30:Tb29,// Quartermaster // rations out any given array of numbers // requires: factorial, round, ratioToCents, ratioToSavarts // inputs an array of numbers // outputs an array of objects, 5 properties quartermaster = (arr) => { var rations = [] var unclean = arr var denominator = unclean.filter(x => typeof x === 'number') var numerator = unclean.filter(x => typeof x === 'number') var ratio = [] var fraction = [] var cents = [] var savarts = [] var centsStd = [] var combined = [] var obj = {Ratio: "", Fraction: "", Cents: "", CentsStd: "", RatioStd: "", Savarts: "", Viz: [], Notes: ""} var uniqueFractions = [] var uniqueCentsStd = [] var counter = 0 var output = Array(counter) function modulo (a) {return ((a%1200)+1200)%1200} // cents[i]%1200 gives remainder, we want modulo // creates a list of unique fractions and their text representations for (var n=0; n < numerator.length; n++){ for (var d=0; d < denominator.length; d++){ // creates array with the division of n by d fraction.push(round(numerator[n]/denominator[d],3)) // Text ratio concatenation var textfrac = numerator[n]+"/"+denominator[d] ratio.push(textfrac) } } // unit conversions cents = fraction.map(ratioToCents) savarts = fraction.map(ratioToSavarts) centsStd = cents.map(modulo) // ensure all values are within 0-1200 range // combine each array using only unique values for fraction for (var i=0; i < fraction.length; i++){ // skip repeated values if (Object.values(uniqueFractions).includes(fraction[i])) {continue} // check whether fraction is repeated if (Object.values(uniqueCentsStd).includes(centsStd[i])) {continue} // check whether centsStd is repeated if (fraction[i]<1) {continue} // skip fractions smaller than 1:1 // skip fractions over 1 if needed //if (fraction[i] > 1) { continue } // for new unique values, adds properties var key = ratio[i] combined[key] = Object.create(obj) combined[key].Ratio = ratio[i] combined[key].Fraction = fraction[i] combined[key].Cents = Math.abs(round(cents[i],3)) combined[key].Savarts = Math.abs(round(savarts[i],3)) //combined[key].Cents = Math.abs(round(ratioToCents(combined[key].Fraction),3)) if (combined[key].Cents > 1200) {continue}; // skip ratios with cents over 1200 //combined[key].Savarts = Math.abs(round(ratioToSavarts(combined[key].Fraction),3)) combined[key].CentsStd = round(centsStd[i],3) if (combined[key].CentsStd < 1) {continue}; // skip fractions where mod is 0 //combined[key].RatioStd = Math.floor(cents[i]/1200) + " + " + combined[key].Viz = [{Blue: centsStd[i], Pink: 1200-centsStd[i]}] uniqueFractions.push(fraction[i]) uniqueCentsStd.push(centsStd[i]) counter++ output.push(combined[key]) } return output }31:[] 2e:{"title":"Quartermaster","cells":[{"id":0,"value":"# Quartermaster\n\nGiven a list of numbers, rations them out.\n\nFinds every unique whole number ratio between every element in an array. Useful for math on musical intervals.\n\nOutputs an array of objects with the following properties:\n- Ratio (key): Text fraction (\"1/2\", \"54/53\", ...)\n- Fraction (unique): Result of the division. Unique on first found.\n- Cents: Conversion of the ratio to musical cents, scale of 1200\n- CentsStd: Remaining cents difference when discounting octaves\n- RatioStd: Octave difference + remaining ratio\n- Savarts: Conversion of the ratio to musical Savarts, scale of 1000\n- Viz: Tuple for inline visualizations\n- Notes: blank, there if needed","pinned":false,"hidden":false,"mode":"md"},{"id":5,"value":"

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

","pinned":false,"hidden":false,"mode":"html"},{"id":18,"value":"## Try it out\nStart at 1 and slide up!","pinned":false,"hidden":false,"mode":"md"},{"id":54,"value":"viewof inputRange = Inputs.range([1, 100], {label: \"Maximum:\", step: 1, value: 5})","pinned":false,"hidden":false,"mode":"ojs"},{"id":81,"value":"viewof search = Inputs.search(demo, {placeholder: \"Look for a number or ratio\"})","pinned":false,"hidden":false,"mode":"ojs"},{"id":85,"value":"viewof rows = Inputs.table(search,{\n format: {\n Viz: x => sparkseesaw(x)\n },\n sort: \"Fraction\"\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":56,"value":"demo = quartermaster(plusOne(inputRange))","pinned":false,"hidden":false,"mode":"ojs"},{"id":247,"value":"## Hear the interval!\nFrequencies lower than 80 might not work on your speakers.","pinned":false,"hidden":false,"mode":"md"},{"id":279,"value":"viewof selectedRatio = Inputs.select(demo, {label: \"Select a ratio to hear\", format: x=>x.Ratio, value: demo.find(t=>t.Ratio === 3/2)})","pinned":false,"hidden":false,"mode":"ojs"},{"id":331,"value":"viewof freq = Inputs.range([40, 1000], {label: \"Frequency 1 (Hz):\", step: 1, value: 440})","pinned":false,"hidden":false,"mode":"ojs"},{"id":377,"value":"viewof dur = Inputs.range([1,30], {label: \"Duration (s):\", value: 3, step:1});","pinned":false,"hidden":false,"mode":"ojs"},{"id":274,"value":"freq2 = round(freq*selectedRatio.Fraction,3)","pinned":false,"hidden":false,"mode":"ojs"},{"id":380,"value":"pluck2tone(freq,freq2,dur)","pinned":false,"hidden":false,"mode":"ojs"},{"id":61,"value":"## Live examples","pinned":false,"hidden":false,"mode":"md"},{"id":45,"value":"// Every ratio between every whole number 1...32\nquartermaster(plusOne(32))","pinned":true,"hidden":false,"mode":"ojs"},{"id":67,"value":"// Every ratio within a given array \n// only keeps numbers\nquartermaster([2, 3, 5, 23, 59, \"foo\", 33, [99, 100]])","pinned":true,"hidden":false,"mode":"ojs"},{"id":7,"value":"## Imports","pinned":false,"hidden":false,"mode":"md"},{"id":9,"value":"import {round} from \"@amagnasco/equal-temperament-generator\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":41,"value":"import {plusOne} from \"@amagnasco/cartesian-limits\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":11,"value":"// factorial function by Gabriele Petrioli 2010\n// https://stackoverflow.com/questions/3959211/what-is-the-fastest-factorial-function-in-javascript?noredirect=1&lq=1\n\n// to do: add memoization?\n\nfactorial = (n) => {\n var rval=1;\n for (var i=2; i<= n; i++){\n rval = rval * i;\n }\n return rval;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":470,"value":"### Optional dependencies for visualization","pinned":false,"hidden":false,"mode":"md"},{"id":94,"value":"// optional cute visualization that can be called with\n// Format: {Viz: x => sparkseesaw(x)}\n// fractions between 0 and 1 only\nimport {sparkseesaw} from \"@hamzaamjad/tiny-charts\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":259,"value":"import {pluck2tone} from \"@amagnasco/pluck-wa\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":14,"value":"## Unit conversions","pinned":false,"hidden":false,"mode":"md"},{"id":28,"value":"ratioToCents = (ratio) => {return Math.log10(ratio)*1200/Math.log10(2)}","pinned":false,"hidden":false,"mode":"ojs"},{"id":30,"value":"ratioToSavarts = (ratio) => {return Math.log10(ratio)*1000}","pinned":false,"hidden":false,"mode":"ojs"},{"id":309,"value":"centsToRatio = (cents) => {\n return Math.pow(10,(1/cents))\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":23,"value":"## Quartermaster","pinned":false,"hidden":false,"mode":"md"},{"id":26,"value":"$30","pinned":true,"hidden":false,"mode":"ojs"}],"files":"$W31","stdlib":"1","titling":"auto"}