on market. Most early electronic organ makers thought it too expensive to manufacture the plurality of oscillators required by additive organs, and began instead to build subtractive ones. In a 1940 Institute of Radio Engineers meeting, the head field engineer of Hammond elaborated on the company's new Novachord as having a "subtractive system" in contrast to the original Hammond organ in which "the final tones were built up by combining sound waves". Alan Douglas used the qualifiers additive and subtractive to describe different types of electronic organs in a 1948 paper presented to the Royal Musical Association. The contemporary wording additive synthesis and subtractive synthesis can be found in his 1957 book The electrical production of music, in which he categorically lists three methods of forming of musical tone-colours, in sections titled Additive synthesis, Subtractive synthesis, and Other forms of combinations. A typical modern additive synthesizer produces its output as an electrical, analog signal, or as digital audio, such as in the case of software synthesizers, which became popular around year 2000. Timeline The following is a timeline of historically and technologically notable analog and digital synthesizers and devices implementing additive synthesis. Discrete-time equations In digital implementations of additive synthesis, discrete-time equations are used in place of the continuous-time synthesis equations. A notational convention for discrete-time signals uses brackets i.e. and the argument can only be integer values. If the continuous-time synthesis output is expected to be sufficiently bandlimited; below half the sampling rate or , it suffices to directly sample the continuous-time expression to get the discrete synthesis equation. The continuous synthesis output can later be reconstructed from the samples using a digital-to-analog converter. The sampling period is . Beginning with (), and sampling at discrete times results in where is the discrete-time varying amplitude envelope is the discrete-time backward difference instantaneous frequency. This is equivalent to where for all and See also Frequency modulation synthesis Subtractive synthesis Speech synthesis Harmonic series (music) References External links Digital Keyboards Synergy Sound synthesis types