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Module:Lumatone mapping intro: Difference between revisions

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


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local tuning = frame.args["edo"]
local tuning = frame.args["edo"]
local et = ET.parse(tuning) or ET.parse(tuning .. "edo") or ET.parse("12edo")
local et = ET.parse(tuning) or ET.parse(tuning .. "edo") or ET.parse("12edo")
local debug_mode = yesno(frame.args["debug"])
local debugg = yesno(frame.args["debug"])
local octave = ET.approximate(et, 2)
local octave = ET.approximate(et, 2)
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local fifth = -octave + twelfth -- 3/2 = [-1 1>
local fifth = -octave + twelfth -- 3/2 = [-1 1>
local fifth_error = ET.cents(et, fifth) - rat.cents(rat.new(3, 2))
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 is_far_fifth = (math.abs(fifth_error) / step_size >= 0.40)


local result = string.format("There are many conceivable ways to map [[%s]] onto the onto the [[Lumatone]] keyboard.", ET.as_string(et))
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)
local rings = gcd(octave, twelfth)
if rings > 1 then
if rings > 1 then
-- If the EDO has multiple rings of fifths
-- If the EDO has multiple rings of fifths
result = result .. string.format(" However, since it has %d mutually-exclusive rings of fifths,", rings)
result = result .. string.format(" However, it has %d mutually-exclusive rings of fifths, ", rings)
.. "the [[Standard Lumatone mapping for Pythagorean]] is not one of them."
.. "so the [[Standard Lumatone mapping for Pythagorean]] is not one of them."
if ET.is_highly_composite(et) then
if ET.is_highly_composite(et) then
-- If the EDO has multiple rings of fifths and is highly composite (multiples of 12 especially)
-- If the EDO has multiple rings of fifths and is highly composite (multiples of 12 especially)
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end
end
elseif is_far_fifth == true then
elseif is_far_fifth == true then
-- Dual-fifth EDOs where the relative error on the closest fit for 3/2 is 40% or higher
-- 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, "
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."
.. "neither the sharp or the flat versions of the [[Standard Lumatone mapping for Pythagorean]] work particularly well."
else
elseif octave ~= 12 then
-- If the EDO can be generated entirely by fifths
-- If the EDO can be generated entirely by fifths
result = result .. " Only one, however, agrees with the [[Standard Lumatone mapping for Pythagorean]]."
result = result .. " Only one, however, agrees with the [[Standard Lumatone mapping for Pythagorean]]."
end
end
return frame:preprocess(debug_mode == true and "<pre>" .. result .. "</pre>" or result)
-- Debugger option
if debugg == true then
result = "<syntaxhighlight lang=\"wikitext\">" .. result .. "</syntaxhighlight>"
end
return frame:preprocess(result)
end
end


return p
return p
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