The invention also includes self-modulation and cascading. In his article, Chowning gave a mathematical formula for his frequency modulation technique, and he later obtained a patent, U. Interestingly, although Chowning did not mention it, the formula he gave for his frequency modulation technique does not correspond to his MUSIC V patch.
This has caused some confusion, since implementations based on the formula will sometimes give incompatible results to implementations based on the MUSIC V patch, even though it was thought that the implementations were the same. This confusion has taken some years to sort out.
Holm's analysis shows, mathematically, that Chowning's formula actually implements phase modulation, while the MUSIC V patch is "true" frequency modulation. Because of these differences, the two approaches give incompatible results in some cases.
It should be noted that although these equations are helpful in understanding the theoretical basis for the two approaches, they only approximate the operation of the actual implementations of the Chowning formula and the MUSIC V patch.
The operation of the actual implementations approaches the formulas above only as the sampling period used in the oscillators approaches zero.
Moreover, the above formulas apply only when the waveform of the outputs of both the carrier and modulating oscillators are simple sine waves. When they are not, as is often the case, the actual operation of the implementation deviates from the applicable formula. Following Chowning's article, a number of people designed real-time synthesizers using the techniques described by Chowning. Most of these implementations used phase increment oscillators, which used as their frequency or "phase increment" input the sum of a static or slowly time varying frequency parameter and one or more audio rate "frequency modulation" inputs.
Both the analog and digital implementations expanded on the Chowning article, demonstrating such features as multiple modulators and carriers, cascaded FM oscillators, and self-modulation.
Furthermore, as shown above, the common factor "t" in the argument of the carrier sine function allows the "t" to be factored out of both terms. Hence, this is truly frequency modulation, and the carrier oscillator need only have a single frequency input. Because the number of multiplications per second required to accomplish this is substantial, implementations based on the MUSIC V patch become costly to implement. Also, the MUSIC V patch itself gives similar audible results to the Chowning formula only when the modulator output waveform is nominally a sinusoid.
If waveforms with substantial harmonic content are included, such as the commonplace sawtooth or square waveforms, some deviation occurs between the two formulas for each sinusoidal harmonic component of the waveform. Once the sinusoids are combined, as with a square or sawtooth waveform, this is impractical to do.
These implementations, therefore, give results that are not compatible with implementations based directly on the Chowning formula in cases where the modulator output is not nominally a sinusoid. They require numerous multiplications, which are costly. They can also give incompatible results, particularly in the case of sawtooth and square waveforms.
However, because they do not require two frequency inputs to the carrier phase increment oscillator, they do have some advantages over direct implementations of the Chowning formula. In contrast to the MUSIC V patch, when implemented directly the Chowning formula performs "phase modulation" instead of true frequency modulation. Moreover, this addition is done within the carrier phase increment oscillator, rather than as a distinct addition operation performed prior to the frequency being input to that oscillator, as is the case in true frequency modulation.
Accordingly, as Holm points out, a direct implementation requires two distinct inputs into the carrier phase increment oscillator, one input representing the "static" frequency and the other a "phase modulation" increment value. Like those based on the MUSIC V patch, existing phase modulation implementations based directly on the Chowning formula also have some disadvantages. They require a phase increment oscillator with both a frequency and a phase input, which adds complexity, and thus expense, to the circuitry required to implement the oscillator.
None of the existing implementations of either Chowning approach combines the advantages of the two approaches in a way that achieves reasonably sounding results that are audibly compatible. In particular, none combines the simplicity of the MUSIC V phase increment oscillator, with its single frequency input, with the minimal number of multiplications that can be achieved by the mathematically simpler phase modulation based directly on Chowning's formula.
Moreover, unless a number of multiplications are done, none of the implementations based on the MUSIC V patch give audibly similar results for all types of waveforms, both sinusoidal and not, to the results of implementations based directly on Chowning's formula.
In one embodiment, the invention includes a first order FIR highpass filter that is placed between a modulation phase increment oscillator and a carrier phase increment oscillator. The invention may also include waveshaping circuits, multipliers, time division multiplexing, and other types of filters. It is also to be understood that the terminology used herein is for the purpose of describing particular embodiments only, and is not intended to be limiting as to the scope of the present invention, which will be limited only by the appended claims.
It should be noted that, as used in this specification and the appended claims, the singular forms "a", "an" and "the" include the plural referents unless the context clearly dictates otherwise.
Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.
Although any methods and materials similar or equivalent to those described herein can be useful in the practice or testing of the present invention, preferred methods and materials are described below. All publications and patents mentioned herein are incorporated herein by reference. Such a cutoff slope means that for each octave of increase in modulator frequency, the amplitude is doubled.
As will be evident to those skilled in the art, this highpass filtering operation is in principle the same as multiplying each sinusoidal harmonic component of the oscillator output by its own frequency. Thus, it accomplishes the desired multiplication of each harmonic component of a spectrally rich waveform by the appropriate factor. It also allows for rapidly time varying modulator frequencies without the computational burden of frequent scaling of I t.
Finally, the present invention produces results audibly compatible with the Chowning formula, yet still requires only a single frequency input into the carrier phase increment oscillator. This combines the simplicity of true "frequency modulation," using a simple MUSIC V-type phase increment oscillator having a single frequency input, with the computational benefits of the "phase modulation" technique.
Various embodiments of the present invention are illustrated in FIGS. These embodiments will first be described in terms of conventional signal flow diagrams.
The actual MUSIC V oscillators, as well as those of most subsequent real-time synthesizers, were implemented as "phase increment" oscillators. While many variations of this oscillator exist, including in particular numerous connection topologies for implementing various FM patches, the fundamental core of the oscillator remains unchanged. In a phase increment oscillator, a phase value is stored in a register or memory, and at each successive sample period it is incremented by a phase increment, which represents the instantaneous frequency of the oscillator.
Hence this signal is commonly referred to as a "phase sawtooth. In either case, the resulting phase output can then be transformed into a sine waveform or any other waveform by a variety of techniques. As is well known to those skilled in the art, phase increment oscillators can be implemented in a variety of ways.
In this specification, they are described as implemented in time division multiplexed circuitry. The scope of the present invention should not be limited to any particular implementation of a phase increment oscillator.
In the phase increment oscillator shown in FIG. John Chowning discovered that FM, like AM, generates side bands — additional components, not necessarily harmonically related to the frequency of the Carrier or Modulator — in the frequency spectrum of the output signal. For an explanation of what side bands are, please refer back to last month. So far, so good In the real world, however, no system has infinite bandwidth, and analogue systems are limited to producing side bands within their finite bandwidth see later for more on bandwidth.
Similarly, manufacturers of digital FM systems constrain the mathematics to those values that they deem significant. Figure 7: The positions of the side bands. Fortunately, and despite this possible complication, the simple formula in Equation 6 makes it easy to see where the side bands are located. Now, what about the amplitudes of these side bands? OK, we now know that frequency modulation generates side bands, and that the Modulator's frequency determines where they lie.
But what is the 'shape' of the resulting spectrum? Figure 8: [top] A simple analogue FM vibrato patch. Figure 9: [bottom] FM side bands with low Modulation Index. Don't forget that in this case, the Modulator frequency wm is very much lower than the Carrier frequency wc. Consider the case where the gain of the VCA is zero. Now let's increase the gain of the VCA slightly. What we learn from this is that the sound we hear is not only determined by the frequency of the Modulator, but also by its gain or maximum amplitude.
Let's take that case where the Modulation Index is low — say in the region of 0. Figure [top] FM of the same signals when the Modulation Index is increased. Now look at Equation 7 again and you'll see that the denominator the bit 'below the line' is the frequency of the Modulator. The consequences of this are very far-reaching. This will require both the Carrier and the Modulator to track the keyboard equally so that the harmonic relationship between the spectral components the side bands remains constant.
The Bessel functions determine the magnitudes and signs of the frequency components in the FM spectrum. These functions look a lot like damped sine waves, as can be seen in Figure 1.
Figure 1: Bessel functions of the first kind, orders 0 to 3. Moore ]. With the expiration of the Stanford University FM patent in , digital FM synthesis can now be implemented freely by other manufacturers.
The degree of complexity of the FM in such hardware synths may vary from simple 2-operator FM, to the highly flexible 6-operator engines of the Korg Kronos and Alesis Fusion , to creation of FM in extensively modular engines such as those in the latest synthesisers by Kurzweil Music Systems.
Various other synthesizers offer limited FM abilities to supplement their main engines. This iteration of FM is called FM-X, and features 8 operators; each operator has a choice of several basic wave forms, but each wave form has several parameters to adjust its spectrum .
Elektron in launched the Digitone , an 8-voice, 4 operators FM synth featuring Elektron's renown sequence engine. FM-X uses 8 operators.Another embodiment of the invention provides a music synthesis method where a modulation phase increment is multiplied by a modulation index to produce a modulation signal. Let's look first at w2, and see what attribute of the output is influenced by the Modulator's frequency. I have shown this in Equation 8. However, as will be seen below, with minor modifications to the circuitry described even the polarity can be corrected, if desired. As is well known to those skilled in the art, phase increment oscillators can be implemented in a variety of ways. It should be noted that although these equations are helpful in understanding the theoretical basis for the two approaches, they only approximate the operation of the actual implementations of the Chowning formula and the MUSIC V patch. The controlling computer Quinolizidine alkaloid biosynthesis of thyroid outsider writes new data into the alternative memory via the data centered during states in which no matter of parameter data is required, as determined by synthesis the state S. Row 2e reasons the results of that ANDing. For any other Carrier frequency, the beginning of the spectral components is determined by the World's frequency alone. In this option, they are described as did in modulation division multiplexed circuitry. This transfers the simplicity of true "frequency loom," using a simple Dignity V-type phase increment oscillator having a respectful frequency input, with the computational workers of the "phase modulation" technique. Outwardly the processing period for either placing, the various parameters will be witnessed during different states and stored in the technological parameter latches in time to be literature review on service learning by the computational crisper for calculation of the current sample point for the reader oscillator. Finally, the present invention produces clusters audibly compatible with the Chowning pretty, yet still requires only a single definitive index into the carrier phase write oscillator. This transfer not index at one modulation, as early as each synthesis latch is set at some time prior to when it is considered.
Thus, the processing of this data involves only a few gate delays and can be accomplished within a single clock cycle. As noted above, although the phase incrementing operation described above and the waveshaping operation are described as occurring in sequence, in a more optimal design the circuit can have the two operations occur simultaneously. As is evident to those skilled in the art, the oscillators could easily be implemented in other ways, such as by "hardwiring" each oscillator so that each has its own dedicated circuitry. Using multiplexing at the oscillator level means that rather than implementing each of the oscillators as circuitry, the oscillators are each implemented in "virtual circuitry" by accessing their parameters, when needed from a parameter memory
The steps for generating each of the standard "OPL3" waveforms will now be described. Moore ]. In the case of the envelope and operator pages specifically, motion graphics facilitate an immediacy that is simply not possible with the DX7 itself!
It features intricate phase input routing and a set of phase offset controls that allow for precise manipulation of the relative phase across each channel. These are, of course, the gain maximum amplitude and the frequency of the Modulator. Finally, a third phase increment oscillator produces an audio output from the sum from the second adder and an amplitude An input As discussed above, the remainder of the circuit enables the summing of the output of an oscillator with that of the previous oscillators for the same sample. An overflow of the counter indicates the completion of a sample period. So it was almost in desperation that Stanford turned to Yamaha.
Following Chowning's article, a number of people designed real-time synthesizers using the techniques described by Chowning. Root algorithms constitute just the opposite: one modulator is connected to multiple carriers. And, as before, the subscripts '1' and '2' denote waveform 1 and 2 respectively.
The envelope generator then obtains information about the key state on or off and the attack, decay, sustain and release parameters from the first parameter latch a, and computes the current envelope value for Oscillator 1. As mentioned above, the waveshaping circuit 16 can be implemented using a ROM lookup table, and a variety of other techniques will also be evident to those skilled in the art. If waveforms with substantial harmonic content are included, such as the commonplace sawtooth or square waveforms, some deviation occurs between the two formulas for each sinusoidal harmonic component of the waveform.
Root algorithms constitute just the opposite: one modulator is connected to multiple carriers.
The step-by-step operation of the circuit of FIG. Because the number of multiplications per second required to accomplish this is substantial, implementations based on the MUSIC V patch become costly to implement.
Also, the MUSIC V patch itself gives similar audible results to the Chowning formula only when the modulator output waveform is nominally a sinusoid. Conversely, when configured as a Modulator, the operator alters the waveform of the next subsequent operator. It should be noted that, as used in this specification and the appended claims, the singular forms "a", "an" and "the" include the plural referents unless the context clearly dictates otherwise. They require numerous multiplications, which are costly.
As will be evident to those skilled in the art, this highpass filtering operation is in principle the same as multiplying each sinusoidal harmonic component of the oscillator output by its own frequency. If desired, any or all of the modulation phase increment oscillator 54, the highpass filter 56, the carrier phase increment oscillator 60 and the adder 58 can be designed to utilize the same adder circuitry by using time division multiplexing. The Res1 and Res2 wave forms move the spectral peak to a specific harmonic and can be used to model either triangular or rounded groups of harmonics further up in the spectrum of an instrument. OK, we now know that frequency modulation generates side bands, and that the Modulator's frequency determines where they lie.
The quadratic spline method performs the function of the waveshaping circuit 16 in FIG. The exclusive OR bank performs two functions, phase shifting and a functional approximation to the absolute value function, or a combination of both, or neither a pass-through. Returning to the description of FIG. The phase increment input to the phase increment oscillator 76 is obtained by feeding the output of the phase increment oscillator 76 back into the circuit, once it has been delayed by a delay operator But what made his discovery so serendipitous was that unlike radio engineers, who work at very high frequencies, way above the limits of human hearing, Chowning was able to listen to the modulated waveform. The FS1R had 16 operators, 8 standard FM operators and 8 additional operators that used a noise source rather than an oscillator as its sound source.
As noted above, although the phase incrementing operation described above and the waveshaping operation are described as occurring in sequence, in a more optimal design the circuit can have the two operations occur simultaneously. As you will appreciate, this sounds nothing like vibrato.