Last month I completed my look at processors which modify the signal level. Now we move on to the more esoteric field of signal frequency modification.

Frequency Doubling.

The frequency of a note, measured in Hertz (Hz), is a measure of its pitch. For example middle C has a frequency of 256 Hz (this means a guitar string, say, does 256 complete vibrations every second to produce a note of middle C pitch) whereas A above middle C has a frequency of 440 Hz. As the frequency rises, so does the pitch. More importantly there is a fixed relationship across the musical octaves — as you double the frequency of a note, it goes up one octave. It is convenient to represent these waveforms by showing the output you would see on an oscilloscope screen. (An oscilloscope isa simplified television that displays electrical signals). If the sound waves were fed into a microphone and the microphone's output was fed into a 'scope then you get an 'electrical picture' of the wave, (see figure one).

If you want to produce a note that is one octave above an existing one you somehow have to double the frequency. For example if you start with middle C (256Hz) you need to synthesize a note of 512 Hz. There are some very flash ways of doing this mainly using digital circuitry — more about that later — but it is possible to put together a pretty fair frequency doubler for practically nothing. For those with an adventurous spirit I put forward a suggestion in figure two. The heart of the circuit is a bridge rectifier such as is used in power supplies, the main difference being that it works better if it uses germanium diodes rather than the more common silicon diodes. (For the technically minded germanium diodes only drop 0.3 volts across themselves whereas silicon diodes drop 0.7 volts). Since the bridge 'loses' some of the input voltage as it operates, it is sensible to put stages of amplification either side of it, the pre amplification to give it a signal of at least four volts to work with and the post stage to make up the signal loss and match the output to the main amplifier (ie buffer it). As you will see from figure three the output is one octave above the input though distorted somewhat.

Octave Dividers

In many ways octave division (ie frequency halving) is a lot simpler but, in its own way, produces other problems. The trick is to produce a circuit that will only switch when it encounters a rising waveform. That is, looking back at figure one, it will only switch at the points marked with dotted lines. Such a circuit is known as a bi-stable, or more commonly, a flip-flop. As flip-flops tend to work much more reliably if the rise of the waveform is very steep, the input signal must first be 'squared off', usually using a device known as a Schmitt trigger, giving a circuit something like figure four. I've added in a second flip-flop which halves the frequency again giving two octaves down. The three signals can then be mixed to give any blend you want. The waveforms at various points in the circuit are shown in figure five.

In theory this should be pretty simple; in practice things get a bit tricky. Firstly a guitar string doesn't produce nice, clean (and very boring sounding) waveforms. A lot of harmonics are present, particularly second harmonics, and at times these can be stronger than the fundamental note. This gives our circuitry all sort of trouble. The second harmonic is one octave above the fundamental and, when this harmonic predominates, the octave divider latches on to it. During a string's decay the second harmonic weaves a mad pattern which the divider dutifully follows. This gives rise to a yodelling sound that any Swiss would be proud of, as the one octave below note (generated from the fundamental) and the played note (divided down from the second harmonic) alternate in an annoying warble. Secondly a square waveform is pure, unadulterated distortion — a Schmitt trigger makes a vicious fuzz box.

The first problem is usually tackled by filtering the input signal before it reaches the Schmitt trigger to remove a lot of the troublesome harmonics. This makes for a fairly boring sound, but at least it's clean. In addition high quality octave dividers often use a second Schmitt trigger in parallel with the first, the first one concentrating on the rising edge and the second one detecting the waveform as it falls. By comparing the rising and falling parts of the waveform it is possible to track the fundamental more accurately.

The second problem is tackled by rounding off the harsh, square output waveform using a suitable resistor/capacitor network — in practice a tone control.

As the more treble there is in a signal the more predominant the second harmonic, octave dividers tend to work best when using the bass pickup and with tone controls turned to bass. Open strings tend to be rich in harmonics so these should also be avoided.

Harmony Synthesizers

Harmony synthesizers produce a complementary harmony line based on an input melody line. They usually do this by digital delay line. If this signal were to be clocked out of the delay line at twice the speed that it went in the effect would be to double the frequency (ie an octave above). As the speed at which the signal is clocked out of the delay line is adjustable the output can be adjusted to any harmony interval required. Similarly the signal can be clocked out at a slower rate than it went in, giving a harmony line below, rather than above, the melody. All this takes time, of course, and all harmony synthesisers (or pitch transposers, call them what you will) will delay the signal by the few milliseconds it takes to process the signal. This is generally an advantage when the processed signal is mixed back with the original as it gives an added thickness and richness of sound. Whereas an octave divider can only handle individual notes, a harmony synthesiser can handle virtually whatever you throw at it including chords. I say virtually everything because I have yet to hear one that convincingly tackles vocals at anything other than a relatively small pitch shift.

Vibrato

Vibrato is a cyclic changing of pitch — sort of like tremolo except that the pitch, rather than the volume, is altered. Unfortunately there is no cheap, electronic way of doing this. The most obvious way is to link up a Low Frequency Oscillator (LFO) to adjust the clocking rate of digital delay line as used in a harmony synthesizer. In the end I have to admit that the best vibrato I've ever heard is our old friend Hank B playing with his (misnamed) tremolo arm.

Next month — Equalisers, Wah-Wahs, Phasers etc.