cpsoct — Converts an octave-point-decimal value to cycles-per-second.


Converts an octave-point-decimal value to cycles-per-second.


cpsoct (oct)  (no rate restriction)

where the argument within the parentheses may be a further expression.


cpsoct and its related opcodes are really value converters with a special function of manipulating pitch data.

Data concerning pitch and frequency can exist in any of the following forms:

Table 7. Pitch and Frequency Values

Name Abbreviation
octave point pitch-class (8ve.pc) pch
octave point decimal oct
cycles per second cps
Midi note number (0-127) midinn

The first two forms consist of a whole number, representing octave registration, followed by a specially interpreted fractional part. For pch, the fraction is read as two decimal digits representing the 12 equal-tempered pitch classes from .00 for C to .11 for B. For oct, the fraction is interpreted as a true decimal fractional part of an octave. The two fractional forms are thus related by the factor 100/12. In both forms, the fraction is preceded by a whole number octave index such that 8.00 represents Middle C, 9.00 the C above, etc. Midi note number values range between 0 and 127 (inclusively) with 60 representing Middle C, and are usually whole numbers. Thus A440 can be represented alternatively by 440 (cps), 69 (midinn), 8.09 (pch), or 8.75 (oct). Microtonal divisions of the pch semitone can be encoded by using more than two decimal places.

The mnemonics of the pitch conversion units are derived from morphemes of the forms involved, the second morpheme describing the source and the first morpheme the object (result). Thus cpspch(8.09) will convert the pitch argument 8.09 to its cps (or Hertz) equivalent, giving the value of 440. Since the argument is constant over the duration of the note, this conversion will take place at i-time, before any samples for the current note are produced.

By contrast, the conversion cpsoct(8.75 + k1) which gives the value of A440 transposed by the octave interval k1. The calculation will be repeated every k-period since that is the rate at which k1 varies.

[Note] Note

The conversion from pch, oct, or midinn into cps is not a linear operation but involves an exponential process that could be time-consuming when executed repeatedly. Csound now uses a built-in table lookup to do this efficiently, even at audio rates. Because the table index is truncated without interpolation, pitch resolution when using one of these opcodes is limited to 8192 discrete and equal divisions of the octave, and some pitches of the standard 12-tone equally-tempered scale are very slightly mistuned (by at most 0.15 cents).


Here is an example of the cpsoct opcode. It uses the file cpsoct.csd.

Example 180. Example of the cpsoct opcode.

See the sections Real-time Audio and Command Line Flags for more information on using command line flags.

; Select audio/midi flags here according to platform
-odac     ;;;RT audio out
;-iadc    ;;;uncomment -iadc if RT audio input is needed too
; For Non-realtime ouput leave only the line below:
; -o cpsoct.wav -W ;;; for file output any platform

sr = 44100
ksmps = 32
nchnls = 2
0dbfs = 1

instr 1 ; Convert octave-point-decimal value into Hz

ioct =	p4
icps =	cpsoct(ioct)
	print icps
asig	oscil 0.7, icps, 1
	outs  asig, asig

;sine wave.
f 1 0 16384 10 1

i 1 0 1 8.75
i 1 + 1 8.77
i 1 + 1 8.79
i 1 + .5 6.30


Its output should include lines like this:

instr 1:  icps = 440.000
instr 1:  icps = 446.110
instr 1:  icps = 452.344
instr 1:  icps = 80.521

See also

Pitch Converters: Functions