I'm curious - in your patch SexyBoy.pch, why is the master/slave cable from the Formant Osc to the three Slave Oscs routed through an amplifier module? What does this do?

For that matter, does anybody know precisely what the master/slave signal is? Is it just the sum of keyboard tracking + any pitch mod input signals present at the master osc, like a control mixer? Or is the data in some format that is different from the sum of control signals present at the master osc?

Digital oscillators are generally of the so called accumulator/divider type. Its a very simple algoritm where one increases a pointer into a wavetable. The pointer is a single memory location or processor register of say 24 bit or 32 bit, depending on the processor used. The 24 bit range can hold a number between -2^23 and 2^23. This range is scaled down to represent -180 degrees and 180 degrees phase position within a single cycle of the waveform. Repeatedly adding a constant value to the pointer register increases the phase position and if the register overflows the so called carry bit is simply thrown away and the remainder of the addition stays in the register. If the pointer register is called P, the increment value is called I and the phase position value at 180 degrees would be R, the function would simply be P = (P + I) modulo R. If the value in P would be taken as the output we would now have an upward ramping sawtooth wave and the frequency would depend on the value I, the bigger a value in I the faster the ramp goes up and the higher the pitch. The value in P can also be used to extract other waveforms, a squarewave can be simply extracted by looking at the sign of P, if positive then the squarewave level is max and if negative its min. The value can also be used as a pointer into a block of memory representing a single cycle of an arbitrary waveform. If there is enough bit depth P can also be used as a pointer into a multicycle waveform like a soundsample in a sampler.

The value in the I register is the pitch parameter and when having a closer look at it it has a linear curve, so not a V/Oct curve but a V/Hertz curve. Although the internal algoritms in the Nord Modular are a well kept factory secret, the grey input response follows exactly the behaviour of the I value in an ccumulator/divider algoritm. The maximum value range in the NM is between -2^23 and 2^23, which are scaled down to -256 and 256 'Clavia' units. Connecting a constant module to a grey input will reveal that if the constant value is 0 the frequency of the oscillator is 0 Hertz, in other words it stopped and the value at the output is the waveform value for the momentary phase position where the oscillator was when stopped, so a red output value somewhere between -64 and 64 units. The frequency of the oscillator when the constant value is set to 1 unit would be expected to be the system samplerate divided by two divided by 256 (256 divided by (1 Unit times 256)) = 187.5 Hz. Every unit that you go higher would increase the frequency by another 187.5 Hz. But in fact the frequency is exactly twice as low on the Nord Modular, my guess is that this has to do with the anti-aliasing algoritm used. So on the NM 1 unit gives a frequency of 93.75 Hz, increasing the constant module to a value of 8 will give exactly 750 Hz (8*93.75), 16 will give 1500 Hz, 32 will give 3000 Hz, 64 will give 6000 Hz, etc. This reveals that the maximum frequency on an oscillator is 24kHz. Putting the output of the constant module through an amplifier module will give the possibility of multiplying the value of 64 units by four to reach the maximum value of 512 that gives this 24kHz.

But the constant value can also be negative and a value of minus 1 unit also gives a tone of 93.75 Hz. The 'mathematical' frequency however is minus 93.75 Hertz. Yes, you can have negative frequencies with digital oscillators! A negative frequency will sound with the same pitch as the normal positive frequency, but the phase is reversed. So the upramping sawwave has now become a downramping sawwave with the same frequency! So applying a negative value to a grey input inverts the waveform the same way as multiplying it with a value of -64 units.

Clavia never expected people to use the grey input for other means as connecting a slave oscillator to exactly track a master oscillator, in fact at the time of the release of the NM they didn't realise that treatments of the grey signal gives very interesting options. E.g. imagine alternating the grey input value between a positive and its negated value. Applying this too a sawwave will make the ramp go up or down in the rate of the modulation. And this is exactly the same as a particular type of softsync found on some analog oscillators. The way to do this is simple. Take a master oscillator set to a squarewave, put the grey output into one input of a gain controller module and the red waveform output in the other input. On the output the grey value is now negated in the rate of the squarewave. Feed this signal into the grey input of a slave oscillator and play with the rate control of the slave oscillator. A smooth syncsweep is the result, which sounds less harsh than using the red sync input of a slave. A popular analog sound was to use this type of softsync with a squarewave as second or slave oscillator.

You will hear a slow drift in the sound, this is due to the fact that in the aritmetic used in DSP's there is a very small roundoff error of one bit, well, actually the negative range has one more bitvalue than the positive range as the total range has an even number of possible value, as one of the positive values is snatched away from the positive range to be used a zero. This drift can be speeded up a little to give a PWM like character to the waveform by supplying a very little bit of a constant value to the FMA input on the slave.

This works as the value on the FMA input is actually added directly to the grey input value on the slave oscillator in the oscillators algoritm. This is nicely demonstrated by first silencing the slave by applying a value of zero to its grey input, then conneting the grey signal to the FMA input instead and setting the inputknob of the FMA input to around 105. This will make the slave track the master, although slightly detuned in a nice 'analog' way.

Whatever you now do to the tune controls on the slave has no effect whatsoever as the internal signalrouting of the slave signal in the slave oscillator is grey input -> scale grey value by Partials knob and Detune knob settings -> add signal from FMA input after being scaled by FMA knob -> use this final value to 'increment' the 'phase pointer' register to calculate the momentary phase of the waveform.

AM modulating the output of the gain controller module in the GreyTest3.pch controls the sysncsweep. Normally one would avoid the grey sigan to become zero, as that would stop the oscillator, so this best to use e.g. two amplifier modules, one set to 1/4 and the other set to 4 and morph with a crossfade mixer between the two outputs of the amplifier modules.

Of course nothing is sacred in NM land, so its much fun modulating this signal in other way and/or combining it with modulating the FMA input.

A very nice feature of the NM oscillators is that if you change the pulsewidth of the squarewave the waveform is shifted in level up or down as well. This nicely compensates detuning features when PMW is applied in the basic softsync patch.

Instead of modulating the grey output signal of a master oscillator by a squarewave any other wave will do just fine as well, although the resulting waves will be more complex 'mathematically'.

A special case is when we connect a sinewave directly to the grey input of a sinewave slave oscillator. This yields the so called formant FM or 'zero frequency' FM. Remember that if the grey input receives a avlue of zero the frequency ogf the oscillator is zero Hertz. If a symmetrical signal is fed to this grey input the slave oscillator is swept between a positive and a negative frequency around zero Hz depending on the level of the signal, e.g. if the signal level is reduced to swing between minus and plus 1 unit the slave is swept between minus and plus 93.75 Hz. So the frequency is swept up from zero to the plus frequency, sewpt down to 0 Hz, swept to the minus frequency and swept back to 0 Hz again in the rhythm of the modulating frequency. The slave will now inherit the pitch of the master oscillator as it is swept in that rhythm, but a strong formant area around the plus/minus frequency. When using sinewaves the math is the same as for FM, but simpler to calculate as one frequency in the FM equations is now zero. The level of the modulating sinewave can be set before the grey input or be set by the Partials and Detune knobs, as those are in fact attenuator knobs for the grey signal. Changing the pitch of the master oscillator reveals that the formant area stays in the same position in the spectrum.

The resulting sound does have a distinct FM-sound quality which is nice for blips etc.

Using the 6-Sines slave oscillator allows for very complex blip patterns.

LFO slaves also have grey inputs and these can be modulated in interesting ways as well. E.g. blocking the grey signal rhythmically starts and stops the LFO.

Or route the grey signal through e.g. an AD envelope to create variation in noodles, etc.

BTW, FMA and FMB are the following accumulator/divider equations: 1: P = (I + FMA + P) modulo R, where the output (phase position) is P 2: P = (I + P) modulo R, where the output (phase position) is (P + FMB)

Hope this all was not too technical and has shed some more light on the (now not so) mysterious grey signals.