User:Ganaram inukshuk/TAMNAMS Extension - Revision history

Ganaram inukshuk: /* Finding an ancestor's step ratio that produces a descandant mos xL ys */

2024-02-10T19:16:33Z

Finding an ancestor's step ratio that produces a descandant mos xL ys

← Older revision		Revision as of 19:16, 10 February 2024
Line 73:		Line 73:

	#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 ''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 ancestor 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.

Line 80:		Line 80:
	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:		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, ~~that is~~ the ~~number~~ of L's and s's from ~~the descendant~~ that make up the large and small ~~step sizes of the ancestor~~.		#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 ''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 }.		##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 ''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'').
	##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~~.		##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 ''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 ancestor mos is ''z''L ''w''s. The step ratio range for the ~~ancestor mos ranges from~~ (uL+ us):(vL+ vs) to uL:vL. If z+w is not less than or equal to n, 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. 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 ==		== Names for mosses with more than 10 notes ==

Ganaram inukshuk: /* Finding an ancestor's step ratio that produces a descandant mos xL ys */

2024-02-10T00:56:51Z

Finding an ancestor's step ratio that produces a descandant mos xL ys

← Older revision		Revision as of 00:56, 10 February 2024
Line 70:		Line 70:

	=== Finding the ancestor of a descendant mos ''x''L ''y''s ===		=== 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 ~~descendant~~ with target note count ''n'' or less:		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 ''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 ===		=== 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, that is the number of L's and s's from the descendant that make up the large and small step sizes of the ancestor.
			##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 ancestor mos ranges from (uL+ us):(vL+ vs) to uL:vL. 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 ==		== Names for mosses with more than 10 notes ==

Ganaram inukshuk: /* Relating a mos and its descendants */

2024-02-09T12:27:17Z

Relating a mos and its descendants

← Older revision		Revision as of 12:27, 9 February 2024
Line 31:		Line 31:
	\| rowspan="2" \|''x''+''y''		\| rowspan="2" \|''x''+''y''
	\| rowspan="2" \|2''x''+''y''		\| rowspan="2" \|2''x''+''y''
	\|''x+y''		\|''x''+''y''
	\|3''x''+2''y''		\|3''x''+2''y''
	\|-		\|-
Line 49:		Line 49:
	\| rowspan="2" \|2''x''+''y''		\| rowspan="2" \|2''x''+''y''
	\| rowspan="2" \|''x''		\| rowspan="2" \|''x''
	\|2''x+y''		\|2''x''+''y''
	\|3''x+y''		\|3''x''+''y''
	\|-		\|-
	\|3''x''+''y''		\|3''x''+''y''

Ganaram inukshuk: /* Relating a mos and its descendants */fixed italicized text

2024-02-09T12:26:20Z

Relating a mos and its descendants: fixed italicized text

← Older revision		Revision as of 12:26, 9 February 2024
Line 27:		Line 27:
	\| 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" \|2''x+y''		\| rowspan="2" \|2''x''+''y''
	\|''x+y''		\|''x+y''
	\|3''x''+2''y''		\|3''x''+2''y''
	\|-		\|-
	\|3''x''+2''y''		\|3''x''+2''y''
	\|''x+y''		\|''x''+''y''
	\|-		\|-
	\| rowspan="2" \|2''x+y''		\| rowspan="2" \|2''x''+''y''
	\| rowspan="2" \|''x+y''		\| rowspan="2" \|''x''+''y''
	\|3''x''+2''y''		\|3''x''+2''y''
	\|2''x+y''		\|2''x''+''y''
	\|-		\|-
	\|2''x+y''		\|2''x''+''y''
	\|3''x''+2''y''		\|3''x''+2''y''
	\|-		\|-
	\| rowspan="4" \|''x''		\| rowspan="4" \|''x''
	\| rowspan="4" \|''x+y''		\| rowspan="4" \|''x''+''y''
	\| rowspan="2" \|2''x+y''		\| rowspan="2" \|2''x''+''y''
	\| rowspan="2" \|''x''		\| rowspan="2" \|''x''
	\|2''x+y''		\|2''x+y''
	\|3''x+y''		\|3''x+y''
	\|-		\|-
	\|3''x+y''		\|3''x''+''y''
	\|2''x+y''		\|2''x''+''y''
	\|-		\|-
	\| rowspan="2" \|''x''		\| rowspan="2" \|''x''
	\| rowspan="2" \|2''x+y''		\| rowspan="2" \|2''x''+''y''
	\|3''x+y''		\|3''x''+''y''
	\|''x''		\|''x''
	\|-		\|-
	\|''x''		\|''x''
	\|3''x+y''		\|3''x''+''y''
	\|}		\|}
	For example, the first three generations of ''diatonic descendants'' can be described as:		For example, the first three generations of ''diatonic descendants'' can be described as:

Ganaram inukshuk at 11:19, 9 February 2024

2024-02-09T11:19:38Z

← Older revision		Revision as of 11:19, 9 February 2024
Line 69:		Line 69:
	* ''Great-grandchildren of 5L 2s'': 5L 17s, 17L 5s, 17L 12s, 12L 17s, 12L 19s, 19L 12s, 12L 7s, and 7L 19s		* ''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 ~~with a target note count ''n'' or less~~ ===		=== 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 descendant with target note count ''n'' or less:		For a mos ''x''L ''y''s, perform the following algorithm to find a familiar descendant with target note count ''n'' or less:

Ganaram inukshuk at 11:18, 9 February 2024

2024-02-09T11:18:39Z

← Older revision		Revision as of 11:18, 9 February 2024
Line 7:		Line 7:

	== Relating a mos and its descendants ==		== 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"		{\| class="wikitable"
	! colspan="2" \|Parent		! colspan="2" \|Parent
Line 25:		Line 25:
	!Small steps		!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 mos ~~ancestor~~ with a target note count ''n'' or less ===		* ''Children of 5L 2s'': 7L 5s and 5L 7s
			* ''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 with a target note count ''n'' or less ===
	For a mos ''x''L ''y''s, perform the following algorithm to find a familiar descendant with target note count ''n'' or less:		For a mos ''x''L ''y''s, perform the following algorithm to find a familiar descendant with target note count ''n'' or less:

Line 71:		Line 76:
	#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 parent 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 ===

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

Ganaram inukshuk: Appendix

2024-02-09T11:03:10Z

Appendix

@@ Line 361: / Line 361: @@
 |}
 == Names for equave-agnostic mosses ==
 {| class="wikitable center-all"
 |-
 ! colspan="5" |6-note mosses
@@ Line 598: / Line 538: @@
 == Appendix ==

Ganaram inukshuk: /* Finding a named ancestor for a descendant mos */

2024-02-08T19:26:09Z

Finding a named ancestor for a descendant mos

← Older revision		Revision as of 19:26, 8 February 2024
Line 64:		Line 64:
	\|}		\|}

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

Ganaram inukshuk at 05:33, 8 February 2024

2024-02-08T05:33:26Z

Show changes

Ganaram inukshuk: /* Relating a mos and its descendants */

2024-02-06T01:38:56Z

Relating a mos and its descendants

← Older revision		Revision as of 01:38, 6 February 2024
Line 7:		Line 7:

	== Relating a mos and its descendants ==		== Relating a mos and its descendants ==
	In the absence of any names, mosses can be ~~instead~~ described by how ~~it relates~~ back to a more familiar mos. In general, all mosses with ''n'' periods relate back to a root mos of ''n''L ''n''s. ~~As it pertains to~~ 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.		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.

	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. For a mos of the form ''x''L ''y''s, its descendants (children, grandchildren, great-grandchildren, etc) contain the following pattern of step counts.