Computer Music: Musc 216
Creating a Simple Bell
Using Additive Synthesis Techniques

In this tutorial you will use SYD to create a patch which will simulate the sound of a large BELL. Using Additive Synthesis techniques. As a background to understand the procedure outlined below, you should read Bell Characteristics.

To synthesize a bell using the application SYD, you will need to add 11 operators: the fundamental frequency (1 operator), 8 separate s (8 operators), an amplitude envelope (1 operator) and a mixer operator (1 operator).

If you have not already done so, please read, Additive Synthesis.

Using a Fundamental Frequency of 200 Hz, here is a formula for creating a simple bell sound using 9 frequencies called PARTIALS. Combine sine waves with these frequency ratios:


9th wave

200 x
814 Hz
8th wave
200 x
752 Hz
7th wave
200 x
600 Hz
6th wave
200 x
548 Hz
5th wave
200 x
400 Hz
4th wave
200 x
342 Hz
3rd wave
200 x
238 Hz
2nd wave
200 x
184 Hz
1st wave
200 x
112 Hz

Figure 1: Frequency Ratios of a Simple Bell

Technically, a PARTIAL is a frequency in the spectrum of a sound which is NOT in the Natural Harmonic Series. Sometimes it is also called a "detuned harmonic" or an "enharmonic." In the chart above, the frequencies that ARE part of the Natural Harmonic Series are represented by whole numbers (2, 3). All the other frequencies are PARTIALS. Often in a bell sound, the true FUNDAMENTAL is MISSING altogether or a SUBHARMONIC is hear (perceived) by the listener instead. The lowest frequency here (the 1st wave) is a SUBHARMONIC; the 2nd frequency is close enough to the Fundamental of the Natural Harmonic Series to be considered a detuned partial.

Apply this envelope:

Figure 2: Amplitude Envelope of a Simple Bell

To begin, create a new SYD patch and add 9 Oscillator Operators, 1 Envelope Generator and 1 Mixer Operator in the configuration shown below:

Figure 3: SYD Patch for Simple Additive Synthesis Bell

The duration of the Sound Output should be 6 seconds. The duration of the Amplitude Envelope should mach the duration of the sound output (6 seconds):

Figure 4: Amplitude Envelope Settings

The Fundamental Frequency of the Bell should be 200 Hz. Please assign the Oscillator Operator at the BOTTOM of the SYD window to the Fundamental Frequency. All the other Oscillator Operators will be assigned as partials.

Figure 5: Fundamental Frequency and 8 Partials

Set the Fundamental Oscillator and the 1st partial Oscillator as indicated below:

Figure 6: Fundamental Settings
Figure 7: First Partial Settings

Continue setting the frequency ratios of the remaining operators according to the table listed in Figure 1 above. When you have finished, click the SYNTHESIZE button in the bottom left corner of the patch window. Then click PLAY to listen to the sound.

Further Experimentation

In this Simple Bell patch, all the partials have the same amplitude provided by the LEVEL setting in the Amplitude Envelope. A better scenario would be to have separate amplitudes for each partial such that the FUNDAMENTAL has the loudest amplitude (.5), the 1st partial is 50% of the amplitude of the FUNDAMENTAL (.25), the 2nd partial is 50% of the amplitude of the 1st partial (.125)...... and so on until you finish all 8 partials. This follows the SPECTRUM of the NATURAL HARMONIC SERIES where the amplitude of each harmonic is inversely proportional to its position in the series.

Experiment with different ways to efficiently set these amplitudes.

In natural sounds, the higher partials tend to have shorter amplitude envelopes (they don't ring as long as the lower partials):

Experiment with different ways to efficiently set separate times for the amplitude envelopes of the various partials. For example, try experimenting with the FUNCTION operator and the EXPRESSION operator. Using these operators, you can pass an EXPRESSION to ALL the amplitude fields simultaneously.

In a REAL bell, one side of the bell may not be cast to the same thickness as the other side. Consequently, there will be mall variations in frequencies which produce BEATING at various frequencies. Experiment with using pairs of slightly detuned operators ("enharmonic" partials) to simulate this BEATING effect.

Further information on SYNTHESIZING BELLS can be found on the Sound On Sound: Synth Secrets site: Synthesizing Bells.

If you have not already done so, please read Bell Characteristics.

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