Module:Chord edo approximation - Revision history

Pailiaq at 01:01, 27 May 2026

2026-05-27T01:01:22Z

← Older revision		Revision as of 01:01, 27 May 2026
Line 214:		Line 214:
	table.insert(padded_errs, pad_left(r._err_strs[i], max_err_w[i]))		table.insert(padded_errs, pad_left(r._err_strs[i], max_err_w[i]))
	end		end
	local CODE_STYLE = ' style="padding:~~1px~~ 2px;white-space:nowrap;"'		local CODE_STYLE = ' style="padding:2px 3px;white-space:nowrap;"'
	local steps_cell = '<code' .. CODE_STYLE .. '>' .. table.concat(padded_steps, SEP) .. '</code>'		local steps_cell = '<code' .. CODE_STYLE .. '>' .. table.concat(padded_steps, SEP) .. '</code>'
	local cents_cell = '<code' .. CODE_STYLE .. '>' .. table.concat(padded_cents, SEP) .. '</code>'		local cents_cell = '<code' .. CODE_STYLE .. '>' .. table.concat(padded_cents, SEP) .. '</code>'

Pailiaq: Undo revision 231145 by Pailiaq (talk)

2026-05-27T00:59:55Z

Undo revision 231145 by Pailiaq (talk)

← Older revision		Revision as of 00:59, 27 May 2026
Line 214:		Line 214:
	table.insert(padded_errs, pad_left(r._err_strs[i], max_err_w[i]))		table.insert(padded_errs, pad_left(r._err_strs[i], max_err_w[i]))
	end		end
	local CODE_STYLE = ' style="padding:1px ~~3px~~;white-space:nowrap;"'		local CODE_STYLE = ' style="padding:1px 2px;white-space:nowrap;"'
	local steps_cell = '<code' .. CODE_STYLE .. '>' .. table.concat(padded_steps, SEP) .. '</code>'		local steps_cell = '<code' .. CODE_STYLE .. '>' .. table.concat(padded_steps, SEP) .. '</code>'
	local cents_cell = '<code' .. CODE_STYLE .. '>' .. table.concat(padded_cents, SEP) .. '</code>'		local cents_cell = '<code' .. CODE_STYLE .. '>' .. table.concat(padded_cents, SEP) .. '</code>'
	local errs_cell = '<code' .. CODE_STYLE .. '>' .. table.concat(padded_errs, SEP) .. '</code>'		local errs_cell = '<code' .. CODE_STYLE .. '>' .. table.concat(padded_errs, SEP) .. '</code>'
	~~local CODE_OPEN = '<span style="font-family:monospace;">'~~
	~~local CODE_CLOSE = '</span>'~~
	~~local steps_cell = CODE_OPEN .. table.concat(padded_steps, SEP) .. CODE_CLOSE~~
	~~-- etc.~~

	-- Steps data attribute for the play button (unpadded, comma-separated)		-- Steps data attribute for the play button (unpadded, comma-separated)
	local steps_data_parts = {"0"}		local steps_data_parts = {"0"}

Pailiaq at 00:59, 27 May 2026

2026-05-27T00:59:35Z

← Older revision		Revision as of 00:59, 27 May 2026
Line 214:		Line 214:
	table.insert(padded_errs, pad_left(r._err_strs[i], max_err_w[i]))		table.insert(padded_errs, pad_left(r._err_strs[i], max_err_w[i]))
	end		end
	local CODE_STYLE = ' style="padding:1px ~~2px~~;white-space:nowrap;"'		local CODE_STYLE = ' style="padding:1px 3px;white-space:nowrap;"'
	local steps_cell = '<code' .. CODE_STYLE .. '>' .. table.concat(padded_steps, SEP) .. '</code>'		local steps_cell = '<code' .. CODE_STYLE .. '>' .. table.concat(padded_steps, SEP) .. '</code>'
	local cents_cell = '<code' .. CODE_STYLE .. '>' .. table.concat(padded_cents, SEP) .. '</code>'		local cents_cell = '<code' .. CODE_STYLE .. '>' .. table.concat(padded_cents, SEP) .. '</code>'
	local errs_cell = '<code' .. CODE_STYLE .. '>' .. table.concat(padded_errs, SEP) .. '</code>'		local errs_cell = '<code' .. CODE_STYLE .. '>' .. table.concat(padded_errs, SEP) .. '</code>'
			local CODE_OPEN = '<span style="font-family:monospace;">'
			local CODE_CLOSE = '</span>'
			local steps_cell = CODE_OPEN .. table.concat(padded_steps, SEP) .. CODE_CLOSE
			-- etc.

	-- Steps data attribute for the play button (unpadded, comma-separated)		-- Steps data attribute for the play button (unpadded, comma-separated)
	local steps_data_parts = {"0"}		local steps_data_parts = {"0"}

Pailiaq at 00:58, 27 May 2026

2026-05-27T00:58:00Z

← Older revision		Revision as of 00:58, 27 May 2026
Line 214:		Line 214:
	table.insert(padded_errs, pad_left(r._err_strs[i], max_err_w[i]))		table.insert(padded_errs, pad_left(r._err_strs[i], max_err_w[i]))
	end		end
	local CODE_STYLE = ' style="padding:1px 2px;"'		local CODE_STYLE = ' style="padding:1px 2px;white-space:nowrap;"'
	local steps_cell = '<code' .. CODE_STYLE .. '>' .. table.concat(padded_steps, SEP) .. '</code>'		local steps_cell = '<code' .. CODE_STYLE .. '>' .. table.concat(padded_steps, SEP) .. '</code>'
	local cents_cell = '<code' .. CODE_STYLE .. '>' .. table.concat(padded_cents, SEP) .. '</code>'		local cents_cell = '<code' .. CODE_STYLE .. '>' .. table.concat(padded_cents, SEP) .. '</code>'

Pailiaq at 00:56, 27 May 2026

2026-05-27T00:56:37Z

← Older revision		Revision as of 00:56, 27 May 2026
Line 203:		Line 203:

	-- === PASS 2: emit padded, em-dash-separated cell content ===		-- === PASS 2: emit padded, em-dash-separated cell content ===
	local SEP = '&~~nbsp;&nbsp~~;'		local SEP = ' '

	for _, r in ipairs(results) do		for _, r in ipairs(results) do

Pailiaq at 00:55, 27 May 2026

2026-05-27T00:55:56Z

← Older revision		Revision as of 00:55, 27 May 2026
Line 214:		Line 214:
	table.insert(padded_errs, pad_left(r._err_strs[i], max_err_w[i]))		table.insert(padded_errs, pad_left(r._err_strs[i], max_err_w[i]))
	end		end
	local steps_cell = '<code>' .. table.concat(padded_steps, SEP) .. '</code>'		local CODE_STYLE = ' style="padding:1px 2px;"'
	local cents_cell = '<code>' .. table.concat(padded_cents, SEP) .. '</code>'		local steps_cell = '<code' .. CODE_STYLE .. '>' .. table.concat(padded_steps, SEP) .. '</code>'
	local errs_cell = '<code>' .. table.concat(padded_errs, SEP) .. '</code>'		local cents_cell = '<code' .. CODE_STYLE .. '>' .. table.concat(padded_cents, SEP) .. '</code>'
			local errs_cell = '<code' .. CODE_STYLE .. '>' .. table.concat(padded_errs, SEP) .. '</code>'
	-- Steps data attribute for the play button (unpadded, comma-separated)		-- Steps data attribute for the play button (unpadded, comma-separated)
	local steps_data_parts = {"0"}		local steps_data_parts = {"0"}

Pailiaq at 00:51, 27 May 2026

2026-05-27T00:51:32Z

← Older revision		Revision as of 00:51, 27 May 2026
Line 203:		Line 203:

	-- === PASS 2: emit padded, em-dash-separated cell content ===		-- === PASS 2: emit padded, em-dash-separated cell content ===
	local SEP = ' — '		local SEP = '  '

	for _, r in ipairs(results) do		for _, r in ipairs(results) do

Pailiaq at 00:49, 27 May 2026

2026-05-27T00:49:28Z

← Older revision		Revision as of 00:49, 27 May 2026
Line 2:		Line 2:
	-- Calculates EDO approximations for JI chords like 4:5:6 or 4:5:6:7		-- Calculates EDO approximations for JI chords like 4:5:6 or 4:5:6:7
	-- Metric: RMS of per-note errors around the optimal reference (least-squares),		-- Metric: RMS of per-note errors around the optimal reference (least-squares),
	-- expressed as % of EDO step (relative) so ~~that~~ smaller EDOs aren't penalized		-- expressed as % of EDO step (relative) so smaller EDOs aren't penalized for
	-- ~~for~~ their inherently coarser resolution.		-- their inherently coarser resolution.
	~~-- Usage: {{#invoke:Chord_EDO_Approximation\|main\|chord=4:5:6\|max_rms=15\|min_edo=5\|max_edo=60}}~~
	local u = require("Module:Utils")		local u = require("Module:Utils")
	local yesno = require("Module:Yesno")		local yesno = require("Module:Yesno")
Line 47:		Line 46:
	end		end

	~~-- Computes both absolute (cents) and relative (% of step) RMS around the~~
	~~-- optimal-reference offset (mean of per-note errors).~~
	local function calculate_chord_approximation(interval_cents_list, edo)		local function calculate_chord_approximation(interval_cents_list, edo)
	local edostep = 1200 / edo		local edostep = 1200 / edo
	local steps = {}		local steps = {}
	local abs_errors = {} ~~-- per-interval (root-relative), for display~~		local abs_errors = {}
	local note_errors = {0} ~~-- including root = 0, for math~~		local note_errors = {0}

	for _, ic in ipairs(interval_cents_list) do		for _, ic in ipairs(interval_cents_list) do
Line 64:		Line 61:
	end		end

	~~-- Optimal-reference offset: mean of note errors (least-squares centering)~~
	local n = #note_errors		local n = #note_errors
	local sum = 0		local sum = 0
Line 70:		Line 66:
	local mean = sum / n		local mean = sum / n

	~~-- RMS of centered errors, in cents and as % of EDO step~~
	local sq_sum = 0		local sq_sum = 0
	for _, e in ipairs(note_errors) do		for _, e in ipairs(note_errors) do
Line 94:		Line 89:
	return string.format("%.2f", value)		return string.format("%.2f", value)
	end		end
			end

			-- Right-align s to width by prepending non-breaking spaces (so HTML preserves them)
			local function pad_left(s, width)
			local need = width - #s
			if need <= 0 then return s end
			return string.rep(" ", need) .. s
	end		end

Line 135:		Line 137:
	if #results == 0 then		if #results == 0 then
	return "No edos found within RMS tolerance of " .. max_rms .. "%"		return "No edos found within RMS tolerance of " .. max_rms .. "%"
			end

			-- === PASS 1: precompute all formatted strings, find max width per position ===
			local n_pos = #(results[1].steps) + 1 -- +1 for the root
			local max_step_w = {}
			local max_cents_w = {}
			local max_err_w = {}
			for i = 1, n_pos do max_step_w[i] = 0; max_cents_w[i] = 0; max_err_w[i] = 0 end

			for _, r in ipairs(results) do
			local edostep = 1200 / r.edo
			local step_strs = {"0"}
			local cents_strs = {"0.00"}
			local err_strs = {"0.00"}
			for i, s in ipairs(r.steps) do
			table.insert(step_strs, tostring(s))
			table.insert(cents_strs, string.format("%.2f", s * edostep))
			table.insert(err_strs, format_error(r.abs_errors[i]))
			end
			for i = 1, n_pos do
			if #step_strs[i] > max_step_w[i] then max_step_w[i] = #step_strs[i] end
			if #cents_strs[i] > max_cents_w[i] then max_cents_w[i] = #cents_strs[i] end
			if #err_strs[i] > max_err_w[i] then max_err_w[i] = #err_strs[i] end
			end
			r._step_strs = step_strs
			r._cents_strs = cents_strs
			r._err_strs = err_strs
	end		end

Line 172:		Line 201:
	.. ' !! RMS ([[cent\|¢]])'		.. ' !! RMS ([[cent\|¢]])'
	.. ' !! RMS ([[relative cent\|%]])')		.. ' !! RMS ([[relative cent\|%]])')

			-- === PASS 2: emit padded, em-dash-separated cell content ===
			local SEP = ' — '

	for _, r in ipairs(results) do		for _, r in ipairs(results) do
	local edo_link = string.format("[[%dedo\|%d]]", r.edo, r.edo)		local edo_link = string.format("[[%dedo\|%d]]", r.edo, r.edo)

	local ~~step_parts~~ = {~~"0"~~}		local padded_steps, padded_cents, padded_errs = {}, {}, {}
	for _, ~~s in ipairs~~(r.~~steps~~) do		for i = 1, n_pos do
	table.insert(~~step_parts~~, ~~tostring~~(s))		table.insert(padded_steps, pad_left(r._step_strs[i], max_step_w[i]))
			table.insert(padded_cents, pad_left(r._cents_strs[i], max_cents_w[i]))
			table.insert(padded_errs, pad_left(r._err_strs[i], max_err_w[i]))
	end		end
	local ~~steps_str~~ = table.concat(~~step_parts~~, ~~" "~~)		local steps_cell = '<code>' .. table.concat(padded_steps, SEP) .. '</code>'
	local ~~steps_data~~ = table.concat(~~step_parts~~, ",")		local cents_cell = '<code>' .. table.concat(padded_cents, SEP) .. '</code>'
			local errs_cell = '<code>' .. table.concat(padded_errs, SEP) .. '</code>'

	~~local edostep = 1200 / r.edo~~		-- Steps data attribute for the play button (unpadded, comma-separated)
	local ~~cents_parts~~ = {"0.00"}		local steps_data_parts = {"0"}
	for _, s in ipairs(r.steps) do		for _, s in ipairs(r.steps) do table.insert(steps_data_parts, tostring(s)) end
	table.insert(~~cents_parts~~, ~~string.format~~(~~"%.2f",~~ s * edostep))		local steps_data = table.concat(steps_data_parts, ",")
	end
	local ~~cents_str~~ = table.concat(~~cents_parts~~, " ")

	~~local err_parts = {}~~
	~~for _~~, ~~e in ipairs(r.abs_errors) do~~
	~~table.insert(err_parts, format_error(e))~~
	~~end~~
	~~local err_str = table.concat(err_parts, "~~ ")

	local rms_c = string.format("%.2f", r.rms_cents)		local rms_c = string.format("%.2f", r.rms_cents)
Line 205:		Line 232:
	table.insert(output, '\|-')		table.insert(output, '\|-')
	table.insert(output, string.format('\| %s \|\| %s \|\| %s \|\| %s \|\| %s \|\| %s \|\| %s',		table.insert(output, string.format('\| %s \|\| %s \|\| %s \|\| %s \|\| %s \|\| %s \|\| %s',
	play_btn, edo_link, ~~steps_str~~, ~~cents_str~~, ~~err_str~~, rms_c, rms_r))		play_btn, edo_link, steps_cell, cents_cell, errs_cell, rms_c, rms_r))
	end		end

Pailiaq at 00:43, 27 May 2026

2026-05-27T00:43:26Z

← Older revision		Revision as of 00:43, 27 May 2026
Line 1:		Line 1:
	-- Chord EDO Approximations Module		-- Chord EDO Approximations Module
	-- Calculates EDO approximations for JI chords like 4:5:6 or 4:5:6:7		-- Calculates EDO approximations for JI chords like 4:5:6 or 4:5:6:7
	-- Metric: RMS of per-note errors around the optimal reference (least-squares).		-- Metric: RMS of per-note errors around the optimal reference (least-squares),
	-- Usage: {{#invoke:Chord_EDO_Approximation\|main\|chord=4:5:6\|max_rms=10\|min_edo=5\|max_edo=60}}		-- expressed as % of EDO step (relative) so that smaller EDOs aren't penalized
			-- for their inherently coarser resolution.
			-- Usage: {{#invoke:Chord_EDO_Approximation\|main\|chord=4:5:6\|max_rms=15\|min_edo=5\|max_edo=60}}
	local u = require("Module:Utils")		local u = require("Module:Utils")
	local yesno = require("Module:Yesno")		local yesno = require("Module:Yesno")
Line 8:		Line 10:

	-- ===== CONFIGURATION VARIABLES =====		-- ===== CONFIGURATION VARIABLES =====
	local DEFAULT_MAX_RMS = 10 -- Max RMS error in ~~cents~~		local DEFAULT_MAX_RMS = 15 -- Max RMS error in % of EDO step
	local DEFAULT_MIN_EDO = 5		local DEFAULT_MIN_EDO = 5
	local DEFAULT_MAX_EDO = 60		local DEFAULT_MAX_EDO = 60
Line 45:		Line 47:
	end		end

	-- ~~For a given EDO and a list of interval-~~cents ~~(from root, length N-1~~),		-- Computes both absolute (cents) and relative (% of step) RMS around the
	~~-- compute the approximation. Note errors include the root~~ (~~= 0~~) so the		-- optimal-reference offset (mean of per-note errors).
	-- optimal-reference ~~math is symmetric across all N notes~~.
	local function calculate_chord_approximation(interval_cents_list, edo)		local function calculate_chord_approximation(interval_cents_list, edo)
	local edostep = 1200 / edo		local edostep = 1200 / edo
Line 63:		Line 64:
	end		end

	-- Optimal reference offset: mean of note errors (least-squares ~~optimum~~)		-- Optimal-reference offset: mean of note errors (least-squares centering)
	local n = #note_errors		local n = #note_errors
	local sum = 0		local sum = 0
Line 69:		Line 70:
	local mean = sum / n		local mean = sum / n

	-- RMS of centered errors ~~(deviation from the best-fit transposition)~~		-- RMS of centered errors, in cents and as % of EDO step
	local sq_sum = 0		local sq_sum = 0
	for _, e in ipairs(note_errors) do		for _, e in ipairs(note_errors) do
Line 75:		Line 76:
	sq_sum = sq_sum + d * d		sq_sum = sq_sum + d * d
	end		end
	local ~~rms~~ = math.sqrt(sq_sum / n)		local rms_cents = math.sqrt(sq_sum / n)
			local rms_relative = (rms_cents / edostep) * 100

	return {		return {
	steps = steps,		steps = steps,
	abs_errors = abs_errors,		abs_errors = abs_errors,
	~~note_errors = note_errors,~~
	mean_offset = mean,		mean_offset = mean,
	~~rms~~ = ~~rms~~,		rms_cents = rms_cents,
			rms_relative = rms_relative,
	}		}
	end		end
Line 125:		Line 127:
	for edo = min_edo, max_edo do		for edo = min_edo, max_edo do
	local data = calculate_chord_approximation(intervals_cents, edo)		local data = calculate_chord_approximation(intervals_cents, edo)
	if data.~~rms~~ <= max_rms then		if data.rms_relative <= max_rms then
	data.edo = edo		data.edo = edo
	table.insert(results, data)		table.insert(results, data)
Line 132:		Line 134:

	if #results == 0 then		if #results == 0 then
	return "No edos found within RMS ~~error~~ tolerance of " .. max_rms .. "¢"		return "No edos found within RMS tolerance of " .. max_rms .. "%"
	end		end

Line 159:		Line 161:

	table.insert(output, '\|+ style="font-size: 105%;" \| ' .. caption_main		table.insert(output, '\|+ style="font-size: 105%;" \| ' .. caption_main
	.. string.format('<br /><span style="font-size: 0.75em;">\'\'intervals: %s · ≤ %dedo, RMS error ≤ %g~~{{c}}~~\'\'</span>',		.. string.format('<br /><span style="font-size: 0.75em;">\'\'intervals: %s · ≤ %dedo, RMS rel. error ≤ %g%%\'\'</span>',
	intervals_display, max_edo, max_rms))		intervals_display, max_edo, max_rms))

Line 168:		Line 170:
	.. ' !! class="unsortable" \| Cents ([[cent\|¢]])'		.. ' !! class="unsortable" \| Cents ([[cent\|¢]])'
	.. ' !! class="unsortable" \| Absolute errors ([[cent\|¢]])'		.. ' !! class="unsortable" \| Absolute errors ([[cent\|¢]])'
	.. ' !! RMS ~~error~~ ([[cent\|¢]])')		.. ' !! RMS ([[cent\|¢]])'
			.. ' !! RMS ([[relative cent\|%]])')

	for _, r in ipairs(results) do		for _, r in ipairs(results) do
Line 193:		Line 196:
	local err_str = table.concat(err_parts, " ")		local err_str = table.concat(err_parts, " ")

	local ~~rms_str~~ = string.format("%.2f", r.~~rms~~)		local rms_c = string.format("%.2f", r.rms_cents)
			local rms_r = string.format("%.2f", r.rms_relative)

	local play_btn = string.format(		local play_btn = string.format(
Line 200:		Line 204:

	table.insert(output, '\|-')		table.insert(output, '\|-')
	table.insert(output, string.format('\| %s \|\| %s \|\| %s \|\| %s \|\| %s \|\| %s',		table.insert(output, string.format('\| %s \|\| %s \|\| %s \|\| %s \|\| %s \|\| %s \|\| %s',
	play_btn, edo_link, steps_str, cents_str, err_str, ~~rms_str~~))		play_btn, edo_link, steps_str, cents_str, err_str, rms_c, rms_r))
	end		end

Pailiaq at 00:34, 27 May 2026

2026-05-27T00:34:50Z

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