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PureData: Frequency


In order to to create sound, each oscillator object takes a numerical input which represents a frequency in Hertz. This number determines the number of times the oscillator will make its waveform during one second. By using a creation argument (a default setting typed into the object box when the object is first created), we can set the initial frequency of an oscillator. And by using an [hslider] (Horizontal Slider), a Number or a Message, we can send numerical messages to change the frequency of the oscillator.


Audio vs Message Cables

In all the examples so far, notice the difference between the cable for messages, which is thin, and the cable for audio, which is thicker. Messages can be sent to audio objects (those with a ~ in their name), but usually audio cannot be sent to message objects (those without a ~ in their name). Attempting to do so will cause Pd to print "error: can't connect signal outlet to control inlet", and it will not allow the connection to be made.


MIDI and Frequency

For many musical applications, the MIDI scale is a useful way of controlling the frequency of an oscillator. One can imagine the MIDI scale as a piano keyboard with 128 keys on it, and each key has been marked with a frequency in Hertz which represents that musical note. Below is a part of the table which makes up the MIDI scale. Three octaves are shown. The most important thing to notice is that a note which is one octave higher than another note (for example, the three A notes of 110 Hz, 220 Hz and 440 Hz) has a frequency which is twice that of the lower note.

    MIDI                 MIDI                   MIDI
    Note   Frequency     Note   Frequency       Note   Frequency

 C  36  65.4063913251    48   130.8127826503    60   261.6255653006
 Db 37  69.2956577442    49   138.5913154884    61   277.1826309769
 D  38  73.4161919794    50   146.8323839587    62   293.6647679174
 Eb 39  77.7817459305    51   155.5634918610    63   311.1269837221
 E  40  82.4068892282    52   164.8137784564    64   329.6275569129
 F  41  87.3070578583    53   174.6141157165    65   349.2282314330
 Gb 42  92.4986056779    54   184.9972113558    66   369.9944227116
 G  43  97.9988589954    55   195.9977179909    67   391.9954359817
 Ab 44  103.8261743950   56   207.6523487900    68   415.3046975799
 A  45  110.0000000000   57   220.0000000000    69   440.0000000000
 Bb 46  116.5409403795   58   233.0818807590    70   466.1637615181
 B  47  123.4708253140   59   246.9416506281    71   493.8833012561

For the complete table, see http://www.phys.unsw.edu.au/jw/notes.html

The object in Pd which turns a MIDI note into a frequency in Hertz is called [mtof], or MIDI to Frequency. When the MIDI note "69" is sent to it, for example, it will output the number "440". Looking at our examples, you can see that each slider has a range of 0-127, and this is converted by an [mtof] object to a frequency which tells the oscillator what to do.

Of course, you aren't limited to the notes that Western music schools teach you are correct. So-called "microtonal" notes are possible as well. If you hold down the Shift key while using the mouse to change a Number, decimal numbers are possible, so that you can tell an [osc~] to play MIDI note number 76.89, for example.

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