Wavetable synthesis
Wavetable synthesis is a sound synthesis technique used to create quasi-periodic waveforms often used in the production of musical tones or notes. It uses a series of waveforms that are digitized as a series of amplitude values. Each waveform normally consists of a single cycle of the wave. Many such digitized waves are collected and stored in a table, often containing a series of slightly modified versions of an original "pure" tone. To produce output, the system selects a starting point within the table and a length, and the system loops through that section of the stored waveforms and plays it repeatedly. Each amplitude value is read from memory in turn, often stored in ROM. The series of numbers being read is sent into an digital-to-analog converter, which converts the value into an electrical signal to produce an audible signal. Most systems include the capability to mix multiple samples together to produce more complex output. One example of the technique is in the Waldorf Microwave synthesizer which had loadable wavetables. One consisted of the statement "nineteen twenty" from a voice synthesizer. By selecting different starting points and lengths within this sample, a wide variety of sounds can be produced.
Wavetable synthesis is a sound synthesis technique used to create quasi-periodic waveforms often used in the production of musical tones or notes. It uses a series of waveforms that are digitized as a series of amplitude values. Each waveform normally consists of a single cycle of the wave. Many such digitized waves are collected and stored in a table, often containing a series of slightly modified versions of an original "pure" tone.
To produce output, the system selects a starting point within the table and a length, and the system loops through that section of the stored waveforms and plays it repeatedly. Each amplitude value is read from memory in turn, often stored in ROM. The series of numbers being read is sent into an digital-to-analog converter, which converts the value into an electrical signal to produce an audible signal. Most systems include the capability to mix multiple samples together to produce more complex output.
One example of the technique is in the Waldorf Microwave synthesizer which had loadable wavetables. One consisted of the statement "nineteen twenty" from a voice synthesizer. By selecting different starting points and lengths within this sample, a wide variety of sounds can be produced.
Development
[edit]Wavetable synthesis was invented by Max Mathews in 1958 as part of MUSIC II. MUSIC II “had four-voice polyphony and was capable of generating sixteen wave shapes via the introduction of a wavetable oscillator.”[1]
Hal Chamberlin discussed wavetable synthesis in Byte's September 1977 issue.[2] Wolfgang Palm of Palm Products GmbH (PPG) developed his version in the late 1970s[3] and published it in 1979.[4] The technique has since been used as the primary synthesis method in synthesizers built by PPG and Waldorf Music and as an auxiliary synthesis method by Ensoniq and Access. It is currently used in hardware synthesizers from Waldorf Music and in software synthesizers for PCs and tablets, including apps offered by PPG and Waldorf, among others.
It was also independently developed by Michael McNabb, who used it in his 1978 composition Dreamsong.[5][6]
Principle
[edit]Electronic synthesizers using digital techniques generally produce sounds by producing a digital value, a number, and then sending that value to an digital-to-analog converter (DAC) that produces a scaled output voltage. For instance, to produce a triangle wave or sawtooth, systems used a register containing a starting value, normally zero, and then periodically increase or decrease the value using an adder or phase accumulator. The value in the register is continually sent to the DAC to produce output. The pitch of the resulting sound can be changed by how rapidly the adder is called.
Wavetable synthesis is a relatively simple modification of this sort of system. Instead of the value at any particular instantly being periodically modified by a simple function like addition, the specific value for any instant is read from memory containing a series of values making up multiple arbitrary, single-cycle waveforms.[7] This allows the waveform to have any shape, not just simple ones like triangles or sines. With that exception, the system is otherwise the same; values are read into the register at a rate that produces the desired pitch, and the output of the register is used to feed a DAC that produces the output signal. In order to produce a different sound, all that has to be changed is a single value pointing to the starting point of the waveform in memory.
Because the table contains many different waveforms, playing a longer sample that includes several different waveforms may result in odd side-effects when the system crosses the boundaries between the individual waveforms. Digital interpolation between adjacent waveforms allows for dynamic and smooth changes of the timbre of the tone produced. Additional effects can be provided by reading the waveform forward or backward, and further controlled in a number of ways, for example, by use of an LFO, envelope, pressure or velocity.
Many wavetables used in PPG and Ensoniq synthesizers can simulate the methods used by analog synthesizers, such as pulse-width modulation by utilising a number of square waves of different duty cycles. In this way, when the wavetable is swept, the duty cycle of the pulse wave will appear to change over time. As the early Ensoniq wavetable synthesizers had non resonant filters (the PPG Wave synthesizers used Curtis analogue resonant filters), some wavetables contained highly resonant waveforms to overcome this limitation of the filters.
Confusion with sample-based synthesis (S&S) and Digital Wave Synthesis
[edit]In 1992, with the introduction of the Creative Labs Sound Blaster 16 the term "wavetable"[8] started to be (incorrectly) applied as a marketing term to their sound card. However, these sound cards did not employ any form of wavetable synthesis,[9] but rather PCM samples and FM synthesis.
S&S (Sample and Synthesis) and Digital Wave Synthesis was the main method of sound synthesis utilised by digital synthesizers starting in the mid 1980s with synthesizers such as Sequential Circuits Prophet VS, Korg DW-6000/8000 (DW standing for Digital Wave), Roland D-50 and Korg M1 through to current synthesizers.
Ableton addressed some confusion in an article:[10]
Wait, so isn't this just sampled synthesis? Let's pause here to address a common confusion. While sampled synthesis involves the use of a static digital sample, wavetable synthesis allows for the (optional) evolution of a waveform; this is to say, while wavetable synths can sound like sampled synthesis, the evolving option (which is enabled by default on most classic wavetable sounds) differentiates it.
User wavetables
[edit]The creation of new wavetables was previously a difficult process unless supported by specialized editing facilities and (near) real-time playback of edited wavetables on the synthesizer. Such editors often required the use of extra hardware devices like the PPG Waveterm or were only present in expensive models like the Waldorf WAVE. More commonly, pre-computed wavetables could be added via memory cards or sent to the synthesizer via MIDI. Today, wavetables can be created more easily by software and auditioned directly on a computer. Since all waveforms used in wavetable synthesis are periodic, the time-domain and frequency-domain representation are exact equivalents of each other and both can be used simultaneously to define waveforms and wavetables.
Practical use
[edit]During playback, the sound produced can be harmonically changed by moving to another point in the wavetable, usually under the control of an envelope generator or low frequency oscillator but frequently by any number of modulators (matrix modulation). Doing this modifies the harmonic content of the output wave in real time, producing sounds that can imitate acoustic instruments or be totally abstract, which is where this method of sound creation excels. The technique is especially useful for evolving synth pads, where the sound changes slowly over time.
It is often necessary to 'audition' each position in a wavetable and to scan through it, forwards and backwards, in order to make good use of it, though selecting random wavetables, start positions, end positions and directions of scan can also produce satisfying musical results. It is worth noting that most wavetable synthesizers also employ other synthesis methods to further shape the output waveform, such as subtractive synthesis (filters), phase modulation, frequency modulation and AM (ring) modulation.
Table-lookup synthesis
[edit] | This section may need to be rewritten to comply with Wikipedia's quality standards. (August 2020) |
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(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.[11]
Table-lookup synthesis[12] (or Wavetable-lookup synthesis[13]) (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
[edit]The term "waveform table" (or "wave shape table" as equivalent) is often abbreviated to "wavetable",[14] and its derived term "wavetable oscillator"[15] 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.
However, the derived term "wavetable synthesis" seems slightly confused by the later developments of derived algorithm.
- (1) Wavetable synthesis[15]
- Its original meaning is essentially the same as "table-lookup synthesis",[16][17][15][18] and possibly several actions on waveform(s) may be expected. ⇒See (2), (3)
- (2) Wavetable-modification algorithm[19]
- For example, Karplus–Strong string synthesis[20] is a simple class of "wavetable-modification algorithm" known as digital waveguide synthesis.[19]
- (3) Multiple wavetable synthesis[21]
- In the late-1970s, Michael McNabb[5][6] and Wolfgang Palm[4] independently developed the multiple wavetable extension on the table-lookup synthesis[note 1] which was typically used on PPG Wave and known as wavetable sweeping.[22] Later, it was referred as "multiple wavetable synthesis" by Horner, Beauchamp & Haken 1993.[21]
- (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 Emulator.
Background
[edit]On the above four terminologies for the classes of sound synthesis methods — i.e., (1) Wavetable synthesis, (2) Wavetable-modification algorithm, (3) Multiple wavetable synthesis, and (4) Sample-based synthesis — if these had been appropriately used to distinguish each other, any confusions could be avoided, but it seems failed historically. In the 1990s at the latest, 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 industry standards (including MPEG-4 Structured Audio algorithmic and wavetable synthesis,[23] and AC97 optional hw acceleration wavetable synth[24]). In the mid-2000s, confusion in terminology cropped up yet-again. 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.[25]
As a result, the difficulty of maintaining consistency between concepts and terminology during rapid technological development is noteworthy. For this reason the term "Table-lookup synthesis" is explained at length in this article.
See also
[edit]Notes
[edit]- ^ "Multiple wavetable synthesis" (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.
References
[edit]- ^ Crab, Simon (2013-12-26). "'MUSIC N', Max Vernon Mathews, USA, 1957". 120 Years of Electronic Music. Retrieved 2022-05-26.
- ^ A sampling of techniques for computer performance of music by Hal Chamberlin, Byte, September 1977
- ^ Palm 2009.
- ^ a b Andresen 1979.
- ^ a b Smith III, Julius O. "Viewpoints on the History of Digital Synthesis: Taxonomy of Digital Synthesis Techniques". Stanford, CA: Stanford University. Retrieved February 24, 2015.
- ^ a b McNabb, Michael. "Dreamsong: The Composition" (PDF). Computer Music Journal. 5 (4). Archived from the original (PDF) on March 4, 2016. Retrieved February 24, 2015.
- ^ Bristow-Johnson 1996.
- ^ "Sound Blaster ISA Cards - Information and Troubleshooting". Creative Worldwide Support. Archived from the original on 2012-02-02.
- ^ "Wavetable Synthesis". WikiAudio. 2018-04-05.
- ^ "The New Wave: An In-Depth Look at Live 10's Wavetable". Ableton. Nov 29, 2017.
- ^ 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. ..."
- ^ 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. ..."
- ^ Roads 1996, p. 125, Sampling Synthesis, "Pitch-shifting ... variation technique as used in 'wavetable-lookup synthesis described in chapter 3."
- ^
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
- ^ a b c
Puckette, Miller (2002). "Max at seventeen" (reprint). Computer Music Journal. 26 (4): 31–43. doi:10.1162/014892602320991356.
"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." - ^
Boulanger, Richard; Lazzarini, Victor, eds. (2010-10-22). "3.2.3 Table-Lookup Oscillators". The Audio Programming Book. Foreword by Max Mathews. MIT Press. p. 335–336. ISBN 978-0-262-28860-6.
In this section ... we will be introduce the table-lookup method for generating waveforms. This method is also called wavetable synthesis ... / 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. ... / 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. ..."
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". - ^
Hosken, Dan (2012). "The Oscillator". Music Technology and the Project Studio: Synthesis and Sampling. Routledge. p. 72–73. ISBN 978-1-136-64435-1.
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.
- ^
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.
(HTML version available) - ^ a b
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.") - ^
Karplus, Kevin; Strong, Alex (Summer 1983). "Digital Synthesis of Plucked-String and Drum Timbres" (PDF). Computer Music Journal. 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.
- ^ a b Horner, Andrew; Beauchamp, James; Haken, Lippold (1993). "Methods for multiple wavetable synthesis of musical instrument tones" (PDF). J. Audio Eng. Soc. 41 (5) (published May 1993): 336–356. Archived from the original (PDF) on 2015-04-02. Retrieved 2017-08-21.
Multiple wavetable synthesis, the subject of this paper, is based on a sum of fixed waveforms or periodic basis functions with time-varying weights.
- ^ 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 — 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. ..."
- ^
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). CiteSeerX 10.1.1.35.2773.
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.
- ^
"1.4 Integrating AC '97 into the System" (PDF). AC '97 Component Specification Revision 2.3 Rev 1.0. 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*
- ^
Cullen & Howell 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: Regarding the previous quotation, a specific wavetable synthesis developed by Wolfgang Palm, known as "multiple wavetable synthesis", is ambiguously referred as "wavetable synthesis".
Bibliography
[edit]- Andresen, Uwe (1979), A New Way in Sound Synthesis, 62nd AES Convention (Brussels, Belgium), Audio Engineering Society (AES)
- Bristow-Johnson, Robert (1996), Wavetable Synthesis 101, A Fundamental Perspective, 101st AES Convention (Los Angeles, California), Audio Engineering Society (AES) Copy on MusicDSP Archived 2013-06-15 at the Wayback Machine
- Cullen, Michael; Howell, Steve (February 2006). "Q. Can you explain the origins of wavetable, S&S and vector synthesis?". Sound on Sound.
- Maunchly, J. William; Charpentier, Albert J. (1987), Practical Considerations in the Design of Music Systems using VLSI, AES 5th International Conference: Music and Digital Technology, Audio Engineering Society (AES)
- Palm, Wolfgang (2009), The PPG Story, Part 4
- PPG Wave 2.2 Owners Manual (english) (PDF), Palm Productions GmbH, archived from the original (PDF) on 2012-02-10, retrieved 2010-02-14
- Roads, Curtis (1996). The Computer Music Tutorial. MIT Press. ISBN 978-0-262-68082-0.
External links
[edit]- "Wavetable Cooker". Archived from the original on February 3, 2014. GPL application with graphical interface written in C by Camille Bassuel, implementing several DSP tools, including DFT to generate a wavetable set
- Hermann Seib (2011-01-07). "PPG Wave 2.2 / 2.3 / EVU Simulator". (VSTi plugIn) along with new Wavetables '08 by Wolfgang Palm, and "WaveSim Demo". (standalone version) worked with "Waveterm C". by Hermann Seib, Paul Maddox and Dave Forward.