Computation time reduction in a polyphonic tone synthesizer

Claim 2

In combination with a musical instrument in which a plurality of data words corresponding to the amplitudes of points defining the waveform of a musical tone are computed during each one of a sequence of computation cycles from a preselected set of harmonic coefficients and are transferred sequentially to a means for conversion into audible musical tones, apparatus for reducing the length of time required for each computation cycle by combining subsets of said preselected set of harmonic coefficients comprising: a first harmonic coefficient memory for storing a first subset of said preselected harmonic coefficients, a second harmonic coefficient memory for storing a second subset of said preselected harmonic coefficients, a memory addressing means for reading out harmonic coefficients stored in said first harmonic coefficient memory and for reading out harmonic coefficients stored in said second harmonic coefficient memory, a waveshape memory means, a word counter means for generating a sequence of word numbers having alternate even and odd numerical values, a complementing means responsive to said sequence of word numbers and responsive to harmonic coefficients read out of said second harmonic coefficient memory whereby a harmonic coefficient is transformed to a corresponding harmonic coefficient having an opposite algebraic sign if a corresponding word number has an odd numerical value and whereby a harmonic coefficient is unaltered if said corresponding word number has an even numerical value, a summing means for combining a harmonic coefficient from said complementing means with a harmonic coefficient read out from said first harmonic coefficient memory to form a combined harmonic coefficient, a means for computing responsive to each of said combined harmonic coefficient and responsive to said sequence of word numbers whereby said plurality of data words corresponding to the amplitude of points defining the waveform of a musical tone are computed during each one of said sequence of computation cycles and stored in said waveshape memory means, and a means for producing audible musical tone responsive to data words stored in said waveshape memory means.

Claim 3

Apparatus according to claim 1 wherein said word counter means comprises; a clock for providing timing signals, and a counter means for counting said timing signals modulo the number of memory addresses in said waveshape memory means.

Claim 4

Apparatus according to claim 2 wherein said means for computing comprises; a harmonic counter incremented each time said counter means returns to its minimal count state and wherein said harmonic counter counts modulo a number which is the maximum of the number of harmonic coefficients in said first subset of harmonic coefficients or the number of harmonic coefficients in said second subset of harmonic coefficients and said maximum number is less than the number of harmonic coefficients in said preselected set of harmonic coefficients, an adder-accumulator means wherein the count state of said harmonic counter is successively added to the contents of an accumulator in response to said timing signals, a sinusoid table for storing a plurality of trigonometric sinusoid values, an address decoder means responsive to the content of said accumulator in said adder-accumulator means for reading out trigonometric sinusoid values from said sinusoid table, a data computing means responsive to trigonometric values read out from said sinusoid table and responsive to each said combined harmonic coefficient whereby said plurality of data words corresponding to the amplitudes of points defining the waveform of a musical tone are computed during each one of said sequence of computation cycles, and a waveshape addressing means responsive to the count state of said counter means whereby said plurality of data words computed by said data computing means are stored in said waveshape memory means.

Claim 5

Apparatus according to claim 3 wherein said memory addressing means comprises; a memory address decoding means whereby harmonic coefficients stored in said first harmonic coefficient memory are read out in response to the contents of said harmonic counter and whereby harmonic coefficients stored in said second harmonic coefficient memory are read out in response to the contents of said harmonic counter.

Claim 6

Apparatus according to claim 1 wherein said first harmonic coefficient memory stores said first subset of preselected harmonic coefficients in memory address locations that increase in number from one to the maximum number of memory address locations and wherein said second harmonic coefficient memory stores said second subset of preselected harmonic coefficients in memory locations that decrease in number from the maximum number of memory address locations to one.

Claim 7

Apparatus according to claim 1 wherein said preselected set of harmonic coefficients correspond to the harmonic number sequence q=1,2, . . . , N where N is the maximum number of harmonics and wherein said first harmonic coefficient memory stores a first subset of said preselected harmonic coefficients at memory address locations corresponding to a harmonic number sequence q=1,2, . . . , N/2 and wherein said second harmonic coefficient memory stores a second subset of preselected harmonic coefficients at memory locations corresponding to said harmonic number sequence and wherein the harmonic coefficient for the harmonic number N-q is stored at a memory location corresponding to the harmonic coefficient associated with the harmonic number q.

Claim 8

Apparatus according to claim 1 wherein said complementing means comprises a 2's complementing logic whereby in response to said word number having an even numerical value a 2's complement logic operation is performed on said corresponding harmonic coefficient expressed in its binary numerical form.

Claim 9

In combination with a musical instrument in which a plurality of data words corresponding to the amplitudes of points defining the waveform of a musical tone are computed from a preselected set of harmonic coefficients at regular time intervals and converted into musical tones, apparatus for reducing the length of time required to compute each one of said data words by combining subsets of said preselected set of harmonic coefficients comprising; a first harmonic coefficient memory for storing a first subset of said preselected harmonic coefficients, a second harmonic coefficient memory for storing a second subset of said preselected harmonic coefficients, a memory addressing means for reading out harmonic coefficients stored in said first harmonic coefficient memory and for reading out harmonic coefficients stored in said second harmonic coefficient memory, a counter means for generating a sequence of word numbers having alternate even and odd numerical values, a complementing means responsive to said sequence of word numbers whereby a harmonic coefficient read out of said second harmonic coefficient memory is transformed to its opposite algebraic sign if a corresponding word number has an even numerical value and whereby said harmonic coefficient is unaltered in algebraic sign if said corresponding word number has an odd numerical value, a summing means for combining a harmonic coefficient from said complementing means with a harmonic coefficient read out from said first harmonic coefficient memory to form a combined harmonic coefficient, a means for computing responsive to each said combined harmonic coefficient and responsive to said sequence of word numbers whereby said plurality of data words corresponding to the said amplitudes of points defining the waveform of a musical tone are computed, and a means for producing a musical tone from said plurality of data words.

Claim 10

In combination with a musical instrument in which a plurality of data words corresponding to the amplitudes of points defining the waveform of a musical tone are computed from a preselected set of harmonic coefficients at regular time intervals and converted into musical tones, apparatus for reducing the length of time required to compute each one of said data words by combining subsets of said preselected set of harmonic coefficients comprising; a first harmonic coefficient memory for storing a first subset of said preselected harmonic coefficients, a second harmonic coefficient memory for storing a second subset of said preselected harmonic coefficients, a memory addressing means for reading out harmonic coefficients stored in said first harmonic coefficient memory and for reading out harmonic coefficients stored in said second harmonic coefficient memory, a counter means for generating a sequence of word numbers having alternate even and odd numerical values, a complementing means responsive to said sequence of word numbers whereby a harmonic coefficient read out of said second harmonic coefficient memory is transformed to its opposite algebraic sign if a corresponding word number has an even numerical value and whereby said harmonic coefficient is unaltered in algebraic sign if said corresponding word number has an odd numerical value, a summing means for combining a harmonic coefficient from said complementing means with a harmonic coefficient read out from said first harmonic coefficient memory to form a combined harmonic coefficient, a means for computing responsive to each said combined harmonic coefficient and responsive to said sequence of word numbers whereby said plurality of data words corresponding to the said amplitudes of points defining the waveform of a musical tone are computed, and a means for producing a musical tone from said plurality of data words.

Claim 11

Apparatus according to claim 8 wherein said counter means comprises; a means for obtaining a frequency number, and a note interval adder wherein said frequency number is successively added to the sum previously contained in said note interval adder and whereby the most significant bits of said sum in binary numerical format generate said sequence of word numbers having alternate even and odd numerical values.

Claim 12

Apparatus according to claim 9 wherein said means for computing comprises; a harmonic interval adder cleared to a zero value before a computation of each one of said plurality of data words wherein the content of said note interval adder is added to the present content of said harmonic interval adder, a sinusoid table for storing a plurality of trigonometric sinusoid values, a table memory addressing means for reading trigonometric sinusoid values from said sinusoid table in response to the content of said harmonic interval adder, and a data computing means responsive to trigonometric values read out of said sinusoid table and responsive to each said combined harmonic coefficient whereby said plurality of data words defining the waveform of a musical tone are computed.

Claim 13

Apparatus according to claim 8 wherein said first harmonic coefficient memory stores said first subset of preselected harmonic coefficients in memory address locations that increase in number from one to the maximum number of memory address locations and wherein said second harmonic coefficient memory stores said second subset of preselected harmonic coefficients in memory locations that decrease in number from the maximum number of memory address locations to one.

Claim 14

Apparatus according to claim 8 wherein said preselected set of harmonic coefficients correspond to the harmonic number sequence q=1,2, . . . , N where N is the maximum number of harmonics, and wherein said first harmonic coefficient memory stores a first subset of said preselected harmonic coefficients at memory address locations corresponding to a harmonic number sequence q=1,2, . . . , N/2 and wherein said second harmonic coefficient memory stores a second subset of preselected harmonic coefficients at memory locations corresponding to said harmonic number sequence and wherein the harmonic coefficient for the harmonic number N-q is stored at a memory location corresponding to the harmonic coefficient associated with the harmonic number q.

Claim 15

Apparatus according to claim 8 wherein said complementing means comprises a 2's complementing logic whereby in response to said word number having an even numerical value a 2's complement logic operation is performed on said corresponding harmonic coefficient expressed in its binary numerical form.

Claim 16

In combination with a musical instrument in which a plurality of data words corresponding to the amplitude of points defining the waveform of a musical tone are computed during each one of a sequence of computation cycles from a preselected set of harmonic coefficients and are transferred sequentially to a means for conversion into audible musical tones, apparatus for reducing the length of time required for each computation cycle by combining subsets of said preselected set of harmonic coefficients comprising; a first harmonic coefficient memory for storing a first subset of said preselected harmonic coefficients, a second harmonic coefficient memory for storing a second subset of said preselected harmonic coefficients, a third harmonic coefficient memory for storing a third subset of said preselected harmonic coefficients, a fourth harmonic coefficient memory for storing a fourth subset of said preselected harmonic coefficients, a memory addressing means for reading out harmonic coefficients stored in said first, second, third, and fourth harmonic coefficient memories, a waveshape memory means, a first coefficient combining means whereby a harmonic coefficient read out from said first harmonic coefficient memory is combined with a harmonic coefficient read out from said second harmonic coefficient memory to form a first combined harmonic coefficient, a second coefficient combining means whereby a harmonic coefficient read out from said third harmonic coefficient memory is combined with a harmonic coefficient read out from said fourth harmonic coefficient memory to form a second combined harmonic coefficient, a first means for computing responsive to each of said first combined harmonic coefficient whereby a first component plurality of data words are computed during each one of said sequence of computation cycles, a second means for computing responsive to each said second combined harmonic coefficient whereby a second component plurality of data words are computed during each one of said sequence of computation cycles, a combining means whereby said first component plurality of data words are combined with said second plurality of data words to form said plurality of data words corresponding to the amplitudes of points defining the waveform of a musical tone and are stored in said waveshape memory means, and a means for producing a musical tone responsive to data words stored in said waveshape memory means.

Claim 17

In combination with a musical instrument in which a plurality of data words corresponding to the amplitude of points defining the waveform of a musical tone are computed during each one of a sequence of computation cycles from a preselected set of harmonic coefficients and are transferred sequentially to a means for conversion into audible musical tones, apparatus for reducing the length of time required for each computation cycle by combining subsets of said preselected set of harmonic coefficients comprising; a first harmonic coefficient memory for storing a first subset of said preselected harmonic coefficients, a second harmonic coefficient memory for storing a second subset of said preselected harmonic coefficients, a third harmonic coefficient memory for storing a third subset of said preselected harmonic coefficients, a fourth harmonic coefficient memory for storing a fourth subset of said preselected harmonic coefficients, a memory addressing means for reading out harmonic coefficients stored in said first, second, third, and fourth harmonic coefficient memories, a waveshape memory means, a first coefficient combining means whereby a harmonic coefficient read out from said first harmonic coefficient memory is combined with a harmonic coefficient read out from said second harmonic coefficient memory to form a first combined harmonic coefficient, a second coefficient combining means whereby a harmonic coefficient read out from said third harmonic coefficient memory is combined with a harmonic coefficient read out from said fourth harmonic coefficient memory to form a second combined harmonic coefficient, a first means for computing responsive to each of said first combined harmonic coefficient whereby a first component plurality of data words are computed during each one of said sequence of computation cycles, a second means for computing responsive to each said second combined harmonic coefficient whereby a second component plurality of data words are computed during each one of said sequence of computation cycles, a combining means whereby said first component plurality of data words are combined with said second plurality of data words to form said plurality of data words corresponding to the amplitudes of points defining the waveform of a musical tone and are stored in said waveshape memory means, and a means for producing a musical tone responsive to data words stored in said waveshape memory means.

Claim 18

Apparatus according to claim 14 wherein said first coefficient combining means comprises; a clock for providing timing signals, and a word counter means for counting said timing signals modulo the number of memory addresses in said waveshape memory means whereby a sequence of word numbers is generated having alternate even and odd numerical values.

Claim 19

Apparatus according to claim 15 wherein said first coefficient combining means comprises; a complementing means responsive to said sequence of word numbers whereby a harmonic coefficient read out from said second harmonic coefficient memory is transformed to its opposite algebraic sign if a corresponding word number has an even numerical value and whereby said harmonic coefficient is unaltered in algebraic sign if said corresponding word number has an odd numerical value, and a summing means for combining a harmonic coefficient from said complementing means with a harmonic coefficient read out from said first harmonic coefficient memory to form a first combined harmonic coefficient.

Claim 20

Apparatus according to claim 15 wherein said second coefficient combining means comprises; a data select means whereby a harmonic coefficient read out from said fourth harmonic coefficient memory is subtracted from a harmonic coefficient read out from said third harmonic coefficient memory in response to an even numerical value for a corresponding word number to form a component harmonic coefficient and whereby a harmonic coefficient read out from said fourth harmonic coefficient is added to a harmonic coefficient read out from said third harmonic coefficient memory in response to an odd numerical value for said corresponding word number to form said component harmonic coefficient, and a complementing means responsive to said sequence of word numbers whereby said component harmonic coefficient is transformed to its opposite algebraic sign if a corresponding word number has an even numerical value and whereby said component harmonic coefficient is unaltered in algebraic sign if said corresponding word number has an odd numerical value.

Claim 21

Apparatus according to claim 15 wherein said first means for computing comprises; a harmonic counter incremented each time said word counter means returns to its minimal count state and wherein said harmonic counter counts modulo a number which is less than the number of harmonic coefficients in said preselected set of harmonic coefficients, an adder-accumulator means wherein the count state of said harmonic counter is successively added to the contents of an accumulator in response to said timing signals, a first sinusoid table for storing a plurality of trigonometric sine function values, an address decoder means responsive to the content of said accumulator in said adder-accumulator means for reading out trigonometric sine function values from said first sinusoid table, and a first data computing means responsive to trigonometric sine values read out from said first sinusoid table and responsive to each said first combined harmonic coefficient whereby said first component plurality of data words are computed during each one of said sequence of computation cycles.

Claim 22

Apparatus according to claim 18 wherein said second means for computing comprises; a second sinusoid table for storing a plurality of trigonometric cosine function values, a table addressing means whereby a trigonometric cosine value is read out from second sinusoid table in response to the content of said accumulator in said adder-accumulator, a function select means whereby said trigonometric sine value read out from said first sinusoid table is selected if said corresponding word number has an even numerical value and whereby said trigonometric cosine value read out from said second sinusoid table is selected if said corresponding word number has an odd numerical value, and a second data computing means responsive to the trigonometric value selected by said function select means and responsive to each said second combined harmonic coefficient whereby said second component plurality of data words are computed during each one of said sequence of computation cycles.

Claim 23

Apparatus according to claim 15 wherein said combining means comprises; an adder for pointwise summing corresponding values of said first component plurality of data words and values of said second component plurality of data words to form said plurality of data words corresponding to the amplitudes of points defining the waveform of a musical tone, and a waveshape addressing means responsive to the content of said word counter means whereby said plurality of data words are stored in said waveshape memory means.