# Module:Harmonics in edo

```local p = {}

local function edoprox(edo, odds, title, prec)
local f = 1/edo
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 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)
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 .. ')')
end
local titleMarkup = ''
if title then
titleMarkup = '|-\n|+ ' .. title .. '\n'

end
return '{| 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' ..
'|}'
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 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;
```