Types of Modulation

1. Types of Modulation Synthesis (continued), Additive Synthesis, Amplitude modulation, Ring modulation, Frequency modulation Music Tech 1, 2012

2. Additive Synthesis • Creation of complex sounds through combination of elementary waveforms (sine waves) • Any method of combining waveforms together to create complex sounds is a type of additive synthesis • 2 Main types of additive synthesis • Fixed waveform synthesis • Time-varying synthesis

3. Fixed waveform additive synthesis • Creates waveforms through harmonic addition, or by adding harmonics to a fundamental frequency • Addition of harmonics changes the wave shape to triangle, sawtooth, square/pulse • Synthesizers create harmonic spectrum, oscillators combine and create the waveform

4. FWAS

5. FWAS • Phase, what is it? • Alignment of two waveforms (sine waves); when the peak of one waveform aligns with the trough of another they are 180 degrees out of phase. • Phase is important in determining the shape of a waveform created through FWAS, but the resultant tone is often indiscernible to human ears.

6. FWAS • Addition of partials can help create more complex waveforms • What are partials? • Partials = overtones of a fundamental that are not integer multiples • How is this different from harmonics? • Harmonics MUST be integer multiples of the fundamental.

7. Time-varying additive synthesis • Involves changing the mixture/combination of sine waves in a complex waveform over a period of time. • What is a constraint of FWAS? • Single constant tone (no change over time) • TVAS allows for greater control of timbre and shape over time. But how?

8. TVAS • FWAS uses multiple oscillators producing a constant waveform. The result is itself, although complex, also a continuous waveform. • TVAS employs many oscillators, each with its own frequency envelope AND amplitude envelope. • What is the result? • A complex waveform whose component waves have constantly shifting frequency values and amplitude envelopes. • Complexity of the composite WF is constantly changing!

9. TVAS • This is why it is called “time-varying” • The complexity of the composite is always VARYING over a given period of TIME • More versatile than FWAS, but also more cumbersome. Advantages vs. disadvantages

10. Issues with additive synthesis • What are some potential issues with additive synthesis • Extremely cumbersome in terms of physicality • Needs an oscillator for each component of the composite waveform • In TVAS you need additional information beyond just the oscillator: envelope information for frequency and amplitude of each sine wave. • Where does the data come from? Table lookup; synthesizers take the information for additive synthesis from tables of stored information for wave forms

11. Issues with additive synthesis • Let’s do the math! • Let’s say we want 24 partials and want up to 16 at one time • 384 oscillators • If the system runs at a sample rate of 48K Hz with 384 osc. • 48,000 x 384 = 18,432,000 samples per second • Each sample requires two operations (multiply/add) • 384 (oscillators) x 2 (operations) = 768 total operations • Multiply your total operations by your necessary samp/sec. • 18,432,000 x 768 = 14,155,776,000 operations per second. WHOA!!!!

12. Solution? • Digital synthesis platforms make this much easier on composers and audio engineers. • The process is still the same, but new technology makes the processing speed and table lookup less of an issue. • New modes of synthesis (especially frequency modulation) to create interesting and complex waveforms.

13. Modulation Basics • Modulation = act of changing something; variation of a property of an electronic signal, such as its frequency, amplitude or phase • Components of modulation • Carrier signal – original signal that is being modulated • Modulator signal – frequency performing the modulation • Modulation index – “amount” of modulation; affects different parameters in all types of modulation • Modulation depth – extent to which the carrier is modulated

14. Types of Modulation • 4 types of modulation: • Amplitude modulation • Ring Modulation • Frequency Modulation • Pulse-width modulation

15. Pulse-width modulation • Only exists in square waves • Involves periodically shifting the the upper polarity of a pulse wave from high voltage to low voltage • Represented as a percentage of how long a pulse wave remains in the high value (square wave is 50%) • In PWM, a modulating frequency varies the pulse width

16. Amplitude Modulation • One of the oldest modulation techniques • Involves the combination of the carrier and modulator to create sidebands • Sidebands = additional frequencies above and below the carrier. Sum and difference of the modulating frequency with the carrier • If the carrier is 800 Hz and the modulator is 200 Hz your sidebands will be at 1000 Hz and 600 Hz. • Sidebands are heard at ½ the amplitude of the carrier

17. Amplitude Modulation

18. Amplitude Modulation LFO results in tremolo (wavering amplitude)

19. Ring Modulation • Type of AM synthesis • Produces two sidebands, like AM synthesis, but the carrier frequency is lost in RM • Resultant sound is a combination of only the sidebands • LFO modulator will result in tremolo in RM as well.

20. Ring Modulation

21. Frequency Modulation • If AM synthesis affects the amplitude of the resultant waveform, what does FM synthesis affect? • Frequency, resulting in vibrato • First discovered by John Chowning (b. 1934) of Stanford University in the late 1960s. Patented the technique and sold it to Yamaha, who put it to use in the very famous Yamaha DX7 synthesizer

22. Frequency Modulation • FM synthesis does not refer to a single technique (like AM and RM), but to a family of techniques and methods involving similar processes • Like AM and RM, FM synthesis also produces sidebands, but it produces multiple bands, allowing for even greater complexity with sounds • Each sideband is spread evenly from the carrier by a multiple of the modulating frequency.

23. Frequency Modulation

24. Frequency Modulation

25. Frequency Modulation • Number of sidebands is dependent on the carrier modulation ratio, or CM ratio • The CM ratio determines the quality of the sidebands in relation to the carrier frequency. • What do I mean by quality? • The sidebands are either harmonic or inharmonic

26. Frequency Modulation • If the CM ratio is a simple integer ratio, such as 2:1 or 4:1 it yields only integer multiples, creating a harmonic spectra • 800 Hz to 200 Hz is a 4:1 ratio, yielding the previous harmonic spectra we saw on the board • If the CM ratio is not made up of simple integers (such as 8:2.1) it yields noninteger multiples, or an inharmonic spectra • This is the case if the carrier is 800 Hz and the modulator is 210 Hz. This yields a more “complex” and less harmonic resultant sound

27. Index and Depth • Modulation index – degree of modulation in a modulating frequency; measured as a whole number of decimal (1, 2.1, etc.) • As the modulation index increases, the number of sidebands increases. • What is the result of more sidebands? • Modulation depth – degree of variation in the modulation; measured in Hz.

28. Calculating the Index • Modulation index is derived by dividing the modulation depth (D) by the modulating frequency (M): I = D/M • We also discuss bandwidth when talking about frequency modulation • Bandwidth = total range of sidebands produced in FM synthesis • Derived with one of two equations. • BW = I + 1 • BW = 2 x (D + M)

29. Index and Bandwidth • If you have a MF of 100 Hz and a D of 100 Hz what is the value of your index? • I = 100/100 = 1.0; Index of 1.0 • If you know the value of the index, depth and modulator you can figure out the bandwidth. • B = 2 x (100 + 100) = 400; BW of 400 Hz. • Or, B = 1 + 1 = 2; BW of 2 pairs of sidebands • In short, you have 2 pairs of sidebands spanning 400 Hz.