Module:Harmonics in edo

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Used in Template:Odd harmonics in edo.

---

local p = {}

local function edoprox(edo, odds, title, prec)
  local f = 1/edo
  local eps = .0001
  local todd = {'! colspan="2" | Odd harmonic '}
  local tapprox = {'! colspan="2" | Approximation '}
  local tabs = {'! rowspan="2" | Error \n! absolute ([[cent|¢]]) '}
  local trel = {'! [[Relative error|relative]] (%) '}
  local tdeg = {'! colspan="2" | Steps ([[octave reduction|reduced]])'}
  local tfs = {'! colspan="2" | [[Fifthspan]]'}
  local fmt_approx = string.format(' %%.%df', prec)
  local fmt_abs = string.format(' %%+.%df', prec)
  local fmt_rel = ' %+.0f'
  for _, p in pairs(odds) do
    s = math.log(p) / math.log(2)
    v = s*edo
    ev = math.floor(v + .5)
    m = math.floor(math.log(3)/math.log(2)*edo + .5)
    table.insert(todd, ' ' .. p )
    table.insert(tapprox, string.format(fmt_approx, 1200*(ev % edo)/edo) )
    table.insert(tabs, string.format(fmt_abs, 1200 * (ev - v ) / edo))
    table.insert(trel, string.format(fmt_rel, 100 * (ev - v)))
    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
  local titleMarkup = ''
  if title then
	titleMarkup = '|-\n|+ ' .. title .. '\n'

  end
  noFifthSpan = '{| class="wikitable center-all"\n' ..
	titleMarkup ..
	'|-\n' ..
	table.concat(todd, '\n!') .. '\n' ..
    '|-\n' ..
    table.concat(tabs, '\n|') .. '\n' ..
    '|-\n' ..
	table.concat(trel, '\n|') .. '\n' ..
    '|-\n' ..
  table.concat(tdeg, '\n|') .. '\n' ..
    '|}'
    if (diatonic_edo) then
    	return noFifthSpan .. 
  table.concat(tfs, '\n|') .. '\n' ..
    '|}'
    else
    	return noFifthspan
    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 }

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

function p.harmonics_in_edo (frame)
  local edo = frame.args[1] or frame.args['edo'] or 12 -- edo (default=12)
  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 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
  return edoprox( edo, {unpack(odds, start, start+columns-1)}, title, prec)
end

return p;