User:Ganaram inukshuk/TAMNAMS Extension: Difference between revisions

This is a system for describing and naming mos scales beyond the set of named TAMNAMS mosses. 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.

*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.

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.

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'':

#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 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 (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)

! colspan="2" |6-note mosses

! colspan="2" |Chromatic mosses

! colspan="2" |Enharmonic mosses

|[[1L 5s]]

|antimachinoid

|[[2L 4s]]

|malic

|2L 6s, 6L 2s

|n/a

|2A 8B, 6A 8B

|n/a

|[[3L 3s]]

|triwood

|[[4L 2s]]

|citric

|4L 6s, 6L 4s

|n/a

|4A 10B, 6A 10B

|n/a

|[[5L 1s]]||machinoid

|mechenharmonic

! colspan="2" |7-note mosses

! colspan="2" |Chromatic mosses

! colspan="2" |Enharmonic mosses

!Pattern!!Name

!Patterns

!Names

!Patterns

!Names

|[[1L 6s]]

|onyx

|1L 7s, 7L 1s

|n/a

|1A 8B, 7A 8B

|[[2L 5s]]

|antidiatonic

|2L 7s, 7L 2s

|n/a

|2A 9B, 7A 9B

|[[3L 4s]]

|mosh

|3L 7s, 7L 3s

|n/a

|3A 10B, 7A 10B

|[[4L 3s]]||smitonic

|4L 7s, 7L 4s

|smichromatic

|4A 11B, 7A 11B

|[[5L 2s]]||diatonic

|5L 7s, 7L 5s

|chromatic

|5A 12B, 7A 12B

|[[6L 1s]]||arch(a)eotonic

|6L 7s, 7L 6s

|archeoromatic

|6A 13B, 7A 13B

! colspan="2" |8-note mosses

! colspan="2" |Chromatic mosses

! colspan="2" |Enharmonic mosses

|[[1L 7s]]

|antipine

|1L 8s, 8L 1s

|n/a

|1A 9B, 8A 9B

|[[2L 6s]]

|subaric

|2L 8s, 8L 2s

|n/a

|2A 10B, 8A 10B

|n/a

|[[4L 4s]]||tetrawood; diminished

|4L 8s, 8L 4s

|chromatic tetrawood

|4A 12B, 8A 12B

|enharmonic tetrawood

|[[5L 3s]]||oneirotonic

|oneirochromatic

|5A 13B, 8A 13B

|oneiroenharmonic

|[[6L 2s]]||ekic

|ekchromatic

|6A 14B, 8A 14B

|ekenharmonic

|[[7L 1s]]||pine

|7L 8s, 8L 7s

! colspan="2" |9-note mosses

! colspan="2" |Chromatic mosses

! colspan="2" |Enharmonic mosses

|[[1L 8s]]

|[[3L 6s]]||tcherepnin

|3L 9s, 9L 3s

|cherchromatic

|3A 12B, 9A 12B

|cherenharmonic

|[[4L 5s]]||gramitonic

|gramchromatic

|4A 13B, 9A 13B

|gramenharmonic

|[[5L 4s]]||semiquartal

|5L 9s, 9L 5s

|chtonchromatic

|5A 14B, 9A 14B

|chtonenharmonic

|[[6L 3s]]||hyrulic

|[[8L 1s]]||subneutralic

|8L 9s, 9L 8s

|bluchromatic

|8A 17B, 9A 17B

|bluenharmonic

! colspan="2" |10-note mosses

! colspan="2" |Chromatic mosses

! colspan="2" |Enharmonic mosses

!Pattern!!Name

|[[6L 4s]]||lemon

|lemchromatic

|[[7L 3s]]||dicoid, zaltertic

|[[8L 2s]]||taric

|8L 10s, 10L 8s

|[[9L 1s]]||sinatonic

{| class="wikitable"

! rowspan="2" |Steps

! rowspan="2" |L:s range

! rowspan="2" |L:s range

!Prefix

!Abbrev.

| rowspan="8" |xL ys

| rowspan="2" |soft-

| rowspan="2" |s-

| rowspan="2" |1:1 to 3:2

| rowspan="4" |soft-

| rowspan="4" |s-

|1:1 to 4:3

|(3x+2y)L (x+y)s

|parasoft-

|ps-

|4:3 to 3:2

| rowspan="2" |(2x+y)L (x+y)s

| rowspan="2" |os-

| rowspan="2" |3:2 to 2:1

|quasisoft-

|qs-

|3:2 to 5:3

|(2x+y)L (3x+2y)s

|minisoft-

|ms-

|5:3 to 2:1

| rowspan="4" |xL (x+y)s

| rowspan="4" |hard-

| rowspan="4" |h-

| rowspan="4" |2:1 to 1:0

| rowspan="2" |(2x+y)L xs

| rowspan="2" |hypohard-

|2:1 to 5:2

|(3x+y)L (2x+y)s

|quasihard-

|qh-

|5:2 to 3:1

| rowspan="2" |xL (2x+y)s

| rowspan="2" |hard-

| rowspan="2" |h-

| rowspan="2" |3:1 to 1:0

|parahard-

|ph-

|xL (3x+y)s

|ultrahard-

|uh-

|4:1 to 1:0

{| class="wikitable"

! colspan="2" |Balzano (parent)

! colspan="2" |Chromatic balzano

! colspan="2" |Enharmonic balzano

! colspan="3" |Subchromatic balzano

!Steps

!Name

!Name

!Steps

| rowspan="8" |2L 7s

|9L 20s

| rowspan="4" |s-balsubchromatic

|us-balsubchromatic

|20L 9s

|ps-balsubchromatic

|11L 20s

|ms-balsubchromatic

| rowspan="4" |h-balsubchromatic

|mh-balsubchromatic

| rowspan="2" |2L 11s

| rowspan="2" |h-balenharmonic

|13L 2s

|ph-balsubchromatic

|2L 13s

|uh-balsubchromatic

==Other mos names==

 

#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.

|hexwud-

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.

 

Mosses in this 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 pseudoequalized step ratio. Continuing with the example of 5L 2s, the smallest edo that can reach 5L 7s is 17edo (where L:s = 2:1, therefore 5L+7s = 17), producing a 5L 2s mos with a step ratio of 3:1, whereas reaching the mos 5L 17s requires the initial mos of 5L 2s to have a step ratio of 5:1.

{| class="wikitable"

! colspan="3" |Trivial families

!Mos

!Name

|1L ns

|monolarge family

|Represents an entire family of mosses formerly unnamed by TAMNAMS

|bilarge family

|Named analogously to the monolarge family

! colspan="3" |Families with 3 large steps

!Mos

!Name

|3L (3n+1)s

|tetralinear family

|Named after tetric, the first mos in this sequence (n=0)

|3L (3n+2)s

|Named after anpentic

! colspan="3" |Families with 4 large steps

!Mos

!Name

|4L (4n+1)s

|manulinear family

|Named after manual

|4L (4n+3)s

|smilinear family

|Named after smitonic

! colspan="3" |Families with 5 large steps

!Mos

!Name

|5L (5n+1)s

|mechlinear family

|Named after machinoid

|5L (5n+2)s

|p-linear family

|Named after p-chromatic rather than diatonic, which has no prefix

|5L (5n+3)s

|oneirolinear family

|Named after oneirotonic

|5L (5n+4)s

|chtonlinear family

|Named after semiquartal (prefix chton-)

! colspan="3" |Families with 6 large steps

|6L (6n+1)s

|Named after xeimtonic, a former name for 6L 5s

!Mos

!Name

|7L (7n+1)s

|pinelinear family

|Named after pine

|7L (7n+2)s

|armlinear family

|Named after armotonic (also called superdiatonic)

|7L (7n+3)s

|dicolinear or zalinear family

|Named after dicotonic (also called zaltertic)

|7L (7n+4)s

|prasmilinear family

|Named after suprasmitonic, a former name for 7L 4s but with a truncated name

|7L (7n+5)s

|Named after m-chromatic rather than diatonic

! colspan="3" |Families with 8 large steps

|8L (8n+1)s

|blulinear family

|Named after subneutralic (prefix blu-)

|8L (8n+3)s

|

|

|8L (8n+5)s

|petrlinear family

|Named after petroid, a former name for 8L 5s

|8L (8n+7)s

|

|

! colspan="3" |Families with 9 large steps

!Mos

!Name

|9L (9n+1)s

|sinalinear family

|Named after sinatonic

|-

|9L (9n+2)s

|9L (9n+4)s

|

|

|9L (9n+5)s

|

|

|9L (9n+7)s

|

|

|-

|9L (9n+8)s

==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 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.

| rowspan="4" |[[7L 5s]]

| rowspan="4" |[[5L 7s]]

|}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.