Module:Harmonics in edo - Revision history

ArrowHead294: Revert to revision 75208 by Inthar (talk)

2024-05-23T18:25:54Z

Revert to revision 75208 by Inthar (talk)

← Older revision		Revision as of 18:25, 23 May 2024
Line 16:		Line 16:
	ev = math.floor(v + .5)		ev = math.floor(v + .5)
	table.insert(todd, ' ' .. p )		table.insert(todd, ' ' .. p )
	table.insert(tapprox, string.format(fmt_approx, 1200*(ev % edo)/edo~~):gsub("-", "−"~~))		table.insert(tapprox, string.format(fmt_approx, 1200*(ev % edo)/edo) )
	table.insert(tabs, string.format(fmt_abs, 1200 * (ev - v ) / edo~~):gsub("-", "−"~~))		table.insert(tabs, string.format(fmt_abs, 1200 * (ev - v ) / edo))
	table.insert(trel, string.format(fmt_rel, 100 * (ev - v)~~):gsub("-", "−"~~))		table.insert(trel, string.format(fmt_rel, 100 * (ev - v)))
	table.insert(tdeg, ' ' .. ~~tostring(~~ev~~):gsub("-", "−")~~ .. ' ('.. ev % edo .. ')')		table.insert(tdeg, ' ' .. ev .. ' ('.. ev % edo .. ')')
	end		end
	local titleMarkup = ''		local titleMarkup = ''
	if title then		if title then
	titleMarkup = '\|-\n\|+ ~~style="font-size: 110%;" \|~~ ' .. title .. '\n'		titleMarkup = '\|-\n\|+ ' .. title .. '\n'

	end		end
Line 47:		Line 47:
	local title = frame.args['title'] or 'Approximation of odd harmonics in ' .. edo .. 'edo'		local title = frame.args['title'] or 'Approximation of odd harmonics in ' .. edo .. 'edo'
	local prec = frame.args['prec'] or 1 -- for now only variable precision for abs error		local prec = frame.args['prec'] or 1 -- for now only variable precision for abs error
	return edoprox( edo, {unpack(odds, start, start + columns - 1)}, title, prec)		return edoprox( edo, {unpack(odds, start, start+columns-1)}, title, prec)
	end		end

	return p;		return p;

ArrowHead294 at 18:23, 23 May 2024

2024-05-23T18:23:11Z

← Older revision		Revision as of 18:23, 23 May 2024
Line 18:		Line 18:
	table.insert(tapprox, string.format(fmt_approx, 1200*(ev % edo)/edo):gsub("-", "−"))		table.insert(tapprox, string.format(fmt_approx, 1200*(ev % edo)/edo):gsub("-", "−"))
	table.insert(tabs, string.format(fmt_abs, 1200 * (ev - v ) / edo):gsub("-", "−"))		table.insert(tabs, string.format(fmt_abs, 1200 * (ev - v ) / edo):gsub("-", "−"))
	table.insert(trel, string.format(fmt_rel, 100 * (ev - v):gsub("-", "−")))		table.insert(trel, string.format(fmt_rel, 100 * (ev - v)):gsub("-", "−"))
	table.insert(tdeg, ' ' .. tostring(ev):gsub("-", "−") .. ' ('.. ev % edo .. ')')		table.insert(tdeg, ' ' .. tostring(ev):gsub("-", "−") .. ' ('.. ev % edo .. ')')
	end		end

ArrowHead294 at 18:22, 23 May 2024

2024-05-23T18:22:39Z

← Older revision		Revision as of 18:22, 23 May 2024
Line 16:		Line 16:
	ev = math.floor(v + .5)		ev = math.floor(v + .5)
	table.insert(todd, ' ' .. p )		table.insert(todd, ' ' .. p )
	table.insert(tapprox, string.format(fmt_approx, 1200*(ev % edo)/edo) )		table.insert(tapprox, string.format(fmt_approx, 1200*(ev % edo)/edo):gsub("-", "−"))
	table.insert(tabs, string.format(fmt_abs, 1200 * (ev - v ) / edo))		table.insert(tabs, string.format(fmt_abs, 1200 * (ev - v ) / edo):gsub("-", "−"))
	table.insert(trel, string.format(fmt_rel, 100 * (ev - v)))		table.insert(trel, string.format(fmt_rel, 100 * (ev - v):gsub("-", "−")))
	table.insert(tdeg, ' ' .. ev .. ' ('.. ev % edo .. ')')		table.insert(tdeg, ' ' .. tostring(ev):gsub("-", "−") .. ' ('.. ev % edo .. ')')
	end		end
	local titleMarkup = ''		local titleMarkup = ''
	if title then		if title then
	titleMarkup = '\|-\n\|+ ' .. title .. '\n'		titleMarkup = '\|-\n\|+ style="font-size: 110%;" \| ' .. title .. '\n'

	end		end
Line 47:		Line 47:
	local title = frame.args['title'] or 'Approximation of odd harmonics in ' .. edo .. 'edo'		local title = frame.args['title'] or 'Approximation of odd harmonics in ' .. edo .. 'edo'
	local prec = frame.args['prec'] or 1 -- for now only variable precision for abs error		local prec = frame.args['prec'] or 1 -- for now only variable precision for abs error
	return edoprox( edo, {unpack(odds, start, start+columns-1)}, title, prec)		return edoprox( edo, {unpack(odds, start, start + columns - 1)}, title, prec)
	end		end

	return p;		return p;

Inthar: can't get the fifthspan thing to work

2021-07-29T03:14:34Z

can't get the fifthspan thing to work

← Older revision		Revision as of 03:14, 29 July 2021
Line 3:		Line 3:
	local function edoprox(edo, odds, title, prec)		local function edoprox(edo, odds, title, prec)
	local f = 1/edo		local f = 1/edo
	~~local eps = .0001~~
	local todd = {'! colspan="2" \| Odd harmonic '}		local todd = {'! colspan="2" \| Odd harmonic '}
	local tapprox = {'! colspan="2" \| Approximation '}		local tapprox = {'! colspan="2" \| Approximation '}
Line 9:		Line 8:
	local trel = {'! [[Relative error\|relative]] (%) '}		local trel = {'! [[Relative error\|relative]] (%) '}
	local tdeg = {'! colspan="2" \| Steps ([[octave reduction\|reduced]])'}		local tdeg = {'! colspan="2" \| Steps ([[octave reduction\|reduced]])'}
	~~local tfs = {'! colspan="2" \| [[Fifthspan]]'}~~
	local fmt_approx = string.format(' %%.%df', prec)		local fmt_approx = string.format(' %%.%df', prec)
	local fmt_abs = string.format(' %%+.%df', prec)		local fmt_abs = string.format(' %%+.%df', prec)
Line 17:		Line 15:
	v = s*edo		v = s*edo
	ev = math.floor(v + .5)		ev = math.floor(v + .5)
	~~m = math.floor(math.log(3)/math.log(2)*edo + .5)~~
	table.insert(todd, ' ' .. p )		table.insert(todd, ' ' .. p )
	table.insert(tapprox, string.format(fmt_approx, 1200*(ev % edo)/edo) )		table.insert(tapprox, string.format(fmt_approx, 1200*(ev % edo)/edo) )
Line 23:		Line 20:
	table.insert(trel, string.format(fmt_rel, 100 * (ev - v)))		table.insert(trel, string.format(fmt_rel, 100 * (ev - v)))
	table.insert(tdeg, ' ' .. ev .. ' ('.. ev % edo .. ')')		table.insert(tdeg, ' ' .. ev .. ' ('.. ev % edo .. ')')
	~~diatonic_edo = m/edo > 4/7 and m/edo < 3/5 and gcd(m, edo) == 1~~
	~~if(diatonic_edo) then -- if the best fifth = m\edo is diatonic AND gcd(m, edo) == 1~~
	~~fs = 0~~
	~~position = 0~~
	~~while (position ~= ev and fs < edo) do~~
	~~fs = fs + 1~~
	~~position = (position + m) % edo~~
	~~end~~
	~~if (fs > edo/2) then~~
	~~fs = fs - edo~~
	~~end~~
	~~table.insert(tfs, ' ' .. fs )~~
	~~end~~
	end		end
	local titleMarkup = ''		local titleMarkup = ''
Line 42:		Line 26:

	end		end
	~~noFifthSpan =~~ '{\| class="wikitable center-all"\n' ..		return '{\| class="wikitable center-all"\n' ..
	titleMarkup ..		titleMarkup ..
	'\|-\n' ..		'\|-\n' ..
Line 53:		Line 37:
	table.concat(tdeg, '\n\|') .. '\n' ..		table.concat(tdeg, '\n\|') .. '\n' ..
	'\|}'		'\|}'
	~~if (diatonic_edo) then~~
	~~return noFifthSpan ..~~
	~~table.concat(tfs, '\n\|') .. '\n' ..~~
	~~'\|}'~~
	~~else~~
	~~return noFifthspan~~
	~~end~~
	end		end

	local odds = { 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43 }		local odds = { 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43 }

	~~function gcd(a, b)~~
	~~if (b ~= 0) then~~
	~~return a~~
	~~else~~
	~~return gcd(y, x%y)~~
	~~end~~
	~~end~~

	function p.harmonics_in_edo (frame)		function p.harmonics_in_edo (frame)

Inthar at 03:12, 29 July 2021

2021-07-29T03:12:14Z

← Older revision		Revision as of 03:12, 29 July 2021
Line 27:		Line 27:
	fs = 0		fs = 0
	position = 0		position = 0
	while position ~= ev do		while (position ~= ev and fs < edo) do
	fs = fs + 1		fs = fs + 1
	position = (position + m) % edo		position = (position + m) % edo

Inthar at 03:11, 29 July 2021

2021-07-29T03:11:42Z

← Older revision		Revision as of 03:11, 29 July 2021
Line 17:		Line 17:
	v = s*edo		v = s*edo
	ev = math.floor(v + .5)		ev = math.floor(v + .5)
	m = math.floor(math.log(3/2)/math.log(2)*edo + .5)		m = math.floor(math.log(3)/math.log(2)*edo + .5)
	table.insert(todd, ' ' .. p )		table.insert(todd, ' ' .. p )
	table.insert(tapprox, string.format(fmt_approx, 1200*(ev % edo)/edo) )		table.insert(tapprox, string.format(fmt_approx, 1200*(ev % edo)/edo) )

Inthar: compute the fifth span for diatonic edos

2021-07-29T03:10:48Z

compute the fifth span for diatonic edos

← Older revision		Revision as of 03:10, 29 July 2021
Line 3:		Line 3:
	local function edoprox(edo, odds, title, prec)		local function edoprox(edo, odds, title, prec)
	local f = 1/edo		local f = 1/edo
			local eps = .0001
	local todd = {'! colspan="2" \| Odd harmonic '}		local todd = {'! colspan="2" \| Odd harmonic '}
	local tapprox = {'! colspan="2" \| Approximation '}		local tapprox = {'! colspan="2" \| Approximation '}
Line 8:		Line 9:
	local trel = {'! [[Relative error\|relative]] (%) '}		local trel = {'! [[Relative error\|relative]] (%) '}
	local tdeg = {'! colspan="2" \| Steps ([[octave reduction\|reduced]])'}		local tdeg = {'! colspan="2" \| Steps ([[octave reduction\|reduced]])'}
			local tfs = {'! colspan="2" \| [[Fifthspan]]'}
	local fmt_approx = string.format(' %%.%df', prec)		local fmt_approx = string.format(' %%.%df', prec)
	local fmt_abs = string.format(' %%+.%df', prec)		local fmt_abs = string.format(' %%+.%df', prec)
Line 15:		Line 17:
	v = s*edo		v = s*edo
	ev = math.floor(v + .5)		ev = math.floor(v + .5)
			m = math.floor(math.log(3/2)/math.log(2)*edo + .5)
	table.insert(todd, ' ' .. p )		table.insert(todd, ' ' .. p )
	table.insert(tapprox, string.format(fmt_approx, 1200*(ev % edo)/edo) )		table.insert(tapprox, string.format(fmt_approx, 1200*(ev % edo)/edo) )
Line 20:		Line 23:
	table.insert(trel, string.format(fmt_rel, 100 * (ev - v)))		table.insert(trel, string.format(fmt_rel, 100 * (ev - v)))
	table.insert(tdeg, ' ' .. ev .. ' ('.. ev % edo .. ')')		table.insert(tdeg, ' ' .. ev .. ' ('.. ev % edo .. ')')
			diatonic_edo = m/edo > 4/7 and m/edo < 3/5 and gcd(m, edo) == 1
			if(diatonic_edo) then -- if the best fifth = m\edo is diatonic AND gcd(m, edo) == 1
			fs = 0
			position = 0
			while position ~= ev do
			fs = fs + 1
			position = (position + m) % edo
			end
			if (fs > edo/2) then
			fs = fs - edo
			end
			table.insert(tfs, ' ' .. fs )
			end
	end		end
	local titleMarkup = ''		local titleMarkup = ''
Line 26:		Line 42:

	end		end
	~~return~~ '{\| class="wikitable center-all"\n' ..		noFifthSpan = '{\| class="wikitable center-all"\n' ..
	titleMarkup ..		titleMarkup ..
	'\|-\n' ..		'\|-\n' ..
Line 37:		Line 53:
	table.concat(tdeg, '\n\|') .. '\n' ..		table.concat(tdeg, '\n\|') .. '\n' ..
	'\|}'		'\|}'
			if (diatonic_edo) then
			return noFifthSpan ..
			table.concat(tfs, '\n\|') .. '\n' ..
			'\|}'
			else
			return noFifthspan
			end
	end		end

	local odds = { 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43 }		local odds = { 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43 }

			function gcd(a, b)
			if (b ~= 0) then
			return a
			else
			return gcd(y, x%y)
			end
			end

	function p.harmonics_in_edo (frame)		function p.harmonics_in_edo (frame)

Inthar: consistent "[n]edo" convention

2021-07-29T02:02:21Z

consistent "[n]edo" convention

← Older revision		Revision as of 02:02, 29 July 2021
Line 45:		Line 45:
	local columns = frame.args['columns'] or 15 -- number of columns (default = 15, harmonics 3 to 31)		local columns = frame.args['columns'] or 15 -- number of columns (default = 15, harmonics 3 to 31)
	local start = frame.args['start'] or 1 -- start column, default: start with harmonic 3		local start = frame.args['start'] or 1 -- start column, default: start with harmonic 3
	local title = frame.args['title'] or 'Approximation of odd harmonics in ' .. edo .. ' ~~EDO~~'		local title = frame.args['title'] or 'Approximation of odd harmonics in ' .. edo .. 'edo'
	local prec = frame.args['prec'] or 1 -- for now only variable precision for abs error		local prec = frame.args['prec'] or 1 -- for now only variable precision for abs error
	return edoprox( edo, {unpack(odds, start, start+columns-1)}, title, prec)		return edoprox( edo, {unpack(odds, start, start+columns-1)}, title, prec)

Inthar at 01:53, 29 July 2021

2021-07-29T01:53:42Z

← Older revision		Revision as of 01:53, 29 July 2021
Line 15:		Line 15:
	v = s*edo		v = s*edo
	ev = math.floor(v + .5)		ev = math.floor(v + .5)
	table.insert(todd, ' ' .. p ~~.. '/'~~ )		table.insert(todd, ' ' .. p )
	table.insert(tapprox, string.format(fmt_approx, 1200*(ev % edo)/edo) )		table.insert(tapprox, string.format(fmt_approx, 1200*(ev % edo)/edo) )
	table.insert(tabs, string.format(fmt_abs, 1200 * (ev - v ) / edo))		table.insert(tabs, string.format(fmt_abs, 1200 * (ev - v ) / edo))

Inthar: use the unreduced odd harmonic

2021-07-29T01:53:21Z

use the unreduced odd harmonic

← Older revision		Revision as of 01:53, 29 July 2021
Line 15:		Line 15:
	v = s*edo		v = s*edo
	ev = math.floor(v + .5)		ev = math.floor(v + .5)
	table.insert(todd, ' ' .. p .. '/' ~~.. 2^math.floor(s)~~ )		table.insert(todd, ' ' .. p .. '/' )
	table.insert(tapprox, string.format(fmt_approx, 1200*(ev % edo)/edo) )		table.insert(tapprox, string.format(fmt_approx, 1200*(ev % edo)/edo) )
	table.insert(tabs, string.format(fmt_abs, 1200 * (ev - v ) / edo))		table.insert(tabs, string.format(fmt_abs, 1200 * (ev - v ) / edo))