*WHITE PAPER* The Sound of Music - How & Why the Speaker Cable Matters


I’ve spent a sizeable amount of the last year putting together this white paper: The Sound of Music and Error in Your Speaker Cables

Yes, I’ve done it for all the naysayers but mainly for all the cable advocates that know how you connect your separates determines the level of accuracy you can part from your system.

I’ve often theorized what is happening but now, here is some proof of what we are indeed hearing in speaker cables caused by the mismatch between the characteristic impedance of the speaker cable and the loudspeaker impedance.

I’ve included the circuit so you can build and test this out for yourselves.

Let the fun begin

Max Townshend 

Townshend Audio

F78318cb 1fc9 49a2 8d02 edd399ef66f5Ag insider logo xs@2xtownshend-audio
Well, there went my morning! ;) 

Seriously, a very good read that explains a lot of what I have heard from different cables.
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Finally an objective, peer reviewed, journal article with no built in conflict of interest demonstrating this is not all snake oil! Oh, wait...my mistake...it’s not. OMG - I’m in absolute shock - OP is in sales! Cables, risers, anti-earthquake bars and platforms - anything your heart desires - money is no object - especially when YOURS is in HIS pocket...
The abstract defines the "error" as the voltage drop between amplifier and speaker.  Isn't that determined solely by the resistance of the speaker and cable?  So the "lowest error" would be obtained with a speaker cable of least resistance?  

Well done, felt much better when I got to the  Oh wait...
Like to “paste” that Everywhere....

@TBakin63 - I believe the intro is an invitation for others test the methods and results for them selves. Perhaps instead of bashing his work you might test for yourself and report back?
Mapleshade used to make flat copper ribbon ICs. I still have a pair. Also, Ed Shilling of Hornshoppe Horns used to make flat copper ribbon speaker cables many, many years ago. Both claimed they sound better than "normal" cables.

All the best,
Rule of thumb says that cable becomes transmission line (reflections from impedance boundaries) when signal propagation one way is longer than 1/8 of the fastest transition time.  When perfect square wave is applied all cables behave like transmission line, but it doesn't happen in real life.  Rise time of the signal is roughly 0.35/BW, being 17.5us for 20kHz bandwidth.
17.5us/8=2.188us  a propagation time of 437.5m  (assuming speed of 5ns/m).   Designers do this calculation in any digital design to determine if wires or traces need termination.  I would worry about transmission line effects in audio when using speaker cables longer than 437.5 meters, unless I'm missing something?

(Another commonly used test is to compare length of the cable to 1/10 of the signal wavelength.  20kHz audio signal has wavelength of 10km, assuming signal speed of 200,000km/s.  1/10 of it is 1000m)
Sorry Mr. G'DAY, you are miles from the truth.

I also spent much time into speaker cables research & analysis.

1. The speaker side is not a part of the analysis. It is only looking into the Amp's output through the cables. 
2. The most important character of C (capacitance) should be zero, when the two cables (black and red) are separated and conducted by two separates. Problem solved.
3. The way to go (tested with multiple cases over here: https://forum.audiogon.com/discussions/no-one-actually-knows-how-to-lculate-what-speaker-cable-they-...about two years ago,
and here: https://forum.audiogon.com/discussions/how-to-select-a-good-speaker-cable
4. What matters is R (resistance) as it's series to the Amps' R out or DF.
If that is kept low the sound improves significantly. Try it.

This white paper is embarrassing in the level of errors, and erroneous conclusions.

The increasing rise in response above 400Hz is due to multiple reflections caused by the mismatchbetween the cable characteristic impedance, Zoand the impedance of the load. Note that the load impedance varies between 4 and 25ohms, which is an approximate match with the 18ohm cable.

Seriously?. This is not at all what is happening. If that was the case, the graphs would go up and down with frequency to match the impedance curve of the load as it mismatches with the cable like the peaks in impedance at 1.5KHz, and 10KHz, but they don’t. Why is that? I know why. The author? Not so much.

Now let’s have a good look at figure 12. The oscillations are 5 oscillations per usec. That’s 5MHz. No speaker puts that out. No human can hear it. Now how long is that cable? It’s 7 meters. * 2 = 14 meters. Waveform propagation speed is mainly related to dielectric, so let’s estimate speed at 0.6C = 180,000,000 meters per second. That’s about 13Mhz if due to transmission line reflections. Now what about the 18ohm impedance? Well it would also have transmission line reflections close to 13Mhz, but it appears to have oscillations close to 50 or 100MHz which if due to transmission line effects would require exceeding the speed of light.

For cable 6, Fig 3, with Zo 476ohms, driving the dummy speaker load with a step input from a square wave (the simplest transient) gives rise to severe ringing that has many oscillations.This is due to the transient reaching the mis-matched speaker load where only a small fraction of the signal is absorbed by the load. The remainder of the signal is reflected back to the source (the amplifier) where it is reflected back to the load. Again, only a small fraction of the now-diminished signal is absorbed by the speaker, with the remainder reflecting back to the source and so on. Over time, all the reflections will eventually be absorbed in the load.

Oh come on, really? That is not how characteristic impedance works at all. I sort of feel bad for the op putting this out. This is not going to go over well. Your simulation is highly flawed.

So, lets go back to the conclusion:

The results show that the principal factor determining the error of a cable is its geometry. Cables with very widely spaced conductors have the greatest error, closer-spaced conductor cables have less error, and very closely-spaced, flat conductor cables have the least, or near zero error.

No, this is not the principal factor at all, nor is it what your results indicate. Geometry (spacing) does play a roll in what is a determining factor and what all your results show.

Everything in your article points to 1 and only one 1 item. Inductance. Not characteristic impedance. Plain, simple inductance. Space conductors far apart, and the inductance is high. Space conductors close together and the inductance is low. Put two flat conductors really close and the inductance is very low (and the capacitance very high which can make some amplifiers unhappy).

The graphs in figure 3 - all inductance.

The oscillations in figure 12 - have nothing to do with transmission line effects, they are just a factor of the high or low source resistance in the simulation damping out the load oscillations slow or fast and impacting the frequency.

Reflections causing roll-off? They are at 13Mhz approximately. In your simulation they settle out completely after 10 microseconds (>100KHz bandwidth).

For low-level interconnect signal transmission, typical cables have an impedance of between 50 and 100ohmsanddrivea 10kilohm to 20 kilohm load. There are reflections from the load, but the source resistance is typically the same as the cable impedance, so the reflections will be absorbed in the source resistance and there will be no further reflections. This is known as “back matching”and usually occurs by default in audio and is de rigueur in video.

Source impedances in audio equipment single ended are typically 600-2000 ohms, some higher. That is not anywhere near 100 ohms or 50 ohms.

A high-loss dielectric distorts the electric field which has a second-order effect on the sound. The best practical insulators are air, PTFE and polyester. The worst is PVC.

Foamed polyethylene is better than basic PTFE which is why it is so common in high frequency cables. Reason PTFE is used in high frequency cables is dimensional stability. Polyester is not at all a good dielectric. It can be worse than PVC, or better, but never good.

This will not work well for a cable and can have huge errors. An LCR meter cannot isolate the L and C when taking a measurement on a cable and hence the measurements for L and C end up wrong.  With a good LCR meter (the DM4070 is not), you can adjust the measurement frequency and use the change over frequency to extract the accurate L and C values.  Of course if you start with a good LCR meter, it will have an impedance measurement function, which will allow you to measure the impedance with the cable shorted and the cable open-circui which can then be used to accurately compute the characteristic impedance.

APPENDIX B: Three Methods of Deriving Characteristic Impedance
METHOD 1–Use a VICI DM4070 LCR Meter or Similar
1.Measure the capacitance (C)of the cable with the cable open circuited.
2.Measure the inductance (L) of the cablewith the endshort circuited.
3.With capacitance in microfarads and inductance in microhenries calculate the impedance by this formula Zo= √L/C ohms.


-So the white paper will work with kindling ?
-What are the survival odds..you at a snake oil convention ?
No comment @1971gto455HO.  I am sure the author meant well and believes what they wrote is accurate. It is not. It is seriously flawed. It would be best to just withdraw it, no burning needed.
This thread is yet another wonderful illustration of why its such a waste of time for audiophiles to talk tech. Its all well and good for engineers and designers. But with audiophiles all that happens is the same BS just different words.  

When we get good sound we love it so much we just can't help but want to know all about it. Only thing, the more we learn the more it remains a mystery. Some guy comes along with a nice story. Might as well admit, its a nice story. Probably even some of it is true. Whatever true means. As if we know even that much.  

Just you who knock it, don't pretend you're any better. When it comes to understanding what's really going on we're all pretty much shivering around the campfire in the darkness hoping the tiger's not too hungry tonight.

All I really want to know, how's it sound?
Why do some people make it out to be so hard to get good sound? It’s really not. The core knowledge base needed is really not that big and is very well documented. The rest is mostly personal preference. Good sounding gear is plentiful and need not cost a fortune. Setting it up well can be tricky but is not rocket science.

I get it. It’s a hobby!  Also folks need to sell things.   A perfect match!

Carry on.
Silversmith Fidelium are garnering some excellent reviews.
Until today I'd never heard of Townsend Isolda.

Probably even some of it is true. Whatever true means. As if we know even that much.

It will never cease to amaze me the mental gymnastics an audiophile will perform to avoid admitting that perhaps they are wrong or don’t know how something works (but someone else does).

Some of it ...which part? The premise is wrong, the conclusions wrong, simulations don’t illustrate what they are supposed to, the impedance measurement method is wrong ... It will be much harder to find something right than something wrong. And that I and many others know these things are wrong shows that yes, many know "that much".

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Does this mean more consideration for matching white van speakers?
Home Depot zip cord #2 instead of #5?

Enjoyed reading your white paper.
A lot of work went into this analysis and I commend you for it!

Question: Why did you use long 7 meter cables?
Most people would use 3-10 feet in their application. (which would skew the results in a positive way for all cables tested)

I use Hales Signature Two's with a 4 ohm input.
For speaker cables, the new Silversmith Fidelium.
Separate positive and negative leads are used in the design, raising the specter of low capacitance and high impedance due to a wide separation between the two conductors. (in my case, varying between 3"-8")
Despite this fact, the cables are amazingly neutral and balanced throughout the frequency spectrum.
The transient response on the leading and especially trailing edges are SOTA.
The imaging and sound stage are killer!
They exhibit no edginess or brightness. (especially when compared to the Straightwire Maestros that I formally used)
I might chalk it up to dumb luck that the impedance's between Amp,. Speaker Cable and Speaker apparently match up well.
But many other people who use this cable in very different set ups, feel the same way about this cable.

I could easily experiment by overlaying the cables and taping them together.
From a sonic POV, what improvements would I expect to hear?

The op seems rather quiet considering the feedback. Was this a run and gun marketing exercise or an honest attempt at a serious white paper?
Let's assume you use an Amp with a DF of 400. It has an output resistance of 8/400=0.02 Ohms.
What Capacitance (F) should make an audible change?
If you use two separate cables, (Not one that are molding the two lines in a single plastic tube), what Capacitance would such a cable have?

Maybe the op brought up capacitance, but no one in this thread has raised it as an issue except w.r.t amplifier stability so not sure where you are trying to go with this?
Like @djones said there's no reflections at audio frequencies.


1 . There is no clear scale used for any of the measurements. 
2. The measurements and conclusions are inverted. 


Weighing in on this discussion - I have been wondering about the possibility of using a Litz wire design for the speaker wires.  If you want the complex impedance of the cable to remain flat over the audio range plus adding in consideration for the higher harmonic frequencies then you need to consider proximity effects (skin effect is the proximity effect that most people are familiar with - there are others).  

The skin depth in copper at 100kHz (the upper BW of most good audio amplifiers) is 0.2mm so this equates to a 32AWG wire.  Assuming you want the equivalent of a 12AWG speaker cable then this would equate to the need for 103 individually insulated strands of 32AWG wire to make the equivalent of 12AWG.

The Litz design that I am considering would be based on using 108 individually insulated strands of 32AWG wire.  From a practical construction perspective I would suggest that the individual insulation is colored - say red for the positive and blue for the negative.

The Litz wire would be made in three levels:

1) Take 3 red and 3 blue 32AWG strands and twist them together to form a 6-bunch.  Make sure that the strands are alternated - red, blue, red, blue, red, blue.
2) Repeat step one 36 times to result in 36 6-bunches.  Each 6-bunch should be twisted the same way (e.g. clockwise) and the number of twists per length should be the same for each 6-bunch.
3) Take six 6-bunches and twist these together to form a 36-bunch.
4)  Repeat step three 6 times to result in six 36-bunches. Each 36-bunch should be twisted the same way (e.g. counterclockwise - the opposite to what was used for the 6-bunches) and the number of twists per length should be the same for each 36-bunch.
5) Take six 36-bunches and twist these together to form a 216-bunch.  This should be twisted the same way as the 6-bunches (e.g. clockwise).
6) Apply a length of woven expandable PET sheathing over the cable to provide some physical protection for the finished speaker cable and secure each end of this sheathing with a short length of heat-shrink tubing - approximately 100mm from the end of the cable. 
7) At the 100mm ends of the cable that are not covered in the sheathing separate out all the individual strands into two bunches - 108 red wires and 108 blue wires.
8) Strip 25mm of the insulation from all of the individual strands.
9) Twist all of the blue strands together to form the negative speaker wire and twist all of the red strands together to form the positive speaker wire.
10) Enjoy!
Why would you want 100KHz flat response. You can't hear it, your speakers cannot recreate, and if they could they would likely distort and modulate distortion to audible frequencies.  100KHz amps are mainly to ensure no phase shift in the audio band (and for marketing).

12 awg stranded only drops in resistance about 50% at 100KHz.  You could just use 2- 12 awg stranded, maybe even 1 - 8awg stranded.  18 - 24 AWG would be just as good at 100Khz as 108-32awg and a lot less work.
w.r.t. a liquid conductor, as long as it has inductance, capacitance and resistance (it will), then it will have a characteristic impedance.  However, the only problem to solve is inductance and that would be hard to interleave (for speaker cables).
Technically there are always reflections, however, the impact on power transfer at audio frequencies is several hundred db down.

erik_squires9,935 posts11-18-2020 6:01pmLike @djones said there's no reflections at audio frequencies.

Is it just me, or do these Townshend cables seem to be quite similar in design to the Goertz Alpha-Core's?:

Get a foil inductor, preferably 12awg, and double sided sticky tape. One inductor builds a lot of speaker cable similar to the Goertz or Townshend.  Just be careful, your amp may not like the several nF of capacitance.
Goertz offers their "RC network" aka zobels.

Of course to simplify all this just get some Canare 4s11 or other good copper speaker wire and stop obsessing. 
Can audio2design explain the change in responses as shown in Fig 3. and the close correlation with Zo, if it is not a transmission line effect?

All conductor pairs have capacitance and inductance so must have a characteristic impedance. There is no frequency component. Read All About Circuits, chapter 14 thoroughly and the two papers associated.

There are long transmission lines and short transmission lines.

Silversmith cables have Zo between 800 and 1800 ohms, depending upon the spacing.

Don't use conditionally stable amplifiers. 10nF is not a difficult load for a competently designed amplifier.

The measurements are of the voltage between the two black terminals at either end of the wire. The short circuit has the least voltage drop and is lower and the cables have a greater voltage due to resistance and are higher on the graph and the treble rise is dependant upon Zo. They are not inverted.

As I suggest, do the experiment your self before guessing.

@townshend-audio - What is the magnitude of the error voltage with respect to the voltage at the load/speaker in your measurements?
Transmission lines.

When do you have to bother?

Answer: long cables or high frequencies. You can completely ignore
transmission line effects if length ≪ u /frequency = wavelength.

Audio (< 20 kHz) never matters.
Computers (1 GHz) usually matters.
Radio/TV usually matters.

One of us has the required education, and experience not to guess at this topic. I don’t need to guess or consult "All About Circuits", though it is for the most part a well designed website.

And yes, I can explain them and I already did. INDUCTANCE. This is well known, and documented by professional wire companies like Kimber and Cardas. (Though to be completely accurate, there may be a fraction of a db here and there for skin resistance).
Everything in your article points to 1 and only one 1 item. Inductance. Not characteristic impedance. Plain, simple inductance. Space conductors far apart, and the inductance is high. Space conductors close together and the inductance is low. Put two flat conductors really close and the inductance is very low (and the capacitance very high which can make some amplifiers unhappy).

Let me point out that your statement, "The results, Fig 3, show the frequency responses of a series of cables from 30Hz to 20kHz, together with their characteristic impedances Z0." is wrong. It does not show the frequency response, it shows the cable voltage drop, which is not the same as frequency response.

As we don’t know what drive level the amplifier is, the spectrum analyzer settings, or even the scale, though it may be in db, but was that dbW, dbm, dbu, dbuv? db without anything else is a relative number only when measured electrically. Again, not a frequency response, a relative voltage drop.

Looking at your round conductors, spaced at 5, 15, 50mm. Depending on the gauge, the ratio of inductance will be close to 1:2:3, with 1 being between about 6 an 20uh, but the construction and dielectric differences in your samples will make for a lot of variation, but first order calcs would show about 5db difference between 5mm and 15mm and a bit less between 15 and 50mm, which is not too far off the 5 or 6db differences you show.

The parallel flat plates of your cables (and Alpha Core Geortz cables), I would estimate as only about 3-5uH. I would need more details on the dimensions, thickness of the dielectric, etc., but rough is going to be 3-5uH. That would be 1/2 the best case close wires, and maybe 1/3 - 1/4 and hence why less voltage drop at 20KHz. .... oops see it is 6.6uH in your document. My 5uh upper end was not a bad estimate. No idea what frequency your LCR measures at though, so that 6.6uH may not be accurate at 20KHz.

No transmission lines, no reflections, just basic physics / electrical engineering. You may notice that as opposed to talking in generalities, I have, in both my posts, brought up very specific numbers. Those weak on a topic guess, those who understand take available information and develop relatively accurate estimates.
Oh, FYI, you show the cable drop as lower at 20KHz than 0Hz so something in your system is dropping 2.1db at 20KHz.

... oops, now I see your cable was 6.6uH. Not bad for my 5uH upper end estimate. However, no idea what frequency your LCR meter measures at, so it could be inaccurate at 20KHz.

The whole graph is a bit wonky. A short is 0V which is not 0db, it is some large negative number as it is log scale. If you use the "short" and offset everything else, you may have been offsetting the noise floor, not the actual measurements. You can’t say your drop was 2.1db more than a "short". That is meaningless. Hence that value of 2.1db, the so called error has no real meaning. It would have been better to have compared it to a fixed resistance or have taken a proper frequency response not a cable drop response without a proper reference.

Oh hey, in your chart, I see the ratio of the inductance of the 3 wires I said would be about 1:2:3 is actually 0.95:2.1:3.  It seems the calculations for inductance work pretty well.
Interesting reading. I have the author's Townshend F1 Fractal speaker cable in my system and it is, without a doubt, by far the best speaker cable I have heard. Good to read the science behind why it sounds so good. 
Cheap add to Townshend cables!
Some of the measurement schematics are stolen from others. They got it wrong. Mr. Townshend copied the mistakes. 
He ends up with C- capacitance. 
Capacitance is defined between two points. If the speaker cable is a joint of the black and red wires, tubed in a plastic encapsulation, there might be some  capacitance. Get two separates, no more any capacitance.
What's the big deal?
But loosing the capacitance will not change much the muddy bass, the unclean mid and highs. Getting a cable with a low resistance ref. to DF will. Garantied.
The abstract defines the "error" as the voltage drop between amplifier and speaker. Isn’t that determined solely by the resistance of the speaker and cable? So the "lowest error" would be obtained with a speaker cable of least resistance?
Look, i’m not defending  costly magic cables. I focus more on really good connections (which typically suck, and are made worse by obstinate fancy cables BTW).  I cannot tell you how many systems i have tightened a connector on or eliminated an intermittently shorting 2-guage speaker cable, or cleaned a grss set of contacts on.  sometimes after saying "this isnt right".

That said, to the above, no. Its reactance. Maybe that’s what you meant but reactance is highly dynamic and also interacts with the hugely reactive load that a speaker poses. Consider this, theoretically, when the voice coil is returning toward its original position, it is provide in back-EMF and therefore a NEGATIVE resistance.

Just saying this is not a simple "measure the ohms on our radio shack meter" sort of thing.
If Radio Shack still existed.

While I have not yet had the time to go through the ""White Paper", the reason for the change in sound may well be related to the following:

Assuming one has a Scope & a Square wave generator, try passing a 20 K HZ Square wave through a cable & Observe the waveform that comes out of the other end.

The closer the wires in a cable are to each other, the more rounded will be the Square Wave coming out of the other end.

Only way to get a matching Square Wave Out, is to space the wires some distance from each other.

As music is not composed of Square Waves, some may hear the effects of this rounding of waveform & enjoy the results; others may think that that the rounding is negative for the sound they hear.

Take your pick & use Speaker Wires that fits your preference.

Meh...mumbo jumbo. I’d rather be listening to music, going for a walk, drinking wine, or visiting my local record store, than spending hours or days trying to prove/disprove a very subjective matter. Let your ears decide; it’s that simple.  My ears can’t hear a difference, but that’s me. 
Meh, mumbo jumbo. I’d rather be reading about technical correlations pertaining to sound on a forum dedicated to sound, than reading about unrelated preferences of a personal nature. Let’s not let our lying ears decide, when empirical evidence can lead us away from personal prejudices, It’s that simple. My mind can tell the difference, but that’s me.
Nobody can see a virus because it's so small. Nobody can tell difference between speaker cables (if they were reasonably well manufactured) because the difference is so small. Expensive cable makers only try to get more profit using so-called audio gurus, who say "I can hear difference". Let's not waste our money for the lairs!
Lots of liars reside in those lairs!
No, not with a load. Inductance usually dominates over capacitance.

The closer the wires in a cable are to each other, the more rounded will be the Square Wave coming out of the other end.

Only way to get a matching Square Wave Out, is to space the wires some distance from each other.