8
Table Of Contents
- Logic Express 8 Instruments and Effects
- Contents
- Introduction to the Logic Express Plugins
- Amp Modeling
- Delay
- Distortion
- Dynamics
- EQ
- Filter
- Imaging
- Metering
- Modulation
- Pitch
- Reverb
- Specialized
- Utility
- EVOC 20 PolySynth
- EFM1
- ES E
- ES M
- ES P
- ES1
- ES2
- The ES2 Parameters
- Tutorials
- Sound Workshop
- Sound Design From Scratch, Filter Settings, Digiwaves
- Three Detuned Sawtooth Oscillators and Unison Mode
- Extremely Detuned Monophonic Analog Sounds, Effects
- Clean Bass Settings With One Oscillator Only
- Distorted Analog Basses
- FM Intensity and Frequency
- Controlling FM Intensity by an Envelope and FM Scaling
- FM With Drive and Filter-FM
- FM With Digiwaves
- FM With Wavetables
- Distorted FM in Monophonic Unison
- FM With Unusual Spectra
- Slow and Fast Pulse Width Modulations With Oscillator 2
- Pulse Width Modulation With Two Oscillators, PWM Strings
- Ring Modulation
- Oscillator Synchronization
- First Steps in Vector Synthesis
- Vector Synthesis—XY Pad
- Vector Synthesis Loops
- Bass Drum With Self-Oscillating Filter and Vector Envelope
- Percussive Synthesizers and Basses With Two Filter Decay Phases
- Templates for the ES2
- Sound Workshop
- EXS24 mkII
- Learning About Sampler Instruments
- Loading Sampler Instruments
- Working With Sampler Instrument Settings
- Managing Sampler Instruments
- Searching for Sampler Instruments
- Importing Sampler Instruments
- Parameters Window
- The Instrument Editor
- Setting Sampler Preferences
- Configuring Virtual Memory
- Using the VSL Performance Tool
- External Instrument
- Klopfgeist
- Ultrabeat
- GarageBand Instruments
- Synthesizer Basics
- Glossary
- Index
Appendix Synthesizer Basics 421
Fourier Theorem and Harmonics
“Every periodic wave can be seen as the sum of sine waves with certain wave lengths
and amplitudes, the wave lengths of which have harmonic relations (ratios of small
numbers).” This is known as the Fourier theorem. Roughly translated into more musical
terms, this means that any tone with a certain pitch can be regarded as a mix of sine
partial tones. This is comprised of the basic fundamental tone and its harmonics
(overtones). As an example: The basic oscillation (the first partial tone) is an “A” at
220 Hz. The second partial has double the frequency (440 Hz), the third one oscillates
three times as fast (660 Hz), the next ones 4 and 5 times as fast, and so on.
You can emphasize the partials around the cutoff frequency by using high resonance
values. The picture below shows an ES1 sawtooth wave with a high resonance setting,
and the cutoff frequency set to around 60%. This tone sounds an octave and a fifth
higher than the basic tone. It’s apparent that exactly three cycles of the strongly
emphasized overtone fit into one cycle of the basic wave:
The effect of the resonating filter is comparable to a graphic equalizer with all faders
higher than 660 Hz pulled all the way down, but with only 660 Hz (Cutoff Frequency)
pushed to its maximum position (resonance). The faders for frequencies below 660 Hz
remain in the middle (0 dB).
If you switch off the oscillator signal, a maximum resonance setting results in the self-
oscillation of the filter. It will then generate a sine wave.