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Berkeley COMPSCI 150 - Final Project Specification MIDI Sound Synthesizer

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University of California at BerkeleyCollege of EngineeringDepartment of Electrical Engineering and Computer SciencesComputer Science DivisionCS 150 J. WawrzynekSpring 2002 Project Info.Final Project SpecificationMIDI Sound SynthesizerVersion 0.51 IntroductionFor the final project you are required to use an FPGA board to build a “box” that takes aMIDI signal as input and generates a audio waveform as output. Figure 1 shows a highlevel view of the synthesizer that you will build. MIDI is an acronym for MusicalInstrument Digital Interface, and a MIDI signal is a bit-serial stream of bytes. The audiowaveform is a mono (as opposed to stereo) signal. It will be strong enough to driveheadphones or small speakers. The MIDI synthesizer is monophonic, meaning that it willtranslate MIDI signals into sound not more than one note at a time, and single channel,meaning that it will produce the voice of only one instrument. The audio waveforms aregenerated using a technique called waveform synthesis; waveforms from actual musicalinstruments are stored in ROM and used to generate sound in response to MIDIcommands. The sound waveforms are stored and played-back using 16-bit data samples.Output sampling rate is 31.25KHz.MIDI InDATAADDRESSWavetableROMDACMusicIsolatorOpto-FPGAAmplifierOscillatorFigure 1: High-level view of the MIDI Synthesizer.Our project is a simplified version of commercial synthesizers. For comparison, a medium1grade commercial sound box has stereo output, is polyphonic, and is capable of generating30 notes simultaneously. Note pitch can be varied continuously, and the voices includenumerous digital filters for adding special effects to the sound output. Such systems costaround several hundred dollars.1.1 Sound and Music TheorySound is air vibrating at an audible frequency, typically 20Hz – 20KHz for an adulthuman. The amount of displacement can be sampled and recorded as a sequence ofmagnitudes over time, and reproduced by speakers or headphones.Our hearing is quite complex in the way we perceive musical tones. Two of the mostimportant characteristics of a musical tone is its loudness and its pitch. To a firstapproximation human hearing is logarithmic in perceiving both loudness and pitch. In thecase of loudness, this means that a we perceive the loudness as being proportional to thelogarithm of the sound wave amplitude.In the case of pitch, the human auditory system is very keen at detecting the logarithmicrelationships between frequency, and “musical” pitch intervals. The simplest interval todetect is the octave, where the higher pitch has double the frequency of the lower pitch.Given those two frequencies, it is possible to subdivide the interval (which is the multiple2) into twelve parts, producing eleven semi-tones in between. These twelve semi-tonesform the chromatic scale of the traditional western twelve-tone scale.These twelve intervals form a geometric series. As we move from one up to the next wecan determine its frequency by multiplying by12√2. After 12 such multiplications we willhave doubled the frequency and reached the octave. Most people can detect a pitchdifference much smaller than these 12 divisions, in fact as small as a few hundredths of asemi-tone. In musical terms a cent is 1/100 of a semi-tone. To increase the pitch of a noteby one cent, multiply its frequency by1200√2.The note called middle C has a frequency of 261.63Hz. The MIDI encoding for that noteis key 60. The note called high C, which is an octave higher, has a double thefrequency—523.25Hz, and it has a MIDI encoding of 72. Others tones can be produced bymultiplying and dividing the frequency by factors of12√2. For example, MIDI notenumber 61 has a frequency of 261.63kHz×12√2.There is one more important aspect to a musical sound, called timbre. Whereas pitch isindication of how often a sound wave repeats, and loudness is the way we perceive theamplitude of a sound, timbre is a perception of the shape of the sound wave. Sometimesthe timbre of a musical tone is called its tone quality or color. Different musicalinstruments have different, and readily identifiable, timbres. Like our perception of othercharacteristics of a musical tone, timbre is complex, but it is deeply related to the way amusical note starts, the shape the waveform takes as it repeats itself, and how it dies out.For many musical instruments, a simple model can be used to describe the shape of thewaveform. The waveform can be split into three parts: an attack, a sustain, and a release.The attack is the most interesting part of a musical sound, corresponding to when a noteis first played. It typically lasts for no more than 300ms, and during this time, thewaveform may be very irregular. Most of the rest of the musical sound is very repetitive,2and it is called the sustain. In the sustain section, not much would be missing to the ear ifjust one cycle were played over and over again for the duration of the rest of the note. Atthe end of the note, there may also be irregularities in the waveform, and the releaseconsists of the dying away of the sound. The release is typically shorter than 100ms.This simple model matches some musical instrument better than others. Notes from flutesand other woodwind instruments and bowed sounds such as from the violin family, fitnicely into this model. However, sounds from instruments that are struck, such as amarimba or even a piano don’t really have a sustain part to their notes. In these cases wecould simply omit the sustain part of the model, or probably more simply represent theentire note as an attack only.1.2 Sampling and StoringA 512KB EPROM will be used to store the sound information. At a sample rate of31.25KHz, and at 2 bytes per sample, the EPROM can store roughly 8 seconds of rawsound. However, it must be capable of reproducing notes of maybe 100 different pitches atvarying durations.The simplest way of getting arbitrary duration is to store an attack, a short section of thesustain, and a release in a note template. Then, to generate a note, the synthesizer willplay the attack and continue playing into the sustain. While the note is held, it willcontinue to play the sustain part by looping. When the key is released, to signal the end ofthe note, the synthesizer will continue playing the sustain to the end of the current loopiteration and then play the release portion of the stored note. This process for playing anote is illustrated in figure 2.One way of generating


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Berkeley COMPSCI 150 - Final Project Specification MIDI Sound Synthesizer

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