Theremin Linearity and Antenna Length...

I am posting the following observations because they came as a surprise to me.. I am not sure of the mechanism to explain the following, and I am not sure if these results apply to 'normal' Theremins.. At the moment I do not have time to fully explore what I am seeing.. But will check back every few days to see if anyone has any ideas.

I have been using pieces of copper pipe for my prototype antennas (amongst other things like lengths of wire etc) - these (for convienience in the lab) have tended to be thin and long (10mm to 15mm diameter max, up to 1m long).

Putting one of my Theremin prototypes into a more respectable case, and making some presentable antennas brought some surprises..

I matched the capacitance of my new antennas to that on the prototype - reducing the length from 70cm to 38cm and increasing the diameter to 19mm..

Everything worked fine - tuning never changed..
But - Linearity changed substantially.
Just out of interest, I replaced the antenna with a disk (a CD in fact..) and found that the linearity became even worse.

It SEEMS to me that a long thin antenna gives better linearity than a short fat one.. The only explanation I can think of is that, with a fat antenna, the capacitance is more focussed on the players hand, and therefore a truer inverse-square law result is obtained..

It SEEMS that with a long thin antenna, the capacitance directly between the hand / antenna is reduced, but there is an angular capacitive component added to this which relates to the capacitance not directly between hand / antenna, but between hand+arm and the sections of the antenna not directly (horizontally) in line with the hand

I think that this may cause the total capacitance change to be smoother when a long antenna is used.

For example - hand in line with bottom of antenna - distance to antenna (d) = (say) 50cm .. distance to top of antenna = sqrt((d squared) + (antenna height squared))

As the hand approaches the antenna, the hypoteneus changes less rapidly than distance (d) and the effect of the capacitance from the upper antenna changes less rapidly than the capacitance due to (d) - the entire upper section has varying degrees of capacitive coupling to the hand AND the arm...

?

Is there any truth in the above ? Anyone noticed this before ? Anyone used this ? Could this be how the 'Lev' antenna works? (could the antenna coil and possible resulting capacitance spread be responsible for improvement in linearity?)

I look forward to trying out a floor mounted theremin with a pitch rod made of Wollaston wire and attached to the ceiling.

It does make sense to me. The equations that describe such things are often based on idealisations (http://en.wikipedia.org/wiki/Spherical_cow) - one dimensional lines of infinite length and so on. As the form of a real object tends towards these ideal conditions so one would expect its behaviour to more closely approximate the behaviour predicted by the equations.

I recall Uncle Howie saying something to the effect of "an antenna of infinite length would be perfectly linear, but only at the tip" some time ago on levnet. (Warning - it was more than a year ago, I could well have remembered it wrong.)

Now I must go and inflate my cows.

"Now I must go and inflate my cows."

Tried that.. but the Theremin goes Moo Moooo not Woo Woooo..

I have done a few more experiments.. I now dont think the effect of antenna height / thickness is a huge factor on linearity, but I think it is a factor.

My Theremin generates a linearity correction voltage - and viewing this voltage led me to believe there was a significant deviation resulting from antenna change.. However, I failed to account for the fact that this correction voltage itself has a non-linear relationship to linearity (if you can get your head 'round that, congratulations! ;-)..

Doing the same experiment with a conventional Theremin (having Equalizing coil for linearity compensation) I THINK I noticed a degradation in linearity when the fat antenna was fitted.. but I am not sure this isnt just me seeing what I expect to see - And dont have time to do scientific measurement right now..

I dont really have time to be here at TW, but I am sitting here surrounded by tools and bits of pipes and wires, total chaos I need to tidy up before I can do owt else.. Sooo boring, so have had a minor relapse and given in to my TW addiction - just one fix every few days is ok ?! 8-{

Please take my comments "with a pich of salt" as I don't really know what I'm talking about - these thoughts (that I've had for some time now) are based just on observation.

It seems to me that the note-field on a theremin is somewhat egg-shaped ... or, at least, I find that each note appears to occupy an egg-shaped area with higher or lower notes either further in or further out (like egg-shaped Russian dolls). I've drawn this conclusion by trying to "trace" each note - running my hand around either side, top and bottom of the ariel - while trying to keep on the exact same note; then trying to trace higher and lower notes in the same way.

Actually, the E-Standard's notefield seems egg-shaped with slightly bowing sides - but the E-Pro's field seems to have "flatter" sides so that the field is perhaps more lozenge-shaped ... although both "curve" at the top and bottom.

When playing, I find the optimum place for reliable notes is wherever the field seems to be least curved, which I find to be in the top third or so on an E-Standard (top two thirds seem ok on the E-Pro). If a player's hand strays into the "curved" area (usually when playing too close to the theremin's top surface) then the notes seem less linear, (to me, at least; and logic suggests that where the "eggs" curve in and get "smaller" with each subsequent higher note, the gaps between notes will not be as consistent as when playing where the "egg" sides are at the flattest). Therefore, it seems to me that the longer the antenna, the greater the "flattest-sided" part of the field would be, and, therefore, the area where playing seems most reliable would be greater in depth, (and so the hand would be less likely to stray out of it into a less consistent areas).

The problem would be that with a VERY long antenna, few would be tall enough to play with ease in the top third of its field, (if the theremin itself is at the usual waist height).

I've notice that some of the Anthony Henk theremins (that look as if they have very long adjustable pitch ariels) are usually played with the theremin "body" lower / closer to the floor than most theremins, (in fact the volume antenna looks as if it comes up on a sort of "stalk" to compensate for the theremin body being at knee height video (http://www.youtube.com/watch?v=YTZK9FNgK74)). The positioning of the theremin and its longer ariels means that the player can stand with his/her hands at a comfortable height but still play in the more reliable "straighter edged" bit of the note field, which probably occupies a fairly good depth ... possibly the top two thirds, (in the video I've linked to above, the antenna is extended (although not fully) to about 3 feet and the player plays about two thirds up. I this video (http://www.youtube.com/watch?v=g72JGUmVoRY) the right hand plays about half way up the antenna). I seem to remember reading somewhere that adjusting the height/length of the Henk theremin antennas altered something about the notefield - it might have been its range, but I can't remember off hand.

It also appears to me that the T-Vox might have a longer antenna than the Moog theremins. I'd certainly like to try Henk and T-Vox theremins sometime and see how they compare with the other makes I've played.

Well, that's how it appears to me ... and I won't be at all surprised (or offended) if most here heartily disagree!

The first time I played the Julius Goldberg RCA theremin with its lightning bolt antennas, I noticed that it was difficult to control because the EM field was as jagged as the antennas that were responsible for emitting it.

Everything is fine as long as your pitch hand plays along an absolutely straight line (parallel to the floor) without deviating either up or down, but if you play slightly angled (which I do) the Christmas tree shaped EM field was confusing.

That's why, whenever I play the instrument, I remove its custom lightning bolt and replace it with a standard RCA straight antenna (which is what I do in the opening seconds of this vid).

Goldberg Theremin (http://www.youtube.com/watch?v=b1jJIUT0vlk)

Do you know if Mr Goldberg played with the jagged antenna ... or did he also replace it when performing?

In theremins without linearization coil, such as the Theremax or the Silicon Chip, the antenna length and thickness is not critical, there is just a pitch shift which can be compensated with the pitch tuning knob. There is also a slight impact on the distance between tones but it is nearly proportional so the (non present) linearity isn't really affected.

In theremins with linearization coil (all Etherwaves, RCAs, Wavefronts) the linearity is affected. A different antenna length or thickness gives another static antenna capacitance which detunes the series tank circuit with the linearization coil. So the ratio between the oscillators tank circuit resonance frequency and the antenna tank circuit resonance frequence is not longer the same and linearity is not longer as before. Modifying the antenna dimension in such a theremin needs also recalculation and adaptation of the linearization coil.

I have no experience with antennas with other shapes than a simple rod, so I can't tell anything about that. But I think that the Goldberg theremin is unique.

[i]"I seem to remember reading somewhere that adjusting the height/length of the Henk theremin antennas altered something about the notefield - it might have been its range.." Thereminstrel [/i]

Thanks for pointing out the Henk Theremin - I have seen this vid before, but never noticed the unusual antennas! LOL! 8-()

[i]"Everything is fine as long as your pitch hand plays along an absolutely straight line" - coalport" [/i] Also interesting.. I would hate to have to do an analysis of the fields 'round those 'bolts!


[i]"In theremins with linearization coil (all Etherwaves, RCAs, Wavefronts) the linearity is affected. A different antenna length or thickness gives another static antenna capacitance which detunes the series tank circuit with the linearization coil... " - Thierry [/i]

I did take the precaution of matching the capacitances of the antennas, and this was confirmed by the fact that the oscillator frequency only changed by a few 100Hz when antennas were swapped.

My experiment which showed this linearity issue consisted of a Theremin WITHOUT linearizing coil.. I generate a voltage proportional to the difference frequency, put this voltage through a non-linear circuit, and feed a portion of this voltage back to the reference oscillator.. This feedback voltage alters the frequency of the reference oscillator, forming a closed loop linearity correcting circuit.. The linearity becomes a function of the law of the non-linear feedback circuit, and the quantity of feedback applied.

Provided the law does not change, linearity can be simply adjusted by changing the quantity of feedback (too much feedback and note distance increases as one gets closer to the antenna, and range is reduced, too little feedback and one moves towards the typical Theremin response where notes compress as one gets closer to the antenna).. What I found was that the law did change when the antennas changed (although not as significantly as I had first thought)..

Trying the same on a Theremin with Equalizing coil, changing (capacitively matched) antennas did seem to make some difference to linearity - but I do not have this theremin set up for easy access to signals, so cannot be sure ... I know that I often hear/see things I expect to see - even if they are not there - so I often trust my instruments more than I trust myself.

Offhand, I'd say that the CD created a very thin, horizontally-polarized field while the vertical one is vertically polarized. It would be amazing if we could have a means of making the field visual on actual real hardware like you can do on a mathematical simulation.

What's the real-world equivalent of "iron filings" for electric fields? WEG>

I wonder if anyone ever tried a spiral-wound piece of tubing ... sort of like an expanded version of the "Lev Antenna"?

Don