34:["$","title",null,{"children":"Interval Movement within Chord Changes | travistingey | Observable"}] 3c:[] 38:{"id":"d95b8d3aa7ad76e0","slug":"interval-movement-within-chord-changes","title":"Interval Movement within Chord Changes","thumbnail":"a333679b24f4fa43294cef7afcc851cf214a4d69f16fc36816dd8032a31ca986","access_level":"public","create_time":"$D2021-03-08T04:55:46.089Z","update_time":"$D2022-02-08T18:42:17.559Z","view_time":null,"first_public_time":"$D2021-03-11T21:59:34.187Z","has_unpublished_edits":null,"fork":{"id":"8b421e46c36d8f33","slug":"using-bitwise-operators-for-music-theory","title":"Using Bitwise Operators for Music Theory","owner":{"id":"ebe2f2222861d30c","login":"travistingey","name":""}},"stars":0,"starred":false,"owner":{"type":"team","id":"ebe2f2222861d30c","login":"travistingey","name":"","avatar_url":"https://avatars-next.observableusercontent.com/f6b1c1a85c172841a109bf5c86c22431e37905fd0d859039d7f12f07d41c64ba","tier":"starter_2024","bio":"","followed_by_you":false,"follows_you":false},"version":2184,"publish_version":2184,"role":null,"authored":false,"authors":[{"type":"individual","id":"212eec5edb545995","login":"travistingey","name":"","avatar_url":"https://avatars-next.observableusercontent.com/f6b1c1a85c172841a109bf5c86c22431e37905fd0d859039d7f12f07d41c64ba","tier":null,"bio":"","followed_by_you":false,"follows_you":false}],"members":[{"type":"individual","id":"212eec5edb545995","login":"travistingey","name":"","avatar_url":"https://avatars-next.observableusercontent.com/f6b1c1a85c172841a109bf5c86c22431e37905fd0d859039d7f12f07d41c64ba","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"titling":"auto","title":"Interval Movement within Chord Changes","cells":[{"id":2135,"value":"md`# Interval Movement within Chord Changes\nLooking into the movement of intervals. The perception of a resolution vs departure lays in the context in which two chords are heard. This analysis attempts to look at the minimum movement of intervals within the chord tones.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2058,"value":"{\n const prog =[\n Chord(2,11),\n Chord(7,10),\n Chord(0,9)\n ]\n \n let forward = format_table(prog) \n let backward = format_table(prog,1)\n \n return html`\n

ii-V-I

Looking Forward

\n ${forward}\n
\n

Looking Backward

\n ${backward}\n `\n \n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2150,"value":"format_table = function(prog,dir){\n let data = []\n \n let look = (dir)? 'to' : 'from'\n \n for(let i = 0; i{\n\n const result = {\n from: d.from.name,\n to: d.to.name,\n shared: \n BitMaskToIntervals(d.common)\n .map(i=>itn(i) + ' (' +nts(i,d[look].root) + ')'),\n distance:\n d.result\n .reduce((a,c)=> a + Math.abs(c.distance),0) \n }\n\n table.push(result)\n \n \n const detail = d.result.map(r=>({from:itn(r.from) +' ('+ nts(r.from, d[look].root) + ')',to: itn(r.to)+' ('+nts(r.to,d[look].root)+')',distance:r.distance}))\n \n table = table.concat(detail)\n })\n return Table(table)\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2067,"value":" Chord = function(root,index){\n\n root = root % 12\n let int = Intervals[index] \n \n let notes = int.intervals.map( d=>(d+root)%12 )\n let mask = IntervalsToBitMask(int.intervals)\n let note_mask = mask << root & 4095 | (mask >>> (12-root) )\n\n return {\n root : root,\n name: itn(root) + Intervals[index].name,\n note_mask : note_mask,\n int_mask : mask,\n intervals: Intervals[index].intervals,\n notes: notes,\n int_bin: mask.toString(2),\n note_bin: note_mask.toString(2)\n }\n\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1885,"value":"ChordMovement = function(a,b) {\n let a_diff = BitMaskToIntervals(a.note_mask & (a.note_mask ^ b.note_mask))\n let b_diff = BitMaskToIntervals(b.note_mask & (a.note_mask ^ b.note_mask))\n \n let result = ChordDistance(a_diff,b_diff)\n \n if(!result){\n result = ChordDistance(b_diff,a_diff)\n result = result.map(r=>({\n to: r.from,\n from: r.to,\n distance: r.distance * -1\n }))\n }\n \n return {\n from: a,\n to: b,\n \n common: a.note_mask & b.note_mask,\n result\n \n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1994,"value":"ChordDistance = function(a, b){\n let row ={}\n a.forEach(one=>{\n row[one] = b.map(two =>{\n let step = two - one\n \n if(step > 6) step = step - 12\n if(step < -6) step = step + 12\n \n return {from: one, to: two, distance : step }\n })\n \n })\n \n a.forEach(index=>{ \n row[index].sort((m,n)=> Math.abs(m.distance) - Math.abs(n.distance) )\n })\n \n let a_res = a.map(i=>row[i][0])\n let a_set = a_res.map(i=>i.to)\n \n if(IntervalsToBitMask(b) == IntervalsToBitMask(a_set)){ \n return a_res\n } else {\n return false\n }\n \n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":395,"value":"Intervals = [\n\n{name: \"major \", intervals: [0,4,7]},\n{name: \"minor\", intervals: [0,3,7]},\n{name: \"°\", intervals: [0,3,6]},\n{name: \"+\", intervals: [0,4,8]},\n{name: \"sus4\", intervals: [0,5,7]},\n\n{name: \"maj7 shell\", intervals: [0,4,11]},\n{name: \"7 shell\", intervals: [0,4,10]},\n{name: \"m7 shell\", intervals: [0,3,10]},\n{name: \"m6 shell\", intervals: [0,3,9]},\n\n{name: \"maj7\", intervals: [0,4,7,11]},\n{name: \"7\", intervals: [0,4,7,10]},\n{name: \"m7\", intervals: [0,3,7,10]},\n{name: \"m6\", intervals: [0,3,7,9]},\n{name: \"ø\", intervals: [0,3,6,10]},\n\n{name: \"tritone\", intervals:[0,6]}\n]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":578,"value":"md`## Appendix`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":949,"value":"md`## Imports`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":955,"value":"d3 = require(\"d3@^5.8\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":723,"value":"import {Button, Checkbox, Toggle, Radio, Range, Select, Text, Search, Table} from \"@observablehq/inputs\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2038,"value":"import {BitMaskToIntervals,IntervalsToBitMask,itn,itc,nts,colorScale} from '@travistingey/using-bitwise-operators-for-music-theory'","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W3c","stdlib":"1"}} 33:null