Τετάρτη, Νοεμβρίου 17, 2004

Tube amplifiers and other audiophile oddities

free statistics

I often see heated discussions on whether tube amplifiers or several oddities like expensive power cables are any good. A secondary tendency that frequently appears especially from technologically educated people is to make fun of audiophiles and their peculiar habits. I do not consider myself and audiophile per se, but neither do I think it is a particularly evil hobby and I believe that some explanations might help clarify the audiophile attitude on music listening.

Listening to music is not a quest for scientific rigor or absolute engineering precision. Quite the contrary, it is a way for us humans to have fun and relax. Music can provide intellectual stimulation but it does not impose specific rules to the listener. Surely, we can all imagine that sound devices that faithfully and accurately reproduce music are more likely to please the listener. However, we should remember that music itself is arbitrary. After all, the sound of animal intestines strung on a piece of wood and played with a bow was not designed by a commitee or a panel of experts. Some people decided that it sounds good and the violin was born.

Technologically inclined people typically put the artist on one end as the absolute and definitive source (which he is not, as he is shaped by social conditions and human reactions to his music) and the listener on the other end, as a passive recipient. In this perception of things any device that intervenes between artist and audience has to convey music with the maximum possible fidelity, as a service to the artist. This is quite reasonable but it is a little bit one-sided. After all, the listener initiates musical communication by concentrating on a listening session. So, he is more than a passive recipient, its his pleasure that matters and it is the listener's privilege to enjoy music in a way that pleases him the most. Just like the artist can arbitrarily choose an old bosendorfer piano instead of a modern steinway, the listener can choose tube amplifiers or electrostatic speakers in his effort to enhance his musical experience. It's really a matter of subjective opinion on a purely subjective experience and I don't see why there has to be an objective judgement on the theoretical merits of someone's choices. Maybe the audiophile people are severely misguided, then again who are we to judge them, if they are having fun with music?

A secondary issue of technological importance that has to be stressed is the fact that musical perception is a complex phenomenon that is at best poorly understood. When we are trying to describe whether device A is more accurate than device B in technical terms (distortion, frequency response etc) we are essentially implying that those measurements are important for the human listener. This is not always clear. Many people are completely unable to hear huge amounts of distortion (>5%) and I'm sure that typically the 1% distortion level is almost inaudible for most. Let us consider computer screens as an analogy : most humans would be hard pressed to discern the dot pitch or tell a 100Hz display from a 120Hz display. Yet everyone is able to tell apart a computer screen from a painting or a printed book. Similarly, some audio measurements matter a little, others matter a lot and yet other qualities which we can perceive yet we are unable to measure make a world of difference. In the end, if many people think that machine A is better than machine B then we should chose those measurements that tell them apart based on people's opinion and not the other way round. In the extremely unpropable yet theoretically possible case where listeners can tell apart a 5$ power cable from a 300$ power cable in a double-blind experiment we should try to find out why the 300$ power cable is better.

Clearly in many cases audiophiles fall victims of the placebo effect. I can understand that. In the rare cases where blind studies were performed--I once observed one--most hi-fi enthusiasts were indeed able to tell apart and choose superior equipment quite reliably. For example it appears that a 300 $ and a 1000 $ amplifier are indeed sonically different. Within a given price range the results can be quite controversial because personal taste becomes a primary motive but do not think that people that pay for expensive equipment are by definition misguided. Power cables, magic CD markers and other "marginal" products of dubious technical properties are indeed ridiculous occasional purchases but I'm sure I could think of many other useless items that people do buy besides hi-fi peripherals.

As a final note allow me to say that the best sound I have ever listened from an audio reproduction system came from Audio Research amplifiers (disclaimer: I am not an experienced audio reviewer so do not take my advice--use and trust your own ears) combined with Martin Logan electrostatic speakers. It really made a difference. I wish I had the $$$$$$ needed for that system. On the other hand, I'd propably buy a steinway piano if I had that amount of money.


Music and mathematics

I'm sure you've encountered a mathematical analysis of some basic musical properties, perhaps rhythm, dynamics or some other quality. What intrigues me, however, is not the use of mathematics on music but a comparison of the cognitive process of mathematical proof and discovery with the similar process of musical composition and interpretation.

I'm not a composer or a mathematician but I love both worlds and it appears to me that they do share important common characters. Certainly everyone has a grasp of basic mathematical knowledge but maybe a few fundamental facts about musical morphology will prove useful.

Classical music is quite simple in that it follows relatively strict rules (=axioms!) that are meant to distinguish pleasant sounds from unpleasant sounds. Several of these rules are immediately obvious to anyone that has tried hitting keys on a piano, while others are perhaps quite cryptic. Obviously the selection of these rules is empirical and is meant to produce an aesthetically acceptable result. Breaking these rules or changing them leads to rather surprising and potentially interesting consequences just like in mathematics where changing a single axiom can generate a host of new applications. Think, for example, atonal music and non-euclidean geometries. Note that a musically "correct" piece is like a grammatically "correct" mathematical proposition: it is well formed but not necessarily interesting.

Now, if we assume that we accept these musical "axioms" we enter a process of musical exposition which is, in a way, similar to mathematical proof. First a musical theme (=idea) is presented in a simple format, just like a mathematical proposition. Then it is attacked from several fronts. A musical theme, which can be quite short and simple, can be manipulated with several fundamental operations like modulation (change of tonality), rythmic variations or even mirroring. Bach's the Art of the Fugue is a very clear example of very thorough processing but it does make your head hurt when you try to play it (quite interesting listening, though, you may give it a try).

The sequence and choice of these operations can augment the musical properties of the initial idea and provide a convincing development of the initial theme into a full piece. Even though the individual ideas are simple, the end result can be quite complex. As an example, Beethoven once responded to a challenge by Diabelli who provided a relatively ... boring musical motif to several musicians to see what they could build from it. Beethoven wrote the famous "Diabelli variations" as a response, to Diabelli's astonishment, composing a multi-page set of 33 exquisite variations.

Musical interpretation can pose similar challenges. Only a solid perception of music's inherent structures can allow a coherent, articulate approach to sophisticated works. Note that this perception can be empirical, sentimental and "right-brained"; "talent" if you'd like, so it's not exactly the same as a rigorous mathematical undertaking.

Absolute nonsense, some people will say at this point. Music is elegant and beautiful, math is (usually) not. This is correct at first sight, but after thorough training one learns to appreciate the delicate implications of the mathematical language. The mathematical means of expression do not offer immediate sensory satisfaction but they do provide the intellectual equivalent of an adventurous and occasionally elegant musical undertaking.

Certainly all the above does not mean to imply that musicians are good in math or that mathematically inclined people would become good musicians. After all, Einstein's violin playing was rumoured to be horrible. It takes different qualities to
succeed in either field, but the basic processes of doing music and working with abstract mathematical entities do share several common characteristics.