@@ Line 10: / Line 10: @@
 * For single-period mosses, the UDP is notated as ''u''|''d'', where ''u'' is the number of bright generators stacked ''above'' the tonic, ''d'' is the number of bright generators stacked ''below'' the tonic, and "|" is pronounced as "pipe". The full name of a mos's mode is '''xL ys u|d'''.
-* For multi-period mosses with ''p'' periods, the UDP of is notated as ''up''|''dp''(''p''). Since there are generators being stacked above and below every mosperiod - not just the tonic - there are in total ''u times p'' and ''d times p'' generators being stacked above and below their respective starting pitches. The full name in this case is '''xL ys up|dp(p)'''.
+* For multi-period mosses with ''p'' periods, the UDP of is notated as ''up''|''dp''(''p''). Since there are generators being stacked above and below every period - not just the tonic - there are in total ''u times p'' and ''d times p'' generators being stacked above and below their respective starting pitches. The full name in this case is '''xL ys up|dp(p)'''.
 To make notation easier, TAMNAMS makes the following modifications to UDP notation:
@@ Line 29: / Line 29: @@
 !Mode
 !Rotational order
-!UDP
+!Simplified UDP
 !mosunison
 !1-mosstep
@@ Line 42: / Line 42: @@
 |LLsLLsLs
 |0
-|<nowiki>7|0</nowiki>
+|<nowiki>7|</nowiki>
 |0 (perfect)
 |L (major)
@@ Line 55: / Line 55: @@
 |LsLLsLsL
 |1
-|<nowiki>4|3</nowiki>
+|<nowiki>4|</nowiki>
 |0 (perfect)
 |L (major)
@@ Line 68: / Line 68: @@
 |sLLsLsLL
 |2
-|<nowiki>1|6</nowiki>
+|<nowiki>1|</nowiki>
 |0 (perfect)
 |s (minor)
@@ Line 81: / Line 81: @@
 |LLsLsLLs
 |3
-|<nowiki>6|1</nowiki>
+|<nowiki>6|</nowiki>
 |0 (perfect)
 |L (major)
@@ Line 94: / Line 94: @@
 |LsLsLLsL
 |4
-|<nowiki>3|4</nowiki>
+|<nowiki>3|</nowiki>
 |0 (perfect)
 |L (major)
@@ Line 107: / Line 107: @@
 |sLsLLsLL
 |5
-|<nowiki>0|7</nowiki>
+|<nowiki>0|</nowiki>
 |0 (perfect)
 |s (minor)
@@ Line 120: / Line 120: @@
 |LsLLsLLs
 |6
-|<nowiki>5|2</nowiki>
+|<nowiki>5|</nowiki>
 |0 (perfect)
 |L (major)
@@ Line 133: / Line 133: @@
 |sLLsLLsL
 |7
-|<nowiki>2|5</nowiki>
+|<nowiki>2|</nowiki>
 |0 (perfect)
 |s (minor)
@@ Line 164: / Line 164: @@
 |LssLssLss
 |<nowiki>3L 6s 2|</nowiki>
-|<nowiki>2|0</nowiki>
+|<nowiki>2|</nowiki>
 |0
 |0 (perfect)
@@ Line 179: / Line 179: @@
 |sLssLssLs
 |<nowiki>3L 6s 1|</nowiki>
-|<nowiki>1|1</nowiki>
+|<nowiki>1|</nowiki>
 |2
 |0 (perfect)
@@ Line 194: / Line 194: @@
 |ssLssLssL
 |<nowiki>3L 6s 0|</nowiki>
-|<nowiki>0|2</nowiki>
+|<nowiki>0|</nowiki>
 |1
 |0 (perfect)
@@ Line 226: / Line 226: @@
 === Complements of intervals ===
-The ''octave complement'' (or ''moscomplement'', or ''complement'') of a mos interval follows the same logic as the [[octave complement]] in regular music theory: in general, for a mos with n pitches, a k-mosstep in its large form has a complement of an (n-k)-mosstep in its small form, and the two intervals are complements of one another. If a mos interval is altered by raising it by some number of chromas, its complement will be lowered by the same number of chromas.
+The ''octave complement'' (or ''equave complement'' for mosses that don't have an octave equivalence interval, or simply ''complement'') of a mos interval follows the same logic as the [[octave complement]] in regular music theory: in general, for a mos with n pitches, a k-mosstep in its large form has a complement of an (n-k)-mosstep in its small form, and the two intervals are complements of one another. Alternatively, if a specific mos interval is thought of as a quantity of large and small steps, then its complement is the number of steps needed to produce the mos pattern of xL ys itself. Additionally, if a mos interval is also altered by raising it by some number of chromas, its complement will be lowered by the same number of chromas, and vice-versa.
-Alternatively, if a specific mos interval is thought of as a quantity of large and small steps, then its complement is the number of steps needed to produce the mos pattern of xL ys itself.
 {| class="wikitable"
-|+Moscomplements of 3L 4s
+|+Interval complements of 3L 4s
 ! colspan="2" |Interval
 ! colspan="2" |Complement
@@ Line 239: / Line 237: @@
 !Size
 |-
-|Perfect 0-mosstep (mosunison)
+|Perfect 0-mosstep (unison)
 |'''0'''
-|Perfect 7-mosstep (mosoctave)
+|Perfect 7-mosstep (octave)
 |'''3L+4s'''
 |-
@@ Line 274: / Line 272: @@
 |'''s'''
 |-
-|Perfect 7-mosstep (mosoctave)
+|Perfect 7-mosstep (octave)
 |'''3L+4s'''
-|Perfect 0-mosstep (mosunison)
+|Perfect 0-mosstep (unison)
 |'''0'''
 |}
@@ Line 336: / Line 334: @@
 |-
 | rowspan="15" |1:1 to 1:0
-| rowspan="7" |1:1 to 2:1 (pansoft or soft)
+| rowspan="7" |1:1 to 2:1 ''(general soft range)''
-| rowspan="3" |1:1 to 3:2 (amphisoft)
+| rowspan="3" |1:1 to 3:2
 |1:1 to 4:3 (ultrasoft)
 |
@@ Line 374: / Line 372: @@
 |Also called quintessential
 |-
-| rowspan="7" |2:1 to 1:0 (panhard or hard)
+| rowspan="7" |2:1 to 1:0 ''(general hard range)''
 | rowspan="3" |2:1 to 3:1 (hypohard)
 |2:1 to 5:2 (minihard)
@@ Line 393: / Line 391: @@
 |Also called monohard
 |-
-| rowspan="3" |3:1 to 1:0 (amphihard)
+| rowspan="3" |3:1 to 1:0
 |3:1 to 4:1 (parahard)
 |
@@ Line 413: / Line 411: @@
 |Trivial/pathological
 |}
-New names for the ranges excluded by hyposoft and hypohard are included: amphisoft and amphihard, named such as they surround the region that hyposoft and hypohard span. The broadest ranges for soft and hard step ratios are called pansoft and panhard, or simply soft and hard.
 === Extended spectrum ===
@@ Line 433: / Line 430: @@
 |-
 | rowspan="21" |1:1 to 1:0
-| rowspan="9" |1:1 to 2:1 (soft)
+| rowspan="9" |1:1 to 2:1 ''(general soft range)''
-| rowspan="5" |1:1 to 3:2 (amphisoft)
+| rowspan="5" |1:1 to 3:2
 | rowspan="3" |1:1 to 4:3 (ultrasoft)
 | colspan="2" |1:1 to 6:5 (pseudoequalized)
@@ Line 481: / Line 478: @@
 |'''2:1 (basic)'''
 |-
-| rowspan="11" |2:1 to 1:0 (hard)
+| rowspan="11" |2:1 to 1:0 ''(general hard range)''
 | rowspan="3" |2:1 to 3:1 (hypohard)
 |2:1 to 5:2 (minihard)
@@ Line 500: / Line 497: @@
 |'''3:1 (hard)'''
 |-
-| rowspan="7" |3:1 to 1:0 (amphihard)
+| rowspan="7" |3:1 to 1:0
 |3:1 to 4:1 (parahard)
 | colspan="2" |3:1 to 4:1 (parahard)
@@ Line 961: / Line 958: @@
 This is a system for describing scales beyond the set of named TAMNAMS scales. Both [[User:Frostburn]] ([[User:Frostburn/TAMNAMS Extension]]) and I have similar systems, with the main difference here being how mosses can be named any number of generations away from a named mos.
-To name mosses that have more than 10 notes, rather than giving mosses unique names, names are based on how they're related to another (named) mos. The following names are used for specific generations - namely child, grandchild, and great-grandchild mosses:
+To name mosses that have more than 10 notes, rather than giving mosses unique names, names are based on how they're related to another (named) mos.
-* A child mos is a ''chromatic mos'', or specifically, ''chromatic (mos name)''. For mosses with up to 3 periods, this can be shortened to ''(mos-prefix)chromatic''. This term collectively refers to 2 possible chromatic mosses, or any one of them.
+* A child mos is a ''chromatic mos''. For the child of a named mos, the name is ''chromatic (mos name)'', which can be shortened to ''(mos-prefix)chromatic'' if the mos has no more than 3 periods. This term collectively refers to 2 possible chromatic mosses, or any one of them.
-* A grandchild mos is an ''enharmonic mos'', or specifically, ''enharmonic (mos name)''. For mosses with up to 3 periods, this can be shortened to ''(mos-prefix)enharmonic''. This term collectively refers to 4 possible enharmonic mosses, or any one of them.
+* A grandchild mos is an ''enharmonic mos''. For the grandchild of a named mos, the name is ''enharmonic (mos name)'', which can be shortened to ''(mos-prefix)enharmonic'' if the mos has no more than 3 periods. This term collectively refers to 4 possible enharmonic mosses, or any one of them.
-* A great-grandchild mos is a ''subchromatic mos'', or specifically, ''subchromatic (mos name)''. For mosses with up to 3 periods, this can be shortened to ''(mos-prefix)subchromatic''. This term collectively refers to 8 possible subchromatic mosses, or any one of them. (Tentative name; open to better suggestions.)
+* A great-grandchild mos is a ''subchromatic mos''. For the great-grandchild of a named mos, the name is ''subchromatic (mos name)'', which can be shortened to ''(mos-prefix)subchromatic'' if the mos has no more than 3 periods. This term collectively refers to 8 possible subchromatic mosses, or any one of them. (Tentative name; open to better suggestions.)
-Any mos more than 3 generations away from a named mos is broadly referred to as a ''mos descendant'', or specifically ''(mos name) descendant'' or, for mosses with up to 3 periods, ''(mos-prefix)descendant''. These terms can also be used for describing multiple mos descendants, possibly across multiple generations, or to broadly describe any one mos descendant regardless of generation. Optionally, the number of generations can be specified, producing ''nth (mos name) descendant'' or ''nth (mos-prefix)descendant'', using the algorithm below:
+A mos that is more than 3 generations away from another mos (eg, a great-great-grandchild mos) or any number of generations from another mos is a ''mos descendant''. For the descendant of a named mos, the name is ''(mos name) descendant'', which can be shortened to ''(mos-prefix)descendant'' if the mos has no more than 3 periods. This term collectively refers to any number of descendants of a mos or any single mos descendant regardless of generation, or any one mos descendant. Optionally, the number of generations away from a named parent can be specified, producing the terms ''nth mos descendant'', ''nth (mos name) descendant,'' and ''nth (mos-prefix)descendant'', using the algorithm below to find ''n'':
 # 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 n = 0, where n is the number of generations away from zL ws.
 # Let m1 be equal to max(z, w) and m2 be equal to min(z, w).
@@ Line 971: / Line 969: @@
 # If the sum of z and w is no more than 10, then the parent mos is zL ws and is n generations from the mos descendant xL ys. If not, repeat the process starting at step 2.
-As diatonic (5L 2s) doesn't have a prefix, the terms ''chromatic'', ''enharmonic'', and ''subchromatic'' by themselves (and with no other context suggesting a non-diatonic mos) refer to 1st, 2nd, and 3rd diatonic descendants. For consistency, mos descendant names apply to mosses whose child mosses exceed 10 notes. Since all mosses ultimately descend from some nL ns mos, every possible descendant up to 5 periods will be related to a named mos.
+As diatonic (5L 2s) doesn't have a prefix, the terms ''chromatic'', ''enharmonic'', and ''subchromatic'' by themselves (and with no other context suggesting a non-diatonic mos) refer to 1st (child), 2nd (grandchild), and 3rd (great-grandchild) diatonic descendants. For consistency, mos descendant names apply to mosses whose child mosses exceed 10 notes. Since all mosses ultimately descend from some nL ns mos, every possible descendant up to 5 periods will be related to a named mos.
 {| class="wikitable center-all"
 |+Mosses whose children have more than 10 notes (1st and 2nd descendants only)
@@ Line 1,403: / Line 1,401: @@
 |}
 === Names for mos descendants with more than 5 periods ===
-To name mos descendants with more than 5 periods, the names for wood mosses are extended to hexawood, heptawood (or septawood), octawood, nonawood (or enneawood), and decawood. Beyond that, the naming scheme becomes 11-wood, 12-wood, and so on, and mosses are referred to ''(number)-wood descendants'', or specifically, ''chromatic (number)-wood'', ''enharmonic (number)-wood'', and ''subchromatic (number)-wood.''
+To name mos descendants with more than 5 periods, the names for wood mosses are extended to hexawood, heptawood (or septawood), octawood, nonawood (or enneawood), and decawood. Beyond that, the naming scheme becomes 11-wood, 12-wood, and so on, and mosses are referred to ''chromatic (number)-wood'', ''enharmonic (number)-wood'', and ''subchromatic (number)-wood.'' The term ''(number)-wood descendants'' is also used, and to refer to ''nth (number)-wood descendants'', the algorithm is used below to find the number of generations:
+# 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 n = 0, where n is the number of generations away from zL ws.
+# Let m1 be equal to max(z, w) and m2 be equal to min(z, w).
+# Assign to z the value m2 and w the value m1-m2. Increment n by 1.
+# If both z and w are equal to 1, then the parent mos is nL ns and is n generations from the mos descendant xL ys. If not, repeat the process starting at step 2.
 {| class="wikitable"
 |+Names for wood scales up to 10 periods
@@ Line 1,436: / Line 1,440: @@
 |dkw
 |}
+=== Other names (in-progress) ===
+* n-monolarge or monolarge - Refers to any mos that is of the form 1L ns. These mosses form an infinite mos family that is itself a singular line.
+* n-polylarge or polylarge - Refers to any mos of the form xL (nx+y)s that is along the pseudocollapsed range of step ratios for a mos xL ys. These mosses form an infinite linear family, similar to monolarge mosses.
 === Reasoning for names ===
 The names for chromatic scales are based on former names for the child mosses of diatonic (5L 2s) - p-chromatic for 5L 7s and m-chromatic for 7L 5s - and was generalized to ''chromatic mos''. The term enharmonic is already in use to describe the grandchild mosses of diatonic, and so was generalized to ''enharmonic mos''. The term subchromatic is a term coined by Mike Battaglia to describe a scale that is more chromatic than either chromatic or enharmonic, and is generalized to ''subchromatic mos''.
-The format of adding a mos's prefix to the terms descendant, chromatic, enharmonic, and subchromatic is best applied to mosses that have no more than three periods. With mosses that directly descend from nL ns mosses especially, this is to keep names from becoming too cumbersome.
+The format of adding a mos's prefix to the terms descendant, chromatic, enharmonic, and subchromatic is best applied to mosses that have no more than three periods. With mosses that descend directly from nL ns mosses especially (4L 4s and above), this is to keep names from being too cumbersome (eg, ''chromatic (number)-wood'' instead of ''(number)-woodchromatic'').
 Various people have suggested the use of p- and m- as prefixes to refer to specific chromatic mosses, as well as the use of f- and s- for enharmonic mosses. Generalizing the pattern to 3rd mos descendants reveals an issue where the letters started to diverge from one another, notably where m- is no longer next to p- and f- and s- are no longer along the extremes. Rather than to use these letters and to maintain temperament agnosticism, prefixes based on step ratios are used instead.
@@ Line 1,547: / Line 1,557: @@
 |
 |A more indirect reference to [[machine]] temperament.
-|Still references machine temperament. May also reference [[Subgroup temperaments|mechanism]] temperament.
+|Still references machine temperament. May also reference [[Subgroup temperaments|mechanism]] temperament. May be too minor of a modification.
 |-
 |3L 7s
@@ Line 1,652: / Line 1,662: @@
 |pel-
 |pel
-|pelotonic
+|pelotonic or peltonic
 |unchagned
 |unchagned

User:Ganaram inukshuk/Notes/TAMNAMS: Difference between revisions