Module:Lumatone mapping intro: Difference between revisions
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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 | |||
result = result .. string.format(" However, since it has %d mutually-exclusive rings of fifths,", rings) | 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." | .. "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) | |||
result = result .. " Since it is [[highly composite]], many other mappings will also fail to cover the whole gamut." | result = result .. " Since it is [[highly composite]], many other mappings will also fail to cover the whole gamut." | ||
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 | |||
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 | else | ||
-- 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 | ||