Math
Arithmetic on any signal, lane by lane: add, multiply, divide, power and more on audio or control operands. The output runs at the rate of its fastest input.
- Utility
- Since 0.2.0
- math
- add
- multiply
- divide
- gain
- arithmetic
- utility
Math does arithmetic on signals, lane by lane. Feed it audio and it works on every sample; feed it control lanes and it works once per block.
What it does#
Operation chooses how lane n of A and lane n of B become lane n of the output. The two-operand operations are Add, Subtract, Multiply, Divide, Modulo, Power, Minimum, Maximum, Average and Absolute difference; the one-operand operations (Negate, Absolute, Floor, Ceiling, Round, Square root, Sign) use A and ignore B.
The inputs follow their cables. If A or B carries audio, the output is audio; if both carry control, or nothing at all, the output is control. A control operand against an audio operand is read lane by lane, so a one-lane control B applies to every audio channel and a two-lane control B applies one value per channel. When B is not connected, every lane of B is B when unconnected. When A is not connected it is 0.
Every operation is defined for every input: dividing by 0 gives 0, the square root and power of a negative number keep its sign, and any result that would not be a finite number becomes 0. Math never outputs NaN or infinity.
When to use it#
Use it to scale a signal (Multiply), to offset a control (Add), to ring-modulate two oscillators (Multiply on two audio inputs), to keep a level inside a limit (Minimum, Maximum) or to quantise a control (Round, Floor). For a plain level control with a public knob, Gain is simpler. To turn a signal into a gate, use Compare.
Ports#
| Port | Direction | Signal | Lanes |
|---|---|---|---|
a | Input | Audio or control (follows the cable) | Inferred from the cable |
b | Input | Audio or control (follows the cable) | Inferred from the cable |
out | Output | Audio or control (follows the cable) | Inferred from the cable |
Parameters#
| Parameter | Label | Range | Default | Unit | Scale | Notes |
|---|---|---|---|---|---|---|
op | Operation | 0 to 16 | 0 | linear | The lane-wise operation. Add through Absolute difference combine A and B; Negate through Sign transform A alone and ignore B. Choices: 0 Add, 1 Subtract, 2 Multiply, 3 Divide, 4 Modulo, 5 Power, 6 Minimum, 7 Maximum, 8 Average, 9 Absolute difference, 10 Negate, 11 Absolute, 12 Floor, 13 Ceiling, 14 Round, 15 Square root, 16 Sign. | |
b_default | B when unconnected | -8 to 8 | 0 | linear | Value used for every lane of B when nothing is connected to it. Multiply with 0.5 halves a signal. Shown when op is 0 or 1 or 2 or 3 or 4 or 5 or 6 or 7 or 8 or 9. |
Operation (op)#
Which arithmetic to apply, a discrete choice. Divide and Modulo give 0 when B is 0; Modulo takes the sign of B; Power and Square root keep the sign of A; Round rounds halves away from zero. Changing it takes effect at the next block.
B when unconnected (b_default)#
The value used for every lane of B when nothing is connected to B, from -8 to 8. Changes are smoothed over 5 ms so moving it does not click. It is hidden for the one-operand operations, which ignore B.
Tips#
- To halve audio, set Operation to Multiply and B when unconnected to 0.5. Every channel is halved.
- For per-channel gain from a control, connect a control bundle with one lane per channel to B and Multiply: lane 1 sets the first channel, lane 2 the second.
- Multiply two audio oscillators for ring modulation: you hear the sum and difference of their frequencies.
- Add B when unconnected to an LFO to move its centre before it reaches a parameter socket.
- Math does not clamp. Follow a boost with a Limiter, or shape a control with Scale.
See also#
Gain, Compare, Scale, Control lanes, Multichannel audio.
Help patches
Each help patch is an ordinary Toy that teaches one idea. The diagram shows the Patch; the preview shows its Frame. Open it in TuneToys to play and edit it.
1. Halve a signal
beginner Teaches: op, b_default
Incoming audio multiplied by 0.5, with a scope before and after.
MIDI1 lane
Audio2ch
Fundamental pitch, capped below Nyquist; detune uses cents. Range: 20–20000 Hz. Default: 220 Hz. Logarithmic scale. Units: Hz.
Hz
Output gain. Range: 0–0.5 ×. Default: 0.12 ×. Linear scale. Units: linear gain.
×
Continuous sine/triangle/saw/pulse morph; only its two neighboring waveforms are evaluated. Range: 0–3. Default: 0. Linear scale. Units: unitless. Marks: 0 Sine, 1 Triangle, 2 Saw, 3 Pulse.
Triangle
Pulse duty cycle with a frequency-dependent safe edge width. Range: 0.05–0.95. Default: 0.5. Linear scale. Units: unitless.
Selects the implemented algorithm. Choices are discrete and are not LFO targets. Range: 0–7. Default: 0. Linear scale. Units: unitless.
Cycle offset; Gate rising edges restart phase from this position. Range: 0–1 cycles. Default: 0 cycles. Linear scale. Units: cycles.
cycles
Pitch offset in cents. Range: -1200–1200 cents. Default: 0 cents. Linear scale. Units: cents.
cents
On or off. A rising edge retriggers; held on runs the oscillator or envelope. A control cable switches it at 0.5. Range: 0–1. Default: 1. Linear scale. Units: unitless.
Semitones a full pitch bend on the MIDI input moves the note, up or down. Range: 0–48 st. Default: 2 st. Linear scale. Units: st.
st
Time constant of the slide from one MIDI note's pitch to the next; 0 jumps. Range: 0–2000 ms. Default: 0 ms. Linear scale. Units: ms.
ms
A2ch
B1 lane
Out2ch
The lane-wise operation. Add through Absolute difference combine A and B; Negate through Sign transform A alone and ignore B. Range: 0–16. Default: 2. Linear scale. Units: unitless.
Value used for every lane of B when nothing is connected to it. Multiply with 0.5 halves a signal. Range: -2–2. Default: 0.5. Linear scale. Units: unitless.
Audio2ch
Connections as text
- Oscillator audio output connected to Math a input
- Math out output connected to Patch outputs audio input
- Nothing is connected to B, so every channel of B is B when unconnected.
- Multiply by 0.5 halves the level of every channel. Compare the two scopes.
- Try Add with a small B for a DC offset, or Minimum to flatten the peaks.
2. Ring modulation
intermediate Teaches: op
Two oscillators multiplied sample by sample into a ring-modulated tone.
MIDI1 lane
Audio2ch
Fundamental pitch, capped below Nyquist; detune uses cents. Range: 20–20000 Hz. Default: 220 Hz. Logarithmic scale. Units: Hz.
Hz
Output gain. Range: 0–0.5 ×. Default: 0.12 ×. Linear scale. Units: linear gain.
×
Selects the implemented algorithm. Choices are discrete and are not LFO targets. Range: 0–7. Default: 0. Linear scale. Units: unitless.
Cycle offset; Gate rising edges restart phase from this position. Range: 0–1 cycles. Default: 0 cycles. Linear scale. Units: cycles.
cycles
Pitch offset in cents. Range: -1200–1200 cents. Default: 0 cents. Linear scale. Units: cents.
cents
On or off. A rising edge retriggers; held on runs the oscillator or envelope. A control cable switches it at 0.5. Range: 0–1. Default: 1. Linear scale. Units: unitless.
Semitones a full pitch bend on the MIDI input moves the note, up or down. Range: 0–48 st. Default: 2 st. Linear scale. Units: st.
st
Time constant of the slide from one MIDI note's pitch to the next; 0 jumps. Range: 0–2000 ms. Default: 0 ms. Linear scale. Units: ms.
ms
MIDI1 lane
Audio2ch
Fundamental pitch, capped below Nyquist; detune uses cents. Range: 20–20000 Hz. Default: 220 Hz. Logarithmic scale. Units: Hz.
Hz
Output gain. Range: 0–0.5 ×. Default: 0.12 ×. Linear scale. Units: linear gain.
×
Selects the implemented algorithm. Choices are discrete and are not LFO targets. Range: 0–7. Default: 0. Linear scale. Units: unitless.
Cycle offset; Gate rising edges restart phase from this position. Range: 0–1 cycles. Default: 0 cycles. Linear scale. Units: cycles.
cycles
Pitch offset in cents. Range: -1200–1200 cents. Default: 0 cents. Linear scale. Units: cents.
cents
On or off. A rising edge retriggers; held on runs the oscillator or envelope. A control cable switches it at 0.5. Range: 0–1. Default: 1. Linear scale. Units: unitless.
Semitones a full pitch bend on the MIDI input moves the note, up or down. Range: 0–48 st. Default: 2 st. Linear scale. Units: st.
st
Time constant of the slide from one MIDI note's pitch to the next; 0 jumps. Range: 0–2000 ms. Default: 0 ms. Linear scale. Units: ms.
ms
A2ch
B2ch
Out2ch
The lane-wise operation. Add through Absolute difference combine A and B; Negate through Sign transform A alone and ignore B. Range: 0–16. Default: 2. Linear scale. Units: unitless.
Value used for every lane of B when nothing is connected to it. Multiply with 0.5 halves a signal. Range: -8–8. Default: 0. Linear scale. Units: unitless.
Audio2ch
Connections as text
- Oscillator “carrier” audio output connected to Math a input
- Oscillator “modulator” audio output connected to Math b input
- Math out output connected to Patch outputs audio input
- Both inputs are audio, so Math runs at audio rate and multiplies every sample.
- Multiply gives the sum and difference frequencies (550 Hz and 110 Hz) instead of the originals.
- Switch to Add to hear the two tones simply mixed, or Minimum for a harsher edge.
3. Control arithmetic
intermediate Teaches: op, b_default
An LFO plus an offset, computed at control rate, sweeps a filter cutoff.
MIDI1 lane
Audio2ch
Fundamental pitch, capped below Nyquist; detune uses cents. Range: 20–20000 Hz. Default: 220 Hz. Logarithmic scale. Units: Hz.
Hz
Output gain. Range: 0–0.5 ×. Default: 0.12 ×. Linear scale. Units: linear gain.
×
Selects the implemented algorithm. Choices are discrete and are not LFO targets. Range: 0–7. Default: 0. Linear scale. Units: unitless.
Cycle offset; Gate rising edges restart phase from this position. Range: 0–1 cycles. Default: 0 cycles. Linear scale. Units: cycles.
cycles
Pitch offset in cents. Range: -1200–1200 cents. Default: 0 cents. Linear scale. Units: cents.
cents
On or off. A rising edge retriggers; held on runs the oscillator or envelope. A control cable switches it at 0.5. Range: 0–1. Default: 1. Linear scale. Units: unitless.
Semitones a full pitch bend on the MIDI input moves the note, up or down. Range: 0–48 st. Default: 2 st. Linear scale. Units: st.
st
Time constant of the slide from one MIDI note's pitch to the next; 0 jumps. Range: 0–2000 ms. Default: 0 ms. Linear scale. Units: ms.
ms
Reset1 lane
Control1 lane
Cycle1 lane
Waveform of the oscillator. The random shapes draw a new value each cycle from a generator seeded by the node path, so every host and replay agrees. Range: 0–5. Default: 0. Linear scale. Units: unitless.
Cycles per second when Beats is 0. Range: 0.01–40 Hz. Default: 1 Hz. Logarithmic scale. Units: Hz.
Hz
Beats per cycle, synced to the shared transport. 0 uses Rate instead. Range: 0–64 beats. Default: 0 beats. Linear scale. Units: beats.
beats
Peak-to-peak amount of the output swing. Range: 0–1. Default: 1. Linear scale. Units: unitless.
Centre of the swing. Range: 0–1. Default: 0.5. Linear scale. Units: unitless.
Starting phase of the cycle, and where a Reset edge restarts it. Range: 0–1. Default: 0. Linear scale. Units: unitless.
Where the Triangle peaks, or how the Saw bends. 0.5 is the plain shape. Range: 0–1. Default: 0.5. Linear scale. Units: unitless.
A1 lane
B1 lane
Out1 lane
The lane-wise operation. Add through Absolute difference combine A and B; Negate through Sign transform A alone and ignore B. Range: 0–16. Default: 0. Linear scale. Units: unitless.
Value used for every lane of B when nothing is connected to it. Multiply with 0.5 halves a signal. Range: -1–1. Default: 0.2. Linear scale. Units: unitless.
Audio2ch
Audio2ch
Filter cutoff, capped at 0.45 times sample rate. Range: 20–20000 Hz. Default: 1200 Hz. Logarithmic scale. Units: Hz.
Hz
State-variable filter Q. Range: 0.5–12 Q. Default: 0.707 Q. Linear scale. Units: Q.
Q
Selects the implemented algorithm. Choices are discrete and are not LFO targets. Range: 0–5. Default: 1. Linear scale. Units: unitless.
One or two cascaded state-variable stages; notch/all-pass retain their response semantics. Range: 0–1. Default: 0. Linear scale. Units: unitless.
Reduces resonant gain as Q increases. Range: 0–1. Default: 0. Linear scale. Units: unitless.
Audio2ch
Connections as text
- Oscillator audio output connected to Filter audio input
- Filter audio output connected to Patch outputs audio input
- Control LFO control output connected to Math a input
- Math out output connected to Filter @cutoff input
- The LFO is a control lane, so Math runs at control rate and its output is a control lane too.
- Add moves the whole sweep up or down; Multiply scales its depth.
- The result drives the Cutoff socket. Lane values from 0 to 1 map across the cutoff range.