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441:, which was used to model acoustic waves in strings, tubes, and membranes. The first set of extensions and generalizations of the Karplus-Strong Algorithm, typically known as the Extended Karplus-Strong (EKS) Algorithm, was presented in a paper in 1982 at the International Computer Music Conference in Venice, Italy, and published in more detail in 1983 in Computer Music Journal in an article entitled "Extensions of the Karplus Strong Plucked String Algorithm," by David A. Jaffe and Julius O. Smith, and in Smith's PhD/EE dissertation.
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The patent was licensed first to Mattel
Electronics, which failed as a company before any product using the algorithm was developed, then to a startup company founded by some of the laid-off Mattel executives. They never got sufficient funding to finish development, and so never brought a product to
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loop. The filter can be a first-order lowpass filter (as pictured). In the original algorithm, the filter consisted of averaging two adjacent samples, a particularly simple filter that can be implemented without a multiplier, requiring only shift and add operations. The filter characteristics are
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While they may not adhere strictly to the algorithm, many hardware components for modular systems have been commercially produced that invoke the basic principles of
Karplus-Strong Synthesis: using an inverted, scaled control system for very small time values in a filtered delay line to create
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market either. Eventually Yamaha licensed the patent, as part of the
Sondius package of patents from Stanford. It is unknown whether any hardware using the algorithm was ever sold, though many software implementations (which did not pay any license fees to the inventors) have been released.
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recognized that the transfer-function of the KS, when viewed as a digital filter, coincided with that of a vibrating string, with the filter in the feedback loop representing the total string losses over one period. He later derived the KS algorithm as a special case of
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may be sharpened or flattened relative to the fundamental frequency. The original algorithm used equal weighting on two adjacent samples, as this can be achieved without multiplication hardware, allowing extremely cheap implementations.
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playable notes in the
Western Tempered tuning system, controlled with volt per octave tracking or MIDI data. The Inventors were not specifically credited, though the term "Karplus-Strong Synthesis" is referenced in some of the manuals.
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conjectured that the
Karplus-Strong (KS) algorithm was in some sense a vibrating string simulation, and they worked on showing that it solved the wave equation for the vibrating string, but this was not completed.
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Hardware components capable of
Karplus-Strong style synthesis include the Moog Clusterflux 108M, Mutable Instruments Elements and Rings, 4ms Company Dual Looping Delay, 2HP Pluck, Make Noise Mimeophon,
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Holding the period (= length of the delay line) constant produces vibrations similar to those of a string or bell. Increasing the period sharply after the transient input produces drum-like sounds.
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filters may be used, but FIR have the advantage that transients are suppressed if the fractional delay is changed over time. The most elementary fractional delay is the
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file. The algorithm used a loop gain of 0.98 with increasingly attenuating first order lowpass filters. The pitch of the note was A2, or 220 Hz.
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analysis can be used to get the pitches and decay times of the harmonics more precisely, as explained in the 1983 paper that introduced the algorithm.
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did the first analysis of how it worked. Together they developed software and hardware implementations of the algorithm, including a custom
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A short excitation waveform (of length L samples) is generated. In the original algorithm, this was a burst of
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The length of any digital delay line is a whole-number multiple of the sampling period. In order to obtain a
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are used with parameters selected to obtain an appropriate phase delay at the fundamental frequency. Either
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that loops a short waveform through a filtered delay line to simulate the sound of a hammered or plucked
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Independently controlled wavetable-modification instrument and method for generating musical sound
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Techniques for
Digital Filter Design and System Identification, with Application to the Violin
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Karplus, Kevin; Strong, Alex (1983). "Digital
Synthesis of Plucked String and Drum Timbres".
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The filtered output is simultaneously mixed into the output and fed back into the delay line.
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A demonstration of the
Karplus-Strong algorithm can be heard in the following
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of the filter must be less than 1 at all frequencies, to maintain a stable
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Wavetable
Modification Instrument and Method for Generating Musical Sound
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503:, Non Linear Circuits Is Carp Lust Wrong?, and the Strymon Starlab.
555: This article incorporates text from a publication now in the
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crucial in determining the harmonic structure of the decaying tone.
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analysis. However, it can also be viewed as the simplest class of
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This excitation is output and simultaneously fed back into a
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676:"Extensions of the Karplus-Strong Plucked String Algorithm"
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chip. They named the algorithm "Digitar" synthesis, as a
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The first musical use of the algorithm was in the work
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often needed for fine tuning the string below JND (
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728:, Alexander R. Strong, Kevin J. Karplus, "
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421:Due to its plucked-string sound in certain modes,
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341:(5)). If the phase delay varies with frequency,
110:At first glance, this technique can be viewed as
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809:David A. Jaffe's music, including sound examples
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204:The output of the delay line is fed through a
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186:or frequency sweep, or a single cycle of a
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674:Jaffe, David A.; Smith, Julius O. (1983).
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567:Dictionary of Greek and Roman Antiquities
80:Learn how and when to remove this message
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43:This article includes a list of general
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130:-modification algorithms now known as
27:Method of physical modelling synthesis
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804:A HTML5 port of the above application
767:. Upper Saddle River: Prentice-Hall.
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273:is therefore calculated according to
799:More sound examples under CC license
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487:for female chorus and tape (1987).
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266:for a given fundamental frequency
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49:it lacks sufficient corresponding
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483:for string quartet and tape, and
461:May All Your Children Be Acrobats
747:, Alexander R. Strong, "
614:"inventor:(Alexander R. Strong)"
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404:Problems playing this file? See
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481:Telegram to the President, 1984
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93:Karplus–Strong string synthesis
718:(PhD/EE). Stanford University.
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175:, but it can also include any
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789:The Karplus-Strong Algorithm
417:Refinements to the algorithm
140:invented the algorithm, and
97:physical modelling synthesis
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751:", published 1986-11-18
732:", published 1987-03-17
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439:digital waveguide synthesis
329:between two samples (e.g.,
302:is the sampling frequency.
132:digital waveguide synthesis
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765:Elements of Computer Music
763:Moore, F. Richard (1990).
745:US application 4622877
726:US application 4649783
311:Just Noticeable Difference
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714:Smith, Julius O. (1983).
537:Karplus & Strong 1983
477:Silicon Valley Breakdown
179:signal, such as a rapid
18:Karplus–Strong algorithm
691:(2). MIT Press: 56–69.
651:(2). MIT Press: 43–55.
64:more precise citations.
684:Computer Music Journal
644:Computer Music Journal
602:Jaffe & Smith 1983
570:. London: John Murray.
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252:{\displaystyle -2\pi }
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152:for "digital guitar".
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962:Karplus–Strong string
447:developed a superior
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315:interpolating filters
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231:fundamental frequency
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118:similar to that of a
112:subtractive synthesis
1013:Software synthesizer
857:Frequency modulation
455:Musical applications
327:linear interpolation
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995:Digital synthesizer
463:written in 1981 by
432:Julius O. Smith III
972:Analog synthesizer
934:Physical modelling
513:Digital delay line
501:Arturia MicroFreak
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1008:Scanned synthesis
947:Digital waveguide
862:Linear arithmetic
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576:cite encyclopedia
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376:Karplus-Strong #1
225:Tuning the string
214:positive feedback
103:or some types of
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350:Z-transform
333:(4.2) = 0.8
261:phase delay
192:square wave
173:white noise
150:portmanteau
124:z-transform
120:comb filter
114:based on a
62:introducing
887:Distortion
623:2019-07-17
519:References
406:media help
199:delay line
105:percussion
45:references
909:Wavetable
524:Citations
449:wavetable
343:harmonics
337:(4) + 0.2
247:π
241:−
181:sine wave
128:wavetable
1028:Category
914:Granular
882:Additive
507:See also
177:wideband
985:Modular
957:Formant
901:Sampler
872:Scanned
705:3680063
665:3680062
559::
396:= 220Hz
208:. The
58:improve
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357:Vorbis
293:where
206:filter
101:string
47:, but
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701:JSTOR
679:(PDF)
661:JSTOR
485:Grass
184:chirp
769:ISBN
589:help
425:and
229:The
210:gain
146:VLSI
122:for
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323:FIR
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
