Shepard-tone-like octave effect?

I would like to have a synth sound whose overtones confuse the listener as to what octave they’re hearing. The desired effect is similar to a Shepard tone. The idea is that you’d go up the chromatic scale from C3 to C4, and that each individual note would sound higher than the previous one, but it would be ambiguous whether C3 or C4 was higher, whether C#3 or C#4 was higher, whether D3 or D4 was higher, and so on.

Here’s why I’m asking: I want a sound that pairs with a circular pitch class representation, so you can go around and around the chromatic scale without seeming to go into higher or lower octaves. I’m sure this is possible with additive synthesis just by selectively filtering lower and higher overtones, but creating such a thing is beyond me. An Ableton-compatible solution would be ideal but am open to all suggestions.

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Maybe Endless Series V3 would work? It’s available in VST format and can do tone generation. I’m not sure about generating notes in a scale though because I don’t own it.

The only other thing I know of that can do Shepard tones in scale is the Expert Sleepers General CV eurorack module. You would need the MIDI breakout in order to get the MIDI out from it into Ableton though. Here’s a demo of the Shepard-Risset mode https://www.youtube.com/watch?v=pBqAt-F_6nQ

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maybe I’d call them ‘Deutsch tones’… after Diana Deutsch who used these pitched/static versions in some psychoacoustic experiments.

Anyway you can do this with additive synthesis, maybe with Max or by writing an external?

For each pitch class (chroma) you have a sum of sine tones, one per octave. For height, you vary the amplitudes of the sine tones according to a Gaussian shape. (A raised cosine is used by Shepard, but the Gaussian is more flexible and works just as well.) The mean and spread (Gaussian standard deviation) are up to you. The perceived ‘height’ is essentially this mean. Obviously, you don’t want the variance to be too small, as then you’d get just a sine wave and not have the ambiguity, but neither do you want it large because then it’s a rich and buzzy spectrum, like a vacuum cleaner, and you can’t fit any other sounds in. Generally the most usable versions sound ‘glassy’. Also, you’re using a finite number of tones, so the amplitude of the lowest and highest frequency partials should be very close to zero, they should be totally masked and inaudible.

There’s also a tradeoff between absolute accuracy and timbral control. You may try instead of sine waves, triangle waves or some other wave. It can break up the ‘glassy’ tone somewhat and make it sound warmer, because using only octaves for partials has a very distinctive and sometimes annoying character, you might easily tire of it. The triangle or other versions has a different spectrum, with partials in non-octave relationships, but may sound more pleasing or just be good for variety. If you’re just after a rough perceptual effect in a piece, and not actually conducting a psychoacoustic experiment you can get away with a lot here. I remember some Prophet VS patches, not at all rigorously constructed, where the exact octave was confusing at least within a 2-3 octave range.

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Make noise Telharmonic has a shepard tone generator as a hidden mode if you use Euro?

This sounds like a few things done with comb filters that track pitch. Set up so it’s evenly spaced and you feed it extremely rich content (noise) you’ll get your note at different octaves. How much emphasis on the root depends on the sound source. If you put a wide bandpass in series you can get a bit more emphasis on the root, or layer an oscillator under where you want it.

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I was able to achieve this by varying the relative amplitudes of the odd and even harmonics. See my pitch circularity page (which includes demos) at http://deutsch.ucsd.edu/psychology/pages.php?i=213 , and the pdf by Deutsch, Dooley and Henthorn (2008) posted on this page.

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So cool to see you post here!! I’m a huge fan!

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Oh wow, thanks for the response! Both because it answers the question, and because I assign the speech-to-sound illusion in the first week of class every semester.

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Thanks for your note - it’s great to hear that you are assigning the illusion in your class!

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Also a huge fan. So glad you’re here!

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