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m Names for mos linear families: Renamed "tetralinear" to "trilarge" because it sounded simpler; clarified mos linear family naming
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== Naming mos descendants ==
== Naming mos descendants ==
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.
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''. For the child of a named mos, the name is ''chromatic (mos name).''
*A child mos is a ''chromatic mos'', ''chromatic (mos name).''
*A grandchild mos is an ''enharmonic mos''. For the grandchild of a named mos, the name is ''enharmonic (mos name)''.
*A grandchild mos is an ''enharmonic mos'' or ''enharmonic (mos name)''.
*A great-grandchild mos is a ''subchromatic mos''. For the great-grandchild of a named mos, the name is ''subchromatic (mos name)''.
*A great-grandchild mos is a ''subchromatic mos'' or ''subchromatic (mos name)''.
*A mos that is more than 3 generations away is called a ''descendant mos''. For the descendant of a named mos, the name is ''(mos name) descendant''. This term can also be used to describe any mos descendant any number of generations away from a named mos.
*A mos that is more than 3 generations away is called a ''descendant mos'' or ''(mos name) descendant''.
These phrases may also be shortened by adding the mos's prefix to the terms chromatic, enharmonic, subchromatic, or descendant respectively, if the named mos has no more than 3 periods.
These phrases may also be shortened by adding the mos's prefix to the terms ''chromatic'', ''enharmonic'', ''subchromatic'', or ''descendant'' respectively, if the named mos has no more than 3 periods. Additionally, the terms ''chromatic'', ''enharmonic'', and ''subchromatic'' may be used generally to refer to an entire generation of mosses (2, 4, or 8 possible mosses respectively) rather than a specific mos. The term ''descendant'' may also be used generally to refer to any mos any number of generations away from a named mos.


Optionally, for the phrase ''mos descendant,'' the number of generations away from a named mos 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'':
Optionally, for the phrase ''mos descendant,'' the number of generations away from a named mos 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'':
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|sinenharmonic
|sinenharmonic
|}
|}
==Names for mos descendants by step ratio==
===Naming mos descendants by step ratio===
The designations of chromatic, enharmonic, and subchromatic by themselves does not describe a specific mos descendant. To do that, the name of a step ratio range can be prefixed to the terms ''chromatic'', ''enharmonic'', and ''subchromatic'' (or ''(mos-prefix)chromatic'', ''(mos-prefix)enharmonic'', and ''(mos-prefix)subchromatic''). Specifying the step ratio is optional, and the names for step ratios can be abbreviated into a one or two-letter prefix. (Frostburn's abbreviations can be used here, too.) These prefixes are used for specific descendants, with the notable exception of ''soft'' and ''hard''. For enharmonic mosses, these describe mosses with a step ratio outside the hyposoft and hypohard range. For subchromatic mosses, these describe mosses within the entire soft and hard ranges, producing terminology more specific than just ''subchromatic'' but not as specific as the specific step ratio ranges. These prefixes must include a hyphen.
The designations of chromatic, enharmonic, and subchromatic by themselves does not describe a specific mos descendant. The name of a step ratio range can be prefixed to the terms ''chromatic'', ''enharmonic'', and ''subchromatic'' (or ''(mos-prefix)chromatic'', ''(mos-prefix)enharmonic'', and ''(mos-prefix)subchromatic''). Specifying the step ratio is optional, and the names for step ratios can be abbreviated into a one or two-letter prefix. (Frostburn's abbreviations can be used here, too.) These prefixes are used for specific descendants, with the notable exception of ''soft'' and ''hard''. For enharmonic mosses, these describe mosses with a step ratio outside the hyposoft and hypohard range. For subchromatic mosses, these describe mosses within the entire soft and hard ranges, producing terminology more specific than just ''subchromatic'' but not as specific as the specific step ratio ranges. These prefixes must include a hyphen.
{| class="wikitable"
{| class="wikitable"
|+Descendant mosses sorted by generation and step ratio
|+Descendant mosses sorted by generation and step ratio
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|}
|}
==Other mos names==
==Other mos names==
This section describes additional names for mosses that have more than 10 notes but are worthy of names.
This section describes additional names for groups of mosses or for mosses or that have more than 10 notes but are worthy of names.


=== Names for mos descendants with more than 5 periods ===
=== Names for mos descendants with more than 5 periods ===
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A mos linear family is a family of related mosses of the form xL (nx + y)s. This family starts with the mos xL ys, where x < y and n = 0, and continue with mosses with the same number of large steps but a linearly growing quantity of small steps. An example of such a family is the mos sequence 5L 2s, 5L 7s, 5L 12s, 5L 17s, etc, where each successive mos has 5 more small steps than the last.
A mos linear family is a family of related mosses of the form xL (nx + y)s. This family starts with the mos xL ys, where x < y and n = 0, and continue with mosses with the same number of large steps but a linearly growing quantity of small steps. An example of such a family is the mos sequence 5L 2s, 5L 7s, 5L 12s, 5L 17s, etc, where each successive mos has 5 more small steps than the last.


Names for these families describe a subset of a mos descendant family, and most mos families go by the name of ''(mos name)'' ''linear family'' or ''(mos-prefix)linear family''. Mosses in a linear family relate to one another by repeated application of the replacement ruleset L->Ls and s->s to the initial mos's step pattern. In terms of step ratio, these mosses relate back to the initial mos if the initial mos has a hard or pseudocollapsed step ratio. The linear family for the child mos (x+y)L xs can be seen as the analogous linear family for the mos's step ratio being soft or pseudoequalized; however, the mos (x+y)L xs is the start of its own linear family.
Mosses in a linear family are based on repeated applications of the replacement ruleset L->Ls and s->s on the initial mos, and reaching the nth member of a linear family requires the initial mos have a hard or pseudocollapsed step ratio. The child mos (x+y)L xs is the start of its own linear family, which relates back to the initial mos xL ys if the initial mos has a step ratio that is soft or pseudoequalized.
 
Names for these families describe a subset of a mos descendant family, and most mos families go by the name of ''(mos name)'' ''linear family'' or ''(mos-prefix)linear family''.
{| class="wikitable"
{| class="wikitable"
|+Names of single-period mos linear families (work-in-progress)
|+Names of single-period mos linear families (work-in-progress)
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|
|
|}
|}
== Reasoning for names ==
The overall motivation for these names is to give names to closely related mosses and refer to individual mosses as some member of a broader family, rather than name individual 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 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 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'').
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.
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 shows the letters diverging from one another, notably where m- is no longer next to p- and f- and s- are no longer along the extremes. Rather than using these letters, as well as being temperament-agnostic, prefixes based on step ratios are used instead. However, temperament-based prefixes may be used specifically for diatonic descendants as alternatives to the prefixes based on step ratios.
{| class="wikitable"
{| class="wikitable"
|+Temperament-based mosdescendant prefixes
|+Prefixes for diatonic descendants
! rowspan="2" |Diatonic scale
! rowspan="2" |Diatonic scale
! colspan="3" |Chromatic mosses
! colspan="3" |Chromatic mosses
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|-
|-
!Steps
!Steps
!Notable temperament
!Temp-based prefix
!Prefix
!Prefix
!Steps
!Steps
!Notable temperament
!Temp-based prefix
!Prefix
!Prefix
!Steps
!Steps
!Notable temperament
!Temp-based prefix
!Prefix
!Prefix
|-
|-
| rowspan="8" |[[5L 2s]]
| rowspan="8" |[[5L 2s]]
| rowspan="4" |[[7L 5s]]
| rowspan="4" |[[7L 5s]]
| rowspan="4" |meantone
| rowspan="4" |m- (from meantone)
| rowspan="4" |m-
| rowspan="4" |s-
| rowspan="2" |[[7L 12s]]
| rowspan="2" |[[7L 12s]]
| rowspan="2" |flattone
| rowspan="2" |f- (from flattone)
| rowspan="2" |f-
| rowspan="2" |s-
|[[7L 19s]]
|[[7L 19s]]
|tridecimal
|t- (from tridecimal)
|t-
|us-
|-
|-
|[[19L 7s]]
|[[19L 7s]]
|flattone
|f- (from flattone)
|f-
|ps-
|-
|-
| rowspan="2" |[[12L 7s]]
| rowspan="2" |[[12L 7s]]
| rowspan="2" |meantone
| rowspan="2" |m- (from meantone)
| rowspan="2" |m-
| rowspan="2" |os-
|[[19L 12s]]
|[[19L 12s]]
|meanpop
|m- (from meanpop)
|m-
|qs-
|-
|-
|[[12L 19s]]
|[[12L 19s]]
|huygens
|h- (from huygens)
|h-
|ms-
|-
|-
| rowspan="4" |[[5L 7s]]
| rowspan="4" |[[5L 7s]]
| rowspan="4" |pythagorean
| rowspan="4" |p- (from pythagorean)
| rowspan="4" |p-
| rowspan="4" |h-
| rowspan="2" |[[12L 5s]]
| rowspan="2" |[[12L 5s]]
| rowspan="2" |pythagorean
| rowspan="2" |p- (from pythagorean)
| rowspan="2" |p-
| rowspan="2" |oh-
|[[12L 17s]]
|[[12L 17s]]
|pythagorean
|p- (from pythagorean)
|p-
|mh-
|-
|-
|[[17L 12s]]
|[[17L 12s]]
|gentle
|g- (from gentle)
|g-
|qh-
|-
|-
| rowspan="2" |[[5L 12s]]
| rowspan="2" |[[5L 12s]]
| rowspan="2" |superpyth
| rowspan="2" |s- (from superpyth)
| rowspan="2" |s-
| rowspan="2" |h-
|[[17L 5s]]
|[[17L 5s]]
|superpyth
|s- (from superpyth)
|s-
|ph-
|-
|-
|[[5L 17s]]
|[[5L 17s]]
|ultrapyth
|u- (from ultrapyth)
|u-
|uh-
|}The temperament-based prefixes may be used specifically for diatonic descendants as alternatives to the prefixes based on step ratios, effectively bringing back the names of p-chromatic and m-chromatic.
|}