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'''FRACNAMS''' ('''''F'''ractal-scale '''NAM'''ing '''S'''ystem''), is a christening system of names for [[Fractal scale]]s devised by the XA Discord in 2024. This naming system is heavily influenced by [[TAMNAMS]], but by nature is more widely defined in the scope of what each name represents. The ultimate goal of this system is to give appropriate names to fractal scales with all notable characteristics.
{{Idiosyncratic terms}}
'''FRACNAMS''' ('''''F'''ractal-scale '''NAM'''ing '''S'''ystem''), is a christening system of names for [[Fractal scale]]s devised by [[User:R-4981|R-4981]] in 2024. This naming system is heavily influenced by [[TAMNAMS]], but by nature is more widely defined in the scope of what each name represents. The ultimate goal of this system is to give appropriate names to fractal scales with all notable characteristics.


== Abstractly generalized names ==
== Agnostic 3-interval pattern ==
 
First, the simplest pattern is considered to be a fractal scale consisting of three intervals L>m>s (e.g., 1:2:3). This pattern is named as '''Gesture'''. There are three possible variants of this pattern, which are named '''Rock''', '''Paper''', and '''Scissors''', in that order.
The following names are the most abstract of the FRACNAMS, each one representing many (in some cases literally infinite) scales. These names were created for clarity and convenience, and therefore have no meaning on their own.
 
=== 3-interval pattern ===
 
First, the simplest pattern is considered to be a fractal scale consisting of three intervals L>m>s (e.g., 1:2:3). This pattern is named as '''Gesture'''. There are three possible variants of this pattern, which are named '''Rock''', '''Scissors''', and '''Paper''', in that order.


{| class="wikitable"
{| class="wikitable"
|+ Modes of Gesture
|+ style="font-size: 105%;" | Modes of Gesture
|-
! Mode rotational order
! Mode rotational order
! Division pattern
! Division pattern
Line 23: Line 20:
| 1
| 1
| m:L:s
| m:L:s
| Scissors
| Paper
| m^2 L*m m*s L*m L^2 m*s m*s L*s s^2
| m^2 L*m m*s L*m L^2 m*s m*s L*s s^2
|-
|-
| 2
| 2
| L:s:m
| L:s:m
| Paper
| Scissors
| L^2 L*s L*m L*s s^2 m*s L*m m*s m^2
| L^2 L*s L*m L*s s^2 m*s L*m m*s m^2
|}
|}


There are also possible subspecies such as L:s:s and L:L:s. These are called '''Neutrino''' and '''Quark''' in that order.
There are also possible subspecies such as L:s:s and L:L:s. These are called '''Downer''' and '''Upper''' in that order.


{| class="wikitable"
{| class="wikitable"
|+ Modes of Neutrino
|+ style="font-size: 105%;" | Modes of Downer
|-
! Mode rotational order
! Mode rotational order
! Division pattern
! Division pattern
Line 43: Line 41:
| 0
| 0
| s:s:L
| s:s:L
| Esp
| Down
| s^2 s^2 L*s s^2 s^2 L*s L*s L*s L^2
| s^2 s^2 L*s s^2 s^2 L*s L*s L*s L^2
|-
|-
| 1
| 1
| s:L:s
| s:L:s
| Tau
| Strange
| s^2 L*s s^2 L*s L^2 L*s s^2 L*s s^2
| s^2 L*s s^2 L*s L^2 L*s s^2 L*s s^2
|-
|-
| 2
| 2
| L:s:s
| L:s:s
| Mu
| Bottom
| L^2 L*s L*s L*s s^2 s^2 L*s s^2 s^2
| L^2 L*s L*s L*s s^2 s^2 L*s s^2 s^2
|}
|}


{| class="wikitable"
{| class="wikitable"
|+ Modes of Quark
|+ style="font-size: 105%;" | Modes of Upper
|-
! Mode rotational order
! Mode rotational order
! Division pattern
! Division pattern
Line 82: Line 81:
Modes can also be constructed in more complex and abstract ways, such as "meta-rotation".
Modes can also be constructed in more complex and abstract ways, such as "meta-rotation".


{{todo|expand|inline=1|comment=Add detailed infomations.}}
{{todo|complete section|add examples|inline=1|comment=Add detailed information and name more patterns or modes.}}
 
=== 2-interval pattern ===
 
{{todo|expand|inline=1}}
 
== Specific names ==
 
[[RedBull]] is the first named Fractal scale and is composed by the ratio 1:√3, but its exact notation by formula deformation is <math>1:\frac{1-\sqrt{3}}{\sqrt{3}}</math>. In addition, the Logarithmic Fractal scale, which consists of 1:φ, has a separate name for each mode and is called '''Oneironic'''.


{| class="wikitable"
== Agnostic 4-interval pattern ==
|+ Modes of Oneironic in 34edo
{{todo|complete section|add examples|inline=1|comment=Name more patterns or modes.}}
! Mode rotational order
! Mode binary numbering
! Division pattern
! FRACNAMS
! [[Step pattern]] (34edo)
! Scale [[degree]]s (34edo)
|-
| 0,0,0
| 0
| 1:φ, 1:φ, 1:φ
| Brazilian
| 8 5 5 3 5 3 3 2
| 8 13 18 21 26 29 32 34
|-
| 0,0,1
| 1
| 1:φ, 1:φ, φ:1
| Carolina
| 5 8 3 5 3 5 2 3
| 5 13 16 21 24 29 31 34
|-
| 0,1,0
| 2
| 1:φ, φ:1, 1:φ
| Georgia
| 5 3 8 5 3 2 5 3
| 5 8 16 21 24 26 31 34
|-
| 0,1,1
| 3
| 1:φ, φ:1, φ:1
| California
| 3 5 5 8 2 3 3 5
| 3 8 13 21 23 26 29 34
|-
| 1,0,0
| 4
| φ:1, 1:φ, 1:φ
| Cariboo
| 5 3 3 2 8 5 5 3
| 5 8 11 13 21 26 31 34
|-
| 1,0,1
| 5
| φ:1, 1:φ, φ:1
| Montana
| 3 5 2 3 5 8 3 5
| 3 8 10 13 18 26 29 34
|-
| 1,1,0
| 6
| φ:1, φ:1, 1:φ
| Bigbend
| 3 2 5 3 5 3 8 5
| 3 5 10 13 18 21 29 34
|-
| 1,1,1
| 7
| φ:1, φ:1, φ:1
| Omineca
| 2 3 3 5 3 5 5 8
| 2 5 8 13 16 21 26 34
|}


[[Category:Naming]]
[[Category:Scale naming]]
{{Stub}}
{{Stub}}
Retrieved from "https://en.xen.wiki/w/FRACNAMS"