Module:Lumatone mapping intro

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This module should not be invoked directly; use its corresponding template instead: Template:Lumatone mapping intro.

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.

Introspection summary for Module:Lumatone mapping intro
Functions provided (1) Line Function Params 7 lum_intro (invokable) (frame)	Lua modules required (4) Variable Module Functions used ET Module:ET parse approximate cents as_string is_highly_composite rat Module:Rational cents new gcd Module:Utils _gcd yesno Module:Yesno yesno

No function descriptions were provided. The Lua code may have further information.

---

local p = {}
local ET = require("Module:ET")
local gcd = require("Module:Utils")._gcd
local rat = require("Module:Rational")
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 debug_mode = 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 >= 0.4)

	local result = 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, since it has %d mutually-exclusive rings of fifths, ", rings)
			.. "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
		-- Dual-fifth EDOs where the relative error on the closest fit for 3/2 is 40% or higher
		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."
	else
		-- If the EDO can be generated entirely by fifths
		result = result .. " Only one, however, agrees with the [[Standard Lumatone mapping for Pythagorean]]."
	end
	
	return frame:preprocess(debug_mode == true and "<pre>" .. result .. "</pre>" or result)
end

return p