Module:Powharmonic series

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Note: Do not invoke this module directly; use the corresponding template instead: Template:Powharmonic series.

Generates a table showing the intervals of a powharmonic series for a given exponent, which is used to model timbres involving stretched or compressed harmonics.

---

local p = {}

function p.powharmonic(frame)
    local n = tonumber(frame.args["n"])
    local expo = tonumber(frame.args["expo"])
    local out_str = "{| class=\"wikitable center-all\"\n"
	    .. "|+ style=\"font-size: 105%;\" | " .. string.format("Intervals of the %s-Powharmonic series\n", expo)
	    .. "|-\n"
	    .. "! rowspan=\"2\" | Pitch !! colspan=\"2\" | Frequency multiplier !! colspan=\"3\" | Pitch\n"
	    .. "|-\n"
	    .. "! Definition !! Decimal !! [[Cent]]s !! Change (cents) !! Octave-reduced (cents)"
	    .. "\n"
    local fmt_cent = string.format("%%.%df", tonumber(frame.args["prec"]))
    local p_prev = 0
    local p_current = 0

    for i = 1, n do
        p_current = 1200 * math.log(i) / math.log(2) * expo
        out_str = out_str
            .. "|-\n"
            .. "| ".. string.format("%s", i)
            .. " || " .. string.format("%s<sup>%s</sup>", i, expo)
            .. " || " .. string.format(fmt_cent, i^expo)
            .. " || " .. string.format(fmt_cent, p_current)
            .. " || " .. string.format(fmt_cent, p_current - p_prev)
            .. " || " .. string.format(fmt_cent, math.fmod(p_current, 1200))
            .. "\n"
        p_prev = p_current
    end

    out_str = out_str .. "|}"
    return out_str
end

return p