ASSORTED QUESTIONS - CONTINUED (2)..

this thread is a continuation from here (http://www.thereminworld.com/forum.asp?cmd=p&T=4094&F=557&p=3)

Coalport posted the following on another thread.. I have taken the liberty (I hope this is ok..) of starting this continuation and pasting Coalports posting here, as it could otherwise be missed..

There is (in my opinion) a dire shortage of hard information and particularly comparative measurements of Theremins..

This is a rare gem.

Link to thread where this was posted (http://www.thereminworld.com/forum.asp?cmd=p&T=4107&F=3)

Direct link to www.peterpringle.com/linearity2.jpeg (http://www.peterpringle.com/linearity2.jpeg)

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Coalport's Posting..
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[i]

I was going to post the following link to the ASSORTED QUESTIONS forum, but it seems that topic is now closed.

This is a comparative linearity (range and spacing) chart for the Ethervox, RCA, Etherwave and Etherwave Pro theremins within an 18 inch playing arc. I made this several years ago but since we had been discussing linearity, I thought it might be of some interest to new Theremin World members who hadn't seen it.

I should add that the Etherwave I used in the chart was purchased in 1996 and it is possible that the linearity of newer models is improved. You can clearly see how the spacing between the notes closest to the pitch antenna are seriously "pinched".


http://www.peterpringle.com/linearity2.jpeg

[/i]

*Back to topic*

I spare you the deciphering of about 40 pages which I scribbled in the last weeks and come rather immediately to the conclusion(s):

a) Yes, there is a formula which describes the perfectly linear theremin.

b) Unfortunately, the same formula shows that the perfectly linear theremin cannot be built with real existing components only between the variable oscillator and the pitch rod.

c) But, when limiting to positive distances between hand and pitch rod (rather academic thought, matches perfectly with the real world) and only within a limited pitch range, one may come very close to perfect linearity.

d) Unfortunately, calculating the best approximation asks me for scribbling at least another 40 pages. So please be patient.

[i]"Unfortunately, calculating the best approximation asks me for scribbling at least another 40 pages. So please be patient." - Thierry [/i]

LOL! - No pressure.. It seems that patience is something everyone must learn when dealing with people like us.. 40 pages of calculations would take me a year, and probably be worthless because it would be wrong!

The [i]"between the variable oscillator and the pitch rod"[/i] implies that the linearization method is either the 'usual' one or a modification thereof.. having a tuned circuit in series with and/or forming part of the antenna.. perhaps a version adding poles to the resonant circuit - I could see how this is extremely difficult to compute!

What puzzles me is your statement that the E-Pro is unlike any other Theremin, and that one could apply the linearization method and build a Theremin less complex than the EW Standard... [i]"Just so far: It is easier to create a EPro theremin circuit with "only" 5 linear octaves and a register switch later for virtually extending this to 7 octaves than building an EStandard, WFClassic or tVCox tour circuit which is expected to have 6 to 7 linear octaves without octave shifting... ;-)
" [/i] ... I cannot see how this fits with any linearization method based on components between the variable oscillator and the pitch rod. Please - I am not arguing here (that may start later - LOL ;-).. I am just intensely curious - and perhaps just a little worried..

I didn't say that the EPro was less complex than the EStandard. I said that due to R. Moog's decision to limit the pitch range to only 5 octaves and to use a register switch made it easier to linearize it than if there were 6 or 7 octaves and no register switch...

[i]"I didn't say that the EPro was less complex than the EStandard. I said that due to R. Moog's decision to limit the pitch range to only 5 octaves and to use a register switch made it easier to linearize it than if there were 6 or 7 octaves and no register switch..." - Thierry [/i]

Thank you for that clarification Thierry.. You have in one paragraph brought my intense curiosity down to a managable level, and dispelled my worry!

;-)

I have been thinking a lot about the idea of range switching since reading Thierry's posting on this matter.

Making a 'standard' Theremin, using an equalizing inductor, it is, as Thierry indicates, quite easy to obtain 5 linear-enough playable octaves.. Problems (with this "simple" equalization method) really become noticable when one wants more than 5 octaves.

Until I played the EW-Pro recently, I was not aware that its linear range was limited to 5 octaves.. What Thierry has said regarding Bob Moog overcoming the problem of linearity by limiting the playing field to 5 octaves, makes good sense..

I do not particularly like the idea of having to switch octaves - and much prefer the Tvox approach.. But I have not managed to get better than 5 linear octaves without a lot of complex circuitry, and this translates to an expensive product.

So - I have been trying to work out how octave switching can be done, with the idea that I could make a lower cost version of my Theremin ( I am still doing my Theremin with full linear coverage of > 7 octaves).

I share my thoughts:

!) Assuming the fixed oscillator is at 455kHz, and the variable (pitch)oscillator ranges from 455khz-32hz (454.968kHz) to 455k-1050Hz(453.950kHz) (Giving a difference frequency range of 32Hz to 1.050kHz, which is 5 octaves)..

1.) I cannot see a way to change the register by simply changing the reference oscillator frequency.. for example, shifting the frequency up to 455.032kHz (455kHz+32Hz) would increase the lowest note to 64Hz (one octave higher) - but this would not shift the other difference frequencies proportionally (with the reference at 455.032kHz and the variable at 453.950kHz, the difference frequency would be 1.082kHz, not the 2.100kHz required.. one would simply be adding 32Hz to all the difference frequencies).

2.)I do not see that Multiplying the reference frequency will achieve what is required.. if the reference frequency is doubled to 910kHz, the difference frequency will range from 455.032kHz to 456.050kHz.. even if one was able to get rid of the 455kHz component, octave shifting would not occur.

3.) It seems to me that one must multiply both the reference and variable oscillator frequencies.. And that this will achieve the desired result:

~~~~~Reference~~~Var max~~~~~~Var Min~~~~~Difference Freq
x1~~~455 kHz~~~454.968 kHz~~~453.95 kHz~~~32Hz to 1.05 kHz
x2~~~910 kHz~~~909.936 kHz~~~907.9 kHz~~~~64Hz to 2.1 kHz
x4~~~1820 kHz~~1819.872 kHz ~~~1815.8 kHz~~128Hz to 4.2 kHz
x8~~~3640 kHz~~3639.744 kHz~~~3631.6 kHz~~ 256Hz to 8.4 kHz
x16~~7280 kHz~~7279.488 kHz~~~7263.2 kHz~~ 512Hz to 16.8 kHz

The above shows how multiplying both the reference and variable oscillator waveforms can give switchable ranges, each covering 5 octaves.

It can be seen that for each of the above ranges, the frequency of the variable (pitch) oscillator remains fixed in the range 453.95kHz to 454.968kHz, making the job of linearizing [b]far[/b] easier than if it was required to span a larger range.

Each multiplier circuit could consist of an analogue multiplier with both inputs tied together - the oscillator is fed into these inputs, and the output is double the frequency of the input.. This is the same type of multiplier as used to extract the difference frequency.. except that, as both inputs are the same, there is no difference frequency, there is only the sum of the frequencies - therefore the input (and all its harmonics) are doubled in frequency.

The output of the first multiplier is fed to the input of the second multiplier.. for as many multipliers as are required - and the range switch selects which signals are taken to the final analogue multiplier for extraction of the difference frequency.

So.. For each switchable range (except the lowest 'original' range) two multipliers are required.. to cover a reasonable range (32Hz to 8.4kHz) a total of 6 mult

There are simpler ways, and Moog has chosen one of them...

They never published schematics or circuit details, so I'm most probably and unfortunately not allowed to give more details here.

[i]"They never published schematics or circuit details, so I'm most probably and unfortunately not allowed to give more details here." - Thierry [/i]

Just email me with a clue, Thierry, and I will take the "risk" and publish it here!

In fact, there is no legal constraint I can think of, which could prevent a person from describing how something works.. You are only restricted from reproducing copyrighted works - but if you read a copyrighted work, and then disclose the ideas in this work, you are not breaking any rules (unless you have a NDA with the producer of such a work).

Fred -

I believe you are correct, at least as far as US copyright laws work. There is no crime in describing or analyzing an invention. However, reproducing it may be illegal if the circuit is protected under copyright.

BTW - 7 octaves is alot of linear range to compress into a 2 foot control distance, and makes the intervals very small (i.e. a more difficult to play instrument). I suspect your idea of 5 octave instrument with switchable range would make for a more user friendly theremin.

Wasn't the RCA only 3.5 octaves? That would be nice!

[i]"BTW - 7 octaves is alot of linear range to compress into a 2 foot control distance, and makes the intervals very small (i.e. a more difficult to play instrument). I suspect your idea of 5 octave instrument with switchable range would make for a more user friendly theremin." -Eitherspiel [/i]

LOL! - And here I am designing a Theremin which can give 10 linear octaves in a 1m playing zone.. :-))

Actually, because of the way I am doing things (generating a linear CV from 0 to 10V over the 1m playing range) the 'output' range and tuning can be set to whatever one wants - My prototype has a switch to select how many octaves the playing zone covers (Simply attenuates the CV) - from 3 to 10 octaves in 1 octave steps.. and there is a seperate switch to select the lowest octave (a 8 position switch which adds 1V to 8V to the CV - each 1V adds 1 octave, and the CV drives a 1V/Octave heterodyning VCO).

BUT - This Theremin is really complex and expensive.. Particularly as I do not have funds to go into volume production.. I am trying to find a simpler way so that I could produce a single-board Theremin I could sell as a kit, and matches the E-Pro's performance.

I also wish to clarify that the "idea of 5 octave instrument with switchable range" is not mine - it seems that Bob Moog implemented it first, in the E-Pro.