Mutable Instruments Elements User Manual

Mutable Instruments | Elements

Elements is a full-blown synthesis voice based on modal synthesis - an under-appreciated flavour of
physical modelling synthesis. With Elements, a sound is designed by specifying a resonant structure
(plate, string, tube…), the properties of the material it is made of (stiffness, absorption…), and how the
structure is excited to produce sound - struck, plucked, blown, bowed…

Elements is raw. The sounds of scratching scrape metal, or the wind in a PVC tube, not a symphonic
orchestra.

Elements is designed for Eurorack synthesizer systems and occupies 34 HP of space. It requires a -12V /
+12V supply (2x5 pin connector), drawing 10mA from the -12V rail and 130mA from the +12V rail. The red
stripe of the ribbon cable must be oriented on the same side as the “Red stripe” marking on the printed
circuit board.

This device complies with part 15 of the FCC Rules. Operation is subject to the following
two conditions: (1) This device may not cause harmful interference, and (2) this device must
accept any interference received, including interference that may cause undesired
operation.

This device meets the requirements of the following standards: EN55032, EN55103-2,
EN61000-3-2, EN61000-3-3, EN62311.

Have you ever made a wine glass sing? And noticed that with just the right speed, the sound gets louder
and louder? Or pushed a child on a swing with just the right timing to give her speed? The physical
phenomenon at play, in both cases, is resonance. When we say that a physical system has a resonance at
a particular frequency, it means that bringing energy to the system at this specific frequency will result in
large oscillations - but if energy is brought at a lower or higher frequency, the oscillations will disappear. It
is as if the system is responding to vibrations transmitted at a specific frequency, but is dissipating
vibrations sent at the other frequencies. Just like a band-pass filter!

This phenomenon is present in strings, drums, or the air column in a flute. These systems do not have one
single resonant frequency, but several, called modes. The shape of the instrument, and the material it is
made of determine the modes. Modes are characterized by their frequency, their amplitude, and their Q

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Mutable Instruments | Elements

(quality) factor - how narrow the resonant frequency peak is.

So what happens when we pluck a string, strike a drum or blow in a tube for a short moment? The short
burst of energy of the blow/impact contains many frequencies. Some of these fall outside of the modes,
and are absorbed. Some of these excite the modes, producing a stable, pitched sound. A sound will be
perceived as pure if the modes have a high Q factor - in this case the spectrum has sharp harmonics, and
everything else is absorbed. The sound will be more muffled or noisy if the modes have low Q. When the
frequencies of the modes are in harmonic ratios, the sound is perceived as very musical and strongly
pitched. When the modes are not located at integer ratios of the fundamental, the sound is perceived as
metallic, and its pitch is ambiguous. If the burst of energy contains only low frequencies, only the lowest
frequency modes will be excited. If the burst of energy contains very high frequency, it might be that some
of the low frequency modes will not sound. So what we hear truly is the interplay between the modes
present of the system, and the spectrum of the excitation which causes them to sound. The modes are like
a mould, they represent a possibility of sound - it’s up to us to fill them with an excitation signal!

Modal synthesis artificially recreates this phenomenon. The modes of a vibrating structure are recreated
with a bank of band-pass filters - one band-pass filter per mode. The frequency of these band-pass filters
determines the pitch (note) which will be heard. The Q factor (resonance) of these filters determines for
how long the system can sustain oscillation after being excited, and how “pure” the sound is. The
perceived timbre is a complex function of the frequency, Q, and gains.

To produce sound, this filter bank is excited by bursty/impulsive signals. These can be synthetic bursts of
noise, clicks/sharp envelopes, or samples. In the rest of this document, we will refer to the filter bank as
the Resonator, and the excitation signal generator as the Exciter.

The idea of sending raw material into a filter might seem very similar to classic analog subtractive
synthesis. But there is a big difference! In traditional analog subtractive synthesis, what determines the
pitch (note) of the sound is the oscillator frequency (the raw material). The role of the filter is only to color
it. In modal synthesis, the raw material is bursty and unpitched. What is truly responsible for the pitch of
the note, and its timbre is the resonator. You might actually have already encountered this situation when
“pitching” white noise by sending it into a resonant filter with high resonance.

The exciter->resonator combination might also remind you of formant synthesis - but once again, what
gives speech its pitched component is the exciter (the vocal cords), not the resonator (the vocal tract).

A classic analog piece of equipment that used modal synthesis is the Roland TR-808 drum machine. The
snare drum is synthesized by sending a narrow pulse into two band-pass filters. One could say that these
two band-pass filters represent two modes of a snare drum; and that the analog pulse “striking” them is
the exciter.

Describing a sound by a set of frequencies and gains should remind you of additive synthesis. Actually,
one could say that modal synthesis is an implementation of additive synthesis, in which we have replaced
all the oscillators by resonant filters. Unlike oscillators, the filters will not self oscillate, so they need to be
“pinged” by an external signal.

To do modal synthesis, one needs to specify the frequencies, Q factors and gains of all modes. The
traditional approach followed in academia consists in pre-computing them through a mathematical
analysis of the instrument and its material (as done for example in the Modalys environment developed at
the IRCAM). Some other research labs performed analyses on audio recordings of an instrument to
identify the modes. These approaches can lead to very realistic sounds, but they are not very suitable to a
modular environment - because they don’t provide the ability to shape the sound at the twist of a knob or
change in a CV.

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Given that a rich, interesting sound can need up to 50 modes, providing individual frequency/amplitude/Q
knobs would lead to a huge, barely usable module. Just like for additive synthesis, “one slider per partial”
is a terrible UI. To solve this quandary, Elements does not use pre-recorded modal “signatures” of real
materials, nor does it offer individual control on each mode. Instead, it generates synthetic signatures from
a small set of parameters. We did our best to make sure that it was still possible to dial in a set of modes
similar to those of real materials and structures - but of course, there’s a large set of tones to explore
outside of that! This philosophy is somewhat similar to those of algorithmic reverberators vs convolution
reverberators - which trade realism and authenticity for tweakability!

To recreate excitation signals evoking different types of musical instruments, Elements’ exciter section
consists of three generators named after three possible actions one can do with an instrument:

The BOW generator synthesizes the sound of a bow scratching a material. Depending on the bow pressure,
this combines a raw, scratching, granular noise with a purer sound resulting from the interaction between the
bow and the material.

The BLOW generator synthesizes continuous, noise-like sounds reminiscent of blowing, breathing, wind…
The STRIKE generator produces impulsive bursts and percussive noises for striking and beating the

resonator.

Elements’ front panel is divided into three sections:

The control/performance section with the most essential inputs/outputs.
The exciter section, in which the excitation signal is synthesized.
The resonator section, which controls, under the hood, the frequencies, amplitudes and Q-factor of modes.

A. Bow/Blow envelope CONTOUR. A simple envelope is applied to the sound generated by the BOW and
BLOW exciters. This knob interpolates between several preset shapes for this envelope: short AD

envelopes getting longer and slower, morphing into slower ADSR envelopes, fading into faster AR
envelopes.

B. Excitation mixer. The BOW knob controls the amplitude of scratching/bowing noise sent to the

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