30:[] 2e:{"title":"Harmonic Series (WIP)","cells":[{"id":0,"value":"# Harmonic Series (WIP)\nEasy-to-use JS tools for the harmonic series in music specifically, and progressions more generally.\n\nInputs: \n- a = first term of progression\n- n = number of terms in progression\n- d = common difference\n- p = precision level for rounding\n","pinned":true,"hidden":false,"mode":"md"},{"id":213,"value":"

This work by Alessandro G. Magnasco is licensed under CC BY-NC-SA 4.0

","pinned":false,"hidden":false,"mode":"html"},{"id":199,"value":"viewof demoHz = Inputs.range([20, 10000], {label: \"Frequency (Hz):\", step: 1, value: 110})","pinned":true,"hidden":false,"mode":"ojs"},{"id":206,"value":"demoNotes = d3.cross([demoHz],harmonicProgression(1,10,1,3))","pinned":true,"hidden":false,"mode":"ojs"},{"id":9,"value":"harmonicFinder = (a, n, d) => {\n // a = first term of progression\n // n = number of terms in progression\n // d = common difference\n return 1/(a+(n-1)*d)\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":12,"value":"harmonicFinder(1,2,3)","pinned":true,"hidden":false,"mode":"ojs"},{"id":17,"value":"harmonicSum = (n) => {\n // sums harmonic series until nth term\n // by Surbhi Tyagi 2022\n var s = 0\n for (var i=1; i<=n; i++){s=s+1/i}\n return s\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":21,"value":"harmonicSum(5)","pinned":true,"hidden":false,"mode":"ojs"},{"id":7,"value":"harmonicProgression = (a, n, d, p) => {\n // a = first term of progression\n // n = number of terms in progression\n // d = common difference\n // p = precision \n\n // when d=1: 1/2, 1/3, 1/4, 1/5...\n // when d=2: 1/2, 1/4, 1/6, 1/8...\n \n var arr = []\n for (var i=1; i<=n; i++){\n var s = (1/(a+(i-1)*d))\n arr.push(round(s,p))\n }\n return arr\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":35,"value":"harmonicProgression(1,10,1,3)","pinned":true,"hidden":false,"mode":"ojs"},{"id":97,"value":"// octaves \n\ngeometricProgression = (a, n, d, p) => {\n // a = first term of progression\n // n = number of terms in progression\n // d = common difference\n // p = precision \n\n // when d=2: 1/2, 1/4, 1/8, 1/16...\n // when d=3: 1/2, 1/6, 1/18, 1/54...\n \n var arr = []\n for (var i=1; i<=n; i++){\n var g = 1/(a*(d**(i-1)))\n arr.push(round(g,p))\n }\n return arr\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":121,"value":"geometricProgression(2,10,2,3)","pinned":true,"hidden":false,"mode":"ojs"},{"id":111,"value":"// payItForward\n// returns a straightforward or reciprocal progression\n// requires round\n\npayItForward = (a,n,d,p,t) => {\n // a = first term of progression\n // n = number of terms in progression\n // d = common difference\n // p = precision \n // t = type\n // types: \"r\" for arithmetic, \"h\" for harmonic (1/arithmetic)\n // \"g\" for geometric, \"gr\" for 1/geometric\n \n var arr = []\n for (var i=1; i<=n; i++){\n var r = a+(i-1)*d\n var h = 1/r\n var g = a*(d**(i-1))\n var gr = 1/g\n switch(t){\n case \"r\": arr.push(round(r,p)); break;\n case \"h\": arr.push(round(h,p)); break;\n case \"g\": arr.push(round(g,p)); break;\n case \"gr\": arr.push(round(gr,p)); break;\n default:\n console.log(`Type of progression required`);\n }\n }\n return arr\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":113,"value":"payItForward(1,10,2,3,\"h\")","pinned":true,"hidden":false,"mode":"ojs"},{"id":5,"value":"// WIP\nharmonicRatios = (a,n,d,p) => {\n // a = first term of progression\n // n = number of terms in progression\n // d = common difference\n // p = precision\n // requires round\n \n var arr = []\n\n // ordinal indicators by Tomas Langkass 2016\n // https://stackoverflow.com/questions/13627308/add-st-nd-rd-and-th-ordinal-suffix-to-a-number\n function nth(n){return[\"st\",\"nd\",\"rd\"][((n+90)%100-10)%10-1]||\"th\"}\n\n for (var i=1; i<=n; i++){\n var s = (1/(a+(i-1)*d))\n var r = 1 + \"/\" + (a+(i-1)*d)\n var o = i + nth(i) + \" harmonic of n+\" + d\n arr.push({Fraction: round(s,p), Ratio: r, Notes: o})\n }\n return arr\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":58,"value":"musicalHarmonics(1,125)","pinned":true,"hidden":false,"mode":"ojs"},{"id":224,"value":"// ordinal indicators by Tomas Langkass 2016\n// https://stackoverflow.com/questions/13627308/add-st-nd-rd-and-th-ordinal-suffix-to-a-number\nfunction nth(n){return[\"st\",\"nd\",\"rd\"][((n+90)%100-10)%10-1]||\"th\"}","pinned":false,"hidden":false,"mode":"ojs"},{"id":228,"value":"// closest powers of two by Zibri 2022\n// https://stackoverflow.com/questions/26965171/fast-nearest-power-of-2-in-javascript\nfunction blpo2(x) {\n x = x | (x >> 1);\n x = x | (x >> 2);\n x = x | (x >> 4);\n x = x | (x >> 8);\n x = x | (x >> 16);\n x = x | (x >> 32);\n return x - (x >> 1);\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":84,"value":"// musicalHarmonics\n// divides every whole number between min...max by the closest power of 2\n// returns an array of objects similar to Quartermaster\n// requires ratioToCents, ratioToSavarts, round\n\nmusicalHarmonics = (min,max) => {\n var arr = []\n\n for (var i=min; i<=max; i++){ \n var p = blpo2(i)\n var r = i + \"/\" + p\n var o = i + nth(i) + \" harmonic\"\n var c = Math.abs(round(ratioToCents(i/p),3))\n var sv = Math.abs(round(ratioToSavarts(i/p),3))\n var viz = [{Blue: c, Pink: 1200-c}]\n arr.push({Fraction: round(i/p,3), Ratio: r, Cents: c, Savarts: sv, Notes: o, Viz: viz})\n }\n return arr\n}","pinned":true,"hidden":false,"mode":"ojs"},{"id":60,"value":"## Imports","pinned":false,"hidden":false,"mode":"md"},{"id":62,"value":"import {round} from \"@amagnasco/equal-temperament-generator\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":171,"value":"import {ratioToCents} from \"@amagnasco/quartermaster\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":184,"value":"import {ratioToSavarts} from \"@amagnasco/quartermaster\"","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W30","stdlib":"1","titling":"auto"}