Coupled Oscillators and the Musical Relativists

Season's greetings folks, thought you might be interested in this;
I've just built an electronic circuit consisting of 2 coupled
negative resistance oscillators.
Whilst mucking around with this arrangement I came across an
interesting effect, when driving oscillator was at a fairly high
audio frequency and the frequency of the driven swept through it's
audio range, it's output was a stepped series of discrete intervals
featuring a perfect minor chord including the octave of the tonic.
Unlike the overtone series the low frequency intervals start close
together and interval distance increases up the series.
Is this an "undertone series"?
If you're interested I'll post the circuit schematic. The circuit is
very simple and easy to build from readily available and cheap parts.

TTFN

John S

on 12/23/04 3:35 AM, jsnelsonone <jsnelsonone@yahoo.co.uk> wrote:

>
>
> Season's greetings folks, thought you might be interested in this;
> I've just built an electronic circuit consisting of 2 coupled
> negative resistance oscillators.
> Whilst mucking around with this arrangement I came across an
> interesting effect, when driving oscillator was at a fairly high
> audio frequency and the frequency of the driven swept through it's
> audio range, it's output was a stepped series of discrete intervals
> featuring a perfect minor chord including the octave of the tonic.
> Unlike the overtone series the low frequency intervals start close
> together and interval distance increases up the series.
> Is this an "undertone series"?

Not likely, I don't think, but even with the schematic the math would be a
bit of work to find out, and also require exact transistor response besides
other component values. Interesting but probably not interesting enough to
get me to do the work! ;)

> If you're interested I'll post the circuit schematic. The circuit is
> very simple and easy to build from readily available and cheap parts.
>
> TTFN
>
> John S

--- jsnelsonone <jsnelsonone@yahoo.co.uk> wrote:

>
> Season's greetings folks, thought you might be interested in this;
> I've just built an electronic circuit consisting of 2 coupled
> negative resistance oscillators.

hum, "negative resistance" ????

> Whilst mucking around with this arrangement I came across an
> interesting effect, when driving oscillator was at a fairly high
> audio frequency and the frequency of the driven swept through it's
> audio range, it's output was a stepped series of discrete intervals
> featuring a perfect minor chord including the octave of the tonic.

well, you can get this effect with some amplitude modulation and a
sweep/siren frequency. also, very cool and interseting. would this be
just signal clipping with your circuit ?

> Unlike the overtone series the low frequency intervals start close
> together and interval distance increases up the series.
> Is this an "undertone series"?

yes, or a reasonable facismile. some of the math nuts haven't figured
out how to deal with typical +/- 10% engineering tolerances...not to
intentionally torment the 'purists' but thats "life".

> If you're interested I'll post the circuit schematic. The circuit is
> very simple and easy to build from readily available and cheap parts.
>

maybe yes and maybe no, certain parts aren't all that available, but i'm
interested enuf to look into it.

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John,
There's an easy way to find out. Record it and post it as an MP3 file, and we'll compare it with the undertone series using our most sensitive audio comparator deconstruction device: our ears.
Prent
----------------------------------------------------------------------
Whilst mucking around with this arrangement I came across an
interesting effect, when driving oscillator was at a fairly high
audio frequency and the frequency of the driven swept through it's
audio range, it's output was a stepped series of discrete intervals
featuring a perfect minor chord including the octave of the tonic.
Unlike the overtone series the low frequency intervals start close
together and interval distance increases up the series.
Is this an "undertone series"?
-------------------------------------------------------------------------
--

Prent Rodgers

Music that's "Fake but Accurate"!
Web page: http://prodgers13.home.comcast.net
Podcast: http://podcast1024.blogspot.com
RSS: http://feeds.feedburner.com/Podcast1024
Music: http://www.soundclick.com/PrentRodgers

on 12/23/04 7:27 PM, Kurt Bigler <kkb@breathsense.com> wrote:

> on 12/23/04 3:35 AM, jsnelsonone <jsnelsonone@yahoo.co.uk> wrote:
>
>> Season's greetings folks, thought you might be interested in this;
>> I've just built an electronic circuit consisting of 2 coupled
>> negative resistance oscillators.
>> Whilst mucking around with this arrangement I came across an
>> interesting effect, when driving oscillator was at a fairly high
>> audio frequency and the frequency of the driven swept through it's
>> audio range, it's output was a stepped series of discrete intervals
>> featuring a perfect minor chord including the octave of the tonic.
>> Unlike the overtone series the low frequency intervals start close
>> together and interval distance increases up the series.
>> Is this an "undertone series"?
>
> Not likely, I don't think, but even with the schematic the math would be a
> bit of work to find out, and also require exact transistor response besides
> other component values. Interesting but probably not interesting enough to
> get me to do the work! ;)

Paul corrected me off-list. Somehow I didn't quite catch on to the
possibility that the one oscillator was locking to the other. So of course
frequency division is possible this way, and so of course you have an
undertone series.

If what you want is just an undertone series you can do that with any clock
source and a non-retriggering 1-shot multivibrator with an adjustable
timing. That's the simplest form of a semi-analog frequency divider. But
what you have going with your circuit probably has a lot more interesting
audible qualities.

-Kurt

Hello jsnelsonone-
I had meant to reply to the initial post earlier, but various preoccupations got in the way. As one of my pricipal obsessions is in the overtone series as produced by various means (brass, string, overtone singing, filter resonance, etc.), I am *extremely* intrigued by the possibility of an instrument which will produce an undertone series! (Particularly as there is of course no acoustic instrument which can do so.) I wonder if you have made any more observations your circuit's capabilities - can you tell have far down in the undertone series it will go, and do the tones remain discrete or do they become unstable or blur as you go down, etc, can you tell how exact it is, etc. I might want to have one built, if you would be interested....:)

Message: 6
Date: Thu, 30 Dec 2004 00:13:45 -0800
From: Kurt Bigler
Subject: Re: Coupled Oscillators and the Musical Relativists

on 12/23/04 7:27 PM, Kurt Bigler wrote:

> on 12/23/04 3:35 AM, jsnelsonone wrote:
>
>> Season's greetings folks, thought you might be interested in this;
>> I've just built an electronic circuit consisting of 2 coupled
>> negative resistance oscillators.
>> Whilst mucking around with this arrangement I came across an
>> interesting effect, when driving oscillator was at a fairly high
>> audio frequency and the frequency of the driven swept through it's
>> audio range, it's output was a stepped series of discrete intervals
>> featuring a perfect minor chord including the octave of the tonic.
>> Unlike the overtone series the low frequency intervals start close
>> together and interval distance increases up the series.
>> Is this an "undertone series"?
>
> Not likely, I don't think, but even with the schematic the math would be a

=== message truncated ===

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Hi Christopher, I added another (independent) oscillator to act as a
drone and indeed the pitches are those of the undertone series and
perfectly in tune with the drone's harmonics (the oscillators produce
a non-linear waveform and sound very similar to bagpipe drones at low
frequencies around 100Hz, giving a rich supply of upper partials)
The series runs from the fundamental down to the 8th sub-harmonic
were a low octave of the tonic is found and a few intervals further
down which become increasingly unstable.
This performance would probably improve with a bit of tinkering.
I made a similar set up using digital Schmitt trigger inverters as
the oscillators and the same thing happened only not so well.
I don't have any way at the moment of posting a schematic here, but
I'm working on it.

TTFN

John S

on 4/1/05 17:04, jsnelsonone at jsnelsonone@yahoo.co.uk wrote:

>
>
> Hi Christopher, I added another (independent) oscillator to act as a
> drone and indeed the pitches are those of the undertone series and
> perfectly in tune with the drone's harmonics (the oscillators produce
> a non-linear waveform and sound very similar to bagpipe drones at low
> frequencies around 100Hz, giving a rich supply of upper partials)
> The series runs from the fundamental down to the 8th sub-harmonic
> were a low octave of the tonic is found and a few intervals further
> down which become increasingly unstable.
> This performance would probably improve with a bit of tinkering.
> I made a similar set up using digital Schmitt trigger inverters as
> the oscillators and the same thing happened only not so well.
> I don't have any way at the moment of posting a schematic here, but
> I'm working on it.
>
> TTFN
>
> John S

This sounds good. I look forward to seeing the circuit diagram when it's
ready.

mopani

Hi Mopani, http://www.moosapotamus.com/tri-
negistor/TriNegSchematic.gif is the schematic of a "Stomp Box" called
the Tri-negistor. My arrangement is pretty much identical to the
first 2 stages with the exception that the capacitor of the first
stage should be say half the value of the second stage driven
oscillator which you take the output from as in the last stage of the
Tri-negistor.
You might need to up the voltage I used 15v and 100k pots with 10k
current limiting resistors.

TTFN

John S

on 5/1/05 17:28, jsnelsonone at jsnelsonone@yahoo.co.uk wrote:

>
>
>
>
> Hi Mopani, http://www.moosapotamus.com/tri-
> negistor/TriNegSchematic.gif is the schematic of a "Stomp Box" called
> the Tri-negistor. My arrangement is pretty much identical to the
> first 2 stages with the exception that the capacitor of the first
> stage should be say half the value of the second stage driven
> oscillator which you take the output from as in the last stage of the
> Tri-negistor.
> You might need to up the voltage I used 15v and 100k pots with 10k
> current limiting resistors.
>
> TTFN
>
> John S
>

Great site. I've downloaded the lot. Lots to twiddle.

best
mopani