Module:ET

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This module depends on the following other modules:

This module provides helper functions for equal-step tunings.

Functions

new: Returns an array consisting of the components of an equal-step tuning.

parse: Designed to convert strings in the format [number of steps]ed[equave] into an ET structure, and returns it via the new function. For example, ET.parse("12edo") returns an array containing {12, 2, "edo"}

as_string: Returns the string representation for an ET structure.

backslash_ratio: Converts steps to a proper ratio as a floating-point number.

backslash_display: Displays an ET structure in backslash form ([steps]\[number of divisions]).

cents: Converts the interval an ET structure represents to cents.

hekts: Converts the interval an ET structure represents to hekts (relative cent of 13edt).

approximate: Returns the floor, round, or ceiling of a particular ratio.

tempers_out: Determines if an ET tempers out a provided rational number.

is_highly_composite: Determines if an ET is highly composite.

is_zeta: Determines if an ET holds any zeta records.

why_zeta: Describes what specific properties an ET has if it is a zeta record ET.

local rat = require('Module:Rational')
local p = {}

local common_suffix = {
	['3/2'] = 'f',
	['2'] = 'o',
	['2/1'] = 'o',
	['3'] = 't',
	['3/1'] = 't',
}
local common_ratio = {
	['f'] = rat.new(3, 2),
	['o'] = 2,
	['t'] = 3
}

function p.new(size, equave, suffix)
	size = size or 12
	equave = equave or 2
	if suffix == nil then
		local equave_n, equave_m = rat.as_pair(equave)
		local equave_ratio = rat.as_ratio(equave)
		suffix = size .. 'ed'
		if common_suffix[equave_ratio] then
			suffix = suffix .. common_suffix[equave_ratio]
		elseif equave_m == 1 then
			suffix = suffix .. equave_n
		else
			suffix = suffix .. equave_ratio
		end
	end
	return { size = size, equave = equave, suffix = suffix }
end

function p.parse(unparsed)
	local size, suffix, equave = unparsed:match('^(%d+)(ed(.+))$')
	if equave == nil then
		return nil
	end
	size = tonumber(size)
	equave = common_ratio[equave] or rat.parse(equave)
	if size == nil or equave == nil then
		return nil
	end
	return p.new(size, equave, suffix)
end

return p