User:Romeolz/Isomorphic layouts: Difference between revisions
modifying operations n misc |
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Note: I am very much a math person and this is very theoretical. I mostly work in a Regular Temperament Theory (RTT) framework (sorry Domin). | Note: I am very much a math person and this is very theoretical for the time being. I mostly work in a Regular Temperament Theory (RTT) framework (sorry Domin). | ||
== TODO: == | |||
* Hobbled layouts | |||
* Coloring (albitonic and kite) | |||
* scale (1 or 2 axis), shear, stretch/half rotate(the weird one) | |||
* ht extensions | |||
* tuning continua | |||
* images and audio examples for everything | |||
== Terminology (that I came up with) == | == Terminology (that I came up with) == | ||
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==== Offset vectors ==== | ==== Offset vectors ==== | ||
Every isomorphic layout can be defined by two offset vectors. I will call them o<sub>v</sub> and o<sub>h</sub>, offset vertical and offset horizontal. Usually they have a length (magnitude) of 1. They correspond to a key next to the origin. It is possible for the offsets to have different magnitudes. Magnitudes of 1 and 1 and an angle of 60 or 120 degrees correspond to a hexagonal layout. An angle of 90 degrees corresponds to a square grid. Every interval's shape can be described as a combination of o<sub>v</sub>:s and o<sub>h</sub>:s in the form of p<sub>a/b</sub> = x*o<sub>h</sub> + y*o<sub>v</sub>. | Every isomorphic layout can be defined by two offset vectors. I will call them o<sub>v</sub> and o<sub>h</sub>, offset vertical and offset horizontal. Usually they have a length (magnitude) of 1. They correspond to a key next to the origin. It is possible for the offsets to have different magnitudes. Magnitudes of 1 and 1 and an angle of 60 or 120 degrees correspond to a hexagonal layout. An angle of 90 degrees corresponds to a square grid. Every interval's shape can be described as a combination of o<sub>v</sub>:s and o<sub>h</sub>:s in the form of p<sub>a/b</sub> = x*o<sub>h</sub> + y*o<sub>v</sub>. | ||
==== Offset conventions for hexagonal keyboards ==== | |||
There are three ways of notating offsets for hexagonal keyboards (with straight rows, zigzag columns). | |||
* "Terpstran": right → and up-right ↗ , the most common afaik, named after the terpstrakeyboard webapp | |||
* "Workshop": right → and up-left ↖ , used by scale workshop as right → and up ↑ for a square grid, but functions like the former because of the QWERTY layout's row offsets | |||
* "Albitonic": right → and down-right ↘ , used by projectivetuningspace, easy to conceptualize albitonic scales | |||
==== Conversions between conventions ==== | |||
asdfghj | |||
==== Interval math with interval vectors ==== | ==== Interval math with interval vectors ==== | ||