Help/Collections/Scale.html

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  39 <p class="p1"><b>Scale</b></p>
  40 <p class="p2"><br></p>
  41 <p class="p3"><b>Inherits from: </b><a href="../Core/Object.html"><span class="s1"><b>Object</b></span></a><b><span class="Apple-converted-space"> </span></b></p>
  42 <p class="p2"><br></p>
  43 <p class="p3">Represents a musical scale. It supports arbitrary octave divisions and ratios, and (in conjunction with <a href="Tuning.html"><span class="s1"><b>Tuning</b></span></a><b> </b>) can generate pitch information in various ways, including as input to Patterns.</p>
  44 <p class="p4"><br></p>
  45 <p class="p5">s.boot;</p>
  46 <p class="p4"><br></p>
  47 <p class="p5">a = <span class="s2">Scale</span>.major;</p>
  48 <p class="p6"><span class="s3">a.degrees; <span class="Apple-tab-span"> </span><span class="Apple-tab-span">    </span></span>// [ 0, 2, 4, 5, 7, 9, 11 ]</p>
  49 <p class="p6"><span class="s3">a.semitones;<span class="Apple-tab-span">        </span><span class="Apple-tab-span">    </span></span>// [ 0, 2, 4, 5, 7, 9, 11 ]</p>
  50 <p class="p6"><span class="s3">a.cents;<span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span></span>// [ 0, 200, 300, 500, 700, 900, 1100 ]</p>
  51 <p class="p6"><span class="s3">a.ratios;<span class="Apple-tab-span">   </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span></span>// [ 1, 1.1224620483089, 1.2599210498937, 1.3348398541685, etc. ]</p>
  52 <p class="p2"><br></p>
  53 <p class="p5"><span class="s2">Pbind</span>(<span class="s4">\scale</span>, a, <span class="s4">\degree</span>, <span class="s2">Pseq</span>((0..7) ++ (6..0) ++ [<span class="s4">\rest</span>], 1), <span class="s4">\dur</span>, 0.25).play;</p>
  54 <p class="p2"><br></p>
  55 <p class="p6">// use non-standard tuning</p>
  56 <p class="p5">a.tuning_(<span class="s4">\just</span>);</p>
  57 <p class="p6"><span class="s3">a.degrees;<span class="Apple-tab-span">  </span><span class="Apple-tab-span">    </span></span>// no change; degrees are independent of tuning</p>
  58 <p class="p6"><span class="s3">a.semitones;<span class="Apple-tab-span">        </span><span class="Apple-tab-span">    </span></span>// [ 0, 2.0391000173077, 3.1564128700055, 4.9804499913461, etc. ]</p>
  59 <p class="p6"><span class="s3">a.ratios.collect(</span><span class="s2">_</span><span class="s3">.round(0.001));<span class="Apple-tab-span">   </span></span>// [ 1, 1.125, 1.2, 1.333, 1.5, 1.667, 1.875 ]</p>
  60 <p class="p2"><br></p>
  61 <p class="p5"><span class="s2">Pbind</span>(<span class="s4">\scale</span>, a, <span class="s4">\degree</span>, <span class="s2">Pseq</span>((0..7) ++ (6..0) ++ [<span class="s4">\rest</span>], 1), <span class="s4">\dur</span>, 0.25).play;</p>
  62 <p class="p2"><br></p>
  63 <p class="p2"><br></p>
  64 <p class="p7"><b><span class="s5">Creation</span></b></p>
  65 <p class="p2"><br></p>
  66 <p class="p3"><b>*major, *minor, *dorian, *chromatic, *todi, *hijaz, *partch_o1, etc.</b></p>
  67 <p class="p4"><br></p>
  68 <p class="p3">Creates a scale from the library stored in <b>ScaleInfo</b>. Each scale comes with an appropriate default <b>Tuning</b>, but alternate tunings can be specified at creation time:</p>
  69 <p class="p4"><br></p>
  70 <p class="p8"><span class="s2">Scale</span><span class="s3">.phrygian(</span>\pythagorean<span class="s3">)</span></p>
  71 <p class="p4"><br></p>
  72 <p class="p3">If the tuning size does not match the scale's <b>pitchesPerOctave</b>, a warning will be thrown, and the scale will use its default tuning.</p>
  73 <p class="p4"><br></p>
  74 <p class="p3">For a complete list of available scales, execute</p>
  75 <p class="p4"><br></p>
  76 <p class="p5"><span class="s2">Scale</span>.directory</p>
  77 <p class="p4"><br></p>
  78 <p class="p3"><b>*choose(size, pitchesPerOctave)</b></p>
  79 <p class="p4"><br></p>
  80 <p class="p3">Creates a random scale from the library, constrained by size and pitchsPerOctave if desired.</p>
  81 <p class="p4"><br></p>
  82 <p class="p6"><span class="s2">Scale</span><span class="s3">.choose;<span class="Apple-converted-space"> <span class="Apple-tab-span"> </span>   </span></span>// could be anything</p>
  83 <p class="p6"><span class="s2">Scale</span><span class="s3">.choose(7); <span class="Apple-converted-space">    </span></span>// will be a seven-note scale in its default tuning (could be any)</p>
  84 <p class="p6"><span class="s2">Scale</span><span class="s3">.choose(7, 12); </span>// will be a seven-note scale in a twelve-tone tuning (usually ET!2)</p>
  85 <p class="p2"><br></p>
  86 <p class="p6">// Random seven-note scale in random twelve-tone tuning</p>
  87 <p class="p5">a = <span class="s2">Scale</span>.choose(7, 12).tuning_(<span class="s2">Tuning</span>.choose(12));<span class="Apple-tab-span">  </span></p>
  88 <p class="p5">a.tuning.name;</p>
  89 <p class="p2"><br></p>
  90 <p class="p3"><b>*new(degrees, pitchesPerOctave, descDegrees, tuning, name)</b></p>
  91 <p class="p4"><br></p>
  92 <p class="p3">Creates a <b>Scale</b> from scratch. <b>degrees</b> should be an array of Integers or scale name. If <b>pitchesPerOctave</b> is nil, will guess the most appropriate number based on degrees. <b>tuning</b> can be an instance of <b>Tuning</b> or a symbol; if nil, will be equal temperament of pitchesPerOctave. Specify <b>descDegrees</b> if the Scale should play differently when descending than when ascending; otherwise it should be nil.</p>
  93 <p class="p4"><br></p>
  94 <p class="p5"><span class="s2">Scale</span>.new(#[0, 1, 3, 6, 8, 10, 11], name: <span class="s6">"My ET12"</span>);<span class="Apple-tab-span">        </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="s7">// will be in ET12</span></p>
  95 <p class="p5"><span class="s2">Scale</span>.new(#[0, 3, 7, 10, 15, 19, 22], name: <span class="s6">"My Quarter-Tone"</span>);<span class="Apple-converted-space">  </span><span class="s7">// will be in ET24</span></p>
  96 <p class="p5"><span class="s2">Scale</span>.new(#[0, 6, 17, 21, 30, 39], 43, <span class="s4">\partch</span>, <span class="s6">"My Partch"</span>);</p>
  97 <p class="p4"><br></p>
  98 <p class="p2"><br></p>
  99 <p class="p7"><b><span class="s5">Instance Methods</span></b></p>
 100 <p class="p9"><br></p>
 101 <p class="p3"><b>tuning_(tuning)</b></p>
 102 <p class="p4"><br></p>
 103 <p class="p3">Sets the tuning of the Scale. <b>tuning</b> argument can be either an instance of <b>Tuning</b> or a symbol matching a library tuning.</p>
 104 <p class="p4"><br></p>
 105 <p class="p3"><b>semitones</b></p>
 106 <p class="p4"><br></p>
 107 <p class="p3">Returns a tuned array of semitone values. <b>as(Array)</b> is equivalent; <b>as(List)</b> returns it as a list, etc.</p>
 108 <p class="p4"><br></p>
 109 <p class="p3"><b>cents</b></p>
 110 <p class="p4"><br></p>
 111 <p class="p3">Returns a tuned array of cent values.</p>
 112 <p class="p4"><br></p>
 113 <p class="p3"><b>ratios</b></p>
 114 <p class="p4"><br></p>
 115 <p class="p3">Returns a tuned array of ratios.</p>
 116 <p class="p4"><br></p>
 117 <p class="p3"><b>as(LocalBuf)</b></p>
 118 <p class="p4"><br></p>
 119 <p class="p3">Useful for server-side work.</p>
 120 <p class="p4"><br></p>
 121 <p class="p5">(</p>
 122 <p class="p5">r = {</p>
 123 <p class="p5"><span class="Apple-tab-span">     </span><span class="s2">var</span> scale = <span class="s2">Scale</span>.choose.postln;</p>
 124 <p class="p10"><span class="s3"><span class="Apple-tab-span">   </span></span>SinOsc<span class="s3">.ar(</span></p>
 125 <p class="p5"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>(</p>
 126 <p class="p10"><span class="s3"><span class="Apple-tab-span">   </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span></span>DegreeToKey<span class="s3">.kr(</span></p>
 127 <p class="p5"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span>scale.as(<span class="s2">LocalBuf</span>),</p>
 128 <p class="p6"><span class="s3"><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span></span><span class="s2">MouseX</span><span class="s3">.kr(0,15), </span>// mouse indexes into scale</p>
 129 <p class="p5"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span>scale.stepsPerOctave,</p>
 130 <p class="p6"><span class="s3"><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span>1, </span>// mul = 1</p>
 131 <p class="p6"><span class="s3"><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span>60 </span>// offset by 72 notes</p>
 132 <p class="p5"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span>)<span class="Apple-converted-space"> </span></p>
 133 <p class="p6"><span class="s3"><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span>+ </span><span class="s2">LFNoise1</span><span class="s3">.kr([3,3], 0.04) </span>// add some low freq stereo detuning</p>
 134 <p class="p6"><span class="s3"><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span>).midicps, </span>// convert midi notes to hertz</p>
 135 <p class="p5"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>0,</p>
 136 <p class="p5"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span>0.25</p>
 137 <p class="p5"><span class="Apple-tab-span">     </span>)</p>
 138 <p class="p5">}.play;</p>
 139 <p class="p5">)</p>
 140 <p class="p4"><br></p>
 141 <p class="p5">r.free;</p>
 142 <p class="p4"><br></p>
 143 <p class="p3"><b>size</b></p>
 144 <p class="p4"><br></p>
 145 <p class="p3">Returns the length of the scale.</p>
 146 <p class="p4"><br></p>
 147 <p class="p5"><span class="s2">Scale</span>.ionian.size; <span class="s7">// 7</span></p>
 148 <p class="p5"><span class="s2">Scale</span>.minorPentatonic.size; <span class="s7">// 5</span></p>
 149 <p class="p5"><span class="s2">Scale</span>.ajam.size; <span class="s7">// 7</span></p>
 150 <p class="p5"><span class="s2">Scale</span>.partch_o1.size; <span class="s7">// 6</span></p>
 151 <p class="p4"><br></p>
 152 <p class="p3"><b>pitchesPerOctave</b></p>
 153 <p class="p4"><br></p>
 154 <p class="p3">Returns the size of the pitch class set from which the tuning is drawn.</p>
 155 <p class="p4"><br></p>
 156 <p class="p5"><span class="s2">Scale</span>.ionian.pitchesPerOctave; <span class="s7">// 12</span></p>
 157 <p class="p5"><span class="s2">Scale</span>.minorPentatonic.pitchesPerOctave; <span class="s7">// 12</span></p>
 158 <p class="p6"><span class="s2">Scale</span><span class="s3">.ajam.pitchesPerOctave; </span>// 24--this is a quarter-tone scale</p>
 159 <p class="p5"><span class="s2">Scale</span>.partch_o1.pitchesPerOctave; <span class="s7">// 43</span></p>
 160 <p class="p4"><br></p>
 161 <p class="p3"><b>stepsPerOctave</b></p>
 162 <p class="p4"><br></p>
 163 <p class="p3">Usually 12, but may be different if the current tuning has a stretched or compressed octave. Needed for degreeToKey.</p>
 164 <p class="p4"><br></p>
 165 <p class="p5"><span class="s2">Scale</span>.new((0..14), 15, tuning: <span class="s4">\wcAlpha</span>).stepsPerOctave;<span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span><span class="s7">// ~ 11.7</span></p>
 166 <p class="p5"><span class="s2">Scale</span>.new(#[0, 3, 6, 9, 12], 13, tuning: <span class="s4">\bp</span>).stepsPerOctave;<span class="Apple-converted-space">  <span class="Apple-tab-span"> </span></span><span class="s7">// ~ 19.02</span></p>
 167 <p class="p4"><br></p>
 168 <p class="p3">but note:</p>
 169 <p class="p4"><br></p>
 170 <p class="p6"><span class="s2">Scale</span><span class="s3">.ajam.stepsPerOctave; <span class="Apple-tab-span"> </span></span>// 12 -- quarter-tone scales have normal octaves</p>
 171 <p class="p4"><br></p>
 172 <p class="p3"><b>at, wrapAt</b></p>
 173 <p class="p4"><br></p>
 174 <p class="p3">These access the array generated by <b>semitones</b>.</p>
 175 <p class="p2"><br></p>
 176 <p class="p5">a = <span class="s2">Scale</span>.major;</p>
 177 <p class="p5">a.wrapAt(4);<span class="Apple-converted-space">  </span><span class="s7">// 7</span></p>
 178 <p class="p5">a.wrapAt(5);<span class="Apple-converted-space">  </span><span class="s7">// 9</span></p>
 179 <p class="p5">a.wrapAt(6);<span class="Apple-converted-space">  </span><span class="s7">// 11</span></p>
 180 <p class="p5">a.wrapAt(7);<span class="Apple-converted-space">  </span><span class="s7">// 0</span></p>
 181 <p class="p2"><br></p>
 182 <p class="p3"><b>degreeToFreq(degree, rootFreq, octave)</b></p>
 183 <p class="p4"><br></p>
 184 <p class="p3">Returns a frequency based on current tuning and <b>rootFreq</b> argument.</p>
 185 <p class="p4"><br></p>
 186 <p class="p5"><span class="s2">Scale</span>.major.degreeToFreq(2, 60.midicps, 1);<span class="Apple-converted-space">  <span class="Apple-tab-span">   </span><span class="Apple-tab-span">    </span></span><span class="s7">// 659.25511...</span></p>
 187 <p class="p5"><span class="s2">Scale</span>.major(<span class="s4">\just</span>).degreeToFreq(2, 60.midicps, 1); <span class="Apple-tab-span">  </span><span class="s7">// 654.06391...</span></p>
 188 <p class="p4"><br></p>
 189 <p class="p3"><b>degreeToRatio(degree, octave)</b></p>
 190 <p class="p4"><br></p>
 191 <p class="p3">Returns a ratio based on current tuning.</p>
 192 <p class="p4"><br></p>
 193 <p class="p5"><span class="s2">Scale</span>.major.degreeToRatio(2, 1).round(0.001);<span class="Apple-tab-span">        </span><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="s7">// 2.52</span></p>
 194 <p class="p5"><span class="s2">Scale</span>.major(<span class="s4">\just</span>).degreeToRatio(2, 1).round(0.001);<span class="Apple-tab-span"> </span><span class="s7">// 2.5</span></p>
 195 <p class="p11"><br></p>
 196 <p class="p2"><br></p>
 197 <p class="p7"><b><span class="s5">Examples</span></b></p>
 198 <p class="p2"><br></p>
 199 <p class="p5">(</p>
 200 <p class="p5">s.waitForBoot({</p>
 201 <p class="p5"><span class="Apple-tab-span">     </span>a = <span class="s2">Scale</span>.ionian;</p>
 202 <p class="p2"><span class="Apple-tab-span">     </span></p>
 203 <p class="p5"><span class="Apple-tab-span">     </span>p = <span class="s2">Pbind</span>(</p>
 204 <p class="p5"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span><span class="s4">\degree</span>, <span class="s2">Pseq</span>([0, 1, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 2, 1, 0, <span class="s4">\rest</span>], <span class="s2">inf</span>),</p>
 205 <p class="p5"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span><span class="s4">\scale</span>, <span class="s2">Pfunc</span>({ a }, <span class="s2">inf</span>),</p>
 206 <p class="p5"><span class="Apple-tab-span">     </span><span class="Apple-tab-span">    </span><span class="s4">\dur</span>, 0.25</p>
 207 <p class="p5"><span class="Apple-tab-span">     </span>);</p>
 208 <p class="p2"><span class="Apple-tab-span">     </span></p>
 209 <p class="p5"><span class="Apple-tab-span">     </span>q = p.play;</p>
 210 <p class="p5">})</p>
 211 <p class="p5">)</p>
 212 <p class="p2"><br></p>
 213 <p class="p6">// change scale</p>
 214 <p class="p5">a = <span class="s2">Scale</span>.phrygian;</p>
 215 <p class="p2"><br></p>
 216 <p class="p6">// change tuning</p>
 217 <p class="p5">a.tuning_(<span class="s4">\just</span>);</p>
 218 <p class="p2"><br></p>
 219 <p class="p6">// can also set tuning at creation time</p>
 220 <p class="p5">a = <span class="s2">Scale</span>.ionian(<span class="s4">\pythagorean</span>);</p>
 221 <p class="p2"><br></p>
 222 <p class="p6">// if you use a tuning with the wrong number of pitches per octave,</p>
 223 <p class="p6">// you get a warning and the scale reverts to default tuning</p>
 224 <p class="p5">a.tuning_(<span class="s4">\partch</span>);</p>
 225 <p class="p2"><br></p>
 226 <p class="p6">// random scale</p>
 227 <p class="p5">(</p>
 228 <p class="p5">a = <span class="s2">Scale</span>.choose(7, 12);</p>
 229 <p class="p5">[a.name, a.tuning.name].postln;</p>
 230 <p class="p5">)</p>
 231 <p class="p2"><br></p>
 232 <p class="p5">(</p>
 233 <p class="p6">// or make up your own arbitrary scales and tunings</p>
 234 <p class="p5">a = <span class="s2">Scale</span>.new(</p>
 235 <p class="p5"><span class="Apple-tab-span">     </span>#[0, 2, 4, 5, 7, 9, 10],</p>
 236 <p class="p5"><span class="Apple-tab-span">     </span>12,</p>
 237 <p class="p5"><span class="Apple-tab-span">     </span><span class="s2">Tuning</span>.new([0, 0.8, 2.1, 3, 4.05, 5.2, 6, 6.75, 8.3, 9, 10.08, 11.5]),</p>
 238 <p class="p12"><span class="s3"><span class="Apple-tab-span">   </span></span>"Custom"<span class="s3"><span class="Apple-converted-space"> </span></span></p>
 239 <p class="p5">);</p>
 240 <p class="p5">)</p>
 241 <p class="p2"><br></p>
 242 <p class="p6">// tuning has its own class</p>
 243 <p class="p5">t = <span class="s2">Tuning</span>.werckmeister;</p>
 244 <p class="p2"><br></p>
 245 <p class="p5">a = <span class="s2">Scale</span>.lydian(t);</p>
 246 <p class="p2"><br></p>
 247 <p class="p5">q.stop;</p>
 248 <p class="p2"><br></p>
 249 <p class="p6">// getting info</p>
 250 <p class="p5">a.name;</p>
 251 <p class="p5">a.degrees;</p>
 252 <p class="p5">a.semitones;</p>
 253 <p class="p5">a.ratios;<span class="Apple-converted-space"> </span></p>
 254 <p class="p2"><br></p>
 255 <p class="p5">a.tuning.name;</p>
 256 <p class="p5">a.tuning.semitones;</p>
 257 <p class="p5">a.tuning.ratios;</p>
 258 <p class="p2"><br></p>
 259 <p class="p6">// cmd-J to see scale and tuning dictionaries in full</p>
 260 <p class="p10">ScaleInfo</p>
 261 <p class="p10">TuningInfo</p>
 262 <p class="p13"><br></p>
 263 <p class="p14">// for ascending/descending scales, use Pavaroh</p>
 264 <p class="p15">(</p>
 265 <p class="p16">Pbind<span class="s3">(</span><span class="s8">\note</span><span class="s3">, </span>Pavaroh<span class="s3">(</span></p>
 266 <p class="p15"><span class="Apple-tab-span">    </span><span class="s9">Pseq</span>([0, 1, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 2, 1, 0, <span class="s8">\rest</span>], 2),</p>
 267 <p class="p15"><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="s9">Scale</span>.melodicMinor,</p>
 268 <p class="p15"><span class="Apple-tab-span">    </span><span class="Apple-tab-span">    </span><span class="s9">Scale</span>.melodicMinorDesc</p>
 269 <p class="p15"><span class="Apple-tab-span">    </span>),</p>
 270 <p class="p15"><span class="Apple-tab-span">    </span><span class="s8">\dur</span>, 0.25</p>
 271 <p class="p15">).play;</p>
 272 <p class="p15">)</p>
 273 </body>
 274 </html>