The goal is to process the guitar signal directly through Eurorack modules without a preamp, using the Befaco A*B+C for amplification and offset control, followed by the Instruo tanh[3] for saturation. We’ll also explore how these modules interact with the harmonic content of the guitar and how they can produce gates, triggers, or CV from the processed signal.
1. The Guitar Signal
When connected directly to a Eurorack module, the guitar produces a low-amplitude signal (approximately 10-50 mV peak-to-peak) with a wide frequency range. With the guitar tuned to 432 Hz, the fundamental frequencies of the open strings are slightly lower than standard tuning (440 Hz):
| String | Note | Fundamental Frequency (f₀) |
|---|---|---|
| 6 | E (E2) | 82.16 Hz |
| 5 | A (A2) | 108 Hz |
| 4 | D (D3) | 144 Hz |
| 3 | G (G3) | 192 Hz |
| 2 | B (B3) | 240.16 Hz |
| 1 | E (E4) | 323.63 Hz |
Each string produces a waveform with a fundamental frequency (f0f₀f0) and harmonics (2f0,3f0,4f0…2f₀, 3f₀, 4f₀…2f0,3f0,4f0…).
2. Befaco A*B+C
The A*B+C module amplifies the guitar signal and adds an offset to shift it into the desired voltage range.
Mathematical Model
The output voltage of the module is defined by:Vout=k⋅Vin+VoffsetV_{out} = k \cdot V_{in} + V_{offset}Vout=k⋅Vin+Voffset
Where:
- VinV_{in}Vin is the input signal (guitar),
- kkk is the amplification factor (set by the potentiometer; typically up to k=20k = 20k=20),
- VoffsetV_{offset}Voffset is a constant voltage offset (adjustable from -5V to +5V).
Example Calculation
For a guitar string producing Vin=20 mVV_{in} = 20 \, \text{mV}Vin=20mV, with:
- k=100k = 100k=100,
- Voffset=1 VV_{offset} = 1 \, \text{V}Voffset=1V:
Vout=100⋅0.02+1=3 VV_{out} = 100 \cdot 0.02 + 1 = 3 \, \text{V}Vout=100⋅0.02+1=3V
This amplified signal is now compatible with Eurorack voltages (typically 0-10V or ±5V).
3. Instruo tanh[3]
The tanh[3] module applies soft clipping to the amplified signal, shaping it with the hyperbolic tangent (tanh\text{tanh}tanh) function.
Mathematical Model
The output of the module is given by:Vout=tanh(Vin)V_{out} = \text{tanh}(V_{in})Vout=tanh(Vin)
- For small signals (∣Vin∣<1|V_{in}| < 1∣Vin∣<1), the tanh function is approximately linear: tanh(Vin)≈Vin\text{tanh}(V_{in}) \approx V_{in}tanh(Vin)≈Vin
- For larger signals (∣Vin∣>1|V_{in}| > 1∣Vin∣>1), the tanh function saturates: tanh(Vin)→±1\text{tanh}(V_{in}) \to \pm 1tanh(Vin)→±1
Impact on Guitar Signals
- Low-frequency signals (e.g., low E string) with higher amplitudes will saturate more quickly, creating a compressed and harmonically rich output.
- High-frequency signals (e.g., high E string) may remain in the linear range, preserving their dynamic range.
4. Consequences for Gates, Triggers, and CV
The saturated output from tanh[3] can be used as:
- Gate or Trigger:
A high-amplitude attack transient from the guitar string can be treated as a gate or trigger when passed through a comparator or envelope follower. - CV Signal:
The processed signal can directly modulate other Eurorack modules (e.g., VCOs, filters) based on the dynamics of the guitar playing.
5. Patch Example
Signal Chain:
- Input: Guitar signal (raw, low-level) →
- Befaco A*B+C: Amplification (kkk) and offset (VoffsetV_{offset}Voffset) →
- Instruo tanh[3]: Soft clipping and dynamic shaping →
- Output: Gate, CV, or audio signal for further processing.
6. Frequencies and Their Behavior in the System
Each string produces different amplitudes and harmonics, leading to distinct interactions with the modules:
- Low E String (82.16 Hz):
Produces a high-amplitude fundamental, quickly saturating the tanh function. - High E String (323.63 Hz):
Produces lower amplitude but rich harmonics, remaining closer to the linear range of the tanh[3].
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