2e:null 2f:["$","title",null,{"children":"Euclidean scales and chords | Wolfgang Sobtzick | Observable"}] 34:T2cf4,htl.html``35:T738,function euclidean_svg(pattern) { const x = d3.scaleLinear().range([30, 60]); const svg = d3.create("svg").attr("viewBox", "15 0 " + width + " 44"); let step = 0 svg .append('g') .selectAll("g") .data(pattern.atoms) .join('g') .call(g => g.append('rect') .attr('fill', 'none') .attr('stroke', '#22222280') .attr('stroke-width', 1) .attr('x', d => x(d.scale) - 15) .attr('y', 11) .attr('rx', 5) .attr('ry', 5) .attr('height', 28) .attr('width', (d, i) => d.interval * 30) ) .call(g => g.append('g') .selectAll('rect') .data(d => d.rhythm) .enter().append('rect') .attr("x", (d, i) => x(step++) - 10) .attr("y", "15px") .attr("width", "20px") .attr("height", "20px") .attr("fill", (d, i) => (d === 1 ? "black" : "white")) .attr("stroke", "black") .attr("stroke-width", (d, i) => (d === 1 ? "none" : "0.8px")) .attr("r", 13) .on('mouseenter', function (evt, d, nodes) { d3.select(this).transition().duration(55).attr('fill', '#44449966') }) .on('mouseleave', function (evt, d, nodes) { d3.select(this).transition().duration(155).attr('fill', (d, i) => (d === 1 ? "black" : "white")) }) ) .call(g => g.append('text') .style('user-select', 'none') .attr('pointer-events','none') .attr('font-size', '10px') .style('fill', 'white') .attr('x', d => x(d.scale) - (d.scale > 9 ? 6 : 3)) .attr('y', 28.5) .text(d => d.scale) ) return svg.node(); }36:Tc00,scales = [ { length: 12, events: 5, offset: 0, name: "major", type: "scale_pentatonic" }, { length: 12, events: 5, offset: 1, name: "blues major", type: "scale_pentatonic" }, { length: 12, events: 5, offset: 2, name: "egyptian", type: "scale_pentatonic" }, { length: 12, events: 5, offset: 3, name: "minor", type: "scale_pentatonic" }, { length: 12, events: 5, offset: 4, name: "blues minor", type: "scale_pentatonic" }, { length: 12, events: 7, offset: 0, name: "locrian", type: "scale_octave" }, { length: 12, events: 7, offset: 1, name: "phrygian", type: "scale_octave" }, { length: 12, events: 7, offset: 2, name: "minor/ aeloian", type: "scale_octave" }, { length: 12, events: 7, offset: 3, name: "dorian", type: "scale_octave" }, { length: 12, events: 7, offset: 4, name: "mixolydian", type: "scale_octave" }, { length: 12, events: 7, offset: 5, name: "major/ ionian", type: "scale_octave" }, { length: 12, events: 7, offset: 6, name: "lydian", type: "scale_octave" }, { length: 24, events: 7, offset: 0, name: "m7b5", type: "chord_euclidean" }, { length: 24, events: 7, offset: 1, name: "minor", type: "chord_euclidean" }, { length: 24, events: 7, offset: 2, name: "major", type: "chord_euclidean" }, { length: 24, events: 7, offset: 3, name: "minor dim triad", type: "chord_euclidean" }, { length: 24, events: 7, offset: 4, name: "major dim triad", type: "chord_euclidean" }, { length: 24, events: 7, offset: 5, name: "_", type: "chord_euclidean" }, { length: 24, events: 7, offset: 6, name: "5/7/9/11", type: "chord_euclidean" }, { length: 24, events: 6, offset: 0, name: "augmented", type: "chord_euclidean" }, { length: 24, events: 8, offset: 0, name: "diminished", type: "chord_euclidean" }, { interval: [2, 5, 5], name: "sus2", type: "chord_interval" }, { interval: [5, 2, 5], name: "sus4", type: "chord_interval" }, { interval: [3, 4, 2, 3], name: "minor 6", type: "chord_interval" }, { interval: [4, 3, 2, 3], name: "major 6", type: "chord_interval" }, { interval: [4, 3, 3, 3, 3], name: "7b9", type: "chord_interval" }, { interval: [10, 4, 3, 4, 3], name: "13", type: "chord_interval" }, { interval: [4, 4, 2, 2], name: "7#5", type: "chord_interval" }, { interval: [4, 2, 4, 2], name: "7b5", type: "chord_interval" }, { interval: [4, 3, 2, 5, 3], name: "69", type: "chord_interval" }, { interval: [4, 3, 7, 4], name: "add 9", type: "chord_interval" } ]37:T913,function euclidean_show_hori(pattern, node, offset) { const x = d3.scaleLinear().range([30, 60]); const new_g = node.append("g"); const offset_name = 80; const col = { scale_pentatonic: "#eeee0022", scale_octave: "#00eeee22", chord_euclidean: "#ee0ee018", chord_interval: "#00ee4422" }; const color = col[pattern.type]; const translate = "translate(" + offset_name + " ," + offset + ")"; new_g.on("mousedown", function (event, d, nodes) { d3.select(this) .attr("transform", translate) .transition() .duration(89) .attr("transform", "translate(132, " + offset + ")") .transition() .duration(89) .attr("transform", translate); play_scale(pattern); }); new_g.attr("transform", translate); new_g .append("text") .style("user-select", "none") .attr("font-size", "12px") .attr("font-weight", 550) .attr("y", 20) .attr("x", -offset_name) .text(pattern.name); new_g .append("text") .style("user-select", "none") .attr("font-size", "10px") .attr("y", 36) .attr("x", -offset_name) .text(pattern.type.includes("interval") ? "" : `[${pattern.length} ${pattern.events} ${pattern.offset}]`); let step = 0; new_g .selectAll("g") .data(pattern.atoms) .join("g") .call((g) => g .append("rect") .attr("fill", color) .attr("stroke", "#22222280") .attr("stroke-width", 2) .attr("x", (d) => x(d.scale) - 15) .attr("y", 11) .attr("height", 28) .attr("width", (d, i) => d.interval * 30) ) .call((g) => g .selectAll("circle") .data((d) => d.rhythm) .enter() .append("circle") .attr("cx", (d, i) => x(step++)) .attr("cy", 25) .attr("fill", (d, i) => (d === 1 ? "black" : "none")) .attr("stroke", "black") .attr("stroke-width", (d, i) => (d === 1 ? "none" : "0.8px")) .attr("r", 13) ) .call((g) => g .append("text") .style("user-select", "none") .attr("font-size", "12px") .style("fill", "white") .attr("x", (d) => x(d.scale) - (d.scale > 9 ? 7 : 3.41)) .attr("y", 29) .text((d) => { return d.scale; }) ); return node; }38:[] 32:{"id":"2b181de19c0a2724","slug":"euclidean-scales-and-chords","title":"Euclidean scales and chords","thumbnail":"590627400d5b7ecc0c056e33ab6d5cc540a476d98d7cc2c0d8e0bc60e8a37cba","access_level":"public","create_time":"$D2022-10-14T21:25:58.906Z","update_time":"$D2022-11-21T23:37:01.343Z","view_time":null,"first_public_time":"$D2022-10-14T22:34:36.281Z","has_unpublished_edits":null,"fork":true,"stars":1,"starred":false,"owner":{"type":"team","id":"5ef04c3ca4d2968f","login":"kompaqt","name":"Wolfgang Sobtzick","avatar_url":"https://avatars-next.observableusercontent.com/be973dee6963f7de4918b6b96fa6775f97bb3b3d9fc7787194e705e7599cf0ce","tier":"starter_2024"},"version":10332,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"e9bbc78a50f0a4ca","login":"kompaqt","name":"Wolfgang Sobtzick","avatar_url":"https://avatars-next.observableusercontent.com/be973dee6963f7de4918b6b96fa6775f97bb3b3d9fc7787194e705e7599cf0ce","tier":null}],"members":[{"type":"individual","id":"e9bbc78a50f0a4ca","login":"kompaqt","name":"Wolfgang Sobtzick","avatar_url":"https://avatars-next.observableusercontent.com/be973dee6963f7de4918b6b96fa6775f97bb3b3d9fc7787194e705e7599cf0ce","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"title":"Euclidean scales and chords","cells":[{"id":6122,"value":"# Euclidean scales and chords","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":10029,"value":"Thanks to Torben Jansens' [notebook](https://observablehq.com/@toja/euclidean-rhythms) on the euclidean rhythm, i decided to publish part of my journey to my computational music theory i started thinking about 2009.\n\nA little top-down view of the elements involved..","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":10211,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":10216,"value":"## This notebook will be all about the frequency branch:\n\nBecause you don't only get rhythmic euclidean patterns from this algorithm. But also melodic ones in the broadest sense.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":10065,"value":"viewof eucl_pattern = view`

Euclidean pattern generator

\n${['length', Inputs.range([1, 30], {step: 1, value:13, label: \"Length\"})]}\n${['events', Inputs.range([1, 30], {step: 1, value:5,label: \"Events\"})]}\n${['offset', Inputs.range([0, 10], {step: 1, value:0,label: \"Offset\"})]}\n${['interval', Inputs.text({label: \"Intervals\"})]}\n

`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":10099,"value":"pattern = Euclidean(eucl_pattern)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":10076,"value":"euclidean_svg(Euclidean(eucl_pattern))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":10093,"value":"## There are actually three different useful representations from an euclidean:\n- **rhythmic** => black and white blocks\n - sequentially as (on and offbeats):\n - ${pattern.atoms.map(d => d.rhythm).toString().replaceAll(',','')}\n- **melodic** => step number in a block\n - **sequentially** as midi frequencey steps (midi 69 as base frequency):\n - ${pattern.atoms.map(d => d.scale + ' ')} -> ${pattern.atoms.map(d => core.mtof(d.scale + 69).toFixed(2) + ', ')}\n - **parallel** as frequency:\n - ${pattern.atoms.map(d => d.scale + ' ')} -> ${pattern.atoms.map(d => core.mtof(d.scale + 69).toFixed(2) + ', ')}\n- **duration(ic)** => blocks around intervals\n - sequentially as time factors (relative duration of the intervals, multiply for actual duration):\n - ${pattern.atoms.map(d => d.interval + ' ')} -> i.e. ${pattern.atoms.map(d => d.interval * 100 + 'ms ')}","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":10147,"value":"## melodic sequentially","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":10042,"value":"You get the classical scales for like pentatonics: ","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":10150,"value":"Euclidean({length: 12, events: 5, offset: 0})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":70,"value":"{\n const off_y = 50;\n const s = scales.slice(0,5)\n let g = d3\n .create(\"svg\")\n .attr(\"viewBox\", `0 0 ${width} ${off_y * s.length}`);\n\n let y = 0;\n for (const value of s.slice(0,5)) {\n const m = Euclidean(value);\n g = euclidean_show_hori(m, g, y);\n y += off_y;\n }\n\n return g.node();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":10054,"value":"But also all the standard 12 tone equal tempered scales just by rotating a single pattern:","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":10152,"value":"Euclidean({length: 12, events: 7, offset: 0})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":10048,"value":"{\n const off_y = 50;\n const s = scales.slice(5,12)\n let g = d3\n .create(\"svg\")\n .attr(\"viewBox\", `0 0 ${width} ${off_y * s.length}`);\n\n let y = 0;\n for (const value of s) {\n const m = Euclidean(value);\n g = euclidean_show_hori(m, g, y);\n y += off_y;\n }\n\n return g.node();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":10170,"value":"## melodic parallel aka chord(ic)","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":10058,"value":"If you now play **all the events in parallel** you even get the prominent chords in western music:","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":10156,"value":"Euclidean({length: 24, events: 7, offset: 0}) // or events: [6, 8] for the last two","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":10049,"value":"{\n const off_y = 50;\n const s = scales.slice(12,21)\n let g = d3\n .create(\"svg\")\n .attr(\"viewBox\", `0 0 ${width} ${off_y * s.length}`);\n\n let y = 0;\n for (const value of s) {\n const m = Euclidean(value);\n g = euclidean_show_hori(m, g, y);\n y += off_y;\n }\n\n return g.node();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":10164,"value":"## Non-euclidean patterns:","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":10158,"value":"{\n const off_y = 50;\n const s = scales.slice(24,32)\n let g = d3\n .create(\"svg\")\n .attr(\"viewBox\", `0 0 ${width} ${off_y * s.length}`);\n\n let y = 0;\n for (const value of s) {\n const m = Euclidean(value);\n g = euclidean_show_hori(m, g, y);\n y += off_y;\n }\n\n return g.node();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":10192,"value":"## Endless patterns\n\nLastly you can loop those patterns over arbitrary ranges use the .as_scale() function:\n\n${d3.range(40).map(i => pattern.as_scale(i) + ' ')}\n\nThis way you could filter the complete midi range by musical key (or any other integer range for that matter).\n\nJust sync the base note of the pattern with the base note of a chord and you would have a flexible way of defining all allowed notes for improvisation.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":10185,"value":"## Helpers","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":56,"value":"play_scale = (pattern) => {\n const is_chord = pattern.type.includes(\"chord\");\n \n chord_or_scale({\n voice: {\n duration: is_chord ? 1666 : 433,\n waveform: 2,\n scale: {\n spacing: is_chord ? 17 : 210,\n scale: pattern\n },\n overtones: {\n num_voices: 1\n }\n }\n }).play();\n }","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":8539,"value":"chord_or_scale = Eventset({\n gain: 0.5,\n voice: {\n waveform: 1,\n duration: 100, \n gain: [0, 0.07, 0.05, 0.001, 0, 0],\n overtones: {\n base: 52, \n num_voices: 8, \n },\n scale: {\n spacing: 17,\n scale_func: (params) => Overtones(params), \n }\n }, \n trigger1: (params) => Scale(Object.assign({}, params, params.voice.scale))\n })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":10062,"value":"$35","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":53,"value":"$36","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2048,"value":"$37","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":10289,"value":"import {core, Eventset, Euclidean, Overtones, Scale} from \"@kompaqt/core\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":10067,"value":"import {view} from \"@tomlarkworthy/view\"","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2056,"value":"style = html``","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W38","stdlib":"1","titling":"auto"}} 33:"$32:body"