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

The easiest and most general way to refer to a mos that descends from another, TAMNAMS-named mos is to refer to it as a ''mosdescendant'', where the prefix of mos- is substituted for the prefix for the mos itself. For consistency, mosdescendant names apply to named TAMNAMS mosses whose child scales exceed 10 notes, shown in the table below in '''bold'''.

|}The number of generations a mos is from a named mos can also be specified, so the child mos is a ''1st-mosdescendant'', its grandchild a ''2nd-mosdescendant'', its great-grandchild a ''3rd-mosdescaendnt'', and so on. The algorithm below explains how to find the number of generations two related mosses are, given the mos descends from a named mos whose child mosses already exceed 10 notes:

* Finding a parent mos zL ws for the mosdescendant xL ys, where x, y, z, and w share a greatest common factor that is no greater than 5:

*# 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 g = 0, where g 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 g by 1.

Since diatonic doesn't have a mos prefix, the phrase ''diatonic descendant'' is used to refer to its mosdescendants.

=== Naming mosdescendants up to 3 generations ===

Although naming scales beyond the current cap of 10 notes is antithetical to the purpose of TAMNAMS, names for mosses greater than 10 notes can be made systematically using existing names. The rules are described as such:

* If the scale is the child of a named parent scale, then the scale is '''moschromatic'''.

* If the scale is the grandchild of a named parent scale, then the scale is '''mosenharmonic.'''

* If the scale is the great-grandchild of a named parent scale, then the scale is '''mosschismic'''. (tentative name; [[Schismatic family|schismic]] refers to a family of temperaments; open to better name suggestions)

* If the scale is more than 3 generations from a named parent scale, or if referring to a scale regardless of number of generations from the parent, then the scale is a '''mosdescendant''' scale.

 

For describing the scales of a named mos, the prefix of mos- is removed and replaced with the mos's prefix instead. For example, the child, grandchild, and great-grandchild scales for the mos 5L 3s (oneirotonic, prefix oneiro-) are oneirochromatic, oneiroenharmonic, and oneiroschismic respectively, and the entire family of mosses related to oneirotonic are oneirodescendants.

 

Additionally, the lack of a prefix will specifically describe the descendant scales of 5L 2s: chromatic, enharmonic, and schismic. Descendants of 5L 2s are referred to as "diatonic descendants" rather than "descendants".

 

Single-letter prefixes for these names are optional, as the single-letter prefixes are meant for specificity. With no prefix specified, moschromatic refers to one of two child scales, mosenharmonic refers to one of four grandchild scales, and mosschismic refers to one of eight great-grandchild scales. The table below shows those prefixes and the mosdescendants for which they apply, as well as the step ratio of the parent mos needed to reach these scales.

! colspan="3" |Parent scale

! colspan="4" |Mosschismic (great-grandchild) scales

!Step ratio for 2:1

!For L:s = 2:1

!For L:s = 2:1

| rowspan="4" |m-moschromatic

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

| rowspan="4" |3:2 (soft)

| rowspan="2" |f-mosenharmonic

|f-mosschismic

|a-mosschismic

| rowspan="2" |m-mosenharmonic

|u-mosschismic

|m-mosschismic

| rowspan="4" |p-moschromatic

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

| rowspan="4" |3:1 (hard)

| rowspan="2" |p-mosenharmonic

|p-mosschismic

|q-mosschismic

| rowspan="2" |s-mosenharmonic

|r-mosschismic

|s-mosschismic

=== Naming mosdescendants for linearly growing scales (work-in-progress) ===

Some noteworthy mosdescendants may be more than 3 generations away, but may have the same number of large steps as a named parent mos. In such cases, the number of notes with each successive mosdescendant grows linearly, and these mosses may be assigned a letter to refer to a specific mosdescendant. Currently, this applies to mosdescendants whose parent mos has a step ratio that is along the extreme edges of the step ratio spectrum, around pseudoequalized and pseudocollapsed, producing '''nth s-mosdescendants''' and '''nth f-mosdescendants'''. The mos family tree better shows which mosses grow linearly, shown in bold, as the upper child of each node is always xL (x+y)s, which becomes of xL (nx+y)s over n generations.

|+Mosdescendants sorted by position on the mos family tree

! colspan="2" |4th-mosdescendant scales

! colspan="2" |5th-mosdescendant scales

The names for moschromatic scales are based on former names for the child scales for diatonic (5L 2s): p-chromatic (5L 7s) and m-chromatic (7L 5s). This was generalized to "chromatic" and "moschromatic", with the prefixes m- and p- for specificity. The names for mosenharmonic scales are based on discussions with xen Discord members for systematically naming the daughter and granddaughter scales of a mos, producing "enharmonic" and "mosenharmonic" with the prefixes f-, m-, p-, and s- for specificity.

Names for mosdescendants are thereby based on replacing the mos- prefix with that for a mos's TAMNAMS name. This effectively brings back the names of m-chromatic and p-chromatic, as TAMNAMS specifically names mosses up to 10 notes. This also names other mosses whose names were lost entirely, mainly kleistonic (4L 7s, now p-smichromatic) and suprasmitonic (7L 4s, now m-smichromatic), two names that were dropped because these mosses had more than 10 notes.

 

The reason why mosdescendants for mosses with 4 periods or greater are not based on their corresponding n-wood scale is because these mosses do not have any child mosses with 10 notes or fewer, and therefore have no named child mosses from which to build mosdescendant names. Rather, names for these mosdescendants are based on period-agnostic names (antrial, trial, antetric, tetric, etc) to reflect that these are scales based on duplicating a base mos multiple times within an octave.

 

!For moschromatic scales

|A from p'''a'''rasoft, as "P" is taken.

|U from q'''u'''asisoft, as "Q" is taken.

| rowspan="2" |M- and p-mosenharmonic scales have a grandparent whose step ratio is close to the "'''m'''id'''p'''oint" of L:s = 2:1.

|-

|Q and R are the only two letters between P and S. Q may stand for '''q'''uasihard.

|s-

|S for '''s'''harp; s-mosenharmonic scales have a grandparent whose pitches are sharper compared to basic (L:s = 2:1).

|"S" for '''s'''harp.

 

 

* Interestingly, there is evidence that another Xen Discord user ([[user:Flirora]]) suggested the same naming system described here up to 3 generations, with only slight differences with 3rd-generation names. As I was part of a discussion on limiting TAMNAMS names to 10-note mosses, which facilitated naming mosdescendants up to two generations (mosenharmonic scales), rather than this earlier suggestion, it's possible that the same proposal for mosenharmonic scales may have been independently developed twice.

* Some names with this system are not finalized, particularly the term "mosschismic" and some of the single-letter prefixes.

** Better names than "mosschismic" include "mossubharmonic" (adapted from the above suggestion which had "prefix-sub-prefix-enharmonic") and "mossubchromatic", possibly shortened to "mossubchromic" (adapted from "subchromatic", as seen in [[Diatonic, Chromatic, Enharmonic, Subchromatic|this page]]).

** An issue with using letter-based prefixes is that many of them are based on temperaments. A temperament-agnostic interpretation will be needed if these letters are to be generalized outside of the diatonic family.

** Yet another issue is that the pattern of f-, m-, p-, and s-, all based on temperaments, does not continue with 3rd-generation mosses in that f- and s- are no longer at the extremes and p- is no longer at the midpoint (see table below). Either 3rd-generation mosses need a different set of prefixes, or a different set of prefixes are needed throughout.

** In the spirit of TAMNAMS being temperament-agnostic, a proper solution may be to not use and shoehorn temperament-suggestive prefixes, but rather use the names for step ratios. This lines up with Frostburn's proposal, but applies to the first three generations, not just the third. (Frostburn's proposed abbreviations may also work.) Under this system, all prefixes can work for all three generations, so soft-chromatic, hyposoft-chromatic, and minisoft-chromatic is allowed, just as soft-subchromatic, hyposoft-subchromatic, and minisoft-subchromatic. The absence of prefixes is also allowed.

*** Hard and soft are preferred over sharp and flat, as those describe accidentals specific to diatonic notation. TAMNAMS and diamond-mos notation has generalized sharps and flats, called amps/ams and ats.

!Notable temperament(s)

!Notable temperament(s)

!Notable temperament(s)

!Would-be prefix

! colspan="3" |Great-grandchild scales

!Name based on step ratio

!Name based on step ratio

!Possible abbrev.

| rowspan="15" |[[5L 2s]]

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

| rowspan="7" |soft-chromatic

| rowspan="7" |s-chromatic

| rowspan="3" |[[7L 12s]]

| rowspan="3" |soft-enharmonic

|[[7L 19s]]

|ultrasoft-subchromatic

|us-subchromatic

|-

| rowspan="3" |[[12L 7s]]

| rowspan="3" |hyposoft-enharmonic

| rowspan="3" |hs-enharmonic

|quasisoft-subchromatic

|qs-subchromatic

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

| rowspan="7" |hard-chromatic

| rowspan="7" |h-chromatic

| rowspan="3" |[[12L 5s]]

| rowspan="3" |hypohard-enharmonic

| rowspan="3" |hh-enharmonic

|minihard-subchromatic

|mh-subchromatic

|-

|-

|quasihard-subchromatic

|qh-subchromatic

|-

|-

| rowspan="3" |hard-enharmonic

| rowspan="3" |h-enharonic

|parahard-subchromatic

|ph-subchromatic

|-

|-

|ultrahard-subchromatic

|uh-subchromatic