnostic mosses are not provided, as they would be repetitions of a smaller step pattern.
 {| class="wikitable center-all"
-! colspan="5" |TAMNAMS-named mosses
-|-
-!Pattern
-!Name
-!Prefix
-!Abbrev.
-!Reasoning
-|-
-|1L 1s
-|trivial
-|triv
-|trv
-|Trivial mos pattern, simplest possible mos pattern
-|-
-|1L 2s
-|antrial
-|
-|
-|
-|-
-|2L 1s
-|trial
-|
-|
-|
-|-
-|1L 3s
-|antetric
-|
-|
-|
-|-
-|3L 1s
-|tetric
-|
-|
-|
-|-
-|1L 4s
-|pedal
-|
-|
-|
-|-
-|2L 3s
-|pentic
-|
-|
-|
-|-
-|3L 2s
-|anpentic
-|
-|
-|
-|-
-|4L 1s
-|manual
-|
-|
-|
 |-
 ! colspan="5" |6-note mosses
@@ Line 598: / Line 554: @@
 == Appendix ==
+The motivation behind these names is from a desire to expand TAMNAMS-like names past the current note limit of 10 steps and, to a lesser extent, preserve former TAMNAMS names given to such mosses.
+The names for mos descendants are given the general terms of ''child'', ''grandchild'', ''great-grandchild'', and so on. Formerly, names based on the terms ''chromatic'' and ''enharmonic'' were prescribed, much in the spirit of ''m-chromatic'' and ''p-chromatic''. These terms, accompanied by single-letter prefixes, such as ''m-'' and ''p-'', and others, were used as bases for the descendants of any mos. However, these names were abandoned since the concept of ''chromatic'' did not generalize well outside the context of chromatic pairs, and the single-letter prefixes were considered temperament-suggestive.
+More unique names have been prescribed by others, but have limited use or acceptance by the xen community as a whole.
+The names ''m-chromatic'' and ''p-chromatic'', as they apply to 7L 5s and 5L 7s, are left unchanged, but can alternatively be described generally as ''child scales of diatonic'', or specifically, the ''child scale of soft diatonic'' and ''child scale of hard diatonic'' respectively.