Editing Wavetable synthesis (section)

=== Terminologies ===
The term "''waveform table''" (or "''wave shape table''" as equivalent) is often abbreviated to "wavetable",<ref name=allesgiugno1977>
{{cite journal
 | last1     = Alles | first1 = H.G.
 | author-link1=Alles Machine
 | last2     = Giugno| first2 = Pepino di
 | author-link2=Giuseppe di Giugno
 | title     = A One-Card 64 Channel Digital Synthesizer
 | jstor       = 40731292
 | journal   = [[Computer Music Journal]]
 | volume    = 1 | issue = 4 
 | date = November 1977
 | pages     =7–9
 | quote     = The samples in the ''wave shape table'' ...", "FIGURE 1 ... 16 K × 14 BIT '''WAVETABLE'''
}}
</ref> and its derived term "''wavetable oscillator''"<ref name=puckette2002/> seems to be almost the same as "''table-lookup oscillator''" mentioned above, although the word "wave" (or "waveform", "wave shape") may possibly imply a nuance of single-cycle waveform<!-- table -->.

However, the derived term "''wavetable synthesis''" seems slightly confused by the later developments of derived algorithm.

;(1) Wavetable synthesis<ref name=puckette2002/>:<!-- &mdash; original, generic meaning (i.e. a single-cycle table-lookup synthesis). -->Its original meaning is essentially the same as "''table-lookup synthesis''",<ref name=Boulanger2012>
{{cite book
 | editor-last1 = Boulanger | editor-first1 = Richard | editor-link1 = Richard Boulanger
 | editor-last2 = Lazzarini | editor-first2 = Victor  | editor-link2 = Victor Lazzarini
 | others    = Foreword by [[Max Mathews]]
 | chapter   = 3.2.3 Table-Lookup Oscillators
 | title     = The Audio Programming Book
 | chapter-url       = https://books.google.com/books?id=BsLxCwAAQBAJ&pg=PA335&dq=%22Table-lookup%20synthesis%22
 | publisher = MIT Press <!-- publication-date = 2010 -->
 | isbn      = 978-0-262-28860-6
 | page      = [https://books.google.com/books?id=BsLxCwAAQBAJ&pg=PA335&dq=%22Table-lookup%20synthesis%22 335]&ndash;336
 | date      = 2010-10-22 
 | quote     = ''In this section ...<!-- we will continue to work with audio streams and  --> we will be introduce the ''table-lookup method'' for generating waveforms. This method is also called ''wavetable synthesis'' ...<!-- and it can be used for both artificial sounds, generated entirely by computer calculations, and for acoustic sounds, recorded with a microphone. --> / Wavetable synthesis is a technique based on reading data that has been stored in blocks of ''contiguous computer-memory locations'', called ''tables''. This sound-synthesis technique was one of the very first software synthesis methods introduced in the MUSIC I-MUSIC V languages developed by Max Mathews at Bell Labs in the late 1950s and the early 1960s. ...<!-- Back then, computers were slow and reading pre-computed samples from memory was much faster than calculating each sample from scratch (as in the case of previous ''hellosine.c'', in which the sin() function was called for each sample of the synthesizer sound). --> / With table-lookup synthesis, it is sufficient to calculate only a single cycle of a waveform, and then store this small set of samples in the table where it serves as a template. ...<!-- In order to playback the actual sound, this stored single cycle of the waveform must be re-read in a loop at desired frequency. Among other things, this method provided a huge advantage over the analog oscillators used in radio and electronic music studios of early 1960s because analog oscillators were capable of producing but a limited set of wave shapes (sinusoid, triangle, sawtooth, and square), whereas with the table-lookup method virtually any wave shape could be synthesized.-->''"<br/>'''Note''': on the preceding quotation, the authors paraphrased the section title "table-lookup oscillators" as follows: "table-lookup method", "wavetable synthesis", and "table-lookup synthesis".
}}</ref><ref name=Hosken2012>
{{cite book
 | author-first = Dan | author-last = Hosken 
 | chapter   = The Oscillator
 | title     = Music Technology and the Project Studio: Synthesis and Sampling
 | chapter-url       = https://books.google.com/books?id=YhypAgAAQBAJ&pg=PA72&dq=%22Table-lookup%20synthesis%22
 | publisher = Routledge
 | date = 2012
 | isbn      = 978-1-136-64435-1
 | page      = [https://books.google.com/books?id=YhypAgAAQBAJ&pg=PA72&dq=%22Table-lookup%20synthesis%22 72]&ndash;73
 | quote     = ''The '''oscillator''' generates a cycle of some waveform the appropriate number of times per second for the desired fundamental frequency. This is referred to variously as fixed-waveform synthesis, table-lookup synthesis, or wavetable synthesis.<!-- The waveform can be one of the standard waveforms (sine, triangle, sawtooth, etc.) or any other shape that represents a single cycle of a waveform (see Figure 4.2). -->''
}}</ref><ref name=puckette2002>
{{cite journal
 | last      = Puckette | first = Miller
 | author-link= Miller Puckette
 | year      = 2002
 | title     = Max at seventeen
 | url       = http://msp.ucsd.edu/Publications/dartmouth-reprint.pdf
 | format    = reprint
 | journal   = [[Computer Music Journal]]
 | volume    = 26 | issue = 4 | pages = 31–43
 | doi       = 10.1162/014892602320991356
}}<br/>"''For example, the '''wavetable oscillator''' used in [http://msp.ucsd.edu/Publications/dartmouth-reprint.dir/img1.png Fig. 1] made its first appearance in Mathews's '''Music II''' (two, not eleven) '''in the late 1950s'''. Music II was only one in a long sequence of MUSIC N programs, but the idea of wavetable synthesis has had a pervasive influence throughout the computer music discipline.''"
</ref><ref>
{{harvnb|Cullen|Howell|2006}}, "''SOS contributor Steve Howell replies: Wavetable synthesis is actually quite easy to understand. In the early days of synthesis, (analogue) oscillators provided a limited range of waveforms, such as sine, triangle, sawtooth and square/pulse, normally selected from a rotary switch. This gave the user a surprisingly wide range of basic sounds to play with, especially when '''different waveforms were combined in various ways'''.''<br/>([http://msp.ucsd.edu/Publications/dartmouth-reprint.dir/ HTML] version available)
</ref> and possibly several actions on waveform(s) may be expected. ⇒''See'' (2), (3)

;(2) Wavetable-modification algorithm<ref name=usapp5212334/>:<!-- &mdash; including [[digital waveguide synthesis]].<br/> -->For example, [[Karplus–Strong string synthesis]]<ref name=karplusstrong1983>
{{cite journal
 | last1     = Karplus | first1 = Kevin
 | author-link1=Kevin Karplus
 | last2     = Strong  | first2 = Alex
 | date      = Summer 1983
 | title     = Digital Synthesis of Plucked-String and Drum Timbres
 | url       = http://compbio.soe.ucsc.edu/~Karplus/papers/digitar.pdf
 | journal   = [[Computer Music Journal]]
 | volume    = 7 | issue = 2
 | doi       = 10.2307/3680062
 | jstor     = 3680062
 | pages     = 45–55
 | quote     = Wavetable Synthesis: ''One standard synthesis technique is the ''wavetable synthesis'' algorithm. ... The wavetable-synthesis technique is very simple but rather dull musically, since it produces purely periodic tones. ... All the algorithms described in this paper '''produce the variation in sound by modifying the wavetable itself'''.''
}}
</ref> is a simple class of "''wavetable-modification algorithm''" known as [[digital waveguide synthesis]].<ref name=usapp5212334>
{{cite patent
 | country   = US
 | number    = 5212334
 | status    = application
 | title     = [https://www.google.co.jp/patents/US5212334 Digital signal processing using closed waveguide networks]
 | pubdate   = 1993-05-18
 | fdate     = 1990-08-16
 | pridate   = 1986-05-02
 | inventor  = [[Julius O. Smith III]]
 | assign1   = [[Yamaha Corporation]]
}}.<br/>(See also the Wikipedia article [[Digital waveguide synthesis]]: "''The term "[[digital waveguide synthesis]]" was coined by [[Julius O. Smith III]] who helped develop it and eventually filed the patent. It represents an extension of the [[Karplus–Strong algorithm]].   [[Stanford University]] owns the patent rights for digital waveguide synthesis and signed an agreement in 1989 to develop the technology with [[Yamaha Corporation|Yamaha]].''")
</ref>

;(3) Multiple wavetable synthesis<ref name=beauchamp1993/>:<!-- &mdash; developed by McNabb and Palm, typically used on [[PPG Wave]]s.<br/> -->In the late-1970s, Michael McNabb<ref name="History of Digital Synthesis"/><ref name="Dreamsong: The Composition"/> and [[Wolfgang Palm]]{{sfn|Andresen|1979}} independently developed the multiple wavetable extension on the table-lookup synthesis<ref group=note>
"Multiple wavetable synthesis" {{harv|Horner|Beauchamp|Haken|1993}} developed by Michael McNabb and [[Wolfgang Palm]] in the late-1970s, is merely one of the techniques employed to realize dynamically-changing waveforms, by using an array of single-cycle waveforms in table-lookup synthesis.  With this synthesis technique, the waveform can be animated in a similar manner as a [[flip book]].
</ref> which was typically used on [[PPG Wave]] and known as ''wavetable sweeping''.<ref name=sosfeb06b>
{{harvnb|Cullen|Howell|2006}}, "''However, in the late '70s, Wolfgang Palm used 'wavetable' digital oscillators in his innovative PPG Wave synths. Instead of having just three or four waveforms, a wavetable oscillator can have many more &mdash; say, 64 &mdash; because they are digitally created and stored in a 'look-up table' ... Now, if the waveforms are sensibly arranged, we can begin to create harmonic movement in the sound. ... you approach something not unlike a traditional filter sweep. ...''"
</ref> Later, it was referred as "''multiple wavetable synthesis''" by {{harvnb|Horner|Beauchamp|Haken|1993}}.<ref name=beauchamp1993>
{{cite journal
 | last1     = Horner    | first1 = Andrew
 | last2     = Beauchamp | first2 = James
 | last3     = Haken     | first3 = Lippold
 | year      = 1993
 | title     = Methods for multiple wavetable synthesis of musical instrument tones
 | url       = http://ems.music.uiuc.edu/beaucham/papers/JAES.05.93.pdf
 | journal   = J. Audio Eng. Soc.
 | volume    = 41 | issue = 5 | publication-date = May 1993
 | pages     = 336–356
 | quote     = '''Multiple wavetable synthesis''', the subject of this paper, is based on a '''sum of fixed waveforms or periodic basis functions with time-varying weights'''.
}}
</ref>

;(4) [[Sample-based synthesis]]:Simultaneously, since the late-1970s, [[sample-based synthesis]] using relatively long samples instead of single-cycle waveforms has become pervasive due to the introduction of the [[Fairlight CMI]] and [[E-mu Systems|E-mu]] [[Emulator]].