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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.
'''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.


== Abstractly generalized names ==
== agnostic 3-interval pattern ==
 
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''', '''Paper''', and '''Scissors''', in that order.
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.
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{{todo|expand|inline=1|comment=Add detailed infomation and name more patterns or modes.}}
{{todo|expand|inline=1|comment=Add detailed infomation and name more patterns or modes.}}


=== 2-interval pattern ===
== agnostic 2-interval pattern ==


{{todo|expand|inline=1|comment=Name more patterns or modes.}}
{{todo|expand|inline=1|comment=Name more patterns or modes.}}
== 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 '''Goldrush'''.
{| class="wikitable"
|+ Modes of Goldrush in 34edo
! 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
|}
{{todo|expand|inline=1|comment=Name more scales.}}


[[Category:Naming]]
[[Category:Naming]]
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