Basics of EW-Pro.. #2 (and related issues)

[i]the "magic" occurs when one feeds the VCO into a divider and takes the dividers output back to the phase comparator.. When in lock, the frequency out of the VCO is the frequency of the input signal * the dividers value (as in /16 will give *16)[/i]

Thank you, Fred. I'm sure I'd have got there eventually, but you saved me a lot of splinters in my fingers from scratching my head about that.

[i]"..you saved me a lot of splinters.."[/i]

LOL! - PLL's are, IMO, one of the most under-used components in electronics - Oh, they are used extensively in RF or near RF applications, but 'rarely' found elsewhere.

I tried useing them many years ago in audio effects units - Trying to get the bloody things to track VCO's and even acoustic sources.. I think a lot of people get badly put-off by doing this sort of thing -

The PLL operates best when it does not see big jumps in its input frequency - And when the input frequencys stay within quite tight bounds.. A couple of octaves is ok.. more, and you are looking at a difficult design.

PLL's are ideal for the kind of frequencies one finds in Theremins.. Tracking a frequency range of say 100kHz to 110kHz is as simple as copying the schematic from the 4046 application notes, running the freely available software app, and building it! Two PLLs (one for reference oscillator, one for variable oscillator) and one 4520 (dual binary counter) allows one to multiply these frequencies by 2,4,8,16 (2,3,4 and 5 octaves) and you can take the outputs from the VCO's to an XOR.. super simple range expansion..

If one has a variable frequency oscillator (antenna controlled) and make it extremely insensitive and highly linear (distance-pitch) a tiny change in oscillator frequency can be multiplied to whatever one wants.. Oscillator varies from say 100k to 101k, tune reference oscillator so difference is 2kHz, you will have a one octave playing field.. which you can multiply to 3 octaves or 7 octaves as you wish.. You can then divide the resulting difference by whatever you wish, to lower the bottom frequency to wherever you wish..

It so damn easy in digital!

"It so damn easy in digital!"

And this is the main reason I [b]had to[/b] disclose the E-Pro 'secret'.. Because without acceptance of digital techniques being VALID for high quality Theremins, Theremin development could not progress!

Dr Bob Moog saw this I am sure - He, ALONE was in a position to launch a Theremin which could be accepted as analogue, even though it was digital - And even He was taking (in my opinion) a huge risk in doing this.

So, there it is.. I have now given away nearly all my secrets - My secret of linearity is the use of extremely insensitive, but linear, front end - anyone with rudementary understanding of capacitive sensing can see how to do this.. It is absolutely useless for conventional Theremins, as one does not get a usable playing field.. but multiply this field, and the linearity is retained.

My trouble is that I spend too much time in my head, and not enough time at the workbench - People are waiting for my Theremins, and I have boxes of them - part finished, abandoned because some *better* idea has distracted me.. I have been "nearly there" for years - and I am probably more fed up with myself than you all are with me!

Anyone want to employ me? You will get an endless stream of designs, schematics and ideas - You just need some Tech to build them, test them, and give feedback - And put the best bits together into production.

Fred.

[i]"It so damn easy in digital!"[/i]

But it isn't exactly digital, is it! It's distinctly analogue in the phase domain, and that's where the all useful information is. But it has a lot of the benefits of digital - you can cheaply construct massive circuits on chips without serious noise issues. (I guess there comes a point where you have to think about how long it takes for a signal to follow different paths through the circuit, but that's nice and predictable.) Which means you could do things that are just impractical in analogue circuits.

So far we have integer multiplication and division - very musically interesting, the basis of harmonics, subharmonics and just intervals. Heck - one could even generate even tempered intervals. Well, pretty good rational approximations thereof. The keyword here is mediant rounding:

(From Forth Scientific Library Algorithm #46, Vulgar Maths Words (http://www.taygeta.com/fsl/library/vulgar.fth) by, uh, yours truly.)

[i]Numbers which cannot be represented exactly are rounded by a mediant rounding scheme as described in The Art of Computer Programming by D E Knuth. (Volume 2, Seminumerical Algorithms 2nd Edition (1981, Addison Wesley), 4.5.3 Analysis of Euclids Algorithm, page 363, exercise 40) which has been shown to generate best possible approximations. (A less rigorous but more accessible description may be found in the hobbyist book "Recreactions in the Theory of Numbers" by A H Beiler, Dover Publications Ltd, 1966.)[/i]

Or even even tempered partials - just like Hammond organs:

(From Tuning, Timbre, Spectrum, Scale By William A. Sethares)

[i]Some electronic organs (the Hammond organ) produce induced 12-tet spectra using a kind of additive synthesis. Sound begins in 12 high-frequency oscillators. A circuit called a "frequency divider" transposes these 12 frequencies down by octaves, and these are combined as partials of the final sound. In effect this quantises the frequencies of the partials to steps of the 12-tet scale. Such organs are the first electronic example of matching spectrum and scale using induced timbres.[/i]

But I am rambling. The real questions are - does this sort of phase-analogue-digital processing have a name? Is there a massive corpus of research and algorithms out there waiting to be utilised, or is it a backwater of research?

What the Hammond organ does is simple additive synthesis. Imagine a mixer which has entries for the base frequency and the first, perhaps 11, overtones. Each combination of settings of the 12 faders will correspond to a different timbre.

The other principle, the generation of the 12 half-tones of the topmost octave (or even above) and dividing them repeatedly by 2 in order to get a new, lower octave at each division is called TOS (Top octave synthesizer) and is still used (in a simpler form) in cheap keyboards today. But these don't normally use the upper octaves in order to combine overtones as the Hammond organ did.

Yup.

I do find it curious that, while Sethares finds this to be a good thing - his goal being increased consonance through spectral tuning, the wikipedia entry (http://en.wikipedia.org/wiki/Hammond_organ#Tone_generation) for Hammond organs describes it as a technical compromise.

The two instruments we had at home when I was a child were a piano (a Steinway upright grand, much like this one (http://www.youtube.com/watch?v=VKM7Veii71Y)) and, later, a Hammond organ. I seem to recall that playing arbitrary collections of notes at the same time (I won't dignify them as chords) was less raucous on the Hammond than on the piano, and perhaps this can be attributed to this "technical compromise."

I also think it would be interesting to hear a theremin with the same "distinctive tone colours" as a Hammond organ, and wonder if the enhanced consonance between notes would make it easier for the thereminist to "lock on" to harmonically related notes when playing in an ensemble or with a looper.

This is all so interesting and confirms what my ears already heard.

I bought one of the first E-Pros when it came out and was never quite happy with the sound. Playability is great, but could never get a "theremin" sound that I was happy with - always seems to bright and not much overtone.

When the E+ came out, I went to BigCityMusic to try one out and was hooked - great playability and I could immediately get the rich sound I was looking for.

Sold both of my E-Pros and have been immensely happy with my E+.

The thing is - if you don't love the sound, then why are you playing?

[i]"But it isn't exactly digital, is it!" - Gordon C[/i]

Hmmm.. Is there really ever a total boundary between analogue and digital?

With PLL frequency multiplication, one requires two digital inputs - these are "digital" in terms of logic levels - but, as you point out, the phase relationship of these signals is analogue (as in, they are not quantized - they have no discreet steps)..

But the same is true for taking signals from variable and reference oscillators, converting these to digital logic levels, dividing them, and feeding the divided signals into an XOR.. There is no quantizing involved - the phase relationships of the signals going into the XOR are analogue, and one could argue that the (after filtering) waveform is analogue.. which it is!

However - WAVE-SHAPE (amplitude) variations (and thereby any unique harmonic content these waveforms carry) are lost in the process of converting the signals to logic levels, and in subsequent digital processing of these signals – So, when the signals are combined to produce their difference frequency, the output will only carry analogue representation of the phase relationships on the input frequencies..

If one is feeding two constant frequencies each having (say) a ramp waveform, into an analogue heterodyning mixer, the output waveform from the mixer will be complex (Something like a ramp put through a LPF) and if one changes either input waveforms shape, the output waveshape will be altered.. Square the input signals and feed them into an XOR, and (after filtering) you will get exactly the same wave-shape as you would get had the input shapes been sine or any other waveform.

However – rapidly change an input frequency being fed into either analogue or XOR mixer, and the output waveform (for both types of mixer) will distort in a similar manner while the resulting difference frequency is changing – This PHASE related analogue data is not lost as a result of converting the input signals to logic levels.

Multiplying using PLL’s has exactly the same effect as dividing – in terms of what data is retained and what data is lost.. The fact that there is another analogue process (the PLL VCO and the analogue integrator) in the PLL scheme, does not change the fact that it is, essentially, a digital process.

My way ‘round this has been to effectively have two “Theremins” in the “system” – One for the front-end (capacitive sensing, but not using any harmonic data from this front end- using it to process the frequencies and pass the resultant ‘phase analogue’ data as a control signal to the ‘second’ “conventional” Theremin, which uses this data instead of an antenna ‘signal’.

But - Back to the point ;-)

Where does one 'draw the line' between what is "digital" and what is "analogue" ?

I think that calling a system which does not involve quantizing (i.e. where there are no discreet steps .. there is no 'word size' into which the data is 'fitted') "analogue" is probably fair - And a system like the E-Pro could, under this definition, be called analogue..

I certainly do not think that every system which involves logic level signals must be deemed "digital", and I do not see any way that systems which involve a discrete number of 'states' representitive of an analogue quantity can be regarded as analogue.. But even here - where does one draw the line?

If one had a digital word size of (say) 64 bits (1.84467E+19
) then,for every practical purpose, there is no difference between this and a non-digitized analogue version of this - the step accuracy will be far smaller than the thermal noise contributed by the circuit (in fact, this would be true even down to perhaps 24 bits).. And if the same kind of resolution was applied to the time domain, and if digital recreation of a waveform was done at high enough speed so that individual cycles were dynamically modified to replicate the distortion generated when

[i]"because I was thinking in EStandard categories where there is no extra filtering section behind the waveshaping circuit." - Thierry [/i]

Little clues slipping out ;-)

When you think about the Epro topology, you think in terms of an EW Standard..

So, Let me hazard this synopsis.. The Epro (in essence) is an EStandard (or EW+ because it has CV) with the following differences?:

Improved oscillators for much better stability and linearity - but for which wave shape is unimportant, because shape does not contribute to the audio harmonics.. so this gives the freedom to optimize for linearity (by oscillators pulling each other) without the constraints one usually need to worry about.

Replacement of the mixer with the digital range switching dividers and XOR mixer

A waveform modifier and possibly combined VCA modelled on the EStandard / EW+ (as in, using LM13700 for waveform distortion )

Analogue switches / multiplexers to select settings for presets, and perhaps for adjustments based on range switch.

This is followed by a section you have not really explored - and this is the reason you said CV was not used.. A section which (if the manual is correct) contains a VCF.

[b]TO ALL READERS OF THIS - EVERYTHING IN THIS POSTING IS A GUESS! - PLEASE DO NOT TAKE IT AS RELIABLE!![/b]

[i]My way ‘round this has been to effectively have two “Theremins” in the “system” – One for the front-end (capacitive sensing, but not using any harmonic data from this front end- using it to process the frequencies and pass the resultant ‘phase analogue’ data as a control signal to the ‘second’ “conventional” Theremin, which uses this data instead of an antenna ‘signal’.[/i]

It occurs to me that one could pass [i]any[/i] simply pitched audio signal through a comparator and use it as data for the "second theremin", along with an envelope follower to track the volume of the signal. Kind of like the opposite of a vocoder.

Playing that instrument could literally be "as easy as whistling". Mwahahaha-haaaa!