Shifting pitch

Yamaha has also patented sampling architectures (see Massie s chapter for more information on sample rate conversion and interpolation in samplers). A recent patent [Fujita, 1996] illustrates how fractional addressing from a phase accumulator is used by an interpolation circuit to perform wide range pitch shifting. 

Asynchronous Pitch Shifting. Asynchronous pitch shifting, the simplest pitch shifting method, simply changes the clock rate of each output digital to analog converter (DAC) to vary the pitch. Each channel requires a separate DAC. Each DAC has its own clock whose rate is determined by the requested frequency for that channel. When a DAC clock occurs, the DAC issues a request to a memory controller that supplies a waveform sample to the DAC. The earliest samplers had a separate memory for each DAC. 

Numerous commercial instruments were built in the early 1980 s that used asynchronous pitch shifting, including the Fairlight Computer Music Instrument [Roads, 1996], Kurzweil 250 [Byrd and Yavelow, 1986], the E-mu Emulator and Emulator 2 [Massie, 1985], and the New England Digital Synclavier. 

Finally, the term pitch shifting is well entrenched to mean simple sample rate conversion within the sampler engineering community. 

To surmount the difficulties of the time domain re-scaling that pitch shifting introduces, techniques such as multi-sampling are used as described below. 

Figure 8.7 Digital Sine function - the frequency response for a zero order hold interpolator sample rate converter with L = 4, which puts the original Nyquist frequency at 0.25 7t. We can see rolloff in the passband of about -3.9 dB and very poor rejection of images outside of the passband, which result in artifacts perceived as pitch shifting distortion.

When the phase increment Ml L is greater than one, and the original signal is being reduced in sample rate, classical sample rate techniques require that the cutoff frequency of the prototype filter change to. One approach is to time- scale the polyphase subfilters, but this increases the computation rate, which is undesirable in a typical VLSI implementation. Another approach is to switch filter tables. In practice, may sampler implementations only have one filter table, and pitch shifting up is restricted to be less than one octave. With this restriction, it is usually OK to use only one filter table with its cutoff equal to f. The artifacts resulting from this compromise are usually acceptable. 

How Many Fractional Phase Register Bits are Needed. The choice of how many bits to make the phase register is an important issue in computer music design. While other authors have covered this issue in relation to traditional sine wave oscillators, there are some subtle differences in the design of sample playback oscillators. Here, the fractional part of the phase register essentially determines how much pitch resolution is available, while the integer part determines how many octaves up the waveform can be transposed (pitch shifted). 

Denoting a > 0 the pitch shift ratio, and assuming that the loop buffer contains one period, the frequency Fout of the output sine wave is simply Fout = (X Fioop where I, denotes the frequency at which the loop samples are output. From this, we derive that relative variations of a and Fout are equal ... 

The smallest available variation of the pitch shift ratio a is given by the number Nf of bits used to represent its fractional part. More specifically,... 

Clearly, the constraint on Nj- is more stringent as a becomes small tuning errors will be more audible in downward pitch shifting than in upward pitch shifting. Unless a limit is imposed on the required amount of downward pitch shifting, an arbitrary large number of bits must be used to represent a. Denoting Noct the maximum number of octaves one wishes to pitch-shift down, we always have a> 2 N°cl and equation (8.10) now reads... 

Bristow-Johnson, 1995] Bristow-Johnson, R. (1995). A detailed analysis of a time-domain formant-corrected pitch-shifting algorithm. J. Audio Eng. Soc., 43(5) 340-352. 

It is difficult to integrate multiple DACs into a single chip, but integrating the pitch shifting circuitry onto a single chip has been economical since the middle 1980 s. Only a single DAC is then required for output, since the data can be mixed in the digital domain. 

These factors motivated a complete shift in sampler design from asynchronous to synchronous pitch shifting techniques in the middle 1980 s. 

Sample rate conversion. All of the synchronous pitch shifting techniques essentially involve sample rate conversion techniques. The theory and practice of sample rate conversion has received extensive coverage in many excellent texts and articles, but it is illuminating to compare the computer music perspective with the traditional sample rate conversion literature. Insights from the sample rate conversion literature provide insights to the computer music perspective, and vice versa. 

With Phaselncrement = 1.0, each sample for the wavetable is read out in turn, so the waveform is played back at its original sampling rate. With Phaselncrement = 0.5, the waveform is reproduced one octave lower in pitch. Each sample is repeated once. With Phaselncrement = 2.0, the waveform is pitch shifted up by one octave, and every other sample is skipped, effectively decimating the waveform by 2. 

This tells us that in order to maintain one cent of accuracy, we need eleven bits more than the maximum number of octaves of downward pitch shift. Typically, implementors do not pitch shift by a large amount. 12 to 16 fractional bits is fairly typical in practice. 

One problem of shifting the sampling rate of a PCM sound is the intrinsic link between pitch and time. Pitch shifting upward by one octave yields a sound which plays at twice as high a pitch, and for half the time. Another problem is the so-called munchkinification ect. This relates to the apparent shift in the perceived sound-producing obj ect when the pitch and time is shifted. For example, the octave-up pitch shift also yields the perception of a talker whose head sounds half the size of a normal person. This other dimension, which has to do with the quality of sounds rather than pitch, loudness, or time, is called timbre. Once we ve learned more about the frequency domain, we ll have better tools to explain munchkimfication and timbre, and we ll also have a lot more tools to avoid (or control independently) all of these dimensions. 

Track 8] Spoken Synthesize, Original and Phoneme Synthesis. [Track 9] Pitch Shifted Speech and Trumpet. 

Track pitch shifting information is also displayed in this area of the track. (See Chapter 9 for a discussion of loop and track types.)... 

The + 5 on the Track Header reveals that this track has already had its pitch shifted up five semitones. 

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