Module:Lumatone mapping intro

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Note: Do not invoke this module directly; use the corresponding template instead: Template:Lumatone mapping intro.

This module depends on the following other modules: Module: ET Module: Rational Module: Utils Module: Yesno

This module automatically fills in the introduction for Lumatone keyboard mappings for EDOs.

Since the Standard Lumatone mapping for Pythagorean is based on the chain of fifths, the intro text will depend on how accurately an EDO approximates 3/2 and how many mutually-exclusive circles of fifths it has.

---

local p = {}
local ET = require("Module:ET")
local rat = require("Module:Rational")
local gcd = require("Module:Utils")._gcd
local yesno = require("Module:Yesno")

function p.lum_intro(frame)
	local tuning = frame.args["edo"]
	local et = ET.parse(tuning) or ET.parse(tuning .. "edo") or ET.parse("12edo")
	local debugg = yesno(frame.args["debug"])
	
	local octave = ET.approximate(et, 2)
	local twelfth = ET.approximate(et, 3)

	local step_size = ET.cents(et, 1)
	local fifth = -octave + twelfth -- 3/2 = [-1 1>
	local fifth_error = ET.cents(et, fifth) - rat.cents(rat.new(3, 2))
	local is_far_fifth = (math.abs(fifth_error) / step_size >= 0.40)

	local result = (octave == 12
		and "The standard mapping of [[12edo]] onto the [[Lumatone]] agrees with the [[Standard Lumatone mapping for Pythagorean]]."
		or string.format("There are many conceivable ways to map [[%s]] onto the onto the [[Lumatone]] keyboard.", ET.as_string(et)))
	
	local rings = gcd(octave, twelfth)
	if rings > 1 then
		-- If the EDO has multiple rings of fifths
		result = result .. string.format(" However, it has %d mutually-exclusive rings of fifths, ", rings)
			.. "so the [[Standard Lumatone mapping for Pythagorean]] is not one of them."
		if ET.is_highly_composite(et) then
			-- If the EDO has multiple rings of fifths and is highly composite (multiples of 12 especially)
			result = result .. " Since it is [[highly composite]], many other mappings will also fail to cover the whole gamut."
		end
	elseif is_far_fifth == true then
		-- EDOs with inaccurate fifth (40% or higher relative error)
		result = result .. " However, as both of its fifths are about as far away from just as possible, "
			.. "neither the sharp or the flat versions of the [[Standard Lumatone mapping for Pythagorean]] work particularly well."
	elseif octave ~= 12 then
		-- If the EDO can be generated entirely by fifths
		result = result .. " Only one, however, agrees with the [[Standard Lumatone mapping for Pythagorean]]."
	end
	
	-- Debugger option
	if debugg == true then
		result = "<syntaxhighlight lang=\"wikitext\">" .. result .. "</syntaxhighlight>"
	end
	
	return frame:preprocess(result)
end

return p