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Frequency modulation synthesis

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Odd1 and Odd2 wave forms, and the Res1 and Res2 wave forms. The sine wave selection works the same as the DX7 wave forms. The All1 and All2 wave forms are a saw-tooth wave form. The Odd1 and Odd2 wave forms are pulse or square waves. These two types of wave forms can be used to model the basic harmonic peaks in the bottom of the harmonic spectrum of most instruments. The Res1 and Res2 wave forms move the spectral peak to a specific harmonic and can be used to model either triangular or rounded groups of harmonics further up in the spectrum of an instrument. Combining an All1 or Odd1 wave form with multiple Res1 (or Res2) wave forms (and adjusting their amplitudes) can model the harmonic spectrum of an instrument or sound.
3664:{\displaystyle {\begin{aligned}&\sin \left(\theta _{c}+\beta \,\sin(\theta _{m})\right)\\&\ =\ \sin(\theta _{c})\cos(\beta \sin(\theta _{m}))+\cos(\theta _{c})\sin(\beta \sin(\theta _{m}))\\&\ =\ \sin(\theta _{c})\left+\cos(\theta _{c})\left\\&\ =\ J_{0}(\beta )\sin(\theta _{c})+J_{1}(\beta )2\cos(\theta _{c})\sin(\theta _{m})+J_{2}(\beta )2\sin(\theta _{c})\cos(2\theta _{m})+J_{3}(\beta )2\cos(\theta _{c})\sin(3\theta _{m})+...\\&\ =\ J_{0}(\beta )\sin(\theta _{c})+\sum _{n=1}^{\infty }J_{n}(\beta )\left\\&\ =\ \sum _{n=-\infty }^{\infty }J_{n}(\beta )\,\sin(\theta _{c}+n\theta _{m})\qquad (\because \ J_{-n}(x)=(-1)^{n}J_{n}(x))\end{aligned}}} 1176: 1769: 801: 41: 580: 562:
could model the sounds produced in the human voice and in a wind instrument, along with making percussion instrument sounds. The FS1R also contained an additional wave form called the Formant wave form. Formants can be used to model resonating body instrument sounds like the cello, violin, acoustic guitar, bassoon, English horn, or human voice. Formants can even be found in the harmonic spectrum of several brass instruments.
1293: 1171:{\displaystyle {\begin{aligned}FM(t)&\ =\ A\,\sin \left(\,\int _{0}^{t}\left(\omega _{c}+B\,\sin(\omega _{m}\,\tau )\right)d\tau \right)\\&\ =\ A\,\sin \left(\omega _{c}\,t-{\frac {B}{\omega _{m}}}\left(\cos(\omega _{m}\,t)-1\right)\right)\\&\ =\ A\,\sin \left(\omega _{c}\,t+{\frac {B}{\omega _{m}}}\left(\sin(\omega _{m}\,t-\pi /2)+1\right)\right)\\\end{aligned}}} 2503: 428: 345: 1764:{\displaystyle {\begin{aligned}FM(t)&\ \approx \ A\,\sin \left(\omega _{c}\,t+\beta \,\sin(\omega _{m}\,t)\right)\\&\ =\ A\left(J_{0}(\beta )\sin(\omega _{c}\,t)+\sum _{n=1}^{\infty }J_{n}(\beta )\left\right)\\&\ =\ A\sum _{n=-\infty }^{\infty }J_{n}(\beta )\,\sin((\omega _{c}+n\,\omega _{m})\,t)\end{aligned}}} 626:, which combines a 128-voice sample-based engine with a 128-voice FM engine. This iteration of FM is called FM-X, and features 8 operators; each operator has a choice of several basic wave forms, but each wave form has several parameters to adjust its spectrum. The Yamaha Montage was followed by the more affordable Yamaha 3860:
At this point we may consider various additional signal modifications that we may wish to make to the series of tones produced by the above example. For instance, if we would like to add frequency modulation to the tones, it is necessary to patch another audio signal into the jack connected by a line
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implemented FM on his instruments in the mid-1960s, prior to Chowning's patent. His 158, 258 and 259 dual oscillator modules had a specific FM control voltage input, and the model 208 (Music Easel) had a modulation oscillator hard-wired to allow FM as well as AM of the primary oscillator. These early
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With the expiration of the Stanford University FM patent in 1995, digital FM synthesis can now be implemented freely by other manufacturers. The FM synthesis patent brought Stanford $ 20 million before it expired, making it (in 1994) "the second most lucrative licensing agreement in Stanford's
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relationship to the original carrier signal. As the amount of frequency modulation increases, the sound grows progressively complex. Through the use of modulators with frequencies that are non-integer multiples of the carrier signal (i.e. inharmonic), inharmonic bell-like and percussive spectra can
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synthesizers in 2016. FM-X uses 8 operators. Each FM-X operator has a set of multi-spectral wave forms to choose from, which means each FM-X operator can be equivalent to a stack of 3 or 4 DX7 FM operators. The list of selectable wave forms includes sine waves, the All1 and All2 wave forms, the
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Combining sets of 8 FM operators with multi-spectral wave forms began in 1999 by Yamaha in the FS1R. The FS1R had 16 operators, 8 standard FM operators and 8 additional operators that used a noise source rather than an oscillator as its sound source. By adding in tuneable noise sources the FS1R
420:, though it would take several years before Yamaha released their FM digital synthesizers. In the 1970s, Yamaha were granted a number of patents, under the company's former name "Nippon Gakki Seizo Kabushiki Kaisha", evolving Chowning's work. Yamaha built the first prototype FM 2234: 2498:{\displaystyle {\begin{aligned}\cos(\beta \sin \theta )&=J_{0}(\beta )+2\sum _{n=1}^{\infty }J_{2n}(\beta )\cos(2n\theta )\\\sin(\beta \sin \theta )&=2\sum _{n=0}^{\infty }J_{2n+1}(\beta )\sin((2n+1)\theta )\end{aligned}}} 2528: 2248: 2152: 1298: 806: 1815: 793: 1228: 1895: 172:
may result in pitch instability. However, FM synthesis can also be implemented digitally, which is more stable and became standard practice. Digital FM synthesis (equivalent to the
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synthesizer, released in 1983, was ubiquitous throughout the 1980s. Several other models by Yamaha provided variations and evolutions of FM synthesis during that decade.
3737: 503:, and other techniques. The degree of complexity of the FM in such hardware synths may vary from simple 2-operator FM, to the highly flexible 6-operator engines of the 622:(2020) and opsix SE (2023) integrating 6 operators FM synthesis with subtractive, analogue modeling, additive, semi-modular and Waveshaping. Yamaha released the 307:
as one of its sound generator chips. Throughout the 2000s, FM synthesis was also used on a wide range of phones to play ringtones and other sounds, typically in the
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Yamaha's engineers began adapting Chowning's algorithm for use in a commercial digital synthesizer, adding improvements such as the "key scaling" method
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Yamaha had patented its hardware implementation of FM in the 1970s, allowing it to nearly monopolize the market for FM technology until the mid-1990s.
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As the basic of these variations, we analyze the spectrum of 2 operators (linear FM synthesis using two sinusoidal operators) on the following.
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applications used analog oscillators, and this capability was also followed by other modular synthesizers and portable synthesizers including
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2-operator demonstration: if the frequency of the modulator is lower than that of the carrier, the output note will be that of the modulator.
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in 1974. Yamaha eventually commercialized FM synthesis technology with the Yamaha GS-1, the first FM digital synthesizer, released in 1980.
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in 2018, with 64-voice, 8 operators FM-X architecture in addition to a 128-voice sample-based engine. Elektron in 2018 launched the
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beginning in 1978, included a digital FM synthesizer, using an FM synthesis algorithm licensed from Yamaha. Yamaha's groundbreaking
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New hardware synths specifically marketed for their FM capabilities disappeared from the market after the release of the
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sound chip (which was also commonly used for arcade machines up to the mid-nineties) with later CX5M units using the
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Buchla Electronic Music System: Users Manual written for CBS Musical Instruments (Buchla 100 Owner's Manual)
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and the Modor NF-1. Various other synthesizers offer limited FM abilities to supplement their main engines.
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in 1973. The implementation commercialized by Yamaha (US Patent 4018121 Apr 1977 or U.S. Patent 4,018,121)
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Programming and Metaprogramming in the Electro-Organism - An Operating Directive for the Music Easel
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but the results end up being equivalent mathematically as both are essentially a special case of
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FM synthesis also became the usual setting for games and software up until the mid-nineties. For
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in 1974, based on FM synthesis, before commercially releasing the Yamaha GS-1 in 1980. The
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synthesizer, released in 1983, brought FM to the forefront of synthesis in the mid-1980s.
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to avoid the introduction of distortion that normally occurred in analog systems during
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The spectrum generated by FM synthesis with one modulator is expressed as follows:
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Realtime Convolution & Modulation (AFM + Sample) and Formant Shaping Synthesis
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series of compact, affordable desktop modules,. More recently Korg released the
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Various operator arrangements (known as "FM Algorithms" in Yamaha terminology)
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Amusement use: FM sound chips on PCs, arcades, game consoles, and mobile phones
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released the Korg Volca FM, a, 3-voice, 6 operators FM iteration of the Korg
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history". FM today is mostly found in software-based synths such as FM8 by
4201:"The Synthesis of Complex Audio Spectra by Means of Frequency Modulation" 1980: 329: 156: 155:
sounds. To synthesize harmonic sounds, the modulating signal must have a
133: 4354: 4174: 4008:"Sounds of the '80s Part 2: The Yamaha DX1 & Its Successors (Retro)" 4324: 427: 300: 284: 69: 3861:
to the middle dial on the Model 158 Dual Sine-Sawtooth Oscillator. ...
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Electronic and experimental music: technology, music, and culture
3821:"The top 10 classic synth presets (and where you can hear them)" 611: 308: 292: 288: 268: 264: 4358: 4330:
Synth Secrets, Part 12: An Introduction To Frequency Modulation
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FM synthesis was the basis of some of the early generations of
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However, well-developed FM synthesis options are a feature of
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If we were to ignore the constant phase terms on the carrier
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Music synthesis approaches sound quality of real instruments
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There are multiple variations of FM synthesis, including:
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Variable Phase Modulation, FM-X Synthesis, Altered FM, etc
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arcade (MVS) and home console (AES) machines. The related
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FM Theory & Applications - By Musicians For Musicians
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Nord Modular & Micro Modular V3.03 tips & tricks
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conversion for CV/oct. interface of analog synthesizers)
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Digital frequency modulation synthesis was developed by
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Computer Music: Synthesis, Composition and Performance
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Parallel FM (multiple modulators, multiple-carriers),
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Synth Secrets, Part 13: More On Frequency Modulation
4534: 4511: 4473: 4436: 144:of an oscillator is altered in accordance with the 4347:F.M. Synthesis including complex operator analysis 3663: 2497: 2228: 2122: 2090: 2050: 1954: 1933: 1889: 1847: 1809: 1763: 1267: 1222: 1170: 787: 4087: 4085: 373:who was trying to create sounds different from 271:was used as main basic sound generator board in 4370: 4035:Stanford University News Service (06/07/94), 1810:{\displaystyle \omega _{c}\,,\,\omega _{m}\,} 474:Popularization after the expiration of patent 457:developed a related form of synthesis called 8: 3797: 3795: 3732: 3730: 3728: 788:{\displaystyle m(t)=B\,\sin(\omega _{m}t)\,} 3705:McGuire, Sam; Matějů, Zbyněk (2020-12-28). 363:. FM synthesis was developed since 1967 at 53:modulated by a 440 Hz modulating tone 4377: 4363: 4355: 3744:. Yamaha Corporation. 2014. Archived from 3692: 2139:The above expression is transformed using 151:FM synthesis can create both harmonic and 4238:Dodge, Charles; Jerse, Thomas A. (1997). 3912: 3910: 3908: 3639: 3629: 3595: 3572: 3556: 3542: 3527: 3517: 3503: 3479: 3470: 3454: 3435: 3404: 3388: 3374: 3354: 3344: 3333: 3317: 3289: 3250: 3225: 3194: 3178: 3153: 3122: 3106: 3084: 3053: 3037: 3009: 2977: 2922: 2912: 2901: 2880: 2850: 2813: 2803: 2792: 2767: 2749: 2710: 2676: 2648: 2614: 2573: 2559: 2547: 2527: 2525: 2434: 2424: 2413: 2332: 2322: 2311: 2286: 2247: 2245: 2151: 2149: 2103: 2071: 2034: 1951: 1946: 1930: 1915: 1909: 1886: 1880: 1871: 1860: 1844: 1828: 1826: 1806: 1800: 1795: 1791: 1785: 1779: 1750: 1741: 1736: 1724: 1707: 1692: 1682: 1668: 1636: 1629: 1620: 1615: 1603: 1581: 1552: 1543: 1538: 1526: 1509: 1489: 1479: 1468: 1454: 1448: 1420: 1382: 1376: 1362: 1352: 1346: 1330: 1297: 1295: 1264: 1256: 1241: 1235: 1223:{\displaystyle \phi _{c}=B/\omega _{m}\,} 1219: 1213: 1204: 1192: 1186: 1137: 1127: 1121: 1095: 1086: 1079: 1073: 1057: 1017: 1011: 985: 976: 969: 963: 947: 907: 901: 887: 875: 860: 855: 850: 838: 805: 803: 784: 772: 758: 738: 4208:Journal of the Audio Engineering Society 4160: 1276: 431:FM digital synthesizer Yamaha DX7 (1983) 267:. For arcade systems and game consoles, 4219:Chowning, John; Bristow, David (1986). 4068:Poyser, Debbie; Johnson, Derek (1998). 3757: 3755: 3742:Yamaha Synth 40th Anniversary - History 3685: 2022: 637:FM-X synthesis was introduced with the 1890:{\displaystyle \beta =B/\omega _{m}\,} 3803:"1978 New England Digital Synclavier" 1280: 7: 4128:Yamaha Montage Product Features Page 2512: 228:. Other computers such as the Sharp 4350:mirror site of F.M. Synthesis, 2019 1268:{\displaystyle \phi _{m}=-\pi /2\,} 545:synths manufactured by Clavia, the 4175:"Frequency Modulation Mathematics" 4094:"FM_Synthesis_of_Real_Instruments" 3809:. Penton Media. September 1, 2006. 3518: 3513: 3345: 2913: 2804: 2425: 2323: 1848:{\displaystyle \,\omega =2\pi f\,} 1683: 1678: 1480: 25: 4342:Paul Wiffens Synth School: Part 3 4266:The Pennsylvania State University 4139:Yamaha MODX Product Features Page 382:was licensed to Japanese company 4106:from the original on 2017-09-25. 3708:The Art of Digital Orchestration 700:Exponential FM (preceded by the 578: 340:John Chowning (late-1960s–1970s) 110: 89: 4092:Zollinger, W. Thor (Dec 2017). 3945:. Clavia DMI AB. Archived from 3581: 2238:and a lemma of Bessel function 2141:trigonometric addition formulas 1934:{\displaystyle J_{n}(\beta )\,} 397:quadrature amplitude modulation 190:New England Digital Corporation 4006:Gordon Reid (September 2001). 3892:"U.S. Patent 4018121 Apr 1977" 3654: 3651: 3645: 3626: 3616: 3610: 3604: 3582: 3578: 3549: 3539: 3533: 3476: 3447: 3432: 3422: 3410: 3381: 3366: 3360: 3323: 3310: 3301: 3295: 3256: 3240: 3231: 3218: 3206: 3200: 3184: 3168: 3159: 3146: 3134: 3128: 3112: 3099: 3090: 3077: 3065: 3059: 3043: 3030: 3021: 3015: 2983: 2970: 2955: 2952: 2943: 2937: 2886: 2873: 2856: 2837: 2828: 2822: 2779: 2773: 2755: 2742: 2719: 2716: 2703: 2691: 2682: 2669: 2657: 2654: 2641: 2629: 2620: 2607: 2579: 2566: 2488: 2482: 2467: 2464: 2455: 2449: 2396: 2381: 2368: 2356: 2347: 2341: 2298: 2292: 2272: 2257: 2173: 2161: 2117: 2105: 2085: 2079: 2045: 2039: 1927: 1921: 1754: 1747: 1717: 1714: 1704: 1698: 1633: 1626: 1596: 1593: 1578: 1568: 1556: 1549: 1519: 1516: 1501: 1495: 1458: 1441: 1432: 1426: 1386: 1369: 1313: 1307: 1145: 1114: 1021: 1004: 911: 894: 821: 815: 781: 765: 749: 743: 683:Various waveform of operators 208:systems, sound cards like the 176:using the time integration of 122:Frequency modulation synthesis 32:FM synthesis using 2 operators 1: 1964:Bessel function of first kind 361:broadcast radio transmissions 4242:. New York: Schirmer Books. 2029:Note that modulation signal 1855:) of carrier and modulator, 450:Related development by Casio 4293:The Computer Music Tutorial 3765:The computer music tutorial 2098:, by time integral between 672:Serial FM (multiple stages) 132:whereby the frequency of a 46:A 220 Hz carrier tone 4591: 1899:frequency modulation index 459:phase distortion synthesis 168:FM synthesis using analog 62:frequency modulation index 60:, with various choices of 4393: 4078:. No. December 1998. 3939:"FM synthesis on Modular" 3847:Dr. Hubert Howe (1960s). 795:, the carrier signal is: 355:By the mid-20th century, 238:Yamaha CX5M computer unit 142:(instantaneous) frequency 3880:. Buchla and Associates. 463:CZ range of synthesizers 148:of a modulating signal. 138:modulating its frequency 2060:instantaneous frequency 178:instantaneous frequency 27:Form of sound synthesis 4321:, by Bill Schottstaedt 4290:Roads, Curtis (1996). 3969:"Early Computer Music" 3874:Atten Strange (1974). 3693:Dodge & Jerse 1997 3665: 3522: 3349: 2917: 2808: 2499: 2429: 2327: 2230: 2124: 2092: 2052: 1956: 1935: 1891: 1849: 1811: 1765: 1687: 1484: 1269: 1224: 1172: 789: 733:For modulation signal 694:Additional modulation 659: 533:sample-based synthesis 513:Kurzweil Music Systems 497:sample-based synthesis 432: 352: 320:Don Buchla (mid-1960s) 279:) and notably used in 140:with a modulator. The 44: 4575:Sound synthesis types 4503:Karplus–Strong string 4319:An Introduction To FM 4257:Kreh, Martin (2012), 4199:Chowning, J. (1973). 4150:Digitone product page 4117:Volca FM product page 3967:Holmes, Thom (2008). 3762:Curtis Roads (1996). 3666: 3499: 3329: 2897: 2788: 2500: 2409: 2307: 2231: 2125: 2093: 2091:{\displaystyle FM(t)} 2053: 1957: 1936: 1892: 1850: 1812: 1766: 1664: 1464: 1270: 1225: 1173: 790: 657: 430: 388:is actually based on 347: 43: 4554:Software synthesizer 4398:Frequency modulation 4018:on 17 September 2011 3977:Taylor & Francis 2524: 2244: 2148: 2102: 2070: 2062:is converted to the 2051:{\displaystyle m(t)} 2033: 1945: 1908: 1859: 1825: 1778: 1294: 1234: 1185: 802: 737: 437:digital synthesizers 417:frequency modulation 409:Expansions by Yamaha 357:frequency modulation 297:Mega Drive (Genesis) 248:sound chip, and the 4536:Digital synthesizer 1986:Digital synthesizer 1955:{\displaystyle n\,} 1819:angular frequencies 865: 686:Sinusoidal waveform 422:digital synthesizer 365:Stanford University 182:digital synthesizer 80:Waveforms for each 34: 4513:Analog synthesizer 4475:Physical modelling 4272:–6, archived from 4259:"Bessel Functions" 4054:Yamaha Corporation 4049:"Yamaha SY99 spec" 3979:. pp. 257–8. 3661: 3659: 2495: 2493: 2226: 2224: 2120: 2088: 2066:of carrier signal 2048: 1976:Additive synthesis 1952: 1931: 1887: 1845: 1807: 1761: 1759: 1265: 1230:and the modulator 1220: 1168: 1166: 851: 785: 660: 590:. You can help by 501:additive synthesis 481:Native Instruments 433: 353: 259:computers use the 188:, manufactured by 45: 30: 4562: 4561: 4549:Scanned synthesis 4488:Digital waveguide 4403:Linear arithmetic 4303:978-0-262-68082-0 4223:. Tokyo: Yamaha. 3986:978-0-415-95781-6 3894:. patft.uspto.gov 3718:978-1-000-28699-1 3590: 3498: 3492: 3421: 3415: 3284: 3278: 3004: 2998: 2735: 2729: 2600: 2594: 1660: 1654: 1567: 1561: 1407: 1401: 1326: 1320: 1101: 1053: 1047: 991: 943: 937: 834: 828: 655: 646:Spectral analysis 608: 607: 537:formant synthesis 367:, California, by 206:IBM PC compatible 119: 118: 101:Spectra for each 73: 16:(Redirected from 4582: 4483:Banded waveguide 4408:Phase distortion 4379: 4372: 4365: 4356: 4338:, by Gordon Reid 4332:, by Gordon Reid 4307: 4286: 4285: 4284: 4278: 4263: 4253: 4234: 4215: 4205: 4185: 4184: 4182: 4181: 4170: 4164: 4158: 4152: 4147: 4141: 4136: 4130: 4125: 4119: 4114: 4108: 4107: 4105: 4098: 4089: 4080: 4079: 4065: 4059: 4058: 4045: 4039: 4033: 4027: 4026: 4024: 4023: 4014:. Archived from 4003: 3997: 3996: 3994: 3993: 3975:(3rd ed.). 3964: 3958: 3957: 3955: 3954: 3934: 3928: 3927: 3925: 3924: 3914: 3903: 3902: 3900: 3899: 3888: 3882: 3881: 3871: 3865: 3864: 3844: 3838: 3837: 3835: 3833: 3817: 3811: 3810: 3799: 3790: 3789: 3787: 3786: 3759: 3750: 3749: 3734: 3723: 3722: 3702: 3696: 3690: 3673: 3670: 3668: 3667: 3662: 3660: 3644: 3643: 3634: 3633: 3603: 3602: 3588: 3577: 3576: 3561: 3560: 3532: 3531: 3521: 3516: 3496: 3490: 3488: 3484: 3480: 3475: 3474: 3459: 3458: 3440: 3439: 3419: 3413: 3409: 3408: 3393: 3392: 3359: 3358: 3348: 3343: 3322: 3321: 3294: 3293: 3282: 3276: 3274: 3255: 3254: 3230: 3229: 3199: 3198: 3183: 3182: 3158: 3157: 3127: 3126: 3111: 3110: 3089: 3088: 3058: 3057: 3042: 3041: 3014: 3013: 3002: 2996: 2994: 2990: 2986: 2982: 2981: 2936: 2935: 2916: 2911: 2885: 2884: 2863: 2859: 2855: 2854: 2821: 2820: 2807: 2802: 2772: 2771: 2754: 2753: 2733: 2727: 2725: 2715: 2714: 2681: 2680: 2653: 2652: 2619: 2618: 2598: 2592: 2590: 2586: 2582: 2578: 2577: 2552: 2551: 2530: 2504: 2502: 2501: 2496: 2494: 2448: 2447: 2428: 2423: 2340: 2339: 2326: 2321: 2291: 2290: 2235: 2233: 2232: 2227: 2225: 2137: 2131: 2129: 2127: 2126: 2123:{\displaystyle } 2121: 2097: 2095: 2094: 2089: 2057: 2055: 2054: 2049: 2027: 2006:Video game music 1991:Electronic music 1966:, respectively. 1961: 1959: 1958: 1953: 1940: 1938: 1937: 1932: 1920: 1919: 1896: 1894: 1893: 1888: 1885: 1884: 1875: 1854: 1852: 1851: 1846: 1816: 1814: 1813: 1808: 1805: 1804: 1790: 1789: 1770: 1768: 1767: 1762: 1760: 1746: 1745: 1729: 1728: 1697: 1696: 1686: 1681: 1658: 1652: 1650: 1646: 1642: 1641: 1637: 1625: 1624: 1608: 1607: 1586: 1585: 1565: 1559: 1548: 1547: 1531: 1530: 1494: 1493: 1483: 1478: 1453: 1452: 1425: 1424: 1405: 1399: 1397: 1393: 1389: 1381: 1380: 1351: 1350: 1324: 1318: 1274: 1272: 1271: 1266: 1260: 1246: 1245: 1229: 1227: 1226: 1221: 1218: 1217: 1208: 1197: 1196: 1177: 1175: 1174: 1169: 1167: 1163: 1159: 1158: 1154: 1141: 1126: 1125: 1102: 1100: 1099: 1087: 1078: 1077: 1051: 1045: 1043: 1039: 1035: 1034: 1030: 1016: 1015: 992: 990: 989: 977: 968: 967: 941: 935: 933: 929: 925: 918: 914: 906: 905: 880: 879: 864: 859: 832: 826: 794: 792: 791: 786: 777: 776: 656: 603: 600: 582: 575: 558: 539:respectively. 419: 399: 392: 390:phase modulation 381: 377: 375:analog synthesis 291:was used in the 174:phase modulation 114: 93: 38: 35: 29: 21: 4590: 4589: 4585: 4584: 4583: 4581: 4580: 4579: 4565: 4564: 4563: 4558: 4544:Analog modeling 4530: 4521:Graphical sound 4507: 4469: 4432: 4389: 4386:Sound synthesis 4383: 4315: 4310: 4304: 4289: 4282: 4280: 4276: 4261: 4256: 4250: 4237: 4231: 4218: 4203: 4198: 4194: 4189: 4188: 4179: 4177: 4172: 4171: 4167: 4159: 4155: 4148: 4144: 4137: 4133: 4126: 4122: 4115: 4111: 4103: 4096: 4091: 4090: 4083: 4067: 4066: 4062: 4047: 4046: 4042: 4034: 4030: 4021: 4019: 4005: 4004: 4000: 3991: 3989: 3987: 3966: 3965: 3961: 3952: 3950: 3936: 3935: 3931: 3922: 3920: 3916: 3915: 3906: 3897: 3895: 3890: 3889: 3885: 3873: 3872: 3868: 3846: 3845: 3841: 3831: 3829: 3819: 3818: 3814: 3801: 3800: 3793: 3784: 3782: 3780: 3772:. p. 226. 3761: 3760: 3753: 3736: 3735: 3726: 3719: 3704: 3703: 3699: 3691: 3687: 3682: 3677: 3676: 3658: 3657: 3635: 3625: 3591: 3568: 3552: 3523: 3486: 3485: 3466: 3450: 3431: 3400: 3384: 3373: 3369: 3350: 3313: 3285: 3272: 3271: 3246: 3221: 3190: 3174: 3149: 3118: 3102: 3080: 3049: 3033: 3005: 2992: 2991: 2973: 2918: 2893: 2889: 2876: 2846: 2809: 2763: 2762: 2758: 2745: 2723: 2722: 2706: 2672: 2644: 2610: 2588: 2587: 2569: 2543: 2542: 2538: 2522: 2521: 2492: 2491: 2430: 2399: 2372: 2371: 2328: 2282: 2275: 2242: 2241: 2223: 2222: 2176: 2146: 2145: 2138: 2134: 2100: 2099: 2068: 2067: 2031: 2030: 2028: 2024: 2019: 2014: 1972: 1943: 1942: 1911: 1906: 1905: 1876: 1857: 1856: 1823: 1822: 1796: 1781: 1776: 1775: 1758: 1757: 1737: 1720: 1688: 1648: 1647: 1616: 1599: 1577: 1539: 1522: 1508: 1504: 1485: 1444: 1416: 1415: 1411: 1395: 1394: 1372: 1342: 1341: 1337: 1316: 1292: 1291: 1237: 1232: 1231: 1209: 1188: 1183: 1182: 1165: 1164: 1117: 1107: 1103: 1091: 1069: 1068: 1064: 1041: 1040: 1007: 997: 993: 981: 959: 958: 954: 931: 930: 897: 871: 870: 866: 849: 845: 824: 800: 799: 768: 735: 734: 728: 708:Oscillator sync 689:Other waveforms 650: 648: 604: 598: 595: 588:needs expansion 573: 568: 540: 521: 476: 471: 452: 414: 411: 406: 394: 387: 379: 372: 342: 322: 317: 220:chips like the 202: 166: 130:sound synthesis 128:) is a form of 58: 51: 28: 23: 22: 15: 12: 11: 5: 4588: 4586: 4578: 4577: 4567: 4566: 4560: 4559: 4557: 4556: 4551: 4546: 4540: 4538: 4532: 4531: 4529: 4528: 4523: 4517: 4515: 4509: 4508: 4506: 4505: 4500: 4495: 4493:Direct digital 4490: 4485: 4479: 4477: 4471: 4470: 4468: 4467: 4462: 4457: 4452: 4446: 4444: 4434: 4433: 4431: 4430: 4425: 4420: 4415: 4410: 4405: 4400: 4394: 4391: 4390: 4384: 4382: 4381: 4374: 4367: 4359: 4353: 4352: 4344: 4339: 4333: 4327: 4322: 4314: 4313:External links 4311: 4309: 4308: 4302: 4287: 4254: 4248: 4235: 4229: 4216: 4195: 4193: 4190: 4187: 4186: 4165: 4163:, pp. 1–2 4153: 4142: 4131: 4120: 4109: 4081: 4075:Sound on Sound 4060: 4057:(in Japanese). 4040: 4028: 4012:Sound on Sound 3998: 3985: 3959: 3929: 3904: 3883: 3866: 3839: 3812: 3791: 3778: 3751: 3748:on 2017-05-11. 3724: 3717: 3697: 3684: 3683: 3681: 3678: 3675: 3674: 3672: 3671: 3656: 3653: 3650: 3647: 3642: 3638: 3632: 3628: 3624: 3621: 3618: 3615: 3612: 3609: 3606: 3601: 3598: 3594: 3587: 3584: 3580: 3575: 3571: 3567: 3564: 3559: 3555: 3551: 3548: 3545: 3541: 3538: 3535: 3530: 3526: 3520: 3515: 3512: 3509: 3506: 3502: 3495: 3489: 3487: 3483: 3478: 3473: 3469: 3465: 3462: 3457: 3453: 3449: 3446: 3443: 3438: 3434: 3430: 3427: 3424: 3418: 3412: 3407: 3403: 3399: 3396: 3391: 3387: 3383: 3380: 3377: 3372: 3368: 3365: 3362: 3357: 3353: 3347: 3342: 3339: 3336: 3332: 3328: 3325: 3320: 3316: 3312: 3309: 3306: 3303: 3300: 3297: 3292: 3288: 3281: 3275: 3273: 3270: 3267: 3264: 3261: 3258: 3253: 3249: 3245: 3242: 3239: 3236: 3233: 3228: 3224: 3220: 3217: 3214: 3211: 3208: 3205: 3202: 3197: 3193: 3189: 3186: 3181: 3177: 3173: 3170: 3167: 3164: 3161: 3156: 3152: 3148: 3145: 3142: 3139: 3136: 3133: 3130: 3125: 3121: 3117: 3114: 3109: 3105: 3101: 3098: 3095: 3092: 3087: 3083: 3079: 3076: 3073: 3070: 3067: 3064: 3061: 3056: 3052: 3048: 3045: 3040: 3036: 3032: 3029: 3026: 3023: 3020: 3017: 3012: 3008: 3001: 2995: 2993: 2989: 2985: 2980: 2976: 2972: 2969: 2966: 2963: 2960: 2957: 2954: 2951: 2948: 2945: 2942: 2939: 2934: 2931: 2928: 2925: 2921: 2915: 2910: 2907: 2904: 2900: 2896: 2892: 2888: 2883: 2879: 2875: 2872: 2869: 2866: 2862: 2858: 2853: 2849: 2845: 2842: 2839: 2836: 2833: 2830: 2827: 2824: 2819: 2816: 2812: 2806: 2801: 2798: 2795: 2791: 2787: 2784: 2781: 2778: 2775: 2770: 2766: 2761: 2757: 2752: 2748: 2744: 2741: 2738: 2732: 2726: 2724: 2721: 2718: 2713: 2709: 2705: 2702: 2699: 2696: 2693: 2690: 2687: 2684: 2679: 2675: 2671: 2668: 2665: 2662: 2659: 2656: 2651: 2647: 2643: 2640: 2637: 2634: 2631: 2628: 2625: 2622: 2617: 2613: 2609: 2606: 2603: 2597: 2591: 2589: 2585: 2581: 2576: 2572: 2568: 2565: 2562: 2558: 2555: 2550: 2546: 2541: 2537: 2534: 2531: 2529: 2518:as following: 2517: 2516: 2505: 2490: 2487: 2484: 2481: 2478: 2475: 2472: 2469: 2466: 2463: 2460: 2457: 2454: 2451: 2446: 2443: 2440: 2437: 2433: 2427: 2422: 2419: 2416: 2412: 2408: 2405: 2402: 2400: 2398: 2395: 2392: 2389: 2386: 2383: 2380: 2377: 2374: 2373: 2370: 2367: 2364: 2361: 2358: 2355: 2352: 2349: 2346: 2343: 2338: 2335: 2331: 2325: 2320: 2317: 2314: 2310: 2306: 2303: 2300: 2297: 2294: 2289: 2285: 2281: 2278: 2276: 2274: 2271: 2268: 2265: 2262: 2259: 2256: 2253: 2250: 2249: 2237: 2236: 2221: 2218: 2215: 2212: 2209: 2206: 2203: 2200: 2197: 2194: 2191: 2188: 2185: 2182: 2179: 2177: 2175: 2172: 2169: 2166: 2163: 2160: 2157: 2154: 2153: 2132: 2119: 2116: 2113: 2110: 2107: 2087: 2084: 2081: 2078: 2075: 2047: 2044: 2041: 2038: 2021: 2020: 2018: 2015: 2013: 2010: 2009: 2008: 2003: 1998: 1993: 1988: 1983: 1978: 1971: 1968: 1950: 1929: 1926: 1923: 1918: 1914: 1883: 1879: 1874: 1870: 1867: 1864: 1843: 1840: 1837: 1834: 1831: 1803: 1799: 1794: 1788: 1784: 1772: 1771: 1756: 1753: 1749: 1744: 1740: 1735: 1732: 1727: 1723: 1719: 1716: 1713: 1710: 1706: 1703: 1700: 1695: 1691: 1685: 1680: 1677: 1674: 1671: 1667: 1663: 1657: 1651: 1649: 1645: 1640: 1635: 1632: 1628: 1623: 1619: 1614: 1611: 1606: 1602: 1598: 1595: 1592: 1589: 1584: 1580: 1576: 1573: 1570: 1564: 1558: 1555: 1551: 1546: 1542: 1537: 1534: 1529: 1525: 1521: 1518: 1515: 1512: 1507: 1503: 1500: 1497: 1492: 1488: 1482: 1477: 1474: 1471: 1467: 1463: 1460: 1457: 1451: 1447: 1443: 1440: 1437: 1434: 1431: 1428: 1423: 1419: 1414: 1410: 1404: 1398: 1396: 1392: 1388: 1385: 1379: 1375: 1371: 1368: 1365: 1361: 1358: 1355: 1349: 1345: 1340: 1336: 1333: 1329: 1323: 1317: 1315: 1312: 1309: 1306: 1303: 1300: 1299: 1263: 1259: 1255: 1252: 1249: 1244: 1240: 1216: 1212: 1207: 1203: 1200: 1195: 1191: 1179: 1178: 1162: 1157: 1153: 1150: 1147: 1144: 1140: 1136: 1133: 1130: 1124: 1120: 1116: 1113: 1110: 1106: 1098: 1094: 1090: 1085: 1082: 1076: 1072: 1067: 1063: 1060: 1056: 1050: 1044: 1042: 1038: 1033: 1029: 1026: 1023: 1020: 1014: 1010: 1006: 1003: 1000: 996: 988: 984: 980: 975: 972: 966: 962: 957: 953: 950: 946: 940: 934: 932: 928: 924: 921: 917: 913: 910: 904: 900: 896: 893: 890: 886: 883: 878: 874: 869: 863: 858: 854: 848: 844: 841: 837: 831: 825: 823: 820: 817: 814: 811: 808: 807: 783: 780: 775: 771: 767: 764: 761: 757: 754: 751: 748: 745: 742: 727: 724: 714: 713: 712: 711: 705: 702:anti-logarithm 698: 692: 691: 690: 687: 681: 680: 679: 676: 673: 670: 647: 644: 639:Yamaha Montage 606: 605: 585: 583: 572: 569: 567: 564: 520: 517: 475: 472: 470: 467: 461:, used in its 451: 448: 410: 407: 405: 402: 341: 338: 321: 318: 316: 313: 305:FM Towns Marty 277:Taito Z System 201: 198: 165: 162: 136:is changed by 117: 116: 108: 107: 105: 96: 95: 87: 86: 84: 75: 74: 56: 49: 26: 24: 18:FM synthesizer 14: 13: 10: 9: 6: 4: 3: 2: 4587: 4576: 4573: 4572: 4570: 4555: 4552: 4550: 4547: 4545: 4542: 4541: 4539: 4537: 4533: 4527: 4524: 4522: 4519: 4518: 4516: 4514: 4510: 4504: 4501: 4499: 4496: 4494: 4491: 4489: 4486: 4484: 4481: 4480: 4478: 4476: 4472: 4466: 4465:Concatenative 4463: 4461: 4458: 4456: 4453: 4451: 4448: 4447: 4445: 4443: 4439: 4435: 4429: 4426: 4424: 4421: 4419: 4416: 4414: 4411: 4409: 4406: 4404: 4401: 4399: 4396: 4395: 4392: 4387: 4380: 4375: 4373: 4368: 4366: 4361: 4360: 4357: 4351: 4348: 4345: 4343: 4340: 4337: 4334: 4331: 4328: 4326: 4323: 4320: 4317: 4316: 4312: 4305: 4299: 4296:. MIT Press. 4295: 4294: 4288: 4279:on 2017-11-18 4275: 4271: 4267: 4260: 4255: 4251: 4249:0-02-864682-7 4245: 4241: 4236: 4232: 4230:4-636-17482-8 4226: 4222: 4217: 4213: 4209: 4202: 4197: 4196: 4191: 4176: 4173:Doering, Ed. 4169: 4166: 4162: 4161:Chowning 1973 4157: 4154: 4151: 4146: 4143: 4140: 4135: 4132: 4129: 4124: 4121: 4118: 4113: 4110: 4102: 4095: 4088: 4086: 4082: 4077: 4076: 4071: 4064: 4061: 4056: 4055: 4050: 4044: 4041: 4038: 4032: 4029: 4017: 4013: 4009: 4002: 3999: 3988: 3982: 3978: 3974: 3970: 3963: 3960: 3949:on 2007-04-07 3948: 3944: 3940: 3937:Rob Hordijk. 3933: 3930: 3919: 3913: 3911: 3909: 3905: 3893: 3887: 3884: 3879: 3878: 3870: 3867: 3863: 3862: 3856: 3852: 3851: 3843: 3840: 3828: 3827: 3822: 3816: 3813: 3808: 3804: 3798: 3796: 3792: 3781: 3779:0-262-68082-3 3775: 3771: 3767: 3766: 3758: 3756: 3752: 3747: 3743: 3739: 3733: 3731: 3729: 3725: 3720: 3714: 3711:. CRC Press. 3710: 3709: 3701: 3698: 3695:, p. 115 3694: 3689: 3686: 3679: 3648: 3640: 3636: 3630: 3622: 3619: 3613: 3607: 3599: 3596: 3592: 3585: 3573: 3569: 3565: 3562: 3557: 3553: 3546: 3543: 3536: 3528: 3524: 3510: 3507: 3504: 3500: 3493: 3481: 3471: 3467: 3463: 3460: 3455: 3451: 3444: 3441: 3436: 3428: 3425: 3416: 3405: 3401: 3397: 3394: 3389: 3385: 3378: 3375: 3370: 3363: 3355: 3351: 3340: 3337: 3334: 3330: 3326: 3318: 3314: 3307: 3304: 3298: 3290: 3286: 3279: 3268: 3265: 3262: 3259: 3251: 3247: 3243: 3237: 3234: 3226: 3222: 3215: 3212: 3209: 3203: 3195: 3191: 3187: 3179: 3175: 3171: 3165: 3162: 3154: 3150: 3143: 3140: 3137: 3131: 3123: 3119: 3115: 3107: 3103: 3096: 3093: 3085: 3081: 3074: 3071: 3068: 3062: 3054: 3050: 3046: 3038: 3034: 3027: 3024: 3018: 3010: 3006: 2999: 2987: 2978: 2974: 2967: 2964: 2961: 2958: 2949: 2946: 2940: 2932: 2929: 2926: 2923: 2919: 2908: 2905: 2902: 2898: 2894: 2890: 2881: 2877: 2870: 2867: 2864: 2860: 2851: 2847: 2843: 2840: 2834: 2831: 2825: 2817: 2814: 2810: 2799: 2796: 2793: 2789: 2785: 2782: 2776: 2768: 2764: 2759: 2750: 2746: 2739: 2736: 2730: 2711: 2707: 2700: 2697: 2694: 2688: 2685: 2677: 2673: 2666: 2663: 2660: 2649: 2645: 2638: 2635: 2632: 2626: 2623: 2615: 2611: 2604: 2601: 2595: 2583: 2574: 2570: 2563: 2560: 2556: 2553: 2548: 2544: 2539: 2535: 2532: 2520: 2519: 2514: 2510: 2506: 2485: 2479: 2476: 2473: 2470: 2461: 2458: 2452: 2444: 2441: 2438: 2435: 2431: 2420: 2417: 2414: 2410: 2406: 2403: 2401: 2393: 2390: 2387: 2384: 2378: 2375: 2365: 2362: 2359: 2353: 2350: 2344: 2336: 2333: 2329: 2318: 2315: 2312: 2308: 2304: 2301: 2295: 2287: 2283: 2279: 2277: 2269: 2266: 2263: 2260: 2254: 2251: 2240: 2239: 2219: 2216: 2213: 2210: 2207: 2204: 2201: 2198: 2195: 2192: 2189: 2186: 2183: 2180: 2178: 2170: 2167: 2164: 2158: 2155: 2144: 2143: 2142: 2136: 2133: 2114: 2111: 2108: 2082: 2076: 2073: 2065: 2061: 2042: 2036: 2026: 2023: 2016: 2011: 2007: 2004: 2002: 1999: 1997: 1994: 1992: 1989: 1987: 1984: 1982: 1979: 1977: 1974: 1973: 1969: 1967: 1965: 1948: 1924: 1916: 1912: 1904: 1900: 1881: 1877: 1872: 1868: 1865: 1862: 1841: 1838: 1835: 1832: 1829: 1820: 1801: 1797: 1792: 1786: 1782: 1751: 1742: 1738: 1733: 1730: 1725: 1721: 1711: 1708: 1701: 1693: 1689: 1675: 1672: 1669: 1665: 1661: 1655: 1643: 1638: 1630: 1621: 1617: 1612: 1609: 1604: 1600: 1590: 1587: 1582: 1574: 1571: 1562: 1553: 1544: 1540: 1535: 1532: 1527: 1523: 1513: 1510: 1505: 1498: 1490: 1486: 1475: 1472: 1469: 1465: 1461: 1455: 1449: 1445: 1438: 1435: 1429: 1421: 1417: 1412: 1408: 1402: 1390: 1383: 1377: 1373: 1366: 1363: 1359: 1356: 1353: 1347: 1343: 1338: 1334: 1331: 1327: 1321: 1310: 1304: 1301: 1290: 1289: 1288: 1286: 1282: 1278: 1277:Chowning 1973 1261: 1257: 1253: 1250: 1247: 1242: 1238: 1214: 1210: 1205: 1201: 1198: 1193: 1189: 1160: 1155: 1151: 1148: 1142: 1138: 1134: 1131: 1128: 1122: 1118: 1111: 1108: 1104: 1096: 1092: 1088: 1083: 1080: 1074: 1070: 1065: 1061: 1058: 1054: 1048: 1036: 1031: 1027: 1024: 1018: 1012: 1008: 1001: 998: 994: 986: 982: 978: 973: 970: 964: 960: 955: 951: 948: 944: 938: 926: 922: 919: 915: 908: 902: 898: 891: 888: 884: 881: 876: 872: 867: 861: 856: 852: 846: 842: 839: 835: 829: 818: 812: 809: 798: 797: 796: 778: 773: 769: 762: 759: 755: 752: 746: 740: 731: 725: 723: 720: 718: 709: 706: 703: 699: 696: 695: 693: 688: 685: 684: 682: 677: 674: 671: 668: 667: 665: 664: 663: 645: 643: 640: 635: 633: 629: 625: 621: 617: 613: 602: 599:February 2023 593: 589: 586:This section 584: 581: 577: 576: 570: 566:2000s–present 565: 563: 559: 556: 552: 548: 547:Alesis Fusion 544: 538: 534: 530: 526: 518: 516: 514: 510: 509:Alesis Fusion 506: 502: 498: 494: 490: 486: 482: 473: 468: 466: 464: 460: 456: 449: 447: 444: 442: 438: 429: 425: 423: 418: 408: 403: 401: 398: 391: 385: 376: 370: 369:John Chowning 366: 362: 358: 351: 350:John Chowning 346: 339: 337: 335: 331: 326: 319: 314: 312: 310: 306: 302: 298: 294: 290: 286: 282: 278: 274: 270: 266: 262: 258: 254: 251: 247: 243: 239: 235: 231: 227: 223: 219: 215: 214:Sound Blaster 211: 207: 199: 197: 195: 191: 187: 183: 179: 175: 171: 163: 161: 158: 154: 149: 147: 143: 139: 135: 131: 127: 123: 115: 113: 106: 104: 100: 99: 98: 97: 94: 92: 85: 83: 79: 78: 77: 76: 71: 67: 63: 59: 52: 42: 37: 36: 33: 19: 4438:Sample-based 4397: 4292: 4281:, retrieved 4274:the original 4265: 4239: 4220: 4211: 4207: 4192:Bibliography 4178:. Retrieved 4168: 4156: 4145: 4134: 4123: 4112: 4073: 4063: 4052: 4043: 4031: 4020:. Retrieved 4016:the original 4011: 4001: 3990:. Retrieved 3972: 3962: 3951:. Retrieved 3947:the original 3942: 3932: 3921:. Retrieved 3896:. Retrieved 3886: 3876: 3869: 3859: 3858: 3849: 3842: 3830:. Retrieved 3824: 3815: 3806: 3783:. Retrieved 3764: 3746:the original 3741: 3707: 3700: 3688: 2508: 2135: 2025: 1773: 1180: 732: 729: 721: 716: 715: 661: 636: 609: 596: 592:adding to it 587: 560: 522: 477: 453: 445: 434: 412: 354: 323: 216:popularized 203: 186:Synclavier I 167: 164:Applications 160:be created. 150: 126:FM synthesis 125: 121: 120: 109: 102: 88: 81: 65: 54: 47: 31: 4418:Subtractive 4325:FM tutorial 4268:, pp.  3832:October 19, 726:2 operators 678:Mix of them 669:2 operators 549:range, the 525:Yamaha SY99 505:Korg Kronos 493:subtractive 404:1970s–1980s 334:ARP Odyssey 309:Yamaha SMAF 170:oscillators 4428:Distortion 4283:2014-08-22 4180:2013-04-11 4022:2011-06-29 3992:2011-06-04 3953:2013-03-23 3923:2017-04-30 3898:2017-04-30 3826:MusicRadar 3785:2011-06-05 2012:References 2001:Sound chip 1996:Sound card 1903:amplitudes 1283:, p.  1281:Roads 1996 551:Korg Oasys 489:Image-Line 325:Don Buchla 240:) use the 194:Yamaha DX7 153:inharmonic 4450:Wavetable 3770:MIT Press 3680:Citations 3620:− 3597:− 3586:∵ 3570:θ 3554:θ 3547:⁡ 3537:β 3519:∞ 3514:∞ 3511:− 3501:∑ 3468:θ 3461:− 3452:θ 3445:⁡ 3426:− 3402:θ 3386:θ 3379:⁡ 3364:β 3346:∞ 3331:∑ 3315:θ 3308:⁡ 3299:β 3248:θ 3238:⁡ 3223:θ 3216:⁡ 3204:β 3176:θ 3166:⁡ 3151:θ 3144:⁡ 3132:β 3104:θ 3097:⁡ 3082:θ 3075:⁡ 3063:β 3035:θ 3028:⁡ 3019:β 2975:θ 2950:⁡ 2941:β 2914:∞ 2899:∑ 2878:θ 2871:⁡ 2848:θ 2835:⁡ 2826:β 2805:∞ 2790:∑ 2777:β 2747:θ 2740:⁡ 2708:θ 2701:⁡ 2695:β 2689:⁡ 2674:θ 2667:⁡ 2646:θ 2639:⁡ 2633:β 2627:⁡ 2612:θ 2605:⁡ 2571:θ 2564:⁡ 2557:β 2545:θ 2536:⁡ 2513:Kreh 2012 2486:θ 2462:⁡ 2453:β 2426:∞ 2411:∑ 2394:θ 2391:⁡ 2385:β 2379:⁡ 2366:θ 2354:⁡ 2345:β 2324:∞ 2309:∑ 2296:β 2270:θ 2267:⁡ 2261:β 2255:⁡ 2217:⁡ 2208:⁡ 2202:± 2196:⁡ 2187:⁡ 2168:± 2159:⁡ 2017:Footnotes 1925:β 1878:ω 1863:β 1839:π 1830:ω 1798:ω 1783:ω 1739:ω 1722:ω 1712:⁡ 1702:β 1684:∞ 1679:∞ 1676:− 1666:∑ 1618:ω 1610:− 1601:ω 1591:⁡ 1572:− 1541:ω 1524:ω 1514:⁡ 1499:β 1481:∞ 1466:∑ 1446:ω 1439:⁡ 1430:β 1374:ω 1367:⁡ 1360:β 1344:ω 1335:⁡ 1322:≈ 1254:π 1251:− 1239:ϕ 1211:ω 1190:ϕ 1135:π 1132:− 1119:ω 1112:⁡ 1093:ω 1071:ω 1062:⁡ 1025:− 1009:ω 1002:⁡ 983:ω 974:− 961:ω 952:⁡ 923:τ 909:τ 899:ω 892:⁡ 873:ω 853:∫ 843:⁡ 770:ω 763:⁡ 697:Linear FM 610:In 2016, 543:Nord Lead 380:algorithm 146:amplitude 4569:Category 4455:Granular 4423:Additive 4101:Archived 1981:Chiptune 1970:See also 632:Digitone 330:Minimoog 311:format. 157:harmonic 134:waveform 4526:Modular 4498:Formant 4442:Sampler 4413:Scanned 710:with FM 624:Montage 315:History 301:Fujitsu 285:Neo Geo 4460:Vector 4300:  4246:  4227:  3983:  3776:  3715:  3589:  3497:  3491:  3420:  3414:  3283:  3277:  3003:  2997:  2734:  2728:  2599:  2593:  2509:Source 1901:, and 1774:where 1659:  1653:  1566:  1560:  1406:  1400:  1325:  1319:  1052:  1046:  942:  936:  833:  827:  555:Kronos 485:Sytrus 384:Yamaha 378:. His 230:X68000 218:Yamaha 103:β 82:β 4388:types 4277:(PDF) 4262:(PDF) 4204:(PDF) 4104:(PDF) 4097:(PDF) 2064:phase 620:opsix 616:Volca 469:1990s 455:Casio 273:Taito 257:PC-98 253:PC-88 210:AdLib 4298:ISBN 4244:ISBN 4225:ISBN 4214:(7). 3981:ISBN 3834:2018 3774:ISBN 3713:ISBN 1962:-th 1817:are 1279:and 628:MODX 612:Korg 553:and 535:and 529:FS1R 527:and 507:and 332:and 299:and 293:Sega 289:OPN2 269:OPNB 265:OPNA 263:and 255:and 232:and 226:OPL3 224:and 222:OPL2 212:and 124:(or 4440:or 3807:Mix 3544:sin 3442:sin 3376:sin 3305:sin 3235:sin 3213:cos 3163:cos 3141:sin 3094:sin 3072:cos 3025:sin 2947:sin 2868:cos 2832:cos 2737:sin 2698:sin 2686:sin 2664:cos 2636:sin 2624:cos 2602:sin 2561:sin 2533:sin 2459:sin 2388:sin 2376:sin 2351:cos 2264:sin 2252:cos 2214:sin 2205:cos 2193:cos 2184:sin 2156:sin 2058:as 1941:is 1897:is 1709:sin 1588:sin 1511:sin 1436:sin 1364:sin 1332:sin 1285:232 1109:sin 1059:sin 999:cos 949:sin 889:sin 840:sin 760:sin 717:etc 594:. 487:by 483:or 441:DX7 303:'s 295:'s 283:'s 281:SNK 261:OPN 250:NEC 246:OPP 242:OPM 234:MSX 4571:: 4264:, 4212:21 4210:. 4206:. 4099:. 4084:^ 4072:. 4051:. 4010:. 3971:. 3941:. 3907:^ 3857:. 3823:. 3805:. 3794:^ 3768:. 3754:^ 3740:. 3727:^ 2511:: 1287:: 719:. 515:. 499:, 495:, 400:. 393:, 371:, 336:. 72:). 70:dB 64:, 4378:e 4371:t 4364:v 4306:. 4270:5 4252:. 4233:. 4183:. 4025:. 3995:. 3956:. 3926:. 3901:. 3855:7 3836:. 3788:. 3721:. 3655:) 3652:) 3649:x 3646:( 3641:n 3637:J 3631:n 3627:) 3623:1 3617:( 3614:= 3611:) 3608:x 3605:( 3600:n 3593:J 3583:( 3579:) 3574:m 3566:n 3563:+ 3558:c 3550:( 3540:) 3534:( 3529:n 3525:J 3508:= 3505:n 3494:= 3482:] 3477:) 3472:m 3464:n 3456:c 3448:( 3437:n 3433:) 3429:1 3423:( 3417:+ 3411:) 3406:m 3398:n 3395:+ 3390:c 3382:( 3371:[ 3367:) 3361:( 3356:n 3352:J 3341:1 3338:= 3335:n 3327:+ 3324:) 3319:c 3311:( 3302:) 3296:( 3291:0 3287:J 3280:= 3269:. 3266:. 3263:. 3260:+ 3257:) 3252:m 3244:3 3241:( 3232:) 3227:c 3219:( 3210:2 3207:) 3201:( 3196:3 3192:J 3188:+ 3185:) 3180:m 3172:2 3169:( 3160:) 3155:c 3147:( 3138:2 3135:) 3129:( 3124:2 3120:J 3116:+ 3113:) 3108:m 3100:( 3091:) 3086:c 3078:( 3069:2 3066:) 3060:( 3055:1 3051:J 3047:+ 3044:) 3039:c 3031:( 3022:) 3016:( 3011:0 3007:J 3000:= 2988:] 2984:) 2979:m 2971:) 2968:1 2965:+ 2962:n 2959:2 2956:( 2953:( 2944:) 2938:( 2933:1 2930:+ 2927:n 2924:2 2920:J 2909:0 2906:= 2903:n 2895:2 2891:[ 2887:) 2882:c 2874:( 2865:+ 2861:] 2857:) 2852:m 2844:n 2841:2 2838:( 2829:) 2823:( 2818:n 2815:2 2811:J 2800:1 2797:= 2794:n 2786:2 2783:+ 2780:) 2774:( 2769:0 2765:J 2760:[ 2756:) 2751:c 2743:( 2731:= 2720:) 2717:) 2712:m 2704:( 2692:( 2683:) 2678:c 2670:( 2661:+ 2658:) 2655:) 2650:m 2642:( 2630:( 2621:) 2616:c 2608:( 2596:= 2584:) 2580:) 2575:m 2567:( 2554:+ 2549:c 2540:( 2515:) 2507:( 2489:) 2483:) 2480:1 2477:+ 2474:n 2471:2 2468:( 2465:( 2456:) 2450:( 2445:1 2442:+ 2439:n 2436:2 2432:J 2421:0 2418:= 2415:n 2407:2 2404:= 2397:) 2382:( 2369:) 2363:n 2360:2 2357:( 2348:) 2342:( 2337:n 2334:2 2330:J 2319:1 2316:= 2313:n 2305:2 2302:+ 2299:) 2293:( 2288:0 2284:J 2280:= 2273:) 2258:( 2220:y 2211:x 2199:y 2190:x 2181:= 2174:) 2171:y 2165:x 2162:( 2130:. 2118:] 2115:t 2112:, 2109:0 2106:[ 2086:) 2083:t 2080:( 2077:M 2074:F 2046:) 2043:t 2040:( 2037:m 1949:n 1928:) 1922:( 1917:n 1913:J 1882:m 1873:/ 1869:B 1866:= 1842:f 1836:2 1833:= 1821:( 1802:m 1793:, 1787:c 1755:) 1752:t 1748:) 1743:m 1734:n 1731:+ 1726:c 1718:( 1715:( 1705:) 1699:( 1694:n 1690:J 1673:= 1670:n 1662:A 1656:= 1644:) 1639:] 1634:) 1631:t 1627:) 1622:m 1613:n 1605:c 1597:( 1594:( 1583:n 1579:) 1575:1 1569:( 1563:+ 1557:) 1554:t 1550:) 1545:m 1536:n 1533:+ 1528:c 1520:( 1517:( 1506:[ 1502:) 1496:( 1491:n 1487:J 1476:1 1473:= 1470:n 1462:+ 1459:) 1456:t 1450:c 1442:( 1433:) 1427:( 1422:0 1418:J 1413:( 1409:A 1403:= 1391:) 1387:) 1384:t 1378:m 1370:( 1357:+ 1354:t 1348:c 1339:( 1328:A 1314:) 1311:t 1308:( 1305:M 1302:F 1262:2 1258:/ 1248:= 1243:m 1215:m 1206:/ 1202:B 1199:= 1194:c 1161:) 1156:) 1152:1 1149:+ 1146:) 1143:2 1139:/ 1129:t 1123:m 1115:( 1105:( 1097:m 1089:B 1084:+ 1081:t 1075:c 1066:( 1055:A 1049:= 1037:) 1032:) 1028:1 1022:) 1019:t 1013:m 1005:( 995:( 987:m 979:B 971:t 965:c 956:( 945:A 939:= 927:) 920:d 916:) 912:) 903:m 895:( 885:B 882:+ 877:c 868:( 862:t 857:0 847:( 836:A 830:= 822:) 819:t 816:( 813:M 810:F 782:) 779:t 774:m 766:( 756:B 753:= 750:) 747:t 744:( 741:m 601:) 597:( 236:( 66:β 57:m 55:f 50:c 48:f 20:)

Index

FM synthesizer

frequency modulation index
dB


sound synthesis
waveform
modulating its frequency
(instantaneous) frequency
amplitude
inharmonic
harmonic
oscillators
phase modulation
instantaneous frequency
digital synthesizer
Synclavier I
New England Digital Corporation
Yamaha DX7
IBM PC compatible
AdLib
Sound Blaster
Yamaha
OPL2
OPL3
X68000
MSX
Yamaha CX5M computer unit
OPM

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