ELECTRIC OPRPHEUS ACADEMY
SPILLING THE BEANS #11 FREQUENCY SHIFT
Frequency shift is a linear shifting of the frequency – a real, reversible transposition by which the frequencies of a sound can be altered without changing its temporal and dynamic progression.
[Please do not confuse it with 'pitch shift,' and not at all with the hazy notions that are repeatedly connected with pitch shift!]
Linear frequency shifting: That means the distances of all frequencies to each other remain, but their proportions (intervals) change. When an upshift takes place, they become smaller; when a downshift occurs, they become bigger.
As a simple example, here is a sound made of 3 sinusoidal tones:
100 Hz – 200 Hz – 400 Hz
Harmonically, these are the fundamental tone, the octave and the double octave.
If we shift this sound 800 Hz upwards, then we get the new frequencies:
800 Hz – 900 Hz – 1200 Hz
These are now a whole tone (9/8) and a fifth (12/8 or 3/2) above the new 'fundamental tone'.
The same one 50 Hz down results in:
50 Hz – 150 Hz - 350 Hz
An interval proportion of 1:3:7 (fundamental tone, fifth + octave, seventh + double octave – namely the somewhat smaller seventh 7/4)
With these examples one can easily see why the process can conflict with a predefined tone system. Not only are the original interval proportions lost, but new ones that do not integrate into the tonal system ordinarily emerge, too.
Unless the overtone series of the integral partial tones would be the tonal system itself, such as with overtone singing. Then the motifs can be brought into another harmonic state by shifting many times over.
Here is an example of an overtone flute:
The flute melody begins with the minor third between the 5th and 6th
overtone. (We assign the number 1 to the fundamental tone, not the octave,
because the intervals are then obvious at a glance).
Through upshifting by the three-fold base frequency, these two initial tones get into the area of the 8th and 9th overtones, thereby forming a major second:
Shifted downwards by a two-fold base frequency, with an alias filter:
[The overtone flute is a long, thin copper pipe with a recorder mouthpiece. By varying the blowing pressure, the different overtones are produced. The 'percussion instrument' is a grill rack which can be found in every next-best stove].
* * *
In regard to the material to be processed, we generally have to differentiate between:
a.) Sound material with an integer overtone structure (practically all stringed, plucked and brass instruments, including the human singing voice)
b.) Sound material with an arbitrarily different partial tone structure (percussion instruments, planar tone generators such as plates, bells, cymbals; prepared instruments; all types of static, water and wind – as well as the ambient noises and sounding of instruments, and the consonants of the human voice)
[In older teaching books one finds the terms 'harmonic' and 'disharmonic' sounds for this differentiation. As long as this is not meant in a judgmental or excluding way, one can use this differentiation as far as I am concerned]
a) Harmonic Sound Material
As just demonstrated, integer overtone series can be aligned with themselves by frequency shifting. In an extreme case, with very sharp, rigid sounds, it works like a filtering. The overtone series apparently remains the same, only the low frequencies are more or less missing.
Displacements with fractions of the base frequency no longer align with the original overtone series, but are in turn interpretable as parts of an integer series with a lower fundamental tone.
The original fundamental tone always remains in the difference frequencies of the successive partial tones, no matter which interval they are just forming. However, that also means with each distortion which leads to combination tones, it is reconstructed! Such distortions can develop through overloading, through bad links in the transmission chain (amplifier, loudspeaker), but also directly in one's ears if a shifted sound is played too loud.
Therefore, one should very carefully use narrow-banded sounds of this type primarily – unless one would like to cause such mostly unpleasant interferences...
If one wants to motivically work with various transpositions of the very same sound, similar to the way it would also be possible with tempo transposition or pitch shift (whereby all frequencies would be proportionally shifted, rather than linearly), then a rare phenomenon arises: There is no harmonic conflict; there is no such thing as 'consonance' and 'dissonance.' Either the partial tones are aligned or not, or they lie so close beside the alignment that a pulse which is the same for all frequency pairs develops.
b) Disharmonic Sounds
Disharmonic sound material behaves in a totally different manner. There are no uniform difference frequencies. From the transposition of a sound, its original state is no longer apparent: It cannot be reconstructed by distortion nor in a psychoacoustic way. Any transposition can melodically or harmonically enter into a relationship with any other, as well as with the original. The only thing is that there is no general 'harmonic theory.' However, that should not mean that regularities would not be found; as a rule, these only apply to the one individual case.
A cut from Limpe Fuchs' 'Watersong' (field recording and lithophone):
The same cut with a 550 Hz upshift
and 550 Hz downshift, with a downstreamed alias filter
A canon-like mix from the original and 3 transpositions (crude):
If one combines frequency shift with proportional frequency changes such as tempo transition or pitch shift, one can thus work in a motivic manner by counterbalancing both of the different processes.
(>> ATEM, Werke 3, ccr403)
Many recordings, even professional ones, have 'offset': this means an amount of extremely low frequencies (below 10 Hz), if not direct current. Normally that does not attract any further attention, because the transmission paths (loudspeakers) cannot bring it. For the frequency shift, however, that is considered as 0 Hz, is correctly shifted, and is then noticeable as a penetrating whistling noise. The bottom line: Use offset filters! (e.g., rmo in VASP or AMP).
Seen from a functional perspective, frequency shift is simply a multiplication. One of its precursors is ring modulation.
[The description is somewhat misleading. It simply refers to a certain circuit technology...]
The ring modulator multiplies both inputs. The frequency shifter also does the same thing, only complexly. (A differentiation of both inputs in 'signal' and 'carrier' has to do with technical problems; basically they are equivalent). While the typical raw sound is created in the ring modulator by the inseparable mix of the upper and lower 'side band' (upshift and downshift), this can be selected in the frequency shift.
Thus, there is nothing against laying arbitrary sound material at both inputs that – complex from now on – multiplies, meaning it is complexly modulated.
One can then imagine the frequency shift in such a way that every frequency of the one sound, together with every frequency of the other sound, forms a new sum frequency. In many cases, however, the level dropouts or envelope modulations, which arise through the multiplication of the amplitudes, are at the forefront.
Here is the complex modulation of the cut with the brass band music that briefly appeared in the previous newsletter:
If the complex operations basically occupy two channels, how does one proceed with stereo material? Very simple: split for both channels, as in the previous example. (The corresponding VASP script can be found below).
(c) Günther Rabl 2011
VASP script for complex modulation in stereo
sfload limpe6.wav "load Limpe's 'Watersong' in buffer A
sfload blasmusik.wav "load the brass band music in buffer B
stsplit "split for both channels from here on
hilb "Hilbert alllpass
hilb "Hilbert allpass
vmul "modulation of both buffers (complex multiplication)
endstspplit "end of the stereo split
"(the indentations only serve for easier readability)