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Source code

local MARGIN = 10
local AMPLITUDE, WAVE_WIDTH = 30, 600
local GAP_BETWEEN_WAVES = 25
local NUM_WAVES = 7
local FONT_SIZE, FONT_FUDGE = 20, 5
local WAVE_STYLE = ' stroke="#000" stroke-width="1.5" fill="none"'
local img_wd = 2 * MARGIN + WAVE_WIDTH
local img_ht = 2 * MARGIN + NUM_WAVES * AMPLITUDE * 2 +
 (NUM_WAVES - 1) * GAP_BETWEEN_WAVES
local PI = math.asin(1) * 2
local XD = PI / 12
local SQRT2 = math.sqrt(2)
local Y1 = (2 * SQRT2) / 7 - 1 / 7
local Y2 = (4 * SQRT2) / 7 - 2 / 7
local Y3 = SQRT2 / 2
local Y4 = (3 * SQRT2) / 7 + 2 / 7
function sine_wave_path (x, y, width, amp, num_half_waves)
 local xmul = width / (num_half_waves * PI)
 local xd = XD * xmul
 local path = 'M' .. coords(x, y)
 for _ = 1, num_half_waves do
 path = path .. ' C' .. coords(x + xd, y + amp * Y1)
 .. ' ' .. coords(x + 2*xd, y + amp * Y2)
 .. ' ' .. coords(x + 3*xd, y + amp * Y3)
 .. ' C' .. coords(x + 4*xd, y + amp * Y4)
 .. ' ' .. coords(x + 5*xd, y + amp)
 .. ' ' .. coords(x + 6*xd, y + amp)
 .. ' C' .. coords(x + 7*xd, y + amp)
 .. ' ' .. coords(x + 8*xd, y + amp * Y4)
 .. ' ' .. coords(x + 9*xd, y + amp * Y3)
 .. ' C' .. coords(x + 10*xd, y + amp * Y2)
 .. ' ' .. coords(x + 11*xd, y + amp * Y1)
 .. ' ' .. coords(x + 12*xd, y)
 x = x + width / num_half_waves
 amp = amp * -1 -- flip over vertically every half wave
 end
 return path
end
function coords (x, y)
 return string.format('%g,%g', x, y)
end
local fh = assert(io.open("Harmonic_partials_on_strings.svg", "wb"))
fh:write('<?xml version="1.0" encoding="UTF-8"?>\n' ..
 '<svg version="1.0" width="', img_wd, '" height="', img_ht,
 '" xmlns="http://www.w3.org/2000/svg">\n')
local y_origin = MARGIN + AMPLITUDE
local wave_labels, pick_circles = '', ''
for n = 1, NUM_WAVES do
 local amp = AMPLITUDE - (n - 1) * AMPLITUDE * 0.1
 fh:write(' <path', WAVE_STYLE, ' d="',
 sine_wave_path(MARGIN, y_origin, WAVE_WIDTH, amp, n), ' ',
 sine_wave_path(MARGIN, y_origin, WAVE_WIDTH, -amp, n),
 '"/>\n')
 if n > 1 then
 local pick_x = MARGIN + WAVE_WIDTH / n
 local pick_r = AMPLITUDE * 0.2
 pick_circles = pick_circles .. ' <circle cx="' .. pick_x ..
 '" cy="' .. y_origin + pick_r ..
 '" r="' .. pick_r .. '"/>\n'
 wave_labels = wave_labels .. ' <text x="' .. pick_x ..
 '" y="' .. y_origin - FONT_SIZE + 2 * FONT_FUDGE ..
 '">1/' .. n .. '</text>\n'
 end
 y_origin = y_origin + 2 * AMPLITUDE + GAP_BETWEEN_WAVES
end
fh:write(' <g stroke="#000" fill="#bbb">\n', pick_circles, ' </g>\n',
 ' <g font-family="Bitstream Vera Sans" font-size="', FONT_SIZE, 'px"',
 ' text-anchor="middle">\n',
 ' <text x="', MARGIN + FONT_FUDGE,
 '" y="', MARGIN + AMPLITUDE - FONT_SIZE + 2 * FONT_FUDGE,
 '">0</text>\n',
 ' <text x="', MARGIN + WAVE_WIDTH - FONT_FUDGE,
 '" y="', MARGIN + AMPLITUDE - FONT_SIZE + 2 * FONT_FUDGE,
 '">1</text>\n',
 wave_labels,
 ' </g>\n',
 '</svg>\n')

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