Module:Infobox chord: Difference between revisions
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local prime_limit = 1 | local prime_limit = 1 | ||
local lcm = 1 | local lcm = 1 | ||
local otonal_odd_limit = 1 | |||
local root_interval_links = {} | local root_interval_links = {} | ||
for i, h in ipairs(harmonics) do | for i, h in ipairs(harmonics) do | ||
-- compute LCM of all harmonics to use as the denominator in utonal form, if needed | |||
lcm = lcm * h / (utils._gcd(lcm, h)) | |||
-- increase otonal odd limit for this harmonic, if needed | |||
local odd = h | |||
while odd > 0 and odd % 2 == 0 do | |||
odd = odd / 2 | |||
end | |||
if odd > otonal_odd_limit then | |||
otonal_odd_limit = odd | |||
end | |||
-- increase prime limit for this harmonic, if needed | |||
for prime, n in pairs(utils.prime_factorization_raw(h)) do | for prime, n in pairs(utils.prime_factorization_raw(h)) do | ||
if prime > prime_limit then | if prime > prime_limit then | ||
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end | end | ||
-- compute ratio of this harmonic relative to the root | |||
local gcd = utils._gcd(h, root) | local gcd = utils._gcd(h, root) | ||
local numer = h / gcd | local numer = h / gcd | ||
| Line 68: | Line 81: | ||
end | end | ||
local | local utonal_odd_limit = 1 | ||
local utonal_intervals = {} | |||
for i, h in ipairs(harmonics) do | |||
local gcd = utils._gcd(lcm, h) | |||
local numer = h / gcd | |||
local denom = lcm / gcd | |||
table.insert(utonal_intervals, numer .. "/" .. denom) | |||
local denom_odd = denom | |||
while denom_odd > 0 and denom_odd % 2 == 0 do | |||
denom_odd = denom_odd / 2 | |||
end | |||
if denom_odd > utonal_odd_limit then | |||
utonal_odd_limit = denom_odd | |||
end | end | ||
end | end | ||
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end | end | ||
while denom % 2 == 0 do | while denom > 0 and denom % 2 == 0 do | ||
denom = denom / 2 | denom = denom / 2 | ||
end | end | ||
| Line 104: | Line 123: | ||
table.insert(infobox_data, {"Harmonics", frame.args["Harmonics"]}) | table.insert(infobox_data, {"Harmonics", frame.args["Harmonics"]}) | ||
table.insert(infobox_data, {"Intervals from root", table.concat(root_interval_links, " ‒ ")}) | table.insert(infobox_data, {"Intervals from root", table.concat(root_interval_links, " ‒ ")}) | ||
if | if (not utils.value_provided(frame.args["Root"])) and (utonal_limit < otonal_limit or utonal_limit < 1000) then | ||
table.insert(infobox_data, {"[[Utonal]] Ratios", table.concat(utonal_intervals, " ‒ ")}) | table.insert(infobox_data, {"[[Utonal]] Ratios", table.concat(utonal_intervals, " ‒ ")}) | ||
end | end | ||
if prime_limit < 96 then | if prime_limit < 96 then | ||
table.insert(infobox_data, {"[[Prime limit]]", "[[" .. prime_limit .. "-limit|" .. prime_limit .. "]]"}) | table.insert(infobox_data, {"[[Prime limit]]", "[[" .. prime_limit .. "-limit|" .. prime_limit .. "]]"}) | ||
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table.insert(infobox_data, {"[[Odd limit]]", odd_limit}) | table.insert(infobox_data, {"[[Odd limit]]", odd_limit}) | ||
end | end | ||
table.insert(infobox_data, "[[Otonal]] odd limit", otonal_limit) | |||
table.insert(infobox_data, "[[Utonal]] odd limit", utonal_limit) | |||
end | end | ||