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\paperwidth 11in \paperheight 8.5in \leftmargin 3.5cm \topmargin 3cm \rightmargin 2cm \bottommargin 3cm \secnumdepth 2 \tocdepth 2 \paragraph_separation indent \paragraph_indentation default \quotes_language english \papercolumns 1 \papersides 1 \paperpagestyle empty \tracking_changes false \output_changes false \html_math_output 0 \html_css_as_file 0 \html_be_strict false \end_header \begin_body \begin_layout Standard \begin_inset ERT status open \begin_layout Plain Layout \backslash begin{textblock*}{ \backslash paperwidth}(0mm,30mm) \end_layout \begin_layout Plain Layout \backslash begin{center} \end_layout \begin_layout Plain Layout \backslash includegraphics[width= \backslash paperwidth-400px]{graphics/logo} \end_layout \begin_layout Plain Layout \backslash end{center} \end_layout \begin_layout Plain Layout \backslash end{textblock*} \end_layout \begin_layout Plain Layout \end_layout \begin_layout Plain Layout \backslash begin{textblock*}{ \backslash paperwidth}(30mm,235mm) \end_layout \begin_layout Plain Layout \backslash noindent \end_layout \begin_layout Plain Layout SAE Berlin \backslash \backslash \end_layout \begin_layout Plain Layout Student Id: 18128 \backslash \backslash \end_layout \begin_layout Plain Layout Course: AED412 \backslash \backslash \end_layout \begin_layout Plain Layout Headinstructor: Boris Kummerer \backslash \backslash \end_layout \begin_layout Plain Layout Berlin, Germany 2012 \backslash \backslash \end_layout \begin_layout Plain Layout \backslash end{textblock*} \end_layout \end_inset \end_layout \begin_layout Standard \begin_inset ERT status open \begin_layout Plain Layout \backslash author{ \end_layout \begin_layout Plain Layout by Karl Pannek \end_layout \begin_layout Plain Layout } \end_layout \begin_layout Plain Layout \end_layout \begin_layout Plain Layout \backslash title{ \backslash LARGE{Prototyping a Modular Analog Synthesizer}} \end_layout \begin_layout Plain Layout \backslash maketitle{ } \end_layout \begin_layout Plain Layout \end_layout \end_inset \end_layout \begin_layout Standard \begin_inset ERT status open \begin_layout Plain Layout \backslash pagenumbering{arabic} \end_layout \begin_layout Plain Layout \backslash setcounter{page}{2} \end_layout \begin_layout Plain Layout \backslash renewcommand \backslash cftpartdotsep{6.6} \end_layout \begin_layout Plain Layout \backslash renewcommand \backslash cftchapdotsep{6.6} \end_layout \end_inset \end_layout \begin_layout Chapter* Table of Contents \end_layout \begin_layout Standard \begin_inset ERT status open \begin_layout Plain Layout \backslash renewcommand \backslash contentsname{} \end_layout \begin_layout Plain Layout \backslash vspace*{-8.5em} \end_layout \begin_layout Plain Layout \backslash tableofcontents \end_layout \end_inset \end_layout \begin_layout Chapter Preface \end_layout \begin_layout Section* Introduction \end_layout \begin_layout Standard This paper constitutes an attempt to summarize the most important facts and information on the topic of analog, modular synthesizers. The range of discussed subjects involves a series of various perspectives, including historical, theoretical, electronic and practical viewpoints. \end_layout \begin_layout Standard Its goal is to convey an understanding of the inner workings of electronic synthesizers and their components. Moreover the reader is guided through the process of creating a small but functional modular synthesizer setup that is fun to play and experiment with. The intention was to investigate the possibilities and limits in designing and building an analog sound device for someone, who had not been in contact with analog synthesizers, let alone building electronics devices before. The project was inspired by the film \emph on moog \emph default \begin_inset ERT status open \begin_layout Plain Layout \backslash cite{Fjellestad:movie} \end_layout \end_inset , a documentary about Dr. Robert Moog, electronic instrument pioneer and inventor. \end_layout \begin_layout Section* Chapter Overview \end_layout \begin_layout Standard The first chapter represents the research on the historical background of analog synthesizers since the beginning of the twentieth century. It was tried to outline important milestones in the historic development from the first electronic sound generating devices until a point in time when manufacturers of modular synthesizers have developed a profitable market. \end_layout \begin_layout Standard Subsequently the most important concepts of subtractive synthesis are summarized. A general overview over common sound generation and processing methods is given, whereby all concepts are applicable to both analog and digital synthesis. In chapter three these concepts are taken one step further and discussed in the context of electronic circuitry. Lastly the process of building an electronic synthesizer prototype is described. \end_layout \begin_layout Standard \begin_inset Note Note status collapsed \begin_layout Plain Layout The process of building the prototype includes working with an oscilloscope to examine and verify the shape of various waveforms before and after modulatio n. \end_layout \begin_layout Plain Layout To make it playable with a keyboard, a MIDI input module is added. It features an Arduino microprocessor to convert digital MIDI messages into control voltage outputs that other modules can connect to. It is the only digital component of the synthesizer, while tone generation and processing are analog. \end_layout \end_inset \end_layout \begin_layout Chapter Historic Evolution of the Synthesizer \end_layout \begin_layout Section Early Development Milestones \end_layout \begin_layout Standard \begin_inset Note Note status collapsed \begin_layout Plain Layout Electric instruments at that time were developed primarily to imitate and evolve the sounds of classical instruments and therefore satisfy traditional ideas of musical writing \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[p.~12]{Manning1985} \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Standard Around 1900 american Thaddeus Cahill initiated a new era of music by inventing a 200 ton machine known as the Dynamophone or Thelharmonium \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[p.~19]{Humpert1987} \end_layout \end_inset . Working against incredible technical difficulties, he succeeded to create an electrical sound generator, that produced alternating sine wave shaped currents of different audio frequencies. A modified electrical dynamo was used in conjunction with several specially geared shafts and inductors to create the signals. The Dynamophone could be played with a polyphonic keyboard and featured special acoustic horns to convert the electrical vibrations into sound \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[p.~1]{Manning1985} \end_layout \end_inset . The timbre of the instrument was manually shaped from fundamentals and overtones. This is known as the principle of additive synthesis \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[p.~730]{Bode1984} \end_layout \end_inset . \end_layout \begin_layout Standard \begin_inset Wrap figure lines 0 placement O overhang 0in width "4.5cm" status collapsed \begin_layout Plain Layout \begin_inset ERT status open \begin_layout Plain Layout \backslash vspace*{-2em} \end_layout \begin_layout Plain Layout \backslash begin{center} \end_layout \end_inset \end_layout \begin_layout Plain Layout \begin_inset Graphics filename graphics/theremin.jpg display false width 4.5cm \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout Leon Theremin performing the Aetherophone \end_layout \end_inset \end_layout \begin_layout Plain Layout \begin_inset ERT status open \begin_layout Plain Layout \backslash end{center} \end_layout \begin_layout Plain Layout \backslash vspace*{-2em} \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Standard In 1924 the russian inventor Leon Theremin created the Aetherophone, which would later be known as the Theremin. Unlike most electric instrument developed around that time, the Theremin had no keyboard. It was played merely by hand motion around two capacitive detecors, that generated electrical fields. These were affected by the electric capacity of the human body. One of these detectors was a vertical rod to control dynamics and the other a horizontal loop to change the pitch \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[p.~3]{Manning1985} \end_layout \end_inset . \begin_inset Quotes eld \end_inset The theatricality of its playing technique and the uniqueness of its sound made the Theremin the most radical musical instrument innovation of the early 20th century. \begin_inset Quotes erd \end_inset \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[p.~6]{Dunn1992} \end_layout \end_inset \end_layout \begin_layout Standard Some organ-like precursors to the synthesizer were the Ondes Martenot and the Trautonium, which were devised just a few years later. The Ondes Martenot is one of the few early electric instruments, that are still in concert- and theatre use in their original design today \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[p.~20]{Humpert1987} \end_layout \end_inset . \end_layout \begin_layout Standard The Givelet (1929) was a commercially more successful instrument, since it was designed as a cheap alternative to pipe organs. These instruments were polyphonic and unified the concepts of the Pianola - a self-playing piano, controlled by pre-punched tape - with electronic sound genaration. The ability to program electronic sounds should lead the way for future devices such as the RCA synthesizer or computer music production in general. However, the Givelet was about to take a back seat, when Laurens Hammond published his Hammond Organ in 1935. Its technical operation principle is reminiscent of the Dynamophone, since it also involved rotating discs in a magnetic field \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[p.~3]{Manning1985} \end_layout \end_inset . \end_layout \begin_layout Standard \begin_inset Wrap figure lines 0 placement O overhang 0in width "4.5cm" status collapsed \begin_layout Plain Layout \begin_inset ERT status open \begin_layout Plain Layout \backslash vspace*{-2em} \end_layout \begin_layout Plain Layout \backslash begin{center} \end_layout \end_inset \end_layout \begin_layout Plain Layout \begin_inset Graphics filename graphics/bode-melochord.jpg display false width 4.5cm \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout Harald Bode tuning his first Melochord \end_layout \end_inset \end_layout \begin_layout Plain Layout \begin_inset ERT status open \begin_layout Plain Layout \backslash end{center} \end_layout \begin_layout Plain Layout \backslash vspace*{-2em} \end_layout \end_inset \end_layout \end_inset The german engineer Harald Bode contributed to the design of several new instruments from the 1930's on, like the warbo formant organ (1937) or later the Melochord (1949). He was primarily interested in providing tools for a wide range of musicians, which is why his contributions straddled between the two major design tradition s of new sounds versus imitation of traditional ones. He turned out to be one of central figures in the history of electronic music, since he was also one of the primary engineers in establishing the classic tape music studio in europe \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[p.~9]{Dunn1992} \end_layout \end_inset . \end_layout \begin_layout Standard Bode was one of the first engineers to grasp the significance of the invention of the solid state transistor for sound synthesis. In an article published in 1961 he draws particular attention to the advanteges of modular design. \begin_inset Quotes eld \end_inset The versatility of transistor-based electronics made it possible to design any number of devices which could be controlled by a common set of voltage characteristics. \begin_inset Quotes erd \end_inset \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[p.~117]{Manning1985} \end_layout \end_inset . But it was not until the early 1960's that major advances in electronic design took shape \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[p.~19]{Dunn1992} \end_layout \end_inset . \end_layout \begin_layout Standard \begin_inset Note Note status open \begin_layout Plain Layout Sakbutt (1948) Hugh LeCaine \end_layout \end_inset \end_layout \begin_layout Section The First Synthesizers \end_layout \begin_layout Standard In 1955 the laboratories of the Radio Corporation of America (RCA) introduced a new and very advanced machine to the public named the Olson-Belar Sound Synthesizer, later known as the RCA Mark I Music Synthesizer. It combined many means of tone generation and sound modification known at the time and is considered the first synthesizer. Mark I was built with the specific intention of imitating traditional instrumen t sounds and to reduce the costs of the production of popular music by replacing musicians. However, the machine proved unsuitable for its original intent and was later used completely for electronic music experimentation and composition \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[p.~15-16]{Dunn1992} \end_layout \end_inset . The synthesizer could not be played in the conventional sense in real time. Instead musical information had to be pre programmed as punched holes in a large paper tape. Harry Olson and Herbert Belar produced an improved Mark II Synthesizer in 1957, which the nickname \emph on Victor \emph default was given \emph on \emph default \begin_inset ERT status open \begin_layout Plain Layout \backslash cite{Bear:website} \end_layout \end_inset . \end_layout \begin_layout Standard Around the same time the outstanding guitarist and inventor Les Paul became famous with his multitrack guitar recordings. He stimulated many innovators not only with the success of his multitrack recorder, but also with his methods of electronic sound processing. Harald Bode was so impressed and inspired by his work, that he built a system consisting of a number of electronic modules for sound modification in late 1959 through 1960. His system featured ring modulator devices, envelope followers and generators, voltage-controlled amplifiers, filters, mixers and others \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[p.~733]{Bode1984} \end_layout \end_inset . The modular concept of his device had proven attractive due to its versatility and predicted the more powerful modular synthesizers that emerged in the early 1960's \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[p.~20]{Dunn1992} \end_layout \end_inset . \end_layout \begin_layout Standard In 1963 Robert Moog, a passionate inventor from Ithaca, New York, was selling kits of transistorized Theremins \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[p.~20]{Dunn1992} \end_layout \end_inset . As he states in the movie about him \begin_inset ERT status open \begin_layout Plain Layout \backslash cite{Fjellestad:movie} \end_layout \end_inset , he had been completely obsessed with building and later designing Theremins since the age of 14. A year later he built a transistor based voltage-controlled oscillator and amplifier for the composer Herbert Deutsch. This led moog to the presentation of a paper entitled \emph on Voltage-Controlled Electronic Music Modules \emph default at the sixteenth annual convention of the Audio Engineering Society, which had stimulated widespread interest \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[p.~117-118]{Manning1985} \end_layout \end_inset . \end_layout \begin_layout Standard \begin_inset Wrap figure lines 0 placement I overhang 0in width "5cm" status collapsed \begin_layout Plain Layout \begin_inset ERT status open \begin_layout Plain Layout \backslash vspace*{-2em} \end_layout \begin_layout Plain Layout \backslash begin{center} \end_layout \end_inset \end_layout \begin_layout Plain Layout \begin_inset Graphics filename graphics/buchla.jpg display false width 5cm \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout Donald Buchla with a Series 100 system in the 1960's \end_layout \end_inset \end_layout \begin_layout Plain Layout \begin_inset ERT status open \begin_layout Plain Layout \backslash end{center} \end_layout \begin_layout Plain Layout \backslash vspace*{-2em} \end_layout \end_inset \end_layout \end_inset Similar developments had been taking place at the west coast of the united states. Morton Subotnick and Ramon Sender started their carreer in electronic music experimentation, and became increasingly dissatisfied with the severe limitatio ns of traditional equipment at the San Francisco Tape Music Center, where they were working. They sought out to hire a competent engineer and met Donald Buchla \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[p.~117-118]{Manning1985}, \backslash citealp[p.~22]{Dunn1992} \end_layout \end_inset . Their discussions resulted in the concept of a modular voltage-controlled system. Buchla's design approach differed significantly from Moog. He rejected the idea of a synthesizing familiar sounds and resisted the word \emph on synthesizer \emph default ever since. It seemed much more interesting to emphasize new timbral possibilities and stress the complexity that could arise from randomness. At the same time Buchla was fascinated with designing control devices other than the standard keyboard, which Moog decided to use for playing \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[p.~20]{Dunn1992} \end_layout \end_inset . \end_layout \begin_layout Standard \begin_inset Wrap figure lines 0 placement O overhang 0in width "5cm" status open \begin_layout Plain Layout \begin_inset ERT status open \begin_layout Plain Layout \backslash vspace*{-2em} \end_layout \begin_layout Plain Layout \backslash begin{center} \end_layout \end_inset \end_layout \begin_layout Plain Layout \begin_inset Graphics filename graphics/switched-on-bach.jpg display false width 5cm \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout \emph on Switched-On Bach \emph default LP artwork \end_layout \end_inset \end_layout \begin_layout Plain Layout \begin_inset ERT status open \begin_layout Plain Layout \backslash end{center} \end_layout \begin_layout Plain Layout \backslash vspace*{-2em} \end_layout \end_inset \end_layout \end_inset In 1966 Bob Moogs first production model was available from the business R.A. Moog Co. that he had founded \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[p.~20]{Dunn1992} \end_layout \end_inset . At this time Walter Carlos, an audio engineer from New York who adviced Bob Moog while perfecting his system, worked with Benjamin Folkman to produce an album of titles by Johann Sebastian Bach interpreted only with Moog synthesizers. With the title \emph on Switched-on Bach \emph default they demonstrated the performance of the system so convincingly, that they hit the popmusic charts and sold a million LP's \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[p.~45]{Ruschkowski1990} \end_layout \end_inset . \end_layout \begin_layout Standard By the end of the decade two other manufactrurers entered the market: ARP in America and EMS Ltd. in England. They had become major rivals for Moog and Buchla. Synthesizer production was dominated by these four companies for several years, whereby each firm struggled for a major share of a highly lucrative, rapidly expanding market \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[p.~118]{Manning1985} \end_layout \end_inset . \end_layout \begin_layout Chapter Theory of Subtractive Synthesis \end_layout \begin_layout Section Sources \end_layout \begin_layout Standard Acoustic events can generally be divided in two groups: noises and tones. Whereas tones - as opposed to noise - are classified as sound waves, that oscillate in a periodic manner. However this is only a theoretical classification, since most natural sounds are a combination of the two \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[p.~52]{Ruschkowski1990} \end_layout \end_inset . \end_layout \begin_layout Subsection Wave Oscillation \end_layout \begin_layout Standard At the root of every artificial tone generating system there is an element that produces an oscillation. This element is mostly described as the oscillator, which represents the very source of what can be heard eventually. The oscillator produces a periodic wave, that moves between an amplitude-minima and -maxima. Its waveform (shape of the wave) determines the overtone structure and therefore the timbre of this basic source sound. Oscillators often provide several waveforms between which it is possible to switch back and forth. The pitch of the output signal is defined by the frequency of the wave and must oscillate between 20Hz and 20kHz in order for it to be audible to humans \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[p.~124]{Friesecke2007} \end_layout \end_inset . The output signal can later be processed and modulated in several ways. \end_layout \begin_layout Standard Oscillators that swing at an infrasonic frequency - meaning a frequency so low, that it is not hearable anymore - are called low frequency oscillators (LFO). They are used to control parameters of different components of the synthesizer periodically. For example to influence the pitch of another oscillator to get a vibrato - or the amplitude to get a tremolo effect. Some oscillators frequencies range from very low to very high, in which case a distinction between oscillator and LFO is unnecessary. \end_layout \begin_layout Standard \begin_inset Note Note status collapsed \begin_layout Plain Layout Difference between poly and monophonic synthesis (voices, mono: store last note value) Voices \end_layout \begin_layout Plain Layout unison \end_layout \begin_layout Plain Layout sync \end_layout \end_inset \end_layout \begin_layout Subsubsection Characteristics of Common Waveforms \end_layout \begin_layout Labeling \labelwidthstring 00.00.0000 sine The most basic waveform is the sine wave. It contains no overtones at all and sounds round and dull. \end_layout \begin_layout Labeling \labelwidthstring 00.00.0000 sawtooth The sawtooth, also known as saw or ramp waveform sounds very bright, sometimes described as trompet-like \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[p.~49]{Anwander2011} \end_layout \end_inset . It consist of a complete series of harmonics and is therefore well suited for subtractive synthesis. There are two types of sawtooth waves: rising and descending. \end_layout \begin_layout Labeling \labelwidthstring 00.00.0000 triangle Composed of only odd harmonics, the triangle wave has a much softer, flute-like sound. \end_layout \begin_layout Labeling \labelwidthstring 00.00.0000 square Also known as rectangle, \begin_inset Note Note status open \begin_layout Plain Layout clearify difference to triangle \end_layout \end_inset the square wave also consists of odd harmonics only. Its timbre reminds of woodwind instruments \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[p.~55]{Ruschkowski1990} \end_layout \end_inset . A true square wave has a 50 % duty cycle - equal high and low periods. However, oscillators often feature a pulse width parameter, trough which the high-low time ratio can be accessed. This has a distinct influence on the wave's timbre. In this case, the square becomes a pulse waveform. \end_layout \begin_layout Subsection Noise Generation \end_layout \begin_layout Standard A different approach on the creation of source audio material is resembled by noise generators, which generate random non-periodic frequencies. Therefore the signal contains no tonal information. \end_layout \begin_layout Subsubsection Noise Types \end_layout \begin_layout Labeling \labelwidthstring 00.00.0000 white Equal power density in any band of the frequency spectrum \end_layout \begin_layout Labeling \labelwidthstring 00.00.0000 pink Power density decreases by 3dB per octave; also referred to as 1/f noise \end_layout \begin_layout Labeling \labelwidthstring 00.00.0000 brown Power density decreases by 6dB per octave; also referred to as 1/f \begin_inset script superscript \begin_layout Plain Layout 2 \end_layout \end_inset noise \end_layout \begin_layout Standard The names of these noise types were derived from the spectral distribution of the correspondingly colored light \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[p.~155]{Friesecke2007} \end_layout \end_inset . \end_layout \begin_layout Subsection Triggering Notes \end_layout \begin_layout Standard In order to use the previously discussed signal generators in a musical context, it is necessary to cut off their stationary signals when no note is being played. This is accomplished by routing the output signal of the generator to an amplifier and providing it with a gate signal. The source of the gate signal can be a keyboard or a sequencer, which would also send a pitch value to the oscillator to set its frequency \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[p.~36]{Anwander2011} \end_layout \end_inset . \end_layout \begin_layout Section Signal Processing \end_layout \begin_layout Standard In their raw shape the mentioned source signals sound rather underwhelming, since they produce fixed timbres lacking of distinctive qualities \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[p.~49]{Manning1985} \end_layout \end_inset . To get a more interesting sound, the signal can be manipulated in acoustic colour or dynamics by one or more processing units. \end_layout \begin_layout Subsection Dynamic Envelopes \end_layout \begin_layout Standard The most important component responsible for shaping the dynamic structure of a note is the envelope. It is triggered by the the gate on/off signal and outputs a control signal that fades between the different state phases of a note. The rapidity of these changes is adjusted by parameters, that represent these states. Its output signal can be used to control an amplifier and therefore shape the dynamic structure of the note. The most common envelope type is the ADSR, which stands for attack, decay, sustain, release. \end_layout \begin_layout Labeling \labelwidthstring 00.00.0000 Attack sets how long the envelope signal rises after a note was triggered \end_layout \begin_layout Labeling \labelwidthstring 00.00.0000 Decay sets how long it takes for the envelope signal to drop from its maximum to the sustain level after the attack phase was completed \end_layout \begin_layout Labeling \labelwidthstring 00.00.0000 Sustain sets the output level for the time period after the decay phase and before the gate signal was terminated \end_layout \begin_layout Labeling \labelwidthstring 00.00.0000 Release sets the length of the fade out after the note has endede \end_layout \begin_layout Standard Envelopes can also be used to control other parameters, for example the cutoff frequency of a filter (see chapter \begin_inset CommandInset ref LatexCommand ref reference "sub:filters" \end_inset ). \end_layout \begin_layout Subsection Filtering \begin_inset CommandInset label LatexCommand label name "sub:filters" \end_inset \end_layout \begin_layout Standard The filter is the processing component responsible for the sound changes, that people associate with \emph on the typical synthesizer sound \emph default \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[p.~53]{Anwander2011} \end_layout \end_inset . They remove a spectrum of frequencies from their input signal above or below the cutoff frequency and are often used in conjunction with an envelope or LFO modulation on the cutoff. This cutoff frequency is an important parameter determining the frequency at which the signal begins to be attenuated. The slew rate sets the slope of the filter - meaning how abrubt frequencies are being cut. \end_layout \begin_layout Standard Filters can generally be devided into two categories: Low pass and high pass filters (also called high cut and low cut). To get a bandpass filter, low- and high pass are connected in series. When connected parallely, they become a bandstop or bandreject filter. Lastly the allpass filter should be mentioned, which does not change the frequency spectrum but merely influences the phase of the signal around its cutoff \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[p.~55]{Anwander2011} \end_layout \end_inset . \begin_inset Note Note status open \begin_layout Plain Layout COVER RESONANCE!!! \end_layout \end_inset \end_layout \begin_layout Section Controllers \end_layout \begin_layout Standard Controllers can be characterized by the way of how humans interact with them and how their output signal is applied in controlling other components of the system \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[Ch.~1A, p.~5]{Hutchins1975} \end_layout \end_inset . A keyboard for example is a manual controller, since it is the movement of the players fingers which are translated into a voltage or control value and then used to control pitch and amplitude of a note. The same applies for rotary knobs and faders or touch sensitive surfaces. \end_layout \begin_layout Standard Sequencers on the other hand are programmable controllers. They are not dependend upon a manual interaction except for their programming and activation. \end_layout \begin_layout Section The Modular Approach \end_layout \begin_layout Standard A modular synthesizer is an electronic instrument, where sound generators, processors and control facilities are presented in separate independent entities called modules. These modules are not wired in a preconceived way, but connected together with patchchords. The second essential aspect is the concept of intermodular controllability, with which modules may modulate or regulate the behaviour of other modules. \end_layout \begin_layout Chapter Analog Synthesis \end_layout \begin_layout Section General \end_layout \begin_layout Standard In the context of audio electronics it is important to be know that sound signals are nothing but currents. \end_layout \begin_layout Standard Voltage \end_layout \begin_layout Standard Control Voltage Audio Signal \end_layout \begin_layout Standard Current \end_layout \begin_layout Standard Rotary Knob \end_layout \begin_layout Standard intermodular stuff like buffering \end_layout \begin_layout Section Modules \end_layout \begin_layout Subsection Oscillator \begin_inset CommandInset label LatexCommand label name "sub:electronic-oscillator" \end_inset \end_layout \begin_layout Subsubsection Natural Resonance \end_layout \begin_layout Standard The most basic form of an oscillator circuit producing a sawtooth signal can be realized with just a few parts. A current charges a capacitor at a certain rate. Between the electrodes of the capacitor a voltage potential rises. The voltage is constantly compared with a reference voltage by a detector (Schmitt trigger). Once it reaches the predefined threshold, an electronic switch (transistor) is activated. This switch short-circuits the capacitor and discharges it, causing the output voltage to drop back to its initial potential. This is happening continiously, wheras the rate of the repetition determines the frequency of the generated signal. \end_layout \begin_layout Standard \begin_inset Float figure wide false sideways false status collapsed \begin_layout Plain Layout \begin_inset ERT status open \begin_layout Plain Layout \backslash begin{center} \end_layout \end_inset \end_layout \begin_layout Plain Layout \begin_inset Graphics filename graphics/sawtooth-oscillator-circuit.png display false width 80text% \end_inset \end_layout \begin_layout Plain Layout \begin_inset ERT status open \begin_layout Plain Layout \backslash end{center} \end_layout \end_inset \begin_inset Caption \begin_layout Plain Layout Abstract circuit scheme of a basic sawtooth oscillator \end_layout \end_inset \end_layout \begin_layout Plain Layout \end_layout \end_inset \end_layout \begin_layout Standard To get a triangle shaped output signal, the current source can be reversed in response to the detector \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[Ch.~5B, p.~3]{Hutchins1975} \end_layout \end_inset . \end_layout \begin_layout Standard \begin_inset Float figure wide false sideways false status collapsed \begin_layout Plain Layout \begin_inset ERT status open \begin_layout Plain Layout \backslash begin{center} \end_layout \end_inset \end_layout \begin_layout Plain Layout \begin_inset Graphics filename graphics/triangle-oscillator-circuit.png display false width 80text% \end_inset \end_layout \begin_layout Plain Layout \begin_inset ERT status open \begin_layout Plain Layout \backslash end{center} \end_layout \end_inset \begin_inset Caption \begin_layout Plain Layout Circuit scheme of a simple triangle oscillator \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Standard Either of these two waveforms can be waveshaped into to other common basic waveforms. All required waveshaping methods are fairly simple and their accuracy is sufficient for musical purposes. The sine wave is an exception, because there is no simple electronic method of creating a pure sine wave. What is generally used is a rounded triangle, which gives at least 1 % of harmonic distortion. In order to get a purer sine wave, the harmonics can be filtered out with a VCF following in the signal chain \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[Ch.~5B, p.~3-4]{Hutchins1975} \end_layout \end_inset . \end_layout \begin_layout Subsubsection Voltage Control \end_layout \begin_layout Standard How fast the capacitor is charged is determined by the intensity of the current that it is being charged with. This current is being extracted from a voltage, which of course can be a control voltage. \end_layout \begin_layout Standard However, creating a stable VCO design presents one of the toughest challenges for musical engineers, because the human ear is extremely sensitive to pitch changes. Also compositional processes like multitrack recording plainly reveal errors in pitch relationships \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[Ch.~5B, p.~1]{Hutchins1975} \end_layout \end_inset . The voltage to pitch distribution curve of an oscillator is determined by its exponential response to the voltage at its CV input. In a volt per octave system an increase by 1 volt at the input must result in a doubling of the oscillation frequency at the output. Thus octave purity is achieved. \end_layout \begin_layout Standard A major issue that oscillator designers have to face are temperature influenced variations of the electrical parameters of the system, causing the oscillator pitch to drift when temperature changes occur. To overcome this problem some kind of temperature compensation should be implemented. \end_layout \begin_layout Subsection Filter \begin_inset CommandInset label LatexCommand label name "sub:electronic-filter" \end_inset \end_layout \begin_layout Subsubsection Passive Filter \end_layout \begin_layout Standard Filter circuits are generally based upon the fact that the transfer of alternati ng currents through a capacitor becomes increasingly weak below a certain frequency. A signal simply passed through a capacitor resembles a high pass filter. If the capacitor is connected to the ground the high frequencies are short circuited and low frequencies remain in the signal path. This is referred to as a resistor-capacitor (RC) element. This simple circuit represents a passive, first-order butterworth filter with a roll-off of 6 dB per octave. \begin_inset Note Note status collapsed \begin_layout Plain Layout The moog filter for example concatenates four of these RC elements in a row and regulates the resistor values \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[p.~57]{Anwander2011} \end_layout \end_inset . \end_layout \end_inset To increase the slope of the filter multiple RC elements can be connected in series \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[p.~57]{Anwander2011} \end_layout \end_inset . \end_layout \begin_layout Standard Nevertheless this poses some disadvantages, because the filter stages influence each other. The resistor of the first filter affects the resistance of the second. This can be dealt with by designing the second filter to have a much higher impedance. Unfortunately a high impedance circuit is much more prone to interferences and signal noise \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[p.~97]{Sontheimer2004} \end_layout \end_inset . \end_layout \begin_layout Subsubsection Active Filter \end_layout \begin_layout Standard \begin_inset Wrap figure lines 0 placement O overhang 0in width "5.5cm" status collapsed \begin_layout Plain Layout \begin_inset ERT status open \begin_layout Plain Layout \backslash vspace*{-2em} \end_layout \begin_layout Plain Layout \backslash begin{center} \end_layout \end_inset \end_layout \begin_layout Plain Layout \begin_inset Graphics filename graphics/Sallen-Key-Filter-Lowpass.png display false width 5.5cm \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout Active Sallen-Key low pass filter circuit scheme \end_layout \end_inset \end_layout \begin_layout Plain Layout \begin_inset ERT status open \begin_layout Plain Layout \backslash end{center} \end_layout \begin_layout Plain Layout \backslash vspace*{-2em} \end_layout \end_inset \end_layout \end_inset A better and more flexible solution is the usage of an active filter design, like the Sallen-Key filter. This is a common second-order filter, which is applicable as a low or high pass, whereby only resistors and capacitors have to be swapped \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[p.~97]{Sontheimer2004} \end_layout \end_inset . Resistor \begin_inset script superscript \begin_layout Plain Layout 2 \end_layout \end_inset and capacitor \begin_inset script superscript \begin_layout Plain Layout 2 \end_layout \end_inset can be identified to form a low pass section \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[Ch.~4B, p.~4]{Hutchins1975} \end_layout \end_inset . \end_layout \begin_layout Standard To be able to change the cutoff frequency via voltage control the frequency defining resistor could be replaced with a voltage controlled resistor \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[p.~198]{Lancaster1975} \end_layout \end_inset . \end_layout \begin_layout Subsection Amplifier \end_layout \begin_layout Subsection Envelope Generator \end_layout \begin_layout Chapter Building a Modular Synthesizer \end_layout \begin_layout Section Introduction \begin_inset CommandInset label LatexCommand label name "sec:building-introduction" \end_inset \end_layout \begin_layout Standard It is relatively easy to find circuits to construct simple oscillators and filters based on the fairly comprehensible concepts of resonant circuits and RC elements (see chapter \begin_inset CommandInset ref LatexCommand ref reference "sub:electronic-oscillator" \end_inset and \begin_inset CommandInset ref LatexCommand ref reference "sub:electronic-filter" \end_inset ). However, as their flexibility and capabilities increase (e.g. controlling the frequency of an oscillator with 1 volt per octave), the circuits tend to get exceedingly complex, requiring solid expertise in electronics. \end_layout \begin_layout Standard This is why it was decided to switch to the usage of pre-designed, professionall y manufactured circuit boards for this project as opposed to elaborating all the circuits on perf boards as originally intended. This made the goal of intermodular controllability attainable more easyily. The downside of this approach are higher costs for boards and parts. However, the quality of the end-product is impressing. Also the time saving using this strategy is not to be underestimated. \end_layout \begin_layout Standard During the research phase of this project the author found out about a modular synthesizer building workshop taking place in berlin monthly. It is organized by a spanish collective from barcelona called \emph on befaco \emph default (http://befaco.org/). At the workshop it was possible to acquire various module kits containing all necessary parts and also receive tips and support while assembling them. \end_layout \begin_layout Standard Since the budget for this project was limited, it was tried to arrange a smaller setup that would still offer lots of sound design possibilities. \end_layout \begin_layout Standard \begin_inset Note Note status collapsed \begin_layout Plain Layout Befaco, help, how well it is documented is important, why the filter was chosen, limited budget \end_layout \end_inset \end_layout \begin_layout Section Formats and Interfaces \end_layout \begin_layout Standard There are several formats for module sizes, power supply plugs or patchchord connectors which emerged out of the production lines of various module manufacturers. For example Doepfer's modules are only compatible with their EuroRack cases, with a height of 128.5mm. These EuroRack modules use jack connectors for patching. A different size format often used in the DIY modular synth scene is the one the serge synthesizers use. They use banana jack connectors instead of mini jack for patching, which have the possibility of stacking banana connectors on top of each other and splitting the signal without having to use a multiplier module. For this project a combination was chosen: The modules are EuroRack size, but using banana plugs. \end_layout \begin_layout Standard \begin_inset Note Note status collapsed \begin_layout Plain Layout For tuned modules it is important to consider whether they use a volt per octave or volt per hertz characteristic. \end_layout \begin_layout Plain Layout Audio Signals ±5Volts \end_layout \begin_layout Plain Layout Buffering 1:10 impedance ratio \end_layout \end_inset \end_layout \begin_layout Section Building and Testing \end_layout \begin_layout Standard To get started with building electronic equipment, one has to obtain some tools first. This includes a soldering iron - best with adjustable temperature, a role of quality soldering tin, a desoldering pump and pliers for cutting and bending wire. \end_layout \begin_layout Standard Soldering is a process of mounting electronic parts onto a circuit board by heating up board and component and then melting the soldering tin into the joint. A good temperature for the soldering iron is between 300° and 350° celsius. The iron should not be pressed onto the joint for too long, because there is a risk of destroying the component if it is sensitive to heat. \end_layout \begin_layout Standard \begin_inset Note Note status collapsed \begin_layout Plain Layout Research beginnings - Easy oscillation circuits. easy filters. how voltage controlled is the problem. How it had been decided not to design all circuits self, but instead use predesigned circuit boards in order to be able to get tuning stability and volt-per-octave possibilities. \end_layout \begin_layout Plain Layout It had been understood how designing circuits requires years of work and experience. \end_layout \begin_layout Plain Layout Module decicion, Getting the Circuit boards, Soldering, Getting Parts, General about parts (capacitors and resistors) \end_layout \end_inset \end_layout \begin_layout Standard \begin_inset Note Note status collapsed \begin_layout Plain Layout Oscilloscope, Multimeter, Tracking faults, measuring \end_layout \end_inset \end_layout \begin_layout Section Power Supply and Case \end_layout \begin_layout Standard For the power unit a universal power supply circuit was chosen from Robert Sontheimers audio circuit technology book \begin_inset ERT status open \begin_layout Plain Layout \backslash cite[p.~74]{Sontheimer2004} \end_layout \end_inset . and mounted onto a perf board. Instead of the 7815 and 7915 voltage regulator ICs the 7812 and 7912 were used in order to get a ±12 volt power supply with a center tap for the ground. The modules can be connected to the four male 16-pin flat ribbon connectors, that were added to make the power supply compliant to the EuroRack standard. Another possibility would be to make a flying bus board by attaching those connectors to a flat ribbon cable that lies in the case. Or even just fix female connectors to the cable and plug them directly into the modules. Additionally it is planned to add an IEC socket and a power switch to it for more comfortable on and off switching and more steady starting current. \end_layout \begin_layout Standard The case is a simple rack constructed from a few pieces of wood that are held together by 19 inch rails equipped with thread rails to fasten the modules. \end_layout \begin_layout Standard \begin_inset ERT status open \begin_layout Plain Layout \backslash pagebreak \end_layout \end_inset \end_layout \begin_layout Section Frontpanels \end_layout \begin_layout Standard \begin_inset Wrap figure lines 0 placement R overhang 0in width "22text%" status collapsed \begin_layout Plain Layout \begin_inset ERT status open \begin_layout Plain Layout \backslash vspace*{-2.5em} \end_layout \begin_layout Plain Layout \backslash begin{center} \end_layout \end_inset \end_layout \begin_layout Plain Layout \begin_inset Graphics filename graphics/output-module-panel.pdf scale 60 \end_inset \end_layout \begin_layout Plain Layout \begin_inset Caption \begin_layout Plain Layout Output module template \end_layout \end_inset \end_layout \begin_layout Plain Layout \begin_inset ERT status open \begin_layout Plain Layout \backslash end{center} \end_layout \begin_layout Plain Layout \backslash vspace*{-2em} \end_layout \end_inset \end_layout \end_inset \end_layout \begin_layout Standard The panels for all modules were made from pre-cut aluminum plates with a white varnish. The labels for knobs and banana sockets are printed on the plates with a method, that is similar to homemade circuit board etching. A mirror-inverted label template is printed onto a piece of high gloss paper for inkjet printers - but with a laser printer. It is cut and placed face down onto the upper side of the panel. By thoroughly pressing down a hot flat iron (for ironing clothes) onto the panel for a few minutes, the toner cartridge particles move to the panel. The paper residues need to be removed by placing the panel in some water and rubbing them off with a sponge. Afterwards the panel is sealed with transparent lacquer. Once the panel is dried, the holes for the knobs, switches, etc. can be prepunched and drilled. Lastly all borholes are deburred. \begin_inset Note Note status open \begin_layout Plain Layout foto vom frontpanel ohne stecker \end_layout \end_inset \end_layout \begin_layout Section BF-22 Filter \end_layout \begin_layout Standard This module is an extended copy of the filter from the legendary Korg MS-20 and is based upon the principle of the Sallen and Key filter (see chapter \begin_inset CommandInset ref LatexCommand ref reference "sub:electronic-filter" \end_inset ). It combines two linkable filter stages in one module. Each stage features cutoff and frequency knobs, as well as several voltage control inputs for cutoff frequency and resonance, whereas the cutoff frequency input can be attenuated and inverted with one knob representing modulation depth (labeled: ×-1 ... 0 ... ×1). The HP/LP switch determines, if the filter is used in high pass or low pass mode. \end_layout \begin_layout Standard When turning resonance up, at one point the filter begins to self-resonate at the given cutoff frequency, which means that the filter can also be utilized as an oscillator. Therefore a volt per octave input for the cutoff control voltage was added, to be able to control the oscillating frequency in a musical context. A look at the oscilloscope shows a sine like waveform with few overtones. Turning the resonance to the maximum, the filter goes into distortion and the wave becomes more square causing the sound to get more rough. The amount of distortion is visually represented by a red LED. \end_layout \begin_layout Standard \begin_inset Note Note status open \begin_layout Plain Layout beispiel patch mit foto und beschreibung \end_layout \end_inset \end_layout \begin_layout Section Midi Input \end_layout \begin_layout Standard Note Source \end_layout \begin_layout Section Output \end_layout \begin_layout Chapter Conclusion \end_layout \begin_layout Section* Summary \end_layout \begin_layout Standard This paper constitutes an attempt to summarize what appeared to be the most important facts and information on the topics of history, theory and electronic s during the research on analog synthesis. Of course for all of the discussed could only scratch the surface. Even only the topic of active filters circuits can (and does) fill entire books. \end_layout \begin_layout Standard Accompanying this research a small synthesizer prototype has been set up, making use of the knowledge aquired during the research. \end_layout \begin_layout Section* Results \end_layout \begin_layout Standard \begin_inset Note Note status open \begin_layout Plain Layout As mentioned in chapter \begin_inset CommandInset ref LatexCommand ref reference "sec:building-introduction" \end_inset the process of building the prototype had not transpired as initially planned. \end_layout \begin_layout Plain Layout cunstruction results - goals attained. \end_layout \begin_layout Plain Layout what could be done better? \end_layout \begin_layout Plain Layout what could be added, what are the next steps? \end_layout \begin_layout Plain Layout problems of with output knob. maybe powersupply. \end_layout \begin_layout Plain Layout describe the journey, discribe the difference and natururality of analog sound as opposed to the digital, which i only knew before. \end_layout \end_inset \end_layout \begin_layout Section* A Personal Journey \end_layout \begin_layout Standard As a trained programmer and web application developer the field of electronic engineering always seemed appealing to me. Hence the assignment for a research paper during the audio engineering course at SAE Institute seemed like a welcome opportunity to dive into the realm of building electronic devices in the context of sound generation and modification. \end_layout \begin_layout Standard The process of writing this paper has been an unexpectedly rewarding and inspiring experience, pushing the boundaries of my own musical and technical understanding. Most notably the concepts of free composition - meaning allowing randomness and therefore putting oneself in the position of reacting to a musical system, influencing it in terms of tendencies, rather than controlling it with a predetermed mindset - has been something that really changed my perseption of musical creativity. This for me seems much more attainable in the analog world, where electrical components and signal chains can be brought to their tipping points, resulting in an unpredictable outcome. That is where sound exploration begins, which is a totally different experience than knowing what will happen. Virtual digital environments, which I was familiar with on the other hand, generally seem to tend persuade the user to feel in control at all times. \end_layout \begin_layout Section* Thanks \end_layout \begin_layout Standard Thanks to Eddi, Derek, Befaco, Richard, David \end_layout \begin_layout Standard \begin_inset FloatList figure \end_inset \end_layout \begin_layout Standard \begin_inset CommandInset bibtex LatexCommand bibtex bibfiles "synth_bibliography" options "karl-second4" \end_inset \end_layout \begin_layout Chapter* Declaration of academic honesty \end_layout \begin_layout Standard I hereby declare that in the attached submission I have not presented anyone else’s work, in whole or in part, as my own using only the admitted resources. Where I have taken advantage of the work of others, I have given full acknowled gement. \end_layout \begin_layout Standard My signature below constitutes my pledge that all of the writing is my own work, with the exception of those portions which are properly documented. \end_layout \begin_layout Chapter* Appendix \end_layout \begin_layout Standard \begin_inset Note Note status open \begin_layout Plain Layout urs hegemann \end_layout \begin_layout Plain Layout future audio workshop - cycle oder circle synthe \end_layout \end_inset \end_layout \end_body \end_document