User:Romeolz/Isomorphic layouts/Diatonic layouts
What is a diatonic layout?
A diatonic layout is any layout that has the 5L2s scale structure as its albitonic scale. The albitonic scale can be in any arrangement that doesn't imply another temperament. A layout implies another temperament when for example the layout physically has a key exactly in the middle of the root and fifth. This would imply that the fifth can be split equally in half, which is a property diatonic doesn't have. I will be navigating the intervals of diatonic through fifths-based notation.
Take the Bosanquet-Wilson layout. It's basically the diatonic layout, as it's the most common, and modelled after the piano. The layout highlights the major and minor seconds.
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We can compress the layout by backtracking by one key at every minor second. This can be thought of as a shear operation (see more).
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If we keep shearing, we get an upside down Wicki-Hayden layout!
image of upside down and normal
Diatonic layouts and their offsets
To be a diatonic layout, the offsets of said layout have to be able to be represented as fifths-based intervals (part of the 2.3 subgroup). Yet, not all layouts that satisfy this condition are valid. todotodotodo (how do i generalize this???)