Author Archive

Audiophilia Harpocrates Review

Thursday, January 16th, 2014

Audiophilia Review

A review of our new Harpocrates amplifier!  We are proud to receive the Audiophilia Star Component Award!

Star Component Award

From Audiophilia’s Martin Appel:

“My first impression was the distinct clarity and separation these new amps offered. The key thing was that it achieved this without resorting to hyper edginess that some equipment exhibit but by pouring forth detail in a natural, easy, uncluttered way making the music more accessible. The ‘lifting of veils’ or the ‘removal of grundge’ are expressions we’ve all used and experienced in the description of this phenomena of increased openness and resolution. In this case, it was wonderfully true.”

Many thanks to Martin Appel and Anthony Kershaw of Audiophilia for their ongoing encouragement and support.  Also, I would like to thank Mike Levy and Karl Sigman who were very active with associated equipment (i.e. Mike Levy’s FRM-1 loudspeaker) and with listening evaluations.  The wonderful people and the honest, straightforward style have served to make Audiophilia my favorite audiophile publication!

The Placebo Effect

Tuesday, June 12th, 2012

Let’s say you are asked to evaluate two computers in terms of user friendliness.  If one is an Apple and the other is a PC, then it’s obvious you need to do something to hide this information from the user.  There’s too much of a preconceived notion that the Apple is more user-friendly to allow for a fair comparison.  No problem, we’ll make it a blind test so the user doesn’t know which is which.  In fact we’ll go one step further and make it a double-blind test, so that the individuals administering the test don’t even know which is which.  So far so good.

Now for the next part we ask the user to shift back and forth from one computer to the other every few seconds.  While they are doing this, the users are asked to make note of any difference in user-friendliness between the two computers.  After the trials are conducted, the users sum up their computer user-friendliness feedback.  After careful statistical analysis the results are: There is no significant difference in user-friendliness between the two computers.  Hooray for the scientific method!

The two computers are then given to somebody to use as he pleases over the next couple of weeks.  He scratches his head as he quickly realizes that one of the machines is more user-friendly than the other.  What’s going on here?  Well, first off everybody knows the way this test was conducted is silly.  How are you supposed to notice subtle differences when you’re jumping from one machine to the other every few seconds?  I should clarify that statement: Everybody outside of the audio industry realizes that this test is silly.  However, in the audio industry it is considered the most somber science to conduct a double-blind (ABX) test that flips back and forth between two units under test every few seconds.

Physicist Richard Feynman had a term for this, he called it “Cargo Cult Science“.  It is the sort of science you do when you appear to go though all the right motions, but are missing the big picture.  You are doing everything you are “supposed to”, but you’re not getting useful results.  For example, I read that Swedish Radio conducted a “double-blind, triple-stimulus, hidden-reference” test over two years with 60 experts to test the transparency of low bit-rate audio codecs.  The result?  No statistically significant difference.  However, another listener was able to quickly identify a 1.5 kHz tone in the processed sample under normal listening conditions (i.e. not double-blind).

What can be done to remedy this situation?  Standard audio ABX tests are of little value except for detecting gross differences.  Conversely, going by “whatever sounds the best” is too much like reading tea leaves.  As I’ve mentioned in a previous post, you really need to be able to live with a piece of audio equipment for a while to detect subtle differences, but that sort of test is very difficult to control.  Ah, control…that makes me think of a control group.  What if there is a way to conduct these long term listening trials while maintaining a control group that is given a “placebo”?  Follow me for a moment and I’ll show how this might work.

The latest, whiz-bang, perfect-sound-forever amplifier is finally out!  The objective measurements are phenomenal and the designer is a Ph.D. who works on quantum chaos in his spare time.  The previous generation of this amplifier is very, very good, but this new one makes it seem like something an orangutan designed, the marketing department claims.  Demo samples are distributed, and true to the manufacturer’s word, the new amplifier is so good that every single person loves it and they all burn their old amplifiers so as not to be tempted to ever again listen to something so vile.

That’s the typical scenario (well, sort-of), but what if instead the manufacturer of the new amplifier did the following: Twenty demo amplifiers are sent to reviewers and early adopters, all eager to hear and comment on the new sound.  They are allowed to spend several weeks with the new amplifiers, enough to detect very subtle differences, and then they are asked their opinion relative to competitor’s amplifiers and even to the manufacturer’s previous generation amplifier.  Good so far, but now for the coup de grace: 50% of the demo amplifiers were in fact the previous generation amplifier inside of the new chassis!  That’s right folks, half of you are part of the control group and have been administered the placebo.

How many manufacturers of audiophile equipment are willing to do this?  Can you imagine the change in tone of audio reviews if this practice became common?  If an amplifier manufacturer spends time, spends money, and adds complexity in order to create a next generation amplifier, then shouldn’t it be able to pass this test?  If improvements in THD+N, or any other objective test you can think of, do not pass this long-term double-blind AB test with placebo, then how can you justify manufacturing it and selling it to your customers?

I’m an engineer, so of course I love the technical challenge of optimizing a given parameter as much as any other engineer.  However, an important difference between research and product development is that in product development any change you make should result in a measurable improvement for the customer (cost, reliability, usability, sound quality, etc.).  Unfortunately, it seems like the only people benefiting from efforts to improve THD+N are those in the marketing department.  The research simply isn’t there to support the practice.

Earl Geddes sums it up very nicely with the following quote from his Dagogo interview:

“My position is that if some manufacturer claims an improvement in some sonic property, subtle or not, then it is their obligation to measure this (even if they have to figure out how to do that) and show in a statistically significant way that it makes an audible difference.”

Auditory Masking

Thursday, December 22nd, 2011


In the previous post I mentioned the importance of level matching when comparing audio equipment with differing amounts of distortion.  Implicit was the assumption that the loudness of the two levels would be matched as long as the RMS levels were made equal.  Unfortunately, a psychoacoustic phenomena called auditory masking comes into play to ruin this simple picture.  Many people know that in order to double the perceived loudness of a single tone, you must increase the power by approximately ten times (+10dB).  However, to double the perceived loudness of a tone by adding a second tone at a much higher frequency, you need only double the power (+3dB)!  The reason for this is the compression from auditory masking in the cochlea.

What does this mean for level matching in the presence of distortion?  It means that to double the perceived loudness of a single tone it will take +10dB from a “distortionless” amplifier and less than +10dB from an amplifier with distortion!  This is one of the reasons that tube amplifiers are perceived as having higher power than a comparable solid-state design: The masking effect of our hearing applies less compression to the distorted sound, as the energy is spread over a broader frequency range.  Does this mean tube amps are inherently flawed, inaccurate, etc?  No, like they say “The proof of the pudding is in the eating.”  No amount of hand-waving from audio purists will ever sway some folks from their tube amps and there’s nothing wrong with that.

There are mathematical models available for this compression process, but when coupled with the typical transfer functions of real audio equipment (not just the simple single transistor example I gave in the previous post), there are no nice closed-form solutions that can be used for accurate auditory level matching.  This is something that could be done with simulation however.  It might be worthwhile trying it to see what types of distortion mechanisms give the highest level of perceived loudness versus RMS level (it seems like higher order distortion would, but this is known to give poor sound quality – I suppose it is loud though).  Overall, the best solution for now is the classic one: Live with a piece of gear for a while to get a good feel for it.

Euphonic Distortion?

Tuesday, May 17th, 2011

Why is it that every time you mention that a piece of audio equipment sounds better than another, the spectre of “euphonic distortion” is invoked?  Is it possible that it is really that simple?  You just add some 2nd harmonic distortion and poof!  Now it sounds better?

Enough hand waving already.  They say low order harmonic distortion makes it sound better, I say it doesn’t.  Who’s right?  Well everybody prepare yourselves because…

That’s right, science!  And there’s nothing you can do to stop me – mwaah ha ha ha!

First off let’s start simple.  Some folks say it sounds better when you add low order harmonic distortion.  One of these words in particular stands out to me: “add”.  Why does this word in particular jump out?  It’s due to the importance of level matching.  Most audiophiles know how critical it is to accurately match audio equipment if there’s any hope to perform a fair comparison, but it seems many people have forgotten in this one area.

If you add distortion, then you must adjust the level so that the RMS level matches that of the original signal!

As a concrete example, let’s consider a very simple audio amplifier: A single bipolar junction transistor.  Here’s an outline of the process to follow:

  • Determine the appropriate function of the distortion mechanism
  • Determine the average value in order to remove any dc component
  • Determine the RMS value and apply a multiplier to compensate

Here is the equation for the single bipolar transistor stage when passing a sine wave of angular frequency $$\omega$$:

$$f(t)=\frac{1}{\alpha }\exp(\alpha \sin(\omega t))$$

Where $$\alpha$$ is the degree of nonlinearity – i.e. lower distortion for smaller $$\alpha$$ and higher distortion for larger $$\alpha$$.

Integrating over a full cycle to get the average (i.e. dc) value:

$$f_{AVG}=\frac{1}{2\pi }\int_{0}^{2\pi }\frac{1}{\alpha }\exp(\alpha \sin(x))dx=\frac{1}{\alpha}I_{0}(\alpha)$$

Where $$I_{0}(\alpha)$$ is a modified Bessel function of the first kind.  Now subtract this dc component from the original equation for the transistor stage to get the ac value:

$$f_{AC}(t)=\frac{1}{\alpha }(\exp(\alpha \sin(\omega t))-I_{0}(\alpha))$$

From this the RMS value can now be calculated.  Here is a general expression for calculating the RMS value of a function:

$$f_{RMS}=\left [ \frac{1}{t_{2}-t_{1}}\int_{t_{1}}^{t_{2}} f^{2}(t)dt \right ]^{1/2}$$

Now using this to calculate the RMS value of the single stage bipolar transistor when passing a sine wave:

$$f_{RMS}=\left [ \frac{1}{2\pi }\int_{0}^{2\pi}f_{AC}^{2}(t)dt \right ]^{1/2}=\frac{1}{\alpha}\left [I_{0}(2\alpha)-I_{0}^{2}(\alpha) \right ]^{1/2}$$

Here’s a plot of this $$f_{RMS}$$ function versus the distortion parameter $$\alpha$$:

So now to make the RMS level of the distorted sine wave equal to that of the undistorted sine wave, you must multiply the amplitude of the pure sine wave by the above $$f_{RMS}$$ expression.  You could instead divide the distorted sine wave by the same value – the point is to make the two RMS levels equal.

For clarity here are the two expressions with differing distortion, but equal RMS level – again $$\alpha$$ is the distortion parameter (distortion → 0 as $$\alpha$$ → 0):

$$f_{UNDISTORTED}(t)=\frac{1}{\alpha}\left [I_{0}(2\alpha)-I_{0}^{2}(\alpha) \right ]^{1/2} \sin(\omega t)$$

$$f_{DISTORTED}(t)=\frac{1}{\alpha }(\exp(\alpha \sin(\omega t))-I_{0}(\alpha))$$

As a further point of interest, the nature of the distortion mechanism considered above is that of a nice descending spectrum of harmonics, as shown in the following FFT plot for $$\alpha$$=0.1:

I’m still doing a bit more work with this, so it is by no means anywhere close to conclusive.  However, it is at least an important, and objective, difference that must be accounted for in order to compare “apples to apples” when evaluating the subjective effect of different distortion mechanisms.

The Scent of an Amplifier

Monday, May 16th, 2011

Recently I tried my hand at perfumery.  As with most disciplines there is so, so much more to it than you would ever think.  Interestingly enough, it reminds me very much of audio amplifier design (funny how many things tend to do that for me…).  Here is a brief summary of my first attempt:

  • Took a look at the original Eu de Cologne recipe as a starting point (or at least the closest thing I could find to it on the internet).
  • Ordered up the necessary essential oils: lemon, orange, tangerine, bergamot, lime, grapefruit, neroli, lavender, rosemary, thyme, petitgrain, jasmine.
  • Added amounts that seemed “about right” to a base of Grey Goose vodka.  Let it rest for a while to let all the scents come together nicely.

The result?  Nice, but not wonderful.  Why?  What did I do that was so different than anybody else?  What are the variables I have control over?  Thinking this over for a bit I came to the following realizations:

  • Simplicity is best!  Whether creating a new culinary experience, a cologne, or an amplifier you should only add the essential.
    • More is not always better, even if it’s more good stuff.  You must have a specific purpose in mind to add even one more thing.
  • Quality is crucial!  All essential oils are not created equal.  I later purchased some very good (and expensive) petitgrain and jasmine.
    • There is no substitute for quality when trying to create the best.  It is a necessary, but not sufficient, requirement.
  • Iteration is necessary!  You can keep it simple and use good quality ingredients, but you still need to try and try again.
    • This is how we learn and how true genius comes about (1% inspiration and 99% perspiration…)

Already you probably see how this applies to the design of audio electronics – specifically audio amplifiers in my case.  Lessons to take from this for amplifier design:

  • “Perfection is achieved, not when there is nothing more to add, but when there is nothing left to take away.” – Antoine de Saint Exupery.
    • Do not add more and more stuff, even if high quality, instead take away everything you can while maintaining the fundamental functionality.
  • Good components are crucial.  Do not waste your efforts by pinching pennies in this area – you will ultimately pay even more in service costs and reputation.
    • For example, a “thick film” resistor in your signal chain can introduce a surprising amount of distortion, yet only saves you less than a penny!
  • Question: “How do I get to Carnegie Hall?”  Answer: “Practice, practice, practice.”
    • Prototype, prototype, prototype.  That amazing zone where theory meets reality.  Do lots of it – it’s fun and results in beautiful audio amplifiers!

As a parting thought, here is another area of perfumery with surprising parallels to audio electronics.  There are three distinct categories of perfume scents, based on the time frame in which they assert themselves: The top notes, the middle or “heart” notes and finally the base notes.

Top Notes

These are the scents that form the initial impression of the perfume.  They dissipate quickly, but are important for the same reason all initial impressions are important.  Audio equipment also has “top notes”.  This is what you first noticed when you first heard the equipment, but which faded from your conscious notice after the break in period.  Now only your friends notice these notes when hearing your system for the first time.  Although if you haven’t listened to the equipment for a while you may be reminded.  These are the traits that it is easy for your brain to adapt to.

Heart Notes

These are the primary scents showcased by the perfume.  Once the ephemeral top notes have dissipated this is mostly what you smell.  With an audio system this is what you are left with after the break-in period.  This is the true nature of the gear – it is for these notes that you love it or hate it.  These are the traits of your audio equipment that are not as readily “filtered out” by your brain.  Maybe that’s a good thing and maybe it isn’t – it all depends on how much you enjoy that particular trait!  It is for these notes that a brand of audio equipment becomes famous or infamous.

Base Notes

The base notes are there to anchor the scent, and they do so in a well designed perfume, however they can also be the unpleasant scents left behind once the top and heart notes have dissipated.  Your audio equipment, which one is it?  Does your listening session start off great, only to lead to disinterest after a while?  “Listener fatigue” perhaps?  Or is your audio equipment the kind that invites you in and doesn’t let go until you really must be moving on to other things…  After everything else has dissipated, this is why you either keep the equipment, or put it up for sale.

The Olympus

Friday, May 6th, 2011


The newest member of the Hephaestus Monaural Amplifier series is now available:  The “Olympus“!  The name is a reflection of the position the Olympus takes at the top of the HMA series.  It is also at the top of the audiophile amplifier world I believe, but my opinion toward both my children and my amplifiers is somewhat biased.  🙂

The Olympus boasts an impressive 2000 Wrms into 4O while still maintaining the miniscule 3.5 pound package of the HMA series.  It also makes use of the premium chassis and connectors of the Keledones.  Best and most important of all though, it maintains the amazing sound of the HMA series, so there’s no worry of sacrificing warmth and beauty for power and headroom.

The Forge page has been updated to better call out the differences between the members of the HMA series.  The naming convention has been simplified too – moving away from engineering-inspired names, such as the “HMA-1000”, toward, well, more name-like names!  The series now consists of the “Hephaestus”, “Aphrodite”, “Keledones” and “Olympus”.

Aphrodite Edition

Sunday, October 31st, 2010

After a little encouragement from Aphrodite, Hephaestus has decided to offer a version of the HMA-1000 that is aesthetically enhanced: The HMA-1000 Aphrodite Edition™!  Now the coveted sound of the HMA-1000 is available with an aesthetic design that may better lend itself to certain audio systems.

The Aphrodite Edition™ is available immediately, however every chassis is custom machined so please allow two weeks from the time of order for shipping.  An upgrade option is available for HMA-1000 owners for the difference in cost between the HMA-1000 and the HMA-1000 AE ($500) – please email if interested.

These Things Can Sound Real!

Tuesday, August 24th, 2010


A friend of mine was visiting last week and asked to see my VK-1 Dipole Loudspeaker.  He has worked in the audio industry and has done live sound on many occasions, but he doesn’t tend to sit down and listen much to high quality two-channel audio.

I put on a track of some big band music from the BBC’s Big Band Orchestra.  After a few moments of listening quietly my friend motioned toward the loudspeakers and electronics and remarked, “I forgot that these things can sound real!”

Yes folks, they can sound very real.  I think many people that have never heard really good two-channel playback, and even those that have heard it but have simply forgotten over the years, are amazed at just how realistic it can sound.

Audio recording and its subsequent playback has come a long, long way since Edison’s cylinder recordings.  But even more exciting is the fact that it still has a long, long way to go.  As much as I love the sound of my VK-1 system, I know it will sound to those of the next century much as Edison’s cylinders sound to us today!

Gratuitous Self Promotion

Tuesday, August 17th, 2010

A review of the HMA-1000 from Audiophilia!

From Audiophilia’s Martin Appel:

“Another preconception these amplifiers dispel is that digital means a non-musical presentation — an analytical edginess to the sound. Sorry, not here. The HMA-1000’s are smooth and non-fatiguing, yet replete with inner texture and detail giving them wonderful resolving power greater then my current amplifiers (which are no slouches in that area). And they do all this with an ease and naturalness that says music, not electronics. Voices are more realistically portrayed with more body, texture and intimacy than I’ve heard before. Choose your favorite singer and be prepared to hear them more clearly and with greater presence then you’ve been accustomed to. The HMA-1000’s bring you another step closer to the real thing.”

Many thanks to both Martin Appel and Anthony Kershaw of Audiophilia.  I have enjoyed working with them so much that I’ve decided to become one of their sponsors – here’s to many happy and fruitful years to come!

Can You Hear What I Hear?

Friday, August 13th, 2010


  • Is Chateau Margaux better than a 95 point California wine?
  • Is Prosciutto di Parma better than the ordinary ham I get at the deli?
  • Is a Stradivarius really worth it compared to a reasonably priced violin?
  • Is an audiophile amplifier different than an ordinary audio amplifier?

This type of question circulates endlessly in both audiophile and non-audiophile circles.  Many folks contend that there is no difference between competently designed audio products, especially adherents to the all-powerful ABX test.  Here’s what I think it comes down to:

  • There are folks that can’t really hear a difference and don’t care
  • There are folks that can’t really hear a difference, but like new toys
  • There are folks that can’t really hear a difference and say you can’t either
  • There are folks that can really hear a difference, whether you like it or not

It’s the last category that annoys people the most.  Nobody likes to think that they have inferior perception compared to another.  “I can’t perceive a difference, therefore no difference exists.”  “He says it sounds better, therefore he’s full of it.”  Yes, there are plenty of times that somebody says something sounds better, but are just fooling themselves.  However, there are also times when it’s true.

A physics professor once told me that most of the significant discoveries in physics have already been made.  I replied that I thought we were standing on the verge of a precipice with an unbelievable new world of science before us.  Which one of us do you think history will show as right?  Along these lines, I came across something a highly regarded amplifier designer wrote:

  • “The time of making great strides in amplifier sound is over.”

If you are an audiophile/audio designer like me, then you probably find this statement a little disturbing, especially coming from an authority on the subject.  However, worry is unnecessary because such claims are made all the time – some examples:

  • “With over fifteen types of foreign cars already on sale here, the Japanese auto industry isn’t likely to carve out a big share of the market for itself.” – Business Week, August 2, 1968
  • “Everything that can be invented has been invented.” – Charles H. Duell, US Patent Office 1899.
  • “It will be dead by June.” – Variety Magazine regarding the ‘Rock and Roll’ fad in 1955.

What are some ways future amplifiers may be significantly better?  As Yogi Berra said, “Prediction is very hard, especially about the future.”, but for a bit of fun speculation, here are a couple of ideas I have: Adaptive Operation and True Accuracy.

  • Adaptive Operation: The amplifier changes its mode of operation to make errors that are less offensive to a given listener.  All audio products have errors and always will, but to a given individual some errors are more tolerable than others.  Do you prefer good imaging?  High resolution?  Warmth?  Musicality?  The amplifier can operate according to YOU.  Is it a quiet evening, or a high-energy party?  The amplifier can adapt its operation accordingly.
  • True Accuracy: For audio products “accuracy” does not mean what the Audio Precision measures, it means what YOUR hearing measures.  Accuracy means presenting the original material as the artist intended it to be perceived by the audience.  With recorded material YOU are the audience.  Recorded audio breaks down spatial and temporal barriers to connect you with the artist.  This has absolutely nothing to do with metrics such as THD+N.

As a parting thought, I like what Alan Kay said regarding the future: “The best way to predict the future is to invent it.”  I’m not interested in debating if there can be better sound or not.  I’m interested in ensuring that there will be better sound.