4ms Company Matthias Puech Ensemble Oscillator User Manual - Page 11
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Detailed Concepts and Usage
Scales and Oscillators
The concept of scales is central to the Ensemble Oscillator. In western music, a scale is a series of notes with the last note
being an octave higher than the first note. The spacing between the notes is always one or more semitones (i.e., half-steps,
whole-steps, minor thirds, etc.) Scales in the Ensemble Oscillator are
similar in concept but don't have to adhere to this form: the notes don't have
to repeat on an octave basis and don't have to be spaced by semitones. In
music theory, a scale can be defined by a sequence of intervals. No matter
what note the scale starts on, the intervals will always be the same for any
given type of scale (major, minor, etc.)
In the Ensemble Oscillator you can also think of a scale as a sequence of
harmonics. It can be shown mathematically that any waveform can be
broken down into a series of sine waves. For instance, a 100Hz square
wave can be created from a 100Hz sine wave, plus a 300Hz sine wave, plus
a 500Hz sine wave, plus a 700Hz sine wave, and so on. Each of these sine
waves is a called a "harmonic". The first harmonic is called the
"fundamental". Any sound, no matter how rich or complex the timbre, can be
represented by its harmonic content. Just like in music theory where the
intervals between notes are always the same for any given scale type, the
intervals between the harmonics are always the same for any given
waveform. Whether you prefer to think of the scales as being composed of
notes or harmonics, we will use the term "note" in this manual for simplicity.
The currently selected scale is used to create a set of notes that the oscillators are allowed to produce. The starting note is
determined by the Pitch knob and jack. The rest of the allowed notes are calculated using the sequence of intervals in the
scale. Once the last interval is reached, the sequence starts over with the first interval. By repeating the pattern of intervals
over and over, the Ensemble Oscillator creates a set of notes to which the oscillators will be quantized.
Oscillators
The first oscillator is called the root oscillator and has the lowest pitch. Its frequency before quantization is determined by
the Root knob and jack. The pitch of the other oscillators is determined by the Spread knob and jack. With Spread all the
way down, the oscillators are all tuned to the same pitch. As Spread is turned up, the space between the oscillators is
widened.
Quantization
When an oscillator is tuned between two allowed notes (which is most of the time), instead of "snapping" to the closest note
like a normal quantizer would do, the oscillator produces two pitches: one tuned to each of the nearest allowed notes. The
amplitude of each pitch is relative to its distance from the nearest note in the scale.
Take a look at the diagram on the next page. In the first box, the eight oscillators are spread by a small amount. The allowed
notes are shown by the bars in the scale. The resulting sound is a collection of pitches, the amplitude of each being relative
to how closely an oscillator is tuned to the corresponding note of the scale. For instance, the purple oscillator has a pre-
quantized frequency that's between the second and third notes of the scale (C# and G). Since it's between two notes, both
will be heard (as shown by the result having some of both). The third note (G) will be louder than the second (C#) because
the oscillator is closer to it.
In the second box, the Spread knob is turned up. The notes in the scale don't change, but the oscillators are spaced further
apart. The resulting frequencies cover a wider range. Notice that the root oscillator (purple) stays in place and all the other
oscillators move upwards.
In the third box, Spread has been turned back down, and the Root knob has been turned up. Notice that the spacing
between the oscillators is the same as in the first box, but they've been shifted up in frequency. The resulting frequencies
cover about the same range as in the first box, but everything is about two octaves higher. While the Root knob is being
turned up, each note in the scale rises and falls in volume as an oscillator passes by it. No pitch-bending or glissando
effects are heard.
What's an interval?
An interval is the distance between two
pitches. In music theory, common intervals
have names such as "major third" and
"perfect fifth". Sometimes intervals are
expressed as a number of octaves, whole-
steps, half-steps, or semitones. In
microtonal music, small intervals are usually
expressed in terms of cents, which are
hundredths of a semitone. In mathematics,
an interval might be expressed as a ratio
between the frequencies. An octave is 2:1,
and a fifth is about 1.5:1, and two notes in a
particular microtonal scale might have the
interval 25:24.
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