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Module:MOS in EDO: Difference between revisions

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Added comments; corrected code regarding degenerate mosses (mosses that become edos)
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local mos = require('Module:MOS')
local rat = require('Module:Rational')
local utils = require('Module:Utils')
local p = {}
local p = {}
local mos = require("Module:MOS")
local step_vis = require("Module:Step vis")
local tamnams = require("Module:TAMNAMS")
local utils = require("Module:Utils")
local yesno = require("Module:Yesno")
-- Global variables for cell colors
-- Dark blue for large steps, light blue for small steps
-- For mosses that are reversed (starts with s and ends with L), use orange instead
p.cell_color_none = "" -- For cells that don't have a color (default cell color applies)
p.cell_color_perfect_size = "" -- Only applies for steps of an edo
p.cell_color_large = "#BDD7EE"
p.cell_color_small = "#DDEBF7"
p.cell_color_lg_rev = "#F8CBAD"
p.cell_color_sm_rev = "#FCE4D6"


-- Helper function
-- Helper function
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end
end
return string.format("%iL %is", large_step_count, small_step_count)
return string.format("%iL %is", large_step_count, small_step_count)


end
end
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-- Primary function
-- Primary function
-- Create a rectangular horogram depicting a mos for a given pair of generators
-- Create a rectangular horogram depicting a mos for a given pair of generators
function p.edo_mos_step_patterns(edo, gen_in_edosteps, number_of_periods, temperament)
function p.mos_in_edo(edo, gen_in_edosteps, number_of_periods, temperament)
local edo = edo or 24
local edo = edo or 24
local gen_in_edosteps = gen_in_edosteps or 14
local gen_in_edosteps = gen_in_edosteps or 14
local number_of_periods = number_of_periods or 1
local number_of_periods = number_of_periods or 1
local temperament = temperament or "meantone"
local temperament = temperament --or "meantone"
-- Check whether the number of periods divides the edo
-- Check whether the number of periods divides the edo
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-- Calculate whether to include temperament names
-- Calculate whether to include temperament names
local show_temperament = temperament ~= ""
local show_temperament = temperament ~= "" and temperament ~= nil
-- Calculate the generator complement
-- Calculate the generator complement
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-- Create table, starting with headers
-- Create table, starting with headers
local result = string.format('{| class="wikitable"\n')
local result = "{| class=\"wikitable center-all\"\n"
result = result .. string.format('|-\n')
.. "|+ style=\"font-size: 105%; white-space: nowrap;\" | " .. string.format("Generators %i\\%i and %i\\%i\n", gen_in_edosteps, edo, comp_in_edosteps, edo)
result = result .. string.format('! colspan="%i" |Steps for generators %i\\%i and %i\\%i\n', edo, gen_in_edosteps, edo, comp_in_edosteps, edo)
.. "|-\n"
result = result .. string.format('!Mos\n')
.. string.format("! colspan=\"%i\" | Steps\n", edo)
result = result .. string.format('!Step ratio\n')
.. "! MOS (name)\n"
result = result .. string.format('!TAMNAMS name\n')
.. "! Step ratio\n"
if show_temperament then
if show_temperament then
result = result .. string.format('!Temperament\n')
result = result .. string.format("! Temperament\n")
end
end


-- Add the step pattern for successive mosses until the pattern becomes that for an edo
-- Add the step pattern for successive mosses until the pattern becomes that for an edo
while current_scale ~= nil and starting_mos_valid do
while current_scale ~= nil and starting_mos_valid do
-- Calculate current step ratio
-- Use this to determine which cell colors to use
local current_step_sizes = p.calculate_step_sizes(current_scale)
local step_ratio_gcd = utils._gcd(current_step_sizes["L"], current_step_sizes["s"])
local large_step_size = current_step_sizes["L"]
local small_step_size = current_step_sizes["s"]
-- Is the first step a large step?
local first_step_is_large_step = current_scale[1] == large_step_size
-- Add the step sizes
-- Add the step sizes
result = result .. string.format('|-\n')
result = result .. "|-\n"
for i = 1, #current_scale do
for i = 1, #current_scale do
local current_step = current_scale[i]
local current_step = current_scale[i]
-- Calculate cell color
local cell_color = "NONE"
if large_step_size == small_step_size then
cell_color = p.cell_color_none
elseif first_step_is_large_step then
if current_step == large_step_size then
cell_color = p.cell_color_large
elseif current_step == small_step_size then
cell_color = p.cell_color_small
end
elseif not first_step_is_large_step then
if current_step == large_step_size then
cell_color = p.cell_color_lg_rev
elseif current_step == small_step_size then
cell_color = p.cell_color_sm_rev
end
end
if current_step == 1 then
if current_step == 1 then
result = result .. string.format('| 1\n')
if large_step_size == small_step_size then
result = result .. "| 1\n"
else
result = result .. string.format("| style=\"background-color: %s;\" | 1\n", cell_color)
end
else
else
result = result .. string.format('| colspan="%i" | %i\n', current_step, current_step)
if cell_color == p.cell_color_none then
result = result .. string.format("| colspan=\"%i\" | %i\n", current_step, current_step)
else
result = result .. string.format("| style=\"background-color: %s\" colspan=\"%i\" | %i\n", cell_color, current_step, current_step)
end
end
end
end
end
-- Add the scale sig
-- Add the scale sig
-- If the mos is an edo, say it's an edo instead
local scale_sig = p.mos_step_pattern_to_scale_sig(current_scale)
local scale_sig = p.mos_step_pattern_to_scale_sig(current_scale)
local current_step_sizes = p.calculate_step_sizes(current_scale)
local step_ratio_gcd = utils._gcd(current_step_sizes["L"], current_step_sizes["s"])
-- Get the tamnams name, if there is one
-- Don't show tamnams names for mosses with 5 notes or fewer (to keep the table from being cluttered)
local tamnams_name = tamnams.lookup_name(scale_sig)
local current_step_count = #current_scale
-- Use step sizes to determine whether the mos is an edo
local reduced_large_step_size = current_step_sizes["L"] / step_ratio_gcd
local reduced_large_step_size = current_step_sizes["L"] / step_ratio_gcd
local reduced_small_step_size = current_step_sizes["s"] / step_ratio_gcd
local reduced_small_step_size = current_step_sizes["s"] / step_ratio_gcd
if reduced_large_step_size == reduced_small_step_size then
if reduced_large_step_size == reduced_small_step_size then
result = result .. string.format("| %iedo\n", edo / step_ratio_gcd)
result = result .. string.format("| [[%iedo]]\n", edo / step_ratio_gcd)
elseif tamnams_name ~= nil and current_step_count > 5 then
result = result .. string.format("| [[%s]] (%s)\n", scale_sig, tamnams_name)
else
else
result = result .. string.format("| [[%s]]\n", scale_sig)
result = result .. string.format("| [[%s]]\n", scale_sig)
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result = result .. string.format("| %s:%s\n", current_step_sizes["L"] / step_ratio_gcd, current_step_sizes["s"] / step_ratio_gcd)
result = result .. string.format("| %s:%s\n", current_step_sizes["L"] / step_ratio_gcd, current_step_sizes["s"] / step_ratio_gcd)
-- Add the tamnams name
-- Add the temperament name, if there is one
local tamnams_name = mos.tamnams_name[scale_sig]
if show_temperament then
if tamnams_name ~= nil then
local current_step_count = #current_scale
result = result .. string.format("| %s\n", tamnams_name)
result = result .. string.format("| %s[%i]\n", temperament, current_step_count)
end
-- Produce the next scale in the sequence
current_scale = p.calculate_next_mos_step_pattern(current_scale)
end
 
result = result .. "|}"
return result
end
 
-- Alternate primary function
-- Instead of a "rectangular horogram", use the same type of visualization shown
-- on the diasem page
function p.mos_in_edo_simplified(edo, gen_in_edosteps, number_of_periods, generation_limit, temperament)
local edo = edo or 24
local gen_in_edosteps = gen_in_edosteps or 14
local number_of_periods = number_of_periods or 1
local generation_limit = generation_limit or edo - 1
local temperament = temperament --or "meantone"
-- Check whether the number of periods divides the edo
-- If so, the starting scale will be a multiperiod mos
local period_in_edosteps = edo
local verified_number_of_periods = 1
if edo % number_of_periods == 0 then
period_in_edosteps = edo / number_of_periods
verified_number_of_periods = number_of_periods
end
-- Check whether the generation limit is valid
-- If it's -1, then show all generations (period_in_edosteps-1)
if generation_limit == -1 then
generation_limit = period_in_edosteps - 1
end
-- Calculate whether to include temperament names
local show_temperament = temperament ~= "" and temperament ~= nil
-- Calculate the generator complement
local comp_in_edosteps = period_in_edosteps - gen_in_edosteps
-- Are the args for the starting mos valid?
-- The number of steps in the generator must be between 1 (inclusive) and the number of steps in the period (exclusive)
local starting_mos_valid = gen_in_edosteps >= 1 and gen_in_edosteps <= period_in_edosteps
-- Calculate the starting mos
local current_scale = {}
for i = 1, number_of_periods do
table.insert(current_scale, gen_in_edosteps)
table.insert(current_scale, comp_in_edosteps)
end
-- Create table, starting with headers
local result = "{| class=\"wikitable center-all\"\n"
.. "|+ style=\"font-size: 105%; white-space: nowrap;\" | " .. string.format("Generators %i\\%i and %i\\%i\n", gen_in_edosteps, edo, comp_in_edosteps, edo)
.. "|-\n"
.. "! Step visualization\n"
.. "! MOS (name)\n" -- Scale sig (and name)
.. "! Step sizes\n" -- Step sizes
.. "! Step ratio\n" -- Step ratio
if show_temperament then
result = result .. "! Temperament\n" -- Temperament, if given
end
 
-- Add the step pattern for successive mosses until the pattern becomes that for an edo
local generation_count = 1
while current_scale ~= nil and starting_mos_valid and generation_count <= generation_limit do
-- Calculate current step ratio
-- Use this to determine which cell colors to use
local current_step_sizes = p.calculate_step_sizes(current_scale)
local step_ratio_gcd = utils._gcd(current_step_sizes["L"], current_step_sizes["s"])
local large_step_size = current_step_sizes["L"]
local small_step_size = current_step_sizes["s"]
-- New row
result = result .. "|-\n"
-- Add the step visualization
local sv = step_vis._step_vis(current_scale)
result = result .. string.format("| %s\n", sv)
-- Add the scale sig
-- Also add tamnams name if there is one
local scale_sig = p.mos_step_pattern_to_scale_sig(current_scale)
local tamnams_name = tamnams.lookup_name(scale_sig)
local current_step_count = #current_scale
if large_step_size == small_step_size then
result = result .. string.format("| [[%iedo]]\n", edo / step_ratio_gcd)
elseif tamnams_name ~= nil and current_step_count > 5 then
result = result .. string.format("| [[%s]] (%s)\n", scale_sig, tamnams_name)
else
else
result = result .. string.format("|\n")
result = result .. string.format("| [[%s]]\n", scale_sig)
end
end
-- Add the step sizes
result = result .. string.format("| %i,&nbsp;%i\n", current_step_sizes["L"], current_step_sizes["s"])
-- Add step ratio
local reduced_large_step_size = large_step_size / step_ratio_gcd
local reduced_small_step_size = small_step_size / step_ratio_gcd
result = result .. string.format("| %s:%s\n", reduced_large_step_size, reduced_small_step_size)
-- Add the temperament name, if there is one
-- Add the temperament name, if there is one
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-- Produce the next scale in the sequence
-- Produce the next scale in the sequence
current_scale = p.calculate_next_mos_step_pattern(current_scale)
current_scale = p.calculate_next_mos_step_pattern(current_scale)
-- Increment the generation (row) count
generation_count = generation_count + 1
end
end


result = result .. string.format('|}\n')
result = result .. "|}"
return result
return result
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-- Function to be called by a template
-- Function to be called by a template
function p.edo_mos_step_patterns_frame(frame)
function p.mos_in_edo_frame(frame)
local edo = tonumber(frame.args["EDO"])
local edo = tonumber(frame.args["EDO"])
local gen_in_edosteps = tonumber(frame.args["Generator"])
local gen_in_edosteps = tonumber(frame.args["Generator"])
local temperament = frame.args["Temperament"]
local temperament = frame.args["Temperament"]
local number_of_periods = tonumber(frame.args["Number of Periods"])
local number_of_periods = tonumber(frame.args["Periods"])
local generation_limit = tonumber(frame.args["Generation Limit"])
local debugg = yesno(frame.args["debug"])
local result = p.mos_in_edo_simplified(edo, gen_in_edosteps, number_of_periods, generation_limit, temperament)
local result = p.edo_mos_step_patterns(edo, gen_in_edosteps, number_of_periods, temperament)
-- Debugger option
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:MOS_in_EDO"