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

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== Naming mosses with more than 10 steps ==

== Proposal: Naming mosses with more than 10 steps ==

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, though this is focused on naming single-period mosses up to three generations after a parent scale.

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

=== Naming mosdescendant scales up to 3 generations ===

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=== Mosdescendants for multi-period mosses ===

TAMNAMS has names for 2-period mosses up to 10 notes, and as such, mosdescendant names apply to mosses whose children have more than 10 notes: '''jaric''', '''taric''', '''ekic''', '''lemon''', and '''lime'''. Likewise, there are 3-period scales up to 9 notes, so mosdescendant names apply to '''tcherepnin''' and '''hyrulic'''.

TAMNAMS has names for 2-period mosses up to 10 notes, and as such, mosdescendant names apply to mosses whose children have more than 10 notes: '''jaric''', '''taric''', '''ekic''', '''lemon''', and '''lime'''. Likewise, there are 3-period scales up to 9 notes, so mosdescendant names apply to '''tcherepnin''' and '''hyrulic''', the only 3-period mosses named under TAMNAMS, apart from triwood.

{| class="wikitable"

|+2 and 3-period mosses for which mosdescendant names apply

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|'''hyrulic (hyru-)'''

|}

Starting at 4 periods, mosdescendant names apply only to n-wood scales (~~triwood,~~ tetrawood, pentawood, etc), where the names of mosdescendants are based on names for single-period mosses up to 5 notes rather than based on moschromatic, mosenharmonic, and mosschismic, and thereby limited to mosdescendants with 5n notes; any descendants after that are referred as to '''n-wood descendants'''.

Starting at 4 periods, mosdescendant names apply only to n-wood scales (tetrawood, pentawood, etc), where the names of mosdescendants are based on names for single-period mosses up to 5 notes rather than based on moschromatic, mosenharmonic, and mosschismic, and thereby limited to mosdescendants with 5n notes; any descendants after that are referred as to '''n-wood descendants'''.

Since the names for single-period mosses up to 5 notes may also be used for non-octave periods, these names are used for multi-period mosses, producing '''n-antrial''', '''n-trial''', '''n-antetric''', '''n-tetric''', '''n-antipentic''', '''n-pentic''', '''n-pedal''', and '''n-manual'''. Note that there are only two named 3rd-generation mosses from nL ns rather than the usual eight; the missing six names (what would be n-smitonic, n-mosh, n-checkertonic, n-oneiorotonic, n-diatonic, and n-antidiatonic) are unsuitable for use for multi-period mos names as these names must refer to an octave period.

The table outlines possible names for n-wood descendants for ~~triwood,~~ tetrawood, pentawood, and, in the general case, n-wood.

The table outlines possible names for n-wood descendants for tetrawood, pentawood, and, in the general case, n-wood. Numeric prefixes may be used for these names, rather than n-.

{| class="wikitable"

|+Possible mosdescendant names for mosses with 4 periods or more

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Each generation has twice as many mosdescendants as the last, so rather than try to name every possible descendant, mosdescendants more than 3 generations from a given parent mos may be referred to how many generations away it is. Mosschismic scales are 3rd mosdescendants, so after that are 4th-mosdescendants, 5th-mosdescendants, and so on. The algorithms below shows how to find how many generations away a mos xL ys is from another scale.

* For mosses with up to 3 periods: finding a parent mos zL ws for the mosdescendant xL ys, where x and ~~y are either coprime (have a greatest common factor of 1) or have~~ a greatest common factor ~~of 2 or~~ 3:

* For mosses with up to 3 periods: 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 3:

*# 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.

*# If the sum of z and w is ~~less~~ than ~~or equal to~~ 10, then the mos ~~name~~ is ~~that assigned to the mos~~ zL ws~~, which is g generations away from xL ys~~. If not, repeat the process starting at step 2.

*# If the sum of z and w is no more than 10, then the parent mos is zL ws and has a TAMNAMS name. If not, repeat the process starting at step 2.

* For mosses with 4 periods or more: finding how many generations away a mosdescendant xL ys is from its n-wood scale, where x and y have a greatest common factor of n that is 4 or greater:

*# Let z and w be assigned the values x and y respectively. Let g = 0, where g is the number of generations away from nL ns.

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*# Assign to z the value m2 and w the value m1-m2. Increment g by 1.

*# If the sum of z and w is exactly 2n, then the mos nL ns is g generations away from xL ys. If not, repeat the process starting at step 2.

=== Naming mosdescendant scales where successive generations of scales grow linearly ===

In cases where the number of notes with each successive mosdescendant grows linearly, these mosses may be assigned a letter to refer to a specific mosdescendant.

{| class="wikitable"

!Parent scale

! colspan="2" |Moschromatic (child) scales

! colspan="2" |Mosenharmonic (grandchild) scales

! colspan="2" |Mosschismic (great-grandchild) scales

|-

! rowspan="2" |Steps

! rowspan="2" |Specific name

! rowspan="2" |Steps

! rowspan="2" |Specific name

! rowspan="2" |Steps

! rowspan="2" |Specific name

|

|-

| rowspan="8" |xL ys

| rowspan="4" |(x+y)L xs

| rowspan="4" |m-moschromatic

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

| rowspan="2" |f-mosenharmonic

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

|f-mosschismic

|

|-

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

|a-mosschismic

|

|-

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

| rowspan="2" |m-mosenharmonic

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

|u-mosschismic

|

|-

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

|m-mosschismic

|

|-

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

| rowspan="4" |p-moschromatic

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

| rowspan="2" |p-mosenharmonic

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

|p-mosschismic

|

|-

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

|q-mosschismic

|

|-

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

| rowspan="2" |s-mosenharmonic

|(3x+y)L xs

|r-mosschismic

|

|-

|xL (3x+y)s

|s-mosschismic

|

|}

=== Reasoning for names ===

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 ~~was reorganized to only name~~ 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.

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.

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|}

== Naming mos modes ==

== Proposal: Naming mos modes ==

=== Current proposal, with amendment for emphasis on dark generator ===

=== Current proposal, with proposed amendment for emphasis on dark generator ===

There is currently a proposed system for naming mos modes as follows: '''xL ys u|''', where x is the number of large steps, y is the number of small steps, u corresponds to the the mode's UDP (the u in u|d), and | is pronounced as "pipe". As an example, the modes of 4L 1s (manual) can be named as the following:

{| class="wikitable"

@@ Line 640: / Line 640: @@
 |}
-== Naming mosses with more than 10 steps ==
+== Proposal: Naming mosses with more than 10 steps ==
 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, though this is focused on naming single-period mosses up to three generations after a parent scale.
+Note: Some names with this system are not finalized, particularly mosschismic and some of the single-letter prefixes.
 === Naming mosdescendant scales up to 3 generations ===
@@ Line 913: / Line 915: @@
 === Mosdescendants for multi-period mosses ===
-TAMNAMS has names for 2-period mosses up to 10 notes, and as such, mosdescendant names apply to mosses whose children have more than 10 notes: '''jaric''', '''taric''', '''ekic''', '''lemon''', and '''lime'''. Likewise, there are 3-period scales up to 9 notes, so mosdescendant names apply to '''tcherepnin''' and '''hyrulic'''.
+TAMNAMS has names for 2-period mosses up to 10 notes, and as such, mosdescendant names apply to mosses whose children have more than 10 notes: '''jaric''', '''taric''', '''ekic''', '''lemon''', and '''lime'''. Likewise, there are 3-period scales up to 9 notes, so mosdescendant names apply to '''tcherepnin''' and '''hyrulic''', the only 3-period mosses named under TAMNAMS, apart from triwood.
 {| class="wikitable"
 |+2 and 3-period mosses for which mosdescendant names apply
@@ Line 967: / Line 969: @@
 |'''hyrulic (hyru-)'''
 |}
-Starting at 4 periods, mosdescendant names apply only to n-wood scales (triwood, tetrawood, pentawood, etc), where the names of mosdescendants are based on names for single-period mosses up to 5 notes rather than based on moschromatic, mosenharmonic, and mosschismic, and thereby limited to mosdescendants with 5n notes; any descendants after that are referred as to '''n-wood descendants'''.
+Starting at 4 periods, mosdescendant names apply only to n-wood scales (tetrawood, pentawood, etc), where the names of mosdescendants are based on names for single-period mosses up to 5 notes rather than based on moschromatic, mosenharmonic, and mosschismic, and thereby limited to mosdescendants with 5n notes; any descendants after that are referred as to '''n-wood descendants'''.
 Since the names for single-period mosses up to 5 notes may also be used for non-octave periods, these names are used for multi-period mosses, producing '''n-antrial''', '''n-trial''', '''n-antetric''', '''n-tetric''', '''n-antipentic''', '''n-pentic''', '''n-pedal''', and '''n-manual'''. Note that there are only two named 3rd-generation mosses from nL ns rather than the usual eight; the missing six names (what would be n-smitonic, n-mosh, n-checkertonic, n-oneiorotonic, n-diatonic, and n-antidiatonic) are unsuitable for use for multi-period mos names as these names must refer to an octave period.
-The table outlines possible names for n-wood descendants for triwood, tetrawood, pentawood, and, in the general case, n-wood.
+The table outlines possible names for n-wood descendants for tetrawood, pentawood, and, in the general case, n-wood. Numeric prefixes may be used for these names, rather than n-.
 {| class="wikitable"
 |+Possible mosdescendant names for mosses with 4 periods or more
@@ Line 1,091: / Line 1,093: @@
 Each generation has twice as many mosdescendants as the last, so rather than try to name every possible descendant, mosdescendants more than 3 generations from a given parent mos may be referred to how many generations away it is. Mosschismic scales are 3rd mosdescendants, so after that are 4th-mosdescendants, 5th-mosdescendants, and so on. The algorithms below shows how to find how many generations away a mos xL ys is from another scale.
-* For mosses with up to 3 periods: finding a parent mos zL ws for the mosdescendant xL ys, where x and y are either coprime (have a greatest common factor of 1) or have a greatest common factor of 2 or 3:
+* For mosses with up to 3 periods: 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 3:
 *# 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.
-*# If the sum of z and w is less than or equal to 10, then the mos name is that assigned to the mos zL ws, which is g generations away from xL ys. If not, repeat the process starting at step 2.
+*# If the sum of z and w is no more than 10, then the parent mos is zL ws and has a TAMNAMS name. If not, repeat the process starting at step 2.
 * For mosses with 4 periods or more: finding how many generations away a mosdescendant xL ys is from its n-wood scale, where x and y have a greatest common factor of n that is 4 or greater:
 *# Let z and w be assigned the values x and y respectively. Let g = 0, where g is the number of generations away from nL ns.
@@ Line 1,101: / Line 1,103: @@
 *# Assign to z the value m2 and w the value m1-m2. Increment g by 1.
 *# If the sum of z and w is exactly 2n, then the mos nL ns is g generations away from xL ys. If not, repeat the process starting at step 2.
+=== Naming mosdescendant scales where successive generations of scales grow linearly ===
+In cases where the number of notes with each successive mosdescendant grows linearly, these mosses may be assigned a letter to refer to a specific mosdescendant.
+{| class="wikitable"
+!Parent scale
+! colspan="2" |Moschromatic (child) scales
+! colspan="2" |Mosenharmonic (grandchild) scales
+! colspan="2" |Mosschismic (great-grandchild) scales
+|-
+! rowspan="2" |Steps
+! rowspan="2" |Steps
+! rowspan="2" |Specific name
+! rowspan="2" |Steps
+! rowspan="2" |Specific name
+! rowspan="2" |Steps
+! rowspan="2" |Specific name
+|
+|-
+|-
+| rowspan="8" |xL ys
+| rowspan="4" |(x+y)L xs
+| rowspan="4" |m-moschromatic
+| rowspan="2" |(x+y)L (2x+y)s
+| rowspan="2" |f-mosenharmonic
+|(x+y)L (3x+2y)s
+|f-mosschismic
+|
+|-
+|(3x+2y)L (x+y)s
+|a-mosschismic
+|
+|-
+| rowspan="2" |(2x+y)L (x+y)s
+| rowspan="2" |m-mosenharmonic
+|(3x+2y)L (2x+y)s
+|u-mosschismic
+|
+|-
+|(2x+y)L (3x+2y)s
+|m-mosschismic
+|
+|-
+| rowspan="4" |xL (x+y)s
+| rowspan="4" |p-moschromatic
+| rowspan="2" |(2x+y)L xs
+| rowspan="2" |p-mosenharmonic
+|(2x+y)L (3x+y)s
+|p-mosschismic
+|
+|-
+|(3x+y)L (2x+y)s
+|q-mosschismic
+|
+|-
+| rowspan="2" |xL (2x+y)s
+| rowspan="2" |s-mosenharmonic
+|(3x+y)L xs
+|r-mosschismic
+|
+|-
+|xL (3x+y)s
+|s-mosschismic
+|
+|}
 === Reasoning for names ===
 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 was reorganized to only name 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.
+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.
@@ Line 1,291: / Line 1,358: @@
 |}
-== Naming mos modes ==
+== Proposal: Naming mos modes ==
-=== Current proposal, with amendment for emphasis on dark generator ===
+=== Current proposal, with proposed amendment for emphasis on dark generator ===
 There is currently a proposed system for naming mos modes as follows: '''xL ys u|''', where x is the number of large steps, y is the number of small steps, u corresponds to the the mode's UDP (the u in u|d), and | is pronounced as "pipe". As an example, the modes of 4L 1s (manual) can be named as the following:
 {| class="wikitable"