421:
48:
413:
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191:, with the difference that in the latter the modulator is shifted to be positive before being multiplied with the carrier, while in the former the unshifted modulator is multiplied with the carrier. This has the effect that ring modulation of two sine waves having frequencies of 1,500 Hz and 400 Hz will produce as output signal the sum of a sine wave with frequency 1,900 Hz and one with frequency 1,100 Hz. These two output frequencies are known as
1359:
33:
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to be ring modulated. Oscillator 1 gets modulated by oscillator 3's frequency, oscillator 2 by oscillator 1's frequency, and oscillator 3 by oscillator 2's frequency. Ring modulation is disabled unless the carrier oscillator is set to produce a triangle wave, but the modulating oscillator can be set
1255:
be an ideal square wave at 300 Hz. The output will then include sine waves at 100±300 Hz, 100±900 Hz, 100±1500 Hz, 100±2100 Hz, etc., at decreasing amplitudes according to the
Fourier expansion of the carrier square wave. If the carrier frequency is less than twice the upper
2042:
analog telephone channels used ring modulators to modify the spectrum of the audio speech signals. One application is spectral inversion, typically of speech; a carrier frequency is chosen to be above the highest speech frequencies (which are low-pass filtered at, say, 3 kHz, for a carrier of
1325:
the other pair. The conducting pair carries the signal from the left transformer secondary to the primary of the transformer at the right. If the left carrier terminal is positive, the top and bottom diodes conduct. If that terminal is negative, then the side diodes conduct, but create a polarity
1476:
Analog multiplier ICs (such as those made by Analog
Devices) would work as ring modulators, of course with regard to such matters as their operating limits and scale factors. Use of multiplier ICs means that the modulation products are largely confined to sum and difference frequency of inputs
2654:
Most of the selections are kept in the rock-jazz climate with the rhythm course being interrupted now and again by an overflowing patch of accumulated layers of electronic and percussive effects (Theme from Jack
Johnson, Prelude). In fact, electronic effects appear repeatedly in the form of
1629:. It was a two-tone melody keyboard instrument with foot controllers and later added a second keyboard for timbre control, featuring a white-noise generator, envelope controller, formant filters and ring modulators for harmonics. The early Melochord was extensively used by
1485:
Any DC component of the carrier will degrade the suppression of the carrier and thus in radio applications the carrier is typically transformer- or capacitor-coupled; in low frequency (e.g., audio) applications the carrier may or may not be desired in the output.
1099:
881:
Two oscillators, whose frequencies were harmonically related and ring modulated against each other, produce sounds that still adhere to the harmonic partials of the notes but contain a very different spectral makeup. When the oscillators' frequencies are
1897:. The music on the album is often atonal, with the ring modulator converting the synthesizer's sound into complex metallic timbres. It remains the most experimental released work by the artist, with reviewers calling it "difficult listening at best".
1769:
which produced a clearer sound by eliminating a side band. These devices were designed to be controlled by voltage, compatible with modular synthesizer architecture also advocated by him, and these modules were licensed to
850:
2043:
perhaps 3.3 kHz), and the sum frequencies from the modulator are removed by more low-pass filtering. The remaining difference frequencies have an inverted spectrum: high frequencies become low, and vice versa.
1455:
to generate any of its available waveforms. However, no matter what waveform you set the modulating oscillator to, the ring modulation will always have the effect of modulating a triangle wave with a square wave.
942:
1489:
Imperfections in the diodes and transformers introduce artifacts of the two input signals. In practical ring modulators, this leakage can be reduced by introducing opposing imbalances (
1598:
1263:
mixer, where both input signals are suppressed (not present in the output)—the output is composed entirely of the sum of the products of the frequency components of the two inputs.
1559:
1337:
A particular elegance of the ring modulator is that it is bidirectional: the signal flow can be reversed allowing the same circuit with the same carrier to be used either as a
387:
3511:
2027:
An early application of the ring modulator was for combining multiple analog telephone voice channels into a single wideband signal to be carried on a single cable using
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2017:
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The ring modulator includes an input stage, a ring of four diodes excited by a carrier signal, and an output stage. The input and output stages typically include
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frequency of the signal then the resulting output signal contains spectral components from both the signal and the carrier that combine in the time domain.
1473:) fed from the square wave outputs of the two oscillators. For the limited case of square or pulse wave signals, this is identical to true ring modulation.
3501:
1589:
1597:
1318:
the diodes in a ring modulator all point in the same clockwise or counterclockwise direction. (See the schematic of a ring modulator in the upper right.)
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1518:
stereo signal, and to heterodyne microwave signals in mobile telephone and wireless networking systems. In this case, the circuit is sometimes called a
1558:
2916:
2124:(London: Macmillan Publishers, 2001): "the ring modulator takes its name from the characteristic ring formation of four diodes in its analog circuit."
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1912:: "The transformation of the child voice into a clarinet was desired. For this purpose, a pitch detector computes the instantaneous frequency
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The ring modulator was invented by Frank A. Cowan in 1934 and patented in 1935 as an improvement on the invention of Clyde R. Keith at
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fed the signal from his
Hammond through a Gibson Ring Modulator unit live on stage, which he described in 1989. Founding member of
1881:, Dik Mik, a self-confessed non-musician, used a ring modulator as his main instrument during his time with the band (1969-1973).
2926:
1376:
3622:
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The carrier, which alternates between positive and negative current, at any given time makes one pair of diodes conduct, and
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3281:
2906:
2158:
1851:
1526:. A ring modulator can be used to generate a double-sideband suppressed-carrier (DSB-SC) wave used in radio transmission.
1604:
On lower modulation frequencies, the ring modulation is perceived as a tremolo effect (as in the first part of the sound)
1094:{\displaystyle c(t)=\sin f_{c}t+{\frac {1}{3}}\sin 3f_{c}t+{\frac {1}{5}}\sin 5f_{c}t+{\frac {1}{7}}\sin 7f_{c}t+\ldots }
3476:
3301:
3218:
3142:
2980:
2655:'bruitistic' whizzes and grinds of the synthi resembling a buzz saw and of the guitar steered through a ring modulator.
1283:
for carrying multiple voice signals over telephone cables. It has since been applied to a wider range of uses, such as
1259:
Because the output contains neither the individual modulator or carrier components, the ring modulator is said to be a
3496:
2911:
2172:
1314:
with center-taps towards the diode ring. It is important to note that while the diode ring has some similarities to a
878:. As well, neither the carrier nor the incoming signal are prominent in the output, and ideally, not present at all.
47:
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1813:
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1738:
1477:(unless the circuit is overdriven), rather than the much more complicated products of the rectifier circuit.
1423:
of the two input waveforms. If the signals are processed digitally, the frequency-domain convolution becomes
2975:
2447:, 2-CD set, Stockhausen Gesamtausgabe/Complete Edition 68A–B (Kürten: Stockhausen-Verlag, 2005): 10 & 51
2379:
1650:
1692:(2003), which ring-modulates flute and trumpet. Other Stockhausen pieces employing ring modulation include
1298:
While the original Cowan patent describes a circuit with a ring of four diodes, later implementations used
3607:
2598:
2407:
1660:(1966) also calls for it. Indeed, several entire compositions by Stockhausen are based around it, such as
727:
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3147:
2661:
1724:
1645:
1523:
929:
392:
2019:. In this case odd harmonics prevail which is similar to the sound of a clarinet in the low register."
1948:
of the voice. Then the child voice passes through a ring modulator, where the frequency of the carrier
874:
of the frequencies present in each waveform. This process of ring modulation produces a signal rich in
332:
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techniques by simply multiplying the time domain signals, producing a nearly-perfect signal output.
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2852:
2693:
2645:
2221:
1630:
184:, except that instead of the diodes facing left or right, they face clockwise or counterclockwise.
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are combined to yield an output signal. One signal, called the carrier, is typically a
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2528:
2173:"Double Balanced Mixer – Theory; Circuit; Operation – Tutorial – Electronics Notes"
2086:
2032:
1888:
1836:
1809:
1787:
1733:(1956). One of the best-known applications of the ring modulator may be its use by
1447:
200:
162:
157:
is an electronic device for ring modulation. A ring modulator may be used in music
1682:(1970), where the sounds from two pianos are routed through ring modulators; and
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860:
856:
845:{\displaystyle \sin(u)\,\sin(v)={\frac {1}{2}}\left(\cos(u-v)-\cos(u+v)\right).}
643:
158:
149:; the other signal is typically more complicated and is called the input or the
122:
94:(middle), producing a variation in amplitude of the sine wave-like frequency on
1637:. Meyer-Eppler mentioned the musical application of ring modulator in his book
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synthesizer (and a few others from that era as well) the ring modulator is an
1436:
887:
17:
2420:
Karlheinz
Stockhausen, "Electroacoustic Performance Practice", translated by
3162:
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1771:
1656:
1470:
1420:
1338:
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1272:
475:
RM, producing a variation in amplitude of the square wave-like frequency on
207:
will generate its own pair of sidebands that won't be harmonically-related.
196:
150:
142:
32:
2485:
2439:
Karlheinz
Stockhausen, "Einführung"/"Introduction", English translation by
1621:
One of the earliest musical instruments utilizing a ring modulator was the
2364:
Elektronische
Klangerzeugung: Elektronische Musik und synthetische Sprache
1782:
included an optional ring modulator in his first modular synthesizer, the
1666:(1964), one of the first compositions for orchestra and live electronics;
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3331:
3321:
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3048:
2798:
2052:
1909:
1884:
1878:
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1428:
933:
204:
192:
176:
originally used to implement this technique takes the shape of a ring: a
146:
3450:
3195:
2039:
1439:
the operation or low-pass filter the signals prior to ring modulation.
1383: in this section. Unsourced material may be challenged and removed.
1326:
inversion between the transformers. This action is much like that of a
1783:
1704:
1662:
138:
2548:
2859:
3516:
3486:
1742:
1419:
products can be generated by carefully selecting and changing the
1193:
at increasing regions of the frequency spectrum. For example, let
419:
411:
391:
173:
46:
41:
31:
2035:
and filter was used to assign channels to different frequencies.
1131:
is at least twice the maximum frequency of the modulating signal
3286:
1816:
1327:
2863:
1908:, and in the first section is applied to a child's voice and a
1672:(1965), where the sounds of choral voices are modulated with a
855:
Alternatively, one can use the fact that multiplication in the
3053:
1352:
1299:
2650:
Jazz Forum: The
Magazine of the International Jazz Federation
2510:
Harald Bode, "European
Electronic Music Instrument Design",
1590:
Ring modulation with an exponential sweep from 0 Hz to 9 kHz
1536:
3395:
890:, often producing bell-like or otherwise metallic sounds.
424:
An example of ring modulation on a sine wave of frequency
2550:
Buchla
Electronic Musical Instruments—Historical Overview
1855:, especially on the track "On the Way Home to Earth". On
1162:, then the resulting output is a series of duplicates of
51:
An example of ring modulation on sine waves of frequency
2533:, (New York: Experimental Television Center Ltd, 2004),
467:, resulting in a complex sound using analog FM known as
1757:
One of the first products dedicated for music was the
1224:
represent a sine wave at 100 Hz, and the carrier
2573:"A Ring Modulator Device for the Performing Musician"
1981:
1954:
1918:
1891:
to improvise his 1978 avant-garde-experimental album
1839:
synthesizers also featured built-in ring modulators.
1231:
1200:
1169:
1138:
1110:
945:
903:
739:
692:
652:
619:
592:
565:
536:
507:
481:
450:
430:
335:
308:
279:
250:
221:
203:), the output will sound quite different, since each
100:
77:
57:
2405:
Ludger Brümmer, "Stockhausen on Electronics, 2004",
1633:
in the early days of the electronic music studio at
3525:
3459:
3383:
3330:
3252:
3194:
3171:
3125:
3067:
3009:
2925:
2897:
1869:ran the sounds he played through a ring modulator.
2011:
1967:
1940:
1506:Ring modulation has also been extensively used in
1411:Some modern ring modulators are implemented using
1246:
1215:
1184:
1153:
1123:
1093:
916:
844:
718:
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634:
605:
578:
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522:
490:
459:
436:
381:
314:
294:
265:
236:
109:
86:
63:
2443:, in booklet accompanying Karlheinz Stockhausen,
2430:34, no. 1 (Winter, 1996): 74–105. Citation on 89.
2116:, page 429, volume 21, second edition, edited by
1723:A ring-modulator was the major component used in
2211:Commodore Programmer's Reference Guide, page 463
1648:used ring modulation in 1956 for some sounds in
2114:The New Grove Dictionary of Music and Musicians
1845:employs the ring modulator heavily in the 1974
1275:. The original application was in the field of
400:Mini-Circuits SBL-1 with four Schottky diodes.
2222:"Synth Secrets, Part 11: Amplitude Modulation"
1794:in the late 1960s, and it became an origin of
1345:, for example in low-cost radio transceivers.
886:harmonically related, ring modulation creates
195:. If one of the input signals has significant
27:Frequency mixing function in signal processing
2875:
2445:Licht-Bilder (3. Szene vom SONNTAG aus LICHT)
1349:Integrated circuit methods of ring modulation
8:
1546:Audio samples of the ring modulation effect:
322:denotes time), ring modulation approximates
3502:Professional Lighting and Sound Association
3092:Comparison of analog and digital recording
2882:
2868:
2860:
2375:
2373:
2295:. Tata McGraw-Hill Education. p. 37.
1334:) switch wired for reversing connections.
363:
2001:
1986:
1980:
1959:
1953:
1923:
1917:
1399:Learn how and when to remove this message
1230:
1199:
1168:
1137:
1115:
1109:
1076:
1053:
1041:
1018:
1006:
983:
971:
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902:
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449:
429:
334:
307:
278:
249:
220:
99:
76:
56:
1741:to produce the distinctive voice of the
168:The name derives from the fact that the
2328:(4), Canadian Electroacoustic Community
2082:
2080:
2078:
2076:
2074:
2072:
2070:
2068:
2064:
2031:. A ring modulator in combination with
932:and a series of reducing-amplitude odd
408:) and RF 1–500 MHz (ADE-1: 0.5–500 MHz)
2670:
2659:
2388:, pp. 124-125. John Wiley & Sons.
2140:, p. 11. Wm. C. Brown Co. Publishers.
1611:
3563:New Interfaces for Musical Expression
1900:Ring modulation is used in the piece
1808:, one of the earliest ring modulator
1493:, variable resistors or capacitors).
7:
2849:"Effects Explained: Ring Modulation"
2289:T G Thomas S Chandra Sekhar (2005).
1569:Ring modulation with a 2500 Hz sound
1381:adding citations to reliable sources
187:Ring modulation is quite similar to
2618:(photo). Edison Music Corporation.
2594:"Session Transcript: Tom Oberheim"
2366:, (Bonn: Ferdinand Dümmlers, 1949)
1612:Problems playing these files? See
25:
3112:Reel-to-reel audio tape recording
2851:. Harmony Central. Archived from
2825:, p.76-7. John Wiley & Sons.
2537:from the original on 19 July 2011
2112:Richard Orton, "Ring Modulator",
3581:
2487:Harald Bode—A Lifetime for Sound
1790:built a ring modulator unit for
1765:. Also in 1964 he developed the
1594:
1573:
1555:
1357:
870:Ring modulators thus output the
559:are sine waves with frequencies
382:{\displaystyle y(t)=x(t)\;c(t).}
3097:Experimental musical instrument
2318:"Harald Bode—A Short Biography"
2029:frequency-division multiplexing
1887:used a ring modulator with his
1778:started in 1963–1964. In 1963,
1435:distortion, so it is common to
1368:needs additional citations for
1281:frequency-division multiplexing
726:. This is a consequence of the
646:) sine waves, one of frequency
444:and a square wave of frequency
215:Denoting the carrier signal by
133:function, an implementation of
3613:Electronic musical instruments
2750:. SAF Publishing. p. 20.
2634:, DiscoFreq's Effects Database
2385:Introduction to Computer Music
2268:. Firewall Media. p. 83.
1998:
1992:
1935:
1929:
1654:and his realization score for
1241:
1235:
1210:
1204:
1179:
1173:
1148:
1142:
955:
949:
831:
819:
807:
795:
768:
762:
752:
746:
629:
623:
546:
540:
517:
511:
373:
367:
360:
354:
345:
339:
289:
283:
260:
254:
231:
225:
180:. The circuit is similar to a
1:
3282:Electronic musical instrument
2241:. Artech House. p. 336.
1852:Visions of the Emerald Beyond
1812:products for guitarists. The
3588:Record production portal
3477:Institute of Broadcast Sound
2822:DAFX - Digital Audio Effects
2631:Maestro RM-1A Ring Modulator
2316:Rebekkah Palov (July 2011),
2159:"Multipliers vs. Modulators"
3497:Musical Electronics Library
2459:Doctor Who: The Early Years
2265:Analog Communication System
2092:The Computer Music Tutorial
1583:Notice the bell-like sound.
1551:Unprocessed original sample
1302:as the switching elements.
893:If the carrier signal is a
719:{\displaystyle f_{c}-f_{x}}
686:and the other of frequency
679:{\displaystyle f_{c}+f_{x}}
396:Double balanced high level
3639:
3244:Sound reinforcement system
3153:Sound reinforcement system
2527:Tom Rhea (21 March 2011),
2340:"The "Melochord" (1947–9)"
2095:, pp. 220-221. MIT Press.
2023:Analogue telephone systems
2012:{\displaystyle f_{0}(n)/2}
1639:Elektrische Klangerzeugung
1104:and the carrier frequency
244:, the modulator signal by
3577:
3467:Audio Engineering Society
3365:Software effect processor
3345:Digital audio workstation
3186:Digital signal processing
2950:Digital audio workstation
2819:Zölzer, Udo; ed. (2002).
2748:Hawkwind: Sonic Assassins
2721:"Interview with Jon Lord"
2553:, Buchla & Associates
2514:Audio Engineering Society
2427:Perspectives of New Music
2352:(description and history)
2344:The Keyboardmuseum Online
1776:Moog modular synthesizers
1413:digital signal processing
1332:double pole, double throw
273:and the output signal by
3558:Professional audio store
3460:People and organizations
3446:Sound recording engineer
2615:Oberheim Music Modulator
1941:{\displaystyle f_{0}(n)}
1739:BBC Radiophonic Workshop
642:will be the sum of two (
2976:Microphone preamplifier
2457:Jeremy Bentham (1986),
2411:32, no. 4 (2008):10–16.
2262:Abhishek Yadav (2008).
1767:Bode Frequency Shifter,
1644:Meyer-Eppler's student
1530:Music and sound effects
1522:, one of many possible
199:(which is the case for
36:Schematic diagram of a
3623:Radio modulation modes
2917:Electronic and digital
2799:"Vangelis - Beaubourg"
2772:"Vangelis - Beaubourg"
2599:Red Bull Music Academy
2465:, 1986), p. 127,
2408:Computer Music Journal
2235:Hamish Meikle (2008).
2013:
1969:
1942:
1727:'s music for the film
1541:
1248:
1217:
1186:
1155:
1125:
1095:
918:
846:
728:trigonometric identity
720:
680:
636:
607:
580:
553:
524:
498:
492:
461:
438:
417:
409:
383:
316:
296:
267:
238:
118:
111:
88:
65:
44:
2746:Ian Abrahams (2004).
2530:Harald Bode Biography
2463:W. H. Allen & Co.
2362:Werner Meyer-Eppler,
2200:U.S. patent 1,855,576
2187:U.S. patent 2,025,158
2014:
1970:
1968:{\displaystyle f_{c}}
1943:
1761:developed in 1961 by
1725:Louis and Bebe Barron
1646:Karlheinz Stockhausen
1641:, published in 1949.
1540:
1427:. If the signals are
1249:
1218:
1187:
1156:
1126:
1124:{\displaystyle f_{c}}
1096:
919:
917:{\displaystyle f_{c}}
847:
721:
681:
637:
613:, respectively, then
608:
606:{\displaystyle f_{x}}
581:
579:{\displaystyle f_{c}}
554:
525:
493:
462:
439:
423:
415:
395:
384:
317:
297:
268:
239:
112:
89:
66:
50:
35:
3375:Software synthesizer
3340:Digital audio editor
3126:Playback transducers
2986:Multitrack recording
2646:Trzaskowski, Andrzej
2571:Thomas E. Oberheim,
2292:Communication Theory
2238:Modern Radar Systems
1979:
1952:
1916:
1847:Mahavishnu Orchestra
1796:Oberheim Electronics
1754:, starting in 1963.
1651:Gesang der Jünglinge
1502:Radio communications
1425:circular convolution
1377:improve this article
1247:{\displaystyle c(t)}
1229:
1216:{\displaystyle x(t)}
1198:
1185:{\displaystyle x(t)}
1167:
1154:{\displaystyle x(t)}
1136:
1108:
943:
901:
737:
690:
650:
635:{\displaystyle y(t)}
617:
590:
563:
552:{\displaystyle x(t)}
534:
523:{\displaystyle c(t)}
505:
479:
448:
428:
404:level +7 dBm (1.41 V
333:
306:
295:{\displaystyle y(t)}
277:
266:{\displaystyle x(t)}
248:
237:{\displaystyle c(t)}
219:
211:Simplified operation
189:amplitude modulation
98:
75:
55:
2855:on 1 December 2005.
2350:on 14 November 2007
1792:his musician friend
1759:Bode Ring Modulator
1631:Werner Meyer-Eppler
1306:Circuit description
491:{\displaystyle 12f}
460:{\displaystyle 12f}
110:{\displaystyle 12f}
87:{\displaystyle 12f}
3426:Re-recording mixer
3229:Keyboard amplifier
2945:Binaural recording
2797:McDonald, Steven.
2493:, Harald Bode News
2038:Early attempts at
2009:
1965:
1938:
1859:' 1975 live album
1542:
1510:, for example, to
1446:chip found in the
1431:, this will cause
1244:
1213:
1182:
1151:
1121:
1091:
914:
872:sum and difference
842:
716:
676:
632:
603:
576:
549:
520:
499:
488:
457:
434:
418:
416:Macro of the ADE-1
410:
379:
312:
292:
263:
234:
145:or another simple
119:
107:
84:
61:
45:
40:, showing ring of
3595:
3594:
3401:Guitar technician
3297:Music workstation
3181:Digital recording
3158:Speaker enclosure
3077:8-track cartridge
3019:Phonograph record
2778:. 7 December 2003
2669:Missing or empty
2583:, No. 708 (G-4).
2302:978-0-07-059091-5
2275:978-81-318-0319-6
2248:978-1-59693-243-2
1747:television series
1689:Sonntag aus Licht
1599:
1578:
1560:
1409:
1408:
1401:
1061:
1026:
991:
926:Fourier expansion
782:
437:{\displaystyle f}
315:{\displaystyle t}
131:signal processing
64:{\displaystyle f}
16:(Redirected from
3630:
3618:Frequency mixers
3586:
3585:
3584:
3472:Goji Electronics
3411:Monitor engineer
3370:Software sampler
3277:Electronic drums
3254:Electronic music
3224:Guitar amplifier
3069:Analog recording
3029:Compact cassette
2991:Music production
2899:Music technology
2891:Music technology
2884:
2877:
2870:
2861:
2856:
2834:
2817:
2811:
2810:
2808:
2806:
2794:
2788:
2787:
2785:
2783:
2768:
2762:
2761:
2743:
2737:
2736:
2734:
2732:
2717:
2711:
2710:
2708:
2706:
2685:
2679:
2678:
2672:
2667:
2665:
2657:
2642:
2636:
2635:
2626:
2620:
2619:
2610:
2604:
2603:
2590:
2584:
2582:
2568:
2562:
2561:
2560:
2558:
2545:
2539:
2538:
2524:
2518:
2508:
2502:
2501:
2500:
2498:
2492:
2482:
2476:
2475:
2454:
2448:
2441:Suzanne Stephens
2437:
2431:
2418:
2412:
2403:
2397:
2377:
2368:
2367:
2359:
2353:
2351:
2346:, archived from
2336:
2330:
2329:
2313:
2307:
2306:
2286:
2280:
2279:
2259:
2253:
2252:
2232:
2226:
2225:
2218:
2212:
2209:
2203:
2202:
2196:
2190:
2189:
2183:
2177:
2176:
2169:
2163:
2162:
2155:
2149:
2138:Electronic Music
2131:
2125:
2110:
2104:
2084:
2018:
2016:
2015:
2010:
2005:
1991:
1990:
1974:
1972:
1971:
1966:
1964:
1963:
1947:
1945:
1944:
1939:
1928:
1927:
1730:Forbidden Planet
1625:(1947) built by
1601:
1600:
1580:
1579:
1562:
1561:
1539:
1524:chopper circuits
1520:ring demodulator
1404:
1397:
1393:
1390:
1384:
1361:
1353:
1316:bridge rectifier
1293:electronic music
1277:analog telephony
1253:
1251:
1250:
1245:
1222:
1220:
1219:
1214:
1191:
1189:
1188:
1183:
1160:
1158:
1157:
1152:
1130:
1128:
1127:
1122:
1120:
1119:
1100:
1098:
1097:
1092:
1081:
1080:
1062:
1054:
1046:
1045:
1027:
1019:
1011:
1010:
992:
984:
976:
975:
923:
921:
920:
915:
913:
912:
865:frequency domain
851:
849:
848:
843:
838:
834:
783:
775:
725:
723:
722:
717:
715:
714:
702:
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685:
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682:
677:
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662:
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641:
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612:
610:
609:
604:
602:
601:
585:
583:
582:
577:
575:
574:
558:
556:
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550:
529:
527:
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521:
497:
495:
494:
489:
466:
464:
463:
458:
443:
441:
440:
435:
388:
386:
385:
380:
321:
319:
318:
313:
301:
299:
298:
293:
272:
270:
269:
264:
243:
241:
240:
235:
182:bridge rectifier
135:frequency mixing
116:
114:
113:
108:
93:
91:
90:
85:
70:
68:
67:
62:
21:
3638:
3637:
3633:
3632:
3631:
3629:
3628:
3627:
3598:
3597:
3596:
3591:
3582:
3580:
3573:
3521:
3455:
3421:Record producer
3406:Mixing engineer
3379:
3326:
3292:MIDI controller
3267:Circuit bending
3248:
3190:
3167:
3143:Monitor speaker
3121:
3063:
3011:Recording media
3005:
2996:Music sequencer
2981:Monitor speaker
2927:Sound recording
2921:
2893:
2888:
2846:
2843:
2838:
2837:
2818:
2814:
2804:
2802:
2796:
2795:
2791:
2781:
2779:
2770:
2769:
2765:
2758:
2745:
2744:
2740:
2730:
2728:
2725:Modern Keyboard
2719:
2718:
2714:
2704:
2702:
2689:"Lord Almighty"
2687:
2686:
2682:
2668:
2658:
2644:
2643:
2639:
2628:
2627:
2623:
2612:
2611:
2607:
2592:
2591:
2587:
2570:
2569:
2565:
2556:
2554:
2547:
2546:
2542:
2526:
2525:
2521:
2512:Journal of the
2509:
2505:
2496:
2494:
2490:
2484:
2483:
2479:
2473:
2456:
2455:
2451:
2438:
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2419:
2415:
2404:
2400:
2378:
2371:
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2356:
2338:
2337:
2333:
2315:
2314:
2310:
2303:
2288:
2287:
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2276:
2261:
2260:
2256:
2249:
2234:
2233:
2229:
2220:
2219:
2215:
2210:
2206:
2198:
2197:
2193:
2185:
2184:
2180:
2171:
2170:
2166:
2157:
2156:
2152:
2132:
2128:
2111:
2107:
2085:
2066:
2061:
2049:
2025:
1982:
1977:
1976:
1955:
1950:
1949:
1919:
1914:
1913:
1904:(1988/1997) by
1843:John McLaughlin
1799:Music Modulator
1635:Bonn University
1619:
1618:
1610:
1608:
1607:
1606:
1605:
1602:
1595:
1592:
1586:
1585:
1584:
1581:
1574:
1571:
1565:
1564:
1563:
1556:
1553:
1547:
1543:
1537:
1532:
1508:radio receivers
1504:
1499:
1483:
1417:Intermodulation
1405:
1394:
1388:
1385:
1374:
1362:
1351:
1308:
1285:voice inversion
1269:
1261:double-balanced
1227:
1226:
1196:
1195:
1165:
1164:
1134:
1133:
1111:
1106:
1105:
1072:
1037:
1002:
967:
941:
940:
904:
899:
898:
859:is the same as
788:
784:
735:
734:
706:
693:
688:
687:
666:
653:
648:
647:
615:
614:
593:
588:
587:
566:
561:
560:
532:
531:
503:
502:
477:
476:
446:
445:
426:
425:
407:
398:frequency mixer
331:
330:
304:
303:
275:
274:
246:
245:
217:
216:
213:
137:, in which two
127:ring modulation
96:
95:
73:
72:
53:
52:
28:
23:
22:
15:
12:
11:
5:
3636:
3634:
3626:
3625:
3620:
3615:
3610:
3600:
3599:
3593:
3592:
3578:
3575:
3574:
3572:
3571:
3566:
3560:
3555:
3550:
3545:
3540:
3535:
3529:
3527:
3526:Related topics
3523:
3522:
3520:
3519:
3514:
3509:
3504:
3499:
3494:
3489:
3484:
3482:Lejaren Hiller
3479:
3474:
3469:
3463:
3461:
3457:
3456:
3454:
3453:
3448:
3443:
3441:Sound operator
3438:
3436:Sound follower
3433:
3431:Sound designer
3428:
3423:
3418:
3413:
3408:
3403:
3398:
3393:
3391:Audio engineer
3387:
3385:
3381:
3380:
3378:
3377:
3372:
3367:
3362:
3357:
3352:
3347:
3342:
3336:
3334:
3328:
3327:
3325:
3324:
3319:
3314:
3309:
3304:
3299:
3294:
3289:
3284:
3279:
3274:
3269:
3264:
3258:
3256:
3250:
3249:
3247:
3246:
3241:
3236:
3231:
3226:
3221:
3216:
3211:
3209:Bass amplifier
3206:
3204:Mixing console
3200:
3198:
3192:
3191:
3189:
3188:
3183:
3177:
3175:
3169:
3168:
3166:
3165:
3160:
3155:
3150:
3145:
3140:
3135:
3129:
3127:
3123:
3122:
3120:
3119:
3114:
3109:
3104:
3099:
3094:
3089:
3084:
3079:
3073:
3071:
3065:
3064:
3062:
3061:
3056:
3051:
3046:
3041:
3036:
3031:
3026:
3021:
3015:
3013:
3007:
3006:
3004:
3003:
2998:
2993:
2988:
2983:
2978:
2973:
2968:
2963:
2958:
2953:
2947:
2942:
2940:Mixing console
2937:
2931:
2929:
2923:
2922:
2920:
2919:
2914:
2909:
2903:
2901:
2895:
2894:
2889:
2887:
2886:
2879:
2872:
2864:
2858:
2857:
2847:Scott Lehman.
2842:
2841:External links
2839:
2836:
2835:
2812:
2789:
2763:
2756:
2738:
2727:. January 1989
2712:
2680:
2637:
2621:
2605:
2601:Barcelona 2008
2585:
2578:AES Convention
2563:
2540:
2519:
2517:9 (1961): 267.
2503:
2477:
2471:
2449:
2432:
2413:
2398:
2369:
2354:
2331:
2308:
2301:
2281:
2274:
2254:
2247:
2227:
2213:
2204:
2191:
2178:
2164:
2150:
2134:Strange, Allen
2126:
2105:
2063:
2062:
2060:
2057:
2056:
2055:
2048:
2045:
2024:
2021:
2008:
2004:
2000:
1997:
1994:
1989:
1985:
1962:
1958:
1937:
1934:
1931:
1926:
1922:
1806:Ring Modulator
1669:Mikrophonie II
1609:
1603:
1593:
1588:
1587:
1582:
1572:
1567:
1566:
1554:
1549:
1548:
1545:
1544:
1535:
1534:
1533:
1531:
1528:
1503:
1500:
1498:
1495:
1482:
1479:
1452:triangle waves
1407:
1406:
1365:
1363:
1356:
1350:
1347:
1323:reverse-biases
1307:
1304:
1268:
1265:
1243:
1240:
1237:
1234:
1212:
1209:
1206:
1203:
1181:
1178:
1175:
1172:
1150:
1147:
1144:
1141:
1118:
1114:
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1101:
1090:
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1071:
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987:
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954:
951:
948:
911:
907:
853:
852:
841:
837:
833:
830:
827:
824:
821:
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815:
812:
809:
806:
803:
800:
797:
794:
791:
787:
781:
778:
773:
770:
767:
764:
761:
758:
754:
751:
748:
745:
742:
713:
709:
705:
700:
696:
673:
669:
665:
660:
656:
631:
628:
625:
622:
600:
596:
573:
569:
548:
545:
542:
539:
519:
516:
513:
510:
487:
484:
469:diode-clipping
456:
453:
433:
405:
390:
389:
378:
375:
372:
369:
366:
362:
359:
356:
353:
350:
347:
344:
341:
338:
324:multiplication
311:
291:
288:
285:
282:
262:
259:
256:
253:
233:
230:
227:
224:
212:
209:
170:analog circuit
155:ring modulator
106:
103:
83:
80:
60:
38:ring modulator
26:
24:
18:Ring modulator
14:
13:
10:
9:
6:
4:
3:
2:
3635:
3624:
3621:
3619:
3616:
3614:
3611:
3609:
3608:Audio effects
3606:
3605:
3603:
3590:
3589:
3576:
3570:
3569:Vehicle audio
3567:
3564:
3561:
3559:
3556:
3554:
3551:
3549:
3546:
3544:
3541:
3539:
3538:High fidelity
3536:
3534:
3531:
3530:
3528:
3524:
3518:
3515:
3513:
3510:
3508:
3505:
3503:
3500:
3498:
3495:
3493:
3490:
3488:
3485:
3483:
3480:
3478:
3475:
3473:
3470:
3468:
3465:
3464:
3462:
3458:
3452:
3449:
3447:
3444:
3442:
3439:
3437:
3434:
3432:
3429:
3427:
3424:
3422:
3419:
3417:
3414:
3412:
3409:
3407:
3404:
3402:
3399:
3397:
3394:
3392:
3389:
3388:
3386:
3382:
3376:
3373:
3371:
3368:
3366:
3363:
3361:
3358:
3356:
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3351:
3348:
3346:
3343:
3341:
3338:
3337:
3335:
3333:
3329:
3323:
3320:
3318:
3315:
3313:
3310:
3308:
3305:
3303:
3300:
3298:
3295:
3293:
3290:
3288:
3285:
3283:
3280:
3278:
3275:
3273:
3270:
3268:
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3263:
3260:
3259:
3257:
3255:
3251:
3245:
3242:
3240:
3237:
3235:
3232:
3230:
3227:
3225:
3222:
3220:
3217:
3215:
3212:
3210:
3207:
3205:
3202:
3201:
3199:
3197:
3193:
3187:
3184:
3182:
3179:
3178:
3176:
3174:
3173:Digital audio
3170:
3164:
3161:
3159:
3156:
3154:
3151:
3149:
3146:
3144:
3141:
3139:
3136:
3134:
3131:
3130:
3128:
3124:
3118:
3117:Tape recorder
3115:
3113:
3110:
3108:
3105:
3103:
3100:
3098:
3095:
3093:
3090:
3088:
3087:Cassette deck
3085:
3083:
3080:
3078:
3075:
3074:
3072:
3070:
3066:
3060:
3057:
3055:
3052:
3050:
3047:
3045:
3042:
3040:
3037:
3035:
3032:
3030:
3027:
3025:
3024:Magnetic tape
3022:
3020:
3017:
3016:
3014:
3012:
3008:
3002:
3001:Outboard gear
2999:
2997:
2994:
2992:
2989:
2987:
2984:
2982:
2979:
2977:
2974:
2972:
2969:
2967:
2964:
2962:
2959:
2957:
2954:
2951:
2948:
2946:
2943:
2941:
2938:
2936:
2935:Audio channel
2933:
2932:
2930:
2928:
2924:
2918:
2915:
2913:
2910:
2908:
2905:
2904:
2902:
2900:
2896:
2892:
2885:
2880:
2878:
2873:
2871:
2866:
2865:
2862:
2854:
2850:
2845:
2844:
2840:
2832:
2831:9780471490784
2828:
2824:
2823:
2816:
2813:
2800:
2793:
2790:
2777:
2773:
2767:
2764:
2759:
2757:9780946719693
2753:
2749:
2742:
2739:
2726:
2722:
2716:
2713:
2700:
2696:
2695:
2690:
2684:
2681:
2676:
2663:
2656:
2651:
2647:
2641:
2638:
2633:
2632:
2625:
2622:
2617:
2616:
2609:
2606:
2602:
2600:
2595:
2589:
2586:
2581:
2580:38 (May 1970)
2579:
2574:
2567:
2564:
2552:
2551:
2544:
2541:
2536:
2532:
2531:
2523:
2520:
2516:
2515:
2507:
2504:
2489:
2488:
2481:
2478:
2474:
2472:0-491-03612-4
2468:
2464:
2460:
2453:
2450:
2446:
2442:
2436:
2433:
2429:
2428:
2423:
2417:
2414:
2410:
2409:
2402:
2399:
2395:
2394:9780470714553
2391:
2387:
2386:
2381:
2380:Collins, Nick
2376:
2374:
2370:
2365:
2358:
2355:
2349:
2345:
2341:
2335:
2332:
2327:
2323:
2319:
2312:
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2298:
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2277:
2271:
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2266:
2258:
2255:
2250:
2244:
2240:
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2231:
2228:
2223:
2217:
2214:
2208:
2205:
2201:
2195:
2192:
2188:
2182:
2179:
2174:
2168:
2165:
2160:
2154:
2151:
2147:
2146:0-697-03612-X
2143:
2139:
2135:
2130:
2127:
2123:
2119:
2118:Stanley Sadie
2115:
2109:
2106:
2102:
2101:9780262680820
2098:
2094:
2093:
2088:
2083:
2081:
2079:
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2071:
2069:
2065:
2058:
2054:
2051:
2050:
2046:
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2041:
2036:
2034:
2030:
2022:
2020:
2006:
2002:
1995:
1987:
1983:
1960:
1956:
1932:
1924:
1920:
1911:
1907:
1906:Luciano Berio
1903:
1898:
1896:
1895:
1890:
1886:
1882:
1880:
1876:
1872:
1868:
1864:
1863:
1858:
1854:
1853:
1848:
1844:
1840:
1838:
1834:
1833:Rhodes Chroma
1830:
1826:
1822:
1818:
1815:
1811:
1807:
1805:
1800:
1797:
1793:
1789:
1785:
1781:
1777:
1773:
1768:
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1760:
1755:
1753:
1752:
1748:
1744:
1740:
1736:
1735:Brian Hodgson
1732:
1731:
1726:
1721:
1719:
1718:
1713:
1712:
1707:
1706:
1701:
1700:Mikrophonie I
1697:
1696:
1691:
1690:
1685:
1681:
1680:
1675:
1674:Hammond organ
1671:
1670:
1665:
1664:
1659:
1658:
1653:
1652:
1647:
1642:
1640:
1636:
1632:
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1570:
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1509:
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1472:
1469:
1466:(formed from
1465:
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1453:
1449:
1445:
1440:
1438:
1434:
1430:
1426:
1422:
1418:
1414:
1403:
1400:
1392:
1389:February 2015
1382:
1378:
1372:
1371:
1366:This section
1364:
1360:
1355:
1354:
1348:
1346:
1344:
1340:
1335:
1333:
1329:
1324:
1319:
1317:
1313:
1305:
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1301:
1296:
1294:
1290:
1286:
1282:
1278:
1274:
1266:
1264:
1262:
1257:
1254:
1238:
1232:
1223:
1207:
1201:
1192:
1176:
1170:
1161:
1145:
1139:
1116:
1112:
1088:
1085:
1082:
1077:
1073:
1069:
1066:
1063:
1058:
1055:
1050:
1047:
1042:
1038:
1034:
1031:
1028:
1023:
1020:
1015:
1012:
1007:
1003:
999:
996:
993:
988:
985:
980:
977:
972:
968:
964:
961:
958:
952:
946:
939:
938:
937:
935:
931:
928:contains the
927:
909:
905:
897:of frequency
896:
891:
889:
885:
879:
877:
873:
868:
866:
862:
858:
839:
835:
828:
825:
822:
816:
813:
810:
804:
801:
798:
792:
789:
785:
779:
776:
771:
765:
759:
756:
749:
743:
740:
733:
732:
731:
729:
711:
707:
703:
698:
694:
671:
667:
663:
658:
654:
645:
644:phase-shifted
626:
620:
598:
594:
571:
567:
543:
537:
514:
508:
485:
482:
474:
470:
454:
451:
431:
422:
414:
403:
399:
394:
376:
370:
364:
357:
351:
348:
342:
336:
329:
328:
327:
325:
309:
286:
280:
257:
251:
228:
222:
210:
208:
206:
202:
198:
194:
190:
185:
183:
179:
175:
171:
166:
164:
160:
156:
152:
148:
144:
140:
136:
132:
128:
124:
104:
101:
81:
78:
58:
49:
43:
39:
34:
30:
19:
3579:
3312:Sound module
3272:Drum machine
3214:Effects unit
3107:Player piano
3034:Compact disc
2956:Effects unit
2853:the original
2820:
2815:
2803:. Retrieved
2792:
2780:. Retrieved
2775:
2766:
2747:
2741:
2729:. Retrieved
2724:
2715:
2703:. Retrieved
2698:
2692:
2683:
2671:|title=
2662:cite journal
2653:
2649:
2640:
2630:
2624:
2614:
2608:
2597:
2588:
2576:
2566:
2555:, retrieved
2549:
2543:
2529:
2522:
2511:
2506:
2495:, retrieved
2486:
2480:
2458:
2452:
2444:
2435:
2425:
2416:
2406:
2401:
2383:
2363:
2357:
2348:the original
2343:
2334:
2325:
2321:
2311:
2291:
2284:
2264:
2257:
2237:
2230:
2216:
2207:
2194:
2181:
2167:
2153:
2137:
2129:
2122:John Tyrrell
2113:
2108:
2090:
2087:Curtis Roads
2037:
2033:carrier wave
2026:
1901:
1899:
1892:
1889:Yamaha CS-80
1883:
1865:, guitarist
1860:
1850:
1841:
1837:Yamaha CS-80
1802:
1798:
1788:Tom Oberheim
1766:
1758:
1756:
1749:
1728:
1722:
1715:
1714:(1967), and
1709:
1703:
1699:
1693:
1687:
1686:(2002) from
1684:Licht-Bilder
1683:
1677:
1667:
1661:
1655:
1649:
1643:
1638:
1622:
1620:
1519:
1505:
1497:Applications
1490:
1488:
1484:
1475:
1464:XOR function
1457:
1448:Commodore 64
1441:
1410:
1395:
1386:
1375:Please help
1370:verification
1367:
1336:
1331:
1320:
1312:transformers
1309:
1297:
1289:transceivers
1270:
1260:
1258:
1225:
1194:
1163:
1132:
1103:
892:
883:
880:
869:
854:
500:
472:
468:
214:
201:square waves
186:
177:
167:
163:effects unit
159:synthesizers
154:
126:
120:
29:
3553:Music store
3548:Home cinema
3507:Robert Moog
3492:Max Mathews
3416:Piano tuner
3384:Professions
3360:Scorewriter
3317:Synthesizer
3133:Loudspeaker
2461:, (London:
2422:Jerome Kohl
1871:Deep Purple
1857:Miles Davis
1763:Harald Bode
1627:Harald Bode
1481:Limitations
1460:ARP Odyssey
1450:allows for
1343:demodulator
930:fundamental
895:square wave
888:inharmonics
861:convolution
857:time domain
153:signal. A
123:electronics
3602:Categories
3543:Home audio
3533:Audiophile
3350:GarageBand
3196:Live music
3138:Headphones
3102:Phonograph
2971:Microphone
2966:Headphones
2912:Electrical
2907:Mechanical
2801:. AllMusic
2776:Synthtopia
2731:21 January
2705:21 January
2557:27 January
2497:27 January
2059:References
1975:is set to
1867:Pete Cosey
1780:Don Buchla
1774:for their
1751:Doctor Who
1717:Kurzwellen
1711:Prozession
1614:media help
1512:demodulate
1471:NAND gates
1437:oversample
178:diode ring
161:and as an
71:(top) and
3307:Sequencer
3234:PA system
3163:Subwoofer
3148:PA system
3082:Amplifier
3044:Hard disk
2961:Equalizer
2805:26 August
2782:26 August
2322:EContact!
1894:Beaubourg
1784:Model 100
1772:R.A. Moog
1657:Telemusik
1623:Melochord
1421:frequency
1339:modulator
1273:Bell Labs
1089:…
1067:
1032:
997:
965:
934:harmonics
817:
811:−
802:−
793:
760:
744:
704:−
197:overtones
193:sidebands
151:modulator
143:sine wave
3355:ProTools
3332:Software
3322:Theremin
3262:Chiptune
3219:Foldback
3049:MiniDisc
2694:Keyboard
2648:(1976).
2535:archived
2382:(2010).
2136:(1972).
2089:(1996).
2053:Theremin
2047:See also
2040:securing
1910:clarinet
1885:Vangelis
1879:Hawkwind
1875:Jon Lord
1825:ARP 2600
1821:Synthi A
1720:(1968).
1708:(1969),
1702:(1964),
1698:(1960),
1695:Kontakte
1433:aliasing
1429:wideband
1287:, radio
924:, whose
876:partials
205:harmonic
147:waveform
117:(bottom)
3451:Tape op
3302:Sampler
1862:Agharta
1829:Odyssey
1804:Maestro
1786:. Also
1745:in the
1737:of the
1267:History
863:in the
473:chopper
302:(where
139:signals
3565:(NIME)
3239:Reverb
2829:
2754:
2701:. 1998
2652:: 74.
2469:
2392:
2299:
2272:
2245:
2144:
2099:
1902:Ofanim
1849:album
1810:effect
1743:Daleks
1705:Hymnen
1679:Mantra
1663:Mixtur
1458:On an
1291:, and
174:diodes
42:diodes
3517:STEIM
3512:SMPTE
3487:IRCAM
2952:(DAW)
2491:(PDF)
129:is a
3287:MIDI
3059:Opus
2827:ISBN
2807:2022
2784:2022
2752:ISBN
2733:2015
2707:2016
2675:help
2559:2011
2499:2011
2467:ISBN
2390:ISBN
2297:ISBN
2270:ISBN
2243:ISBN
2142:ISBN
2120:and
2097:ISBN
1835:and
1817:VCS3
1801:and
1491:e.g.
1468:four
1442:The
1328:DPDT
1300:FETs
1279:for
586:and
530:and
3054:MP3
3039:DAT
1873:'s
1814:EMS
1514:an
1444:SID
1379:by
1341:or
1064:sin
1029:sin
994:sin
962:sin
884:not
814:cos
790:cos
757:sin
741:sin
501:If
471:or
406:p-p
172:of
121:In
3604::
3396:DJ
2774:.
2723:.
2699:24
2697:.
2691:.
2666::
2664:}}
2660:{{
2596:,
2575:,
2424:,
2372:^
2342:,
2326:13
2324:,
2320:,
2067:^
1831:,
1827:,
1823:,
1819:,
1676:;
1516:FM
1295:.
936::
867:.
730::
483:12
452:12
402:LO
326::
165:.
125:,
102:12
79:12
2883:e
2876:t
2869:v
2833:.
2809:.
2786:.
2760:.
2735:.
2709:.
2677:)
2673:(
2396:.
2305:.
2278:.
2251:.
2224:.
2175:.
2161:.
2148:.
2103:.
2007:2
2003:/
1999:)
1996:n
1993:(
1988:0
1984:f
1961:c
1957:f
1936:)
1933:n
1930:(
1925:0
1921:f
1616:.
1402:)
1396:(
1391:)
1387:(
1373:.
1330:(
1242:)
1239:t
1236:(
1233:c
1211:)
1208:t
1205:(
1202:x
1180:)
1177:t
1174:(
1171:x
1149:)
1146:t
1143:(
1140:x
1117:c
1113:f
1086:+
1083:t
1078:c
1074:f
1070:7
1059:7
1056:1
1051:+
1048:t
1043:c
1039:f
1035:5
1024:5
1021:1
1016:+
1013:t
1008:c
1004:f
1000:3
989:3
986:1
981:+
978:t
973:c
969:f
959:=
956:)
953:t
950:(
947:c
910:c
906:f
840:.
836:)
832:)
829:v
826:+
823:u
820:(
808:)
805:v
799:u
796:(
786:(
780:2
777:1
772:=
769:)
766:v
763:(
753:)
750:u
747:(
712:x
708:f
699:c
695:f
672:x
668:f
664:+
659:c
655:f
630:)
627:t
624:(
621:y
599:x
595:f
572:c
568:f
547:)
544:t
541:(
538:x
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515:t
512:(
509:c
486:f
455:f
432:f
377:.
374:)
371:t
368:(
365:c
361:)
358:t
355:(
352:x
349:=
346:)
343:t
340:(
337:y
310:t
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287:t
284:(
281:y
261:)
258:t
255:(
252:x
232:)
229:t
226:(
223:c
105:f
82:f
59:f
20:)
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