Skip to content
Permalink
Browse files

add pitch division graphic.

  • Loading branch information...
delta-6400 committed Jun 7, 2019
1 parent 8f0df9e commit 80284bec86445e3578e12507059c0dfe78a9a757
Binary file not shown.
@@ -200,15 +200,17 @@ Many synthesists are likely familiar with the [overtone](https://en.wikipedia.or

The undertone (or subharmonic) series is created by *dividing* the fundamental frequency by integers, rather than multiplying it. For a given frequency `f`, the undertone series would be all frequencies `f/n`, where `n` is an integer. For example at `100Hz`, the undertone series would be `50Hz, 33Hz, 25Hz, 20Hz, ...` The intervals correspond to moving down an octave, followed by moving down a fifth, then down by a fourth, and so on.

MANGROVE can create the undertone series by setting the impulse duration to exceed the period of the oscillator core. Begin by setting *FORMANT* to noon and *BARREL* to minimum (CW) (indicated on the panel by *utone*, a helpful reminder for when you want to create the undertone series!). Set *AIR* to noon, switch to *constant wave*, and monitor the *FORMANT* output. The output should be a ramp wave - every time the impulse is triggered by the oscillator core, it ramps slowly to its maximum and then falls immediately to its minimum before being retriggered.
MANGROVE can create the undertone series by setting the impulse duration to exceed the period of the oscillator core. Begin by setting *FORMANT* to noon and *BARREL* to minimum (CW) (indicated on the panel by *utone*, a helpful reminder for when you want to create the undertone series!). Set *AIR* to noon, switch to *constant wave*, and monitor the *FORMANT* output. The output should be a ramp wave - every time the impulse is triggered by the oscillator core, it ramps slowly to its maximum and then falls immediately to its minimum before being retriggered. Slowly decrease *FORMANT* (CCW), which increases the duration of each impulse. Eventually, this duration will exceed the oscillator core frequency, and you will hear the *FORMANT* output drop an octave.

Slowly decrease *FORMANT* (CCW), which increases the duration of each impulse. Eventually, this duration will exceed the oscillator core frequency, and you will hear the *FORMANT* output drop an octave. Because the impulse duration is longer than the oscillator core period, two clock cycles of the oscillator core must complete before the impulse generator is available to be retriggered. As such, MANGROVE is now generating a new waveform with a period of repetition twice as long as that of the oscillator core, meaning the frequency of this new waveform is half the oscillator core! Halving the frequency drops the pitch by an octave.
![Pitch Division Waveforms](./graphics/waveform_pitch_division.jpg)

Because the impulse duration is longer than the oscillator core period, two clock cycles of the oscillator core must complete before the impulse generator is available to be retriggered. As such, MANGROVE is now generating a new waveform with a period of repetition twice as long as that of the oscillator core, meaning the frequency of this new waveform is half the oscillator core! Halving the frequency drops the pitch by an octave.

Continuing to decrease *FORMANT* will cause the impulse duration to exceed two periods of the oscillator core. The impulse generator will not be retriggered until after the oscillator core completes three cycles, creating a waveform at 1/3 the frequency of the oscillator core.

Further decreasing *FORMANT* will drop the frequency to 1/4 the oscillator core, then 1/5, and so on, filling out the rest of the undertone series!

![Frequency Division Spectrogram](./spectra/pitch_divisions.png)
![Pitch Division Spectrogram](./spectra/pitch_divisions.png)

Mixing the *FORMANT* output in this state with the *SQUARE* output (which remains at the oscillator core frequency as it is unaffected by the *BARREL* and *FORMANT* controls) is an effective way to fatten your synth voice with subharmonics that are spectrally richer than typical squarewave subharmonics generated by a clock divider or flip flop.

@@ -317,7 +319,7 @@ The rhythmic pattern before the modulator pitch starts rising represents an undu

![Audio-rate modulation of*AIR* with ratio sweep, spectrogram](./spectra/air_arm_ratio_sweep.png)

Finally, *AIR* is modulated by an audio rate sine wave tuned to MANGROVE. *FORMANT* and *BARREL* are both swept by hand using the knobs. The sound is reminiscent of traditional FM but with less atonality, instead animating the harmonic content of the signal.
Finally, *AIR* is modulated by an audio rate sine wave tuned to MANGROVE. *FORMANT* and *BARREL* are both swept by hand using the knobs. The sound is reminiscent of traditional FM but with less atonality, instead animating the harmonic content of the signal. Notice that the effect of the audio-rate modulation changes drastically as the *FORMANT* and *BARREL* settings are changed.

![Audio-rate modulation of *AIR* with handswept *FORMANT/BARREL*, spectrogram](./spectra/air_arm_formant_and_barrel_sweep.png)

BIN +1.15 MB (190%) mangrove/mangrove.pdf
Binary file not shown.

0 comments on commit 80284be

Please sign in to comment.
You can’t perform that action at this time.