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| View Original: | Harmonic partials on strings.svg (620x590) | |||
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| Keywords: Harmonic partials on strings.svg Illustration of harmonic overtones on the wave set up along a string when it is held steady in certain places as when a guitar string is plucked while lightly held exactly half way along its length Own work by uploader based on design of bitmap image Image Overtone jpg Qef 2008-07-08 Massive JPEG bitmap version Image Overtone jpg Source code Created by a specially written program in the Lua programming language To recreate the image just run the program and it will write the SVG into a file There are various parameters that can be adjusted at the start of the code The sine-wave approximation using Bezier curves is derived from http //www tinaja com/glib/bezsine pdf Bezier curve sinewave approximation PDF by Jim Fitzsimmons <source lang lua > 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' </source> Qef Sensory Neuroscience Hearing and speech Standing waves on strings Harmonic series Images with Lua source code Sine function Music diagrams Overtones Amplitude | ||||
