Table-lookup synthesis

For other uses, see Wavetable and Wavetable synthesis.
An example of lookup table, where the data at addresses from 63 to 67 are zoomed.
(based on Figure 2.1 on Nelson 2000) On Csound, it is called f-table (function table), and used for various purposes including: wavetable-lookup synthesis, waveshaping, MIDI note mapping, and storing ordered pitch-class sets.[1]

Table-lookup synthesis[2] (or Wavetable-lookup synthesis[3]) (Roads 1996) is a class of sound synthesis methods using the waveform tables by table-lookup, called "table-lookup oscillator" technique. The length of waveforms or samples may be varied by each sound synthesis method, from a single-cycle up to several minutes.

Terminologies

The term "waveform table" (or "wave shape table" as equivalent) is often abbreviated to "wavetable",[4] and its derive term "wavetable oscillator"[5] seems to be almost same as "table-lookup oscillator" mentioned above, although the word "wave" (or "waveform", "wave shape") may possibly imply a nuance of single-cycle waveform.

However, a derive term "wavetable synthesis" seems slightly confusing. In a natural usage of words, its original meaning is basically same as "table-lookup synthesis",[5] and possibly several actions on waveform(s) may be expected,[6] as seen on a paper about Karplus–Strong string synthesis[7] (a simplest class of "wavetable-modification algorithm" known as digital waveguide synthesis[8]). Then in the late-1970s, Michael McNabb[9][10] and Wolfgang Palm[11] independently develop the multiple-wavetable extension on the table-lookup synthesis[note 1] which was typically used on PPG Wave and known with wavetable sweeping,[12] and it was later referred as "multiple wavetable synthesis" by Horner, Beauchamp & Haken 1993.[13] Simultaneously since late-1970s, also the sample-based synthesis using relatively long samples instead of single-cycle waveforms, have become influential by the introductions of the Fairlight CMI and E-mu Emulator.

Background

On the above four terminologies for the classes of sound synthesis methods, i.e.,

  1. Wavetable synthesis[5] — original, generic meaning (i.e. a single-cycle table-lookup synthesis).
  2. Multiple wavetable synthesis[13] — developed by McNabb and Palm, typically used on PPG Waves.
  3. Wavetable-modification algorithm[8] — including digital waveguide synthesis.
  4. Sample-based synthesis

if these had been appropriately used to distinguish each other, any confusions could be avoided, but it seems failed historically. At latest in the 1990s, several influential sample-based synthesis products were marketed under the trade names similar to "wavetable synthesis" (including Gravis Ultrasound wavetable card, Creative Wave Blaster wavetable daughterboard, and Microsoft GS Wavetable SW Synth), and these confusions have further affected on the several industry standards (including MPEG-4 Structured Audio algorithmic and wavetable synthesis,[14] and AC97 optional hw acceleration wavetable synth[15]). As a rebound of these, at the latest since the mid-2000s, a new confusion seem to begin flourish. Merely a subclass of generic wavetable synthesis, i.e. McNabb and Palm's multiple wavetable synthesis, tends to be erroneously referred as if it was a generic class of whole wavetable synthesis family, exclusively.[16]

As a background of these confusions, the difficulties of maintaining the consistencies between concepts and terminologies during the rapid developments of technology, may be significant. And it is a reason why this slightly classical terminology "Table-lookup synthesis" is explained on here.

See also

Footnotes

  1. ↑ "Multiple wavetable synthesis" (Horner, Beauchamp & Haken 1993) developed by Michael McNabb and Wolfgang Palm in the late-1970s, is merely one of the efficient implementation techniques to realize dynamically changing waveforms, by using an array of single-cycle waveforms on a table-lookup synthesis. On this synthesis technique, the waveform can be animated in a similar manner as a flip book.

References

  1. ↑ Nelson, Jon Christopher (2000). "2. Understanding and Using Csound's GEN Routines". The Csound book. Cambridge, MA, USA: MIT Press. pp. 65–97. ISBN 0-262-52261-6.
    "Csound uses lookup tables for musical applications as diverse as wavetable synthesis, waveshaping, mapping MIDI note numbers and storing ordered pitch-class sets. These function tables (f-tables) contain everything from periodic waveforms to arbitrary polynomials and randomly generated values. The specific data are created with Csound's f-table generator subroutines, or GEN routines. ..."
  2. ↑ Roads 1996, p. 87, Introduction to Digital Sound Synthesis, "This chapter outlines the fundamental methods of digital sound production. Following a brief historical overview, we present the theory of table-lookup synthesis—the core of most synthesis algorithms. ..."
  3. ↑ Roads 1996, p. 125, Sampling Synthesis, "Pitch-shifting ... variation technique as used in 'wavetable-lookup synthesis described in chapter 3."
  4. ↑ Alles, H.G.; Giugno, Pepino di (November 1977). "A One-Card 64 Channel Digital Synthesizer". Computer Music Journal. 1 (4): 7–9. JSTOR 40731292. The samples in the wave shape table ...", "FIGURE 1 ... 16 K × 14 BIT WAVETABLE
  5. 1 2 3 Puckette, Miller (2002). "Max at seventeen" (reprint). Computer Music Journal. 26 (4): 31–43. (HTML version available) "For example, the wavetable oscillator used in 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."
  6. ↑ Cullen, Michael. "Q. Can you explain the origins of wavetable, S&S and vector synthesis?". Sound On Sound (February 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.
  7. ↑ Karplus, Kevin; Strong, Alex (1983). "Digital Synthesis of Plucked-String and Drum Timbres" (PDF). Computer Music Journal (published Summer 1983). 7 (2): 45–55. doi:10.2307/3680062. JSTOR 3680062. 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.
  8. 1 2 US application 5212334, Julius O. Smith, III, "Digital signal processing using closed waveguide networks", published 1993-05-18, assigned to Yamaha Corporation.
    (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.”)
  9. ↑ Smith III, Julius O. "Viewpoints on the History of Digital Synthesis: Taxonomy of Digital Synthesis Techniques". Stanford, CA: Stanford University. Retrieved February 24, 2015.
  10. ↑ McNabb, Michael. "Dreamsong: The Composition" (PDF). Computer Music Journal. 5 (4). Retrieved February 24, 2015.
  11. ↑ Andresen, Uwe (Palm Productions) (1979). "A New Way in Sound Synthesis". 62nd Audio Engineering Society (AES) Convention (Brussels, Belgium).
  12. ↑ Sound On Sound (February 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 — say, 64 — 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. ..."
  13. 1 2 Horner, Andrew; Beauchamp, James; Haken, Lippold (1993). "Methods for multiple wavetable synthesis of musical instrument tones" (PDF). J. Audio Eng. Soc. (published May 1993). 41 (5): 336–356. Multiple wavetable synthesis, the subject of this paper, is based on a sum of fixed waveforms or periodic basis functions with time-varying weights.
  14. ↑ Scheirer, Eric D. (MIT Media Lab); Ray, Lee (Joint E-Mu/Creative Technology Center) (1998). "Algorithmic and Wavetable Synthesis in the MPEG-4 Multimedia Standard". 105th Audio Engineering Society (AES) Convention (San Francisco, California). 2.2 Wavetable synthesis with SASBF: The SASBF wavetable-bank format had a somewhat complex history of development. The original specification was contributed by E-Mu Systems and was based on their “SoundFont” format [15]. After integration of this component in the MPEG-4 reference software was complete, the MIDI Manufacturers Association (MMA) approached MPEG requesting that MPEG-4 SASBF be compatible with their “Downloaded Sounds” format [13]. E-Mu agreed that this compatibility was desirable, and so a new format was negotiated and designed collaboratively by all parties.
  15. ↑ "1.4 Integrating AC '97 into the System". AC ‘97 Component Specification Revision 2.3 Rev 1.0 (PDF). Intel Corporation. April 2002. p. 11. Figure 2. AC ‘97 System Diagram: AC ‘97 Digital Controller / Optional hw acceleration / SRC*, mix*, 3D positional*, wavetable synth*
  16. ↑ Sound On Sound (February 2006), "Other synths have employed wavetable synthesis in one guise or another since then and there are several software synths available today which incorporate wavetable synthesis capabilities."
    Note: on the above quotation, a specific wavetable synthesis developed by Wolfgang Palm, known as "multiple wavetable synthesis", is ambiguously referred as "wavetable synthesis".

Bibliography

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