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Module:JI ratios in ED: Difference between revisions

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local utils = require('Module:Utils')
local interval = require('Module:Interval')
local rat = require('Module:Rational')
local jiraf = require('Module:JI ratio finder')
local tip = require('Module:Template input parse')
local p = {}
local p = {}


function p.find_ratios_in_ed_by_primes(ed, primes, equave, tenney_height, denominator_limit)
local et = require("Module:ET")
local ed = ed or 7
--local interval = require('Module:Harmonic entropy')
local primes = primes or { 2, 3, 7, 11 }
local jiraf = require("Module:JI ratio finder")
local equave = equave or rat.new(3, 2)
local rat = require("Module:Rational")
local tenney_height = tenney_height or 10
local tip = require("Module:Template input parse")
local denominator_limit = denominator_limit or 99
local utils = require("Module:Utils")
local yesno = require("Module:Yesno")
 
-- Helper function
-- Given a prime limit, return an array of all primes between (and including) 2
-- and that limit
-- EG, 7-limit becomes { 2, 3, 5, 7 }
function p.primes_within_prime_limit(prime_limit)
local prime_limit = prime_limit or 7
local equave_in_cents = rat.cents(equave)
local primes = {}
local tolerance = equave_in_cents / ed * 0.4
for i = 2, prime_limit do
if utils.is_prime(i) then
-- Find candidate ratios; filter later
table.insert(primes, i)
local max_prime = primes[#primes]
end
local candidate_ratios = jiraf.find_candidate_ratios_within_subgroup(equave_in_cents, denominator_limit, primes)
-- Equave as text
local equave_as_text = rat.as_ratio(equave)  
if equave_as_text == "2/1" then
equave_as_text = "edo"
elseif equave_as_text == "3/1" then
equave_as_text = "edt"
elseif equave_as_text == "3/2" then
equave_as_text = "edf"
end
end
return primes
end
-- Helper function
-- Converts a set of primes (typically a prime subgroup) into text
function p.subgroup_as_text(primes)
local primes = primes or { 2, 3, 5, 7 }
-- Build table headers
local subgroup = ""
local result = string.format('{| class="wikitable center-all"\n')
result = result .. string.format('|+ Intervals of %d%s\n', ed, equave_as_text)
result = result .. string.format('|-\n')
result = result .. string.format('! rowspan="2" | [[Degree]]\n')
result = result .. string.format('! rowspan="2" | [[Cent]]s\n')
result = result .. string.format('! colspan="%d" | Approximated [[JI]] intervals ([[error]] in cents)\n', #primes)
result = result .. string.format('|-\n')
-- Add table headers for prime limits (technically harmonic classes)
for i = 1, #primes do
for i = 1, #primes do
local current_prime = primes[i]
if i ~= #primes then
result = result .. string.format('! [[%d-limit]]\n', current_prime)
subgroup = subgroup .. string.format("%d.", primes[i])
else
subgroup = subgroup .. primes[i]
end
end
end
result = result .. string.format('|-\n')
return subgroup
end
 
-- Helper function
-- Creates the non-header cells in the table
function p.ji_ratio_in_ed_content_cells(steps, equave, candidate_ratios, primes, tolerance)
local steps = steps or 12
local equave = equave or rat.new(2)
local candidate_ratios = candidate_ratios or { rat.new(1), rat.new(2), rat.new(3, 2), rat.new(4, 3), rat.new (5, 4), rat.new (9, 7)}
local primes = primes or { 2, 3, 7 }
local tolerance = tolerance or 20
-- Build the rows for each edstep, showing ratios by limit
-- Calculate equave
for i = 1, ed + 1 do
local equave_in_cents = rat.cents(equave)
local edstep = i - 1
local edstep_in_cents = (edstep / ed) * equave_in_cents
-- Build the rows for each step, showing ratios by limit
local result = ""
for i = 1, steps + 1 do
local step = i - 1
-- Table headers
local step_in_cents = (step / steps) * rat.cents(equave)
result = result .. string.format("| %d\n", step)
result = result .. string.format("| %.3f\n", step_in_cents)
-- If this is the first or last step, only use the unison or equave
-- respectively; otherwise, filter ratios by whether they're within the
-- current step
local filtered_ratios = {}
local filtered_ratios = {}
if step == 0 then
-- Override ratios for edsteps for the unison and equave
filtered_ratios = { rat.new(1) }
-- Otherwise, filter ratios by range
elseif step == steps then
if i == 1 then
filtered_ratios = { equave }
filtered_ratios = { rat.new(1, 1) }
else  
elseif i == ed + 1 then
filtered_ratios = jiraf.filter_ratios_by_range(candidate_ratios, step_in_cents - tolerance, step_in_cents + tolerance)
filtered_ratios = { rat.copy(equave) }
else
filtered_ratios = jiraf.filter_ratios_by_range(candidate_ratios, edstep_in_cents - tolerance, edstep_in_cents + tolerance)
end
end
result = result .. string.format('| %d\n', edstep)
result = result .. string.format('| %.3f\n', edstep_in_cents)
-- Add ratios according to harmonic class
-- Add ratios according to harmonic class
for j = 1, #primes do
for j = 1, #primes do
local current_prime = primes[j]
local current_prime = primes[j]
-- For each prime, filter by harmonic class
-- For the first column, filter by prime limit instead
local prime_filtered_ratios = {}
local prime_filtered_ratios = {}
-- The first column filters by prime limit
-- Successive columns are filered by harmonic class
if j == 1 then
if j == 1 then
prime_filtered_ratios = jiraf.filter_ratios_by_prime_limit(filtered_ratios, current_prime)
prime_filtered_ratios = jiraf.filter_ratios_by_prime_limit(filtered_ratios, primes[j])
else
else
prime_filtered_ratios = jiraf.filter_ratios_by_harmonic_class(filtered_ratios, current_prime)
prime_filtered_ratios = jiraf.filter_ratios_by_harmonic_class(filtered_ratios, primes[j])
end
end
 
-- Filter ratios by complement-agnostic tenney height
local ratios_as_text = jiraf.ratios_to_text(prime_filtered_ratios, "<br>", true)
prime_filtered_ratios = jiraf.filter_ratios_by_complement_agnostic_tenney_height(prime_filtered_ratios, tenney_height, equave)
result = result .. string.format("| %s\n", ratios_as_text)
-- Add ratios to cells
local ratios_as_text = jiraf.ratios_to_text_with_error(prime_filtered_ratios, edstep_in_cents, "<br>", true)
result = result .. string.format('| %s\n', ratios_as_text)
end
end
result = result .. string.format('|-\n')
result = result .. string.format("|-\n")
end
return result
end
 
-- Main function variant for prime limit
function p.ji_ratios_in_ed_by_prime_limit(input_et, int_limit, prime_limit, tenney_height, threshold)
local input_et = input_et or et.parse("12edo")
local prime_limit = prime_limit or 7
local tenney_height = tenney_height or 10
local int_limit = int_limit or 99
local threshold = threshold or 0.3
-- Get the number of divisions, equave, and et as text (eg edo, edt, etc)
local steps = input_et["size"]
local equave = input_et["equave"]
if tonumber(equave) ~= nil then
equave = rat.new(equave)
end
end
local et_as_string = et.as_string(input_et)
-- Calculate equave and tolerance
-- Tolerance is a percentage (threshold) of the step size
local equave_in_cents = rat.cents(equave)
local tolerance = equave_in_cents / steps * threshold
-- Calculate candidate ratios
-- Then filter based on whether their complements exceed the int limit
-- Then filter candidate ratios by tenney height (excludes equave factors)
local candidate_ratios = jiraf.find_candidate_ratios_within_prime_limit(equave_in_cents, int_limit, prime_limit)
candidate_ratios = jiraf.filter_ratios_by_equave_complement_int_limit(candidate_ratios, int_limit, equave)
candidate_ratios = jiraf.filter_ratios_by_no_equave_factors_tenney_height(candidate_ratios, tenney_height, equave)
-- Get the primes
local primes = p.primes_within_prime_limit(prime_limit)
result = result .. string.format('|}\n')
-- Build table headers
local result = "{| class=\"wikitable center-all\"\n"
.. "|+ style=\"font-size: 105%;\" | "
.. string.format("Intervals of %s (as a %d-limit temperament)\n", et_as_string, prime_limit)
.. "|-\n"
.. "! rowspan=\"2\" | [[Degree]]\n"
.. "! rowspan=\"2\" | [[Cent]]s\n"
.. string.format("! colspan=\"%d\" | Approximated [[JI]] intervals\n", #primes)
.. "|-\n"
-- Add footnotes
-- Build header cells for each prime limit
local subgroup_as_text = ""
for i = 1, #primes do
for i = 1, #primes do
if i ~= #primes then
result = result .. string.format("! [[%d-limit]]\n", primes[i])
subgroup_as_text = subgroup_as_text .. string.format("%d.", primes[i])
else
subgroup_as_text = subgroup_as_text .. primes[i]
end
end
end
result = result .. string.format("Based on treating %d%s as a %s subgroup temperament. Other approaches are possible.\n", ed, equave_as_text, subgroup_as_text)
result = result .. string.format("|-\n")
-- Add rest of table
result = result .. p.ji_ratio_in_ed_content_cells(steps, equave, candidate_ratios, primes, tolerance)
result = result .. string.format("|}\n")
return result
return result
end
end


function p.parse_ed(unparsed)
-- Main function variant for prime subgroup
local unparsed = unparsed or "12edo"
function p.ji_ratios_in_ed_by_prime_subgroup(input_et, int_limit, primes, tenney_height, threshold)
local input_et = input_et or et.parse("12edo")
local primes = primes or { 2, 3, 5, 11 }
local tenney_height = tenney_height or 10
local int_limit = int_limit or 99
local threshold = threshold or 0.3
-- Get the number of divisions, equave, and et as text (eg edo, edt, etc)
local steps = input_et["size"]
local equave = input_et["equave"]
if tonumber(equave) ~= nil then
equave = rat.new(equave)
end
local et_as_string = et.as_string(input_et)
-- Calculate equave and tolerance
-- Tolerance is a percentage (threshold) of the step size
local equave_in_cents = rat.cents(equave)
local tolerance = equave_in_cents / steps * threshold
local ed = tonumber(unparsed) or unparsed:match('(%d+)ed')
-- Calculate candidate ratios
 
-- Then filter based on whether their complements exceed the int limit
return ed
-- Then filter candidate ratios by tenney height (excludes equave factors)
end
local candidate_ratios = jiraf.find_candidate_ratios_within_subgroup(equave_in_cents, int_limit, primes)
 
candidate_ratios = jiraf.filter_ratios_by_equave_complement_int_limit(candidate_ratios, int_limit, equave)
function p.parse_equave(unparsed)
candidate_ratios = jiraf.filter_ratios_by_no_equave_factors_tenney_height(candidate_ratios, tenney_height, equave)
local unparsed = unparsed or "10ed4"
-- Get subgroup as text
local subgroup_as_text = p.subgroup_as_text(primes)
-- Build table headers
local result = "{| class=\"wikitable center-all\"\n"
.. "|+ style=\"font-size: 105%;\" | "
.. string.format("Intervals of %s (as a %s subgroup temperament)\n", et_as_string, subgroup_as_text)
.. "|-\n"
.. "! rowspan=\"2\" | [[Degree]]\n"
.. "! rowspan=\"2\" | [[Cent]]s\n"
.. string.format("! colspan=\"%d\" | Approximated [[JI]] intervals\n", #primes)
.. "|-\n"
local equave_unparsed = ""
-- Build header cells for each prime limit
if string.match(unparsed, "edo") or tonumber(unparsed) ~= nil then
for i = 1, #primes do
equave_unparsed = "2/1"
result = result .. string.format("! [[%d-limit]]\n", primes[i])
elseif string.match(unparsed, "edt") then
equave_unparsed = "3/1"
elseif string.match(unparsed, "edf") then
equave_unparsed = "3/2"
else
equave_unparsed = unparsed:match('[%d]+ed([%d]+/[%d]+)') or unparsed:match('[%d]+ed([%d]+)')
end
end
result = result .. "|-\n"
-- Add rest of table
result = result .. p.ji_ratio_in_ed_content_cells(steps, equave, candidate_ratios, primes, tolerance)
return rat.parse(equave_unparsed)
result = result .. string.format("|}\n")
return result
end
end


-- Wrapper function for primary function; to be called by template
function p.ji_ratios_in_ed_frame(frame)
function p.ji_ratios_in_ed_frame(frame)
-- Parse the ed; if it's just a number, interpret it as an edo
local input_et_unparsed = frame.args["ED"] or 12
if tonumber(input_et_unparsed) ~= nil then
input_et_unparsed = input_et_unparsed .. "edo"
end
local input_et = et.parse(input_et_unparsed)
local ed = p.parse_ed(frame.args["ED"])
local tenney_height = tonumber(frame.args["Tenney Height"]) or 10
local equave = p.parse_equave(frame.args["ED"])
local int_limit = tonumber(frame.args["Integer Limit"]) or 99
local threshold = tonumber(frame.args["Threshold"]) or 0.3


local primes_as_text = "2.3.5.7.11.13"
local primes = tonumber(frame.args["Prime Limit"]) or 5
if string.len(frame.args["Primes"]) > 0 then
local temperament_type = "Prime Limit"
primes_as_text = frame.args["Primes"]
if string.len(frame.args["Subgroup"]) > 0 then  
primes = tip.parse_numeric_entries(frame.args["Subgroup"], ".") or tip.parse_numeric_entries(frame.args["Subgroup"], ",")
temperament_type = "Subgroup"
end
end
local primes = tip.parse_numeric_entries(primes_as_text, '.') or tip.parse_numeric_entries(primes_as_text, ',')
local tenney_height = tonumber(frame.args["Tenney Height"]) or 10
local result = ""
local denominator_limit = tonumber(frame.args["Denominator Limit"]) or 99
if temperament_type == "Subgroup" then
result = p.ji_ratios_in_ed_by_prime_subgroup(input_et, int_limit, primes, tenney_height, threshold)
elseif temperament_type == "Prime Limit" then
result = p.ji_ratios_in_ed_by_prime_limit(input_et, int_limit, primes, tenney_height, threshold)
end
local result = p.find_ratios_in_ed_by_primes(ed, primes, equave, tenney_height, denominator_limit)
local debugg = yesno(frame.args["debug"])
if debugg == true then
return result
result = "<syntaxhighlight lang=\"wikitext\">" .. result .. "</syntaxhighlight>"
end
return frame:preprocess(result)
end
end


return p
return p
Retrieved from "https://en.xen.wiki/w/Module:JI_ratios_in_ED"