FMINST

Basic FM synthesis.

in RTcmix/insts/std

quick syntax:

FMINST(outsk, dur, AMP, CARFREQ (Hz/oct.pc), MODFREQ (Hz/oct.pc), LOWINDEX, HIGHINDEX[, PAN, WAVETABLE, INDEXENV])

CAPITALIZED parameters are pfield-enabled for table or dynamic control (see the maketable or makeconnection scorefile commands). Parameters after the [bracket] are optional and default to 0 unless otherwise noted.

Param Field Parameter Units Dynamic Optional Notes
p0 start time seconds no no  
p1 duration seconds no no  
p2 amplitude absolute, for 16-bit soundfiles: 0-32768 yes no  
p3 frequency of carrier Hz or oct.pc* yes no * see note
p4 frequency of modulator Hz or oct.pc* yes no * see note
p5 FM index low point - yes no  
p6 FM index high point - yes no  
p7 pan 0-1 stereo; 0.5 is middle yes yes default: 0
p8 carrier and modulator wavetable reference to a pfield table-handle yes no  
p9 index envelope reference to a pfield table-handle yes no  

NOTE: oct.pc format generally will not work as you expect for p3 and p4 (osc freq) if the pfield changes dynamically. Use Hz instead in that case.

Parameters labled as Dynamic can receive dynamic updates from a table or real-time control source.

Author Brad Garton, rev for v4, JGG, 7/12/04

FMINST creates sound output usig frequency modulation: a type of distortion synthesis where the ‘pitch’ of one waveform (the carrier) of frequency fc is modulated by another waveform (the modulator) with frequency fm and modulation index I (defined by the maximum amplitude deviation of the modulator oscillator divided by its frequency). The resultant sound consists of the carrier frequency as well as a number of sidebands of frequencies fc ± kfm, where k is an integer series increasing from 0 (the carrier frequency). The amplitude of the sidebands over time is determined by a Bessel function of the first kind Jk(I). The modulation index I is a rough guide to how many sidebands will be present in the resultant signal. Negative frequencies are possible, resulting in a 180° out-of-phase sideband at the absolute value of that frequency. Negative amplitudes are also possible, resulting in a reversal of phase at that sideband (paraphrased from Dodge and Jerse, 1985). Note that when negative-amplitude sidebands are added to the corresponding positive-amplitude sidebands that the resultant amplitude of the sideband will be modified (probably reduced).

Usage Notes

FM has traditionally been considered a computationally efficient method to create complex, time-varying spectra using just two oscillators. A very low modulation index and/or frequency will result in vibrato on the carrier signal. As the modulation increases, the spectrum will become increasingly richer. FMINST provides for a time-varying index of modulation based on the index control envelope (p9) in conjunction with p4 and p5 of the instrument (which define the low point and high points of the index envelope).

Sample Scores

very basic:

   rtsetparams(44100, 2)
   load("FMINST")
   
   dur = 7
   amp = 30000
   carfreq = cpspch(8.00)
   modfreq = 179
   minindex = 0
   maxindex = 10
   
   env = maketable("line", 1000, 0, 0, 3.5,1, 7,0)
   wavetable = maketable("wave", 1000, "sine")
   guide = maketable("line", "nonorm", 1000, 0,1, 7,0)
   
   FMINST(0, dur, amp * env, carfreq, modfreq, minindex, maxindex, pan=0.5,
      wavetable, guide)

slightly more advanced:

   rtsetparams(44100, 2)
   load("FMINST")
   
   print_off()
   
   notedur = 0.5
   
   maxamp = 5000
   amp = maketable("linebrk", "nonorm", 1000, 0, 500, maxamp, 500, 0)
   
   wavetable = maketable("wave", 1000, "sine")
   guide = maketable("line", 1000, 0,1, 2,0)
   
   freq = 8.00
   for (start = 0; start < 60; start = start + 0.1) {
      pan = random()
      FMINST(start, notedur, amp, freq, 179, 0, 10, pan, wavetable, guide)
      freq = freq + 0.002
   }

See Also

maketable, AMINST, MULTIFM, MULTIWAVE, WAVETABLE, WAVESHAPE, WAVY, WIGGLE