FRACNAMS

FRACNAMS (Fractal-scale NAMing System), is a christening system of names for Fractal scales 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

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.

Modes of Gesture

Mode rotational order	Division pattern	FRACNAMS	Abstract step pattern from order-2
0	s:m:L	Rock	s^2 m*s L*s m*s m^2 L*m L*s L*m L^2
1	m:L:s	Scissors	m^2 L*m m*s L*m L^2 m*s m*s L*s s^2
2	L:s:m	Paper	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.

Modes of Neutrino

Mode rotational order	Division pattern	FRACNAMS	Abstract step pattern from order-2
0	s:s:L	Esp	s^2 s^2 L*s s^2 s^2 L*s L*s L*s L^2
1	s:L:s	Tau	s^2 L*s s^2 L*s L^2 L*s s^2 L*s s^2
2	L:s:s	Mu	L^2 L*s L*s L*s s^2 s^2 L*s s^2 s^2

Modes of Quark

Mode rotational order	Division pattern	FRACNAMS	Abstract step pattern from order-2
0	s:L:L	Up	s^2 L*s L*s L*s L^2 L^2 L*s L^2 L^2
1	L:s:L	Charm	L^2 L*s L^2 L*s s^2 L*s L^2 L*s L^2
2	L:L:s	Top	L^2 L^2 L*s L^2 L^2 L*s L*s L*s s^2

Modes can also be constructed in more complex and abstract ways, such as "meta-rotation".

Todo: expand Add detailed infomations.

2-interval pattern

Todo: expand

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]\displaystyle{ 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.

Modes of Oneironic in 34edo

Mode rotational order	Mode binary numbering	Division pattern	FRACNAMS	Step pattern (34edo)	Scale degrees (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

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