DWGS 'Endless' Wave & Shepard Tones

tpantano · Post by **tpantano** » Tue Jan 10, 2012 7:54 pm

Hello-

I was wondering if someone would mind helping me wrap my mind around the concept of Shepard Tones and how the R3 uses them for its endless wave.

While I'd like to know some generic confirmation about the concept, one thing I'm curious about is wether each note contains the same frequencies. Does C2 = C3 = C4 = C5, or is it an illusion in our brain?

axxim · Post by **axxim** » Tue Jan 10, 2012 8:28 pm

I am not sure and never have analyzed this, but I thing this can be made wit two tones where one starts on lets say C2 and constantly sweeps its pitch to C5. When this tone reaches C4, the second begins in synchronization with the first at C2 and sweeps the same as the first while the first one fades out reaching C5. Then the first tone begins the same procedure when tone2 reaches C4 and so forth.

Due to the fact that both tones sweep synchronous, you only know the pitch is increasing, but you definitely can't say what frequency it has exactly because there is a second sub (or over-) tone that acts like a harmonic.

A good comparison could be a rotating helicoid (screw shape): you get the impression it is moving from one side to the other.

It would be a good task to find out, but I'm still at work

axxim · Post by **axxim** » Tue Jan 10, 2012 11:35 pm

Well I read about this Shepard tone and it needs more oscillators, not only 2, but I was on the right way. I tried with the Radias using 4 timbres, but the LFO's initial phase only can be set between 0 and 180 degrees, so you can't place their phase equidistant in one period (0, 90, 180, 270). Neither the inverting some phases will work due the saw is not symetrical in the time axis like sine or triangle.

X-Trade · Post by **X-Trade** » Tue Jan 10, 2012 11:57 pm

The 'Endless' waveform present in DWGS and in the Radias PCM section consists of several pitches stacked across almost every octave. This is one reason why in for example the microKorg and MS2000 it was popular to synthesize pipe organ sounds. Interesting combined with RingMod and a BPF or waveshaper.

Anyway, because it covers every octave, as you go up the notes the pitches at the top of the scale become inaudible at the same time that lower pitches come in. With this kind of setup, it is possible to only need one waveform or sample to cover one octave. That same sample can then be mapped repeatedly across all octaves because it doesn't make a difference.

Note that octaves only contain a subset of all harmonics. Whilst a sawtooth contains all harmonics (each one at half the linear amplitude as the last), Octaves only contain powers of 2.
The easiest way to define such a scale is to start at the lowest desirable note.

So for example we can have 55Hz as our base note.
The first partial is 55Hz (technically speaking)
The second harmonic is 110Hz (one octave up)
The fourth harmonic is 220Hz (two octaves up)
The eighth harmonic is 440Hz (three octaves up)
The sixteenth harmonic is 880Hz (four octaves up)
The thirty-second harmonic is 1760Hz (five octaves up)
..3520
..7040
..14080
The five-hundred-and-twelfth harmonic is at 28160Hz which is nine octaves up and is inaudible, thus not needed.

Note that a shepard tone can be achieved quite simply with only two (or more) partials by crossfading over the course of an octave - by the time you reach the top of the octave, the higher note is inaudible but a lower note has been brought in)

axxim · Post by **axxim** » Wed Jan 11, 2012 1:15 am

Well the issue with the limited start phase of the LFO trapped me. I passed to use the Mod Sequencer instead to create the ramps for the pitch and the amplitude curves like this (explication below the pic):

Each timbre uses two mod seqencers, the upper for the pitch and the second for the amp level. The first timbre modseq starts with 0° phase, the phase of the other 3 are incrementally shifted in 90° steps (=4, 8, 12 seq. steps) .

Due the range limitation in the mod values for the pitch -24 to 24 the sweep has only 4 octaves. The four timbrers have the same setting: Osc1=Saw with no other setting. It works pretty good with any wave type even the PCM ones, provided they are not percussive.

The sound can be heard here: http://www.axxim.de/media/EndlessPad.mp3

If someone wants to test/modify this Radias patch, it is here http://www.axxim.de/media/EndlessPad.rdp

Synthoid · Post by **Synthoid** » Wed Jan 11, 2012 9:01 pm

Here's an article about it:

http://en.wikipedia.org/wiki/Shepard_tone

tpantano · Post by **tpantano** » Wed Jan 11, 2012 9:46 pm

axxim wrote:The sound can be heard here: http://www.axxim.de/media/EndlessPad.mp3

That is... intensely confusing o.o

My mind keeps wanting to think the sound restarts but then it listens and feels like it's a continuous linear upward motion, so then I listen again and my mind think it's restarting again. >.>

Re-Member · Post by **Re-Member** » Thu Jan 12, 2012 12:23 am

X-Trade wrote:Anyway, because it covers every octave, as you go up the notes the pitches at the top of the scale become inaudible at the same time that lower pitches come in. With this kind of setup, it is possible to only need one waveform or sample to cover one octave. That same sample can then be mapped repeatedly across all octaves because it doesn't make a difference.

Knowing that the Endless wave is only one octave of samples, you'd only need one Mod Sequencer set at 12 steps changing the pitch to create the Shepard Tone effect. Just set it to repeat smoothly.

Re-Member · Post by **Re-Member** » Thu Jan 12, 2012 3:19 am

Re-Member wrote:Knowing that the Endless wave is only one octave of samples, you'd only need one Mod Sequencer set at 12 steps changing the pitch to create the Shepard Tone effect. Just set it to repeat smoothly.

Scratch that idea. Just tried it out and it has an abrupt gap when it reaches the end of it cycle and tries to repeat itself.

axxim · Post by **axxim** » Thu Jan 12, 2012 10:37 pm

Re-Member wrote:...
Scratch that idea. Just tried it out and it has an abrupt gap when it reaches the end of it cycle and tries to repeat itself....

I was near to post a reply to you, telling it would'tn work, but having this forum trouble yesterday, I thought you would test it anyway

If you make a simple octave sweep, then you have to play and hold the same key in each octave at the same time . The only problem would then be, that the lowest one starts every sweep period with full volume which would be audible. For that you need the second mod sequencer, to smooth the start and the end volume. To avoid the tremolo effect which destroys the endless illusion, you have to generate several waves and distribute their start across the sweep period.