Yes. And I can answer yes to both questions because I believe that sine wave testing is a very good indicator of a components performance. I don't want to put words in your mouth, but it seems that you don't believe that. Also, I know of no way to test the linearity of a single component while playing music.
Tim
Tim, I’m a bit loath to say what I “believe”, but I’m happy to share what I think I know (that is: what I currently understand but am willing to modify if presented with additional information) as well as what I’ve experienced, even allowing that both those things are often held in tension against one another, however uncomfortable that may sometimes be. “Belief” is perhaps best reserved for those who feel a need to assert their values on others, and I personally have no interest in doing that.
What I can say, is that I think the theory of linearity seems fairly scientifically robust. As I’m sure you already know, a function is linear if and only if the following equation holds: af(x+y) = f(ax) + f(ay)
That is, in order for a function to be linear it must contain two properties 1) Additivity: f(x+y) = f(x) +f(y) and 2) Homogeneity af(x) = f(ax).
No problem with that.
But given that we’re discussing the nature of music reproduction systems - designed primarily, as they are, for playing back music - it’s important for me to ask: Can the mechanism of transducer/amplifier/transducer be considered to be truly linear when playing back a medium in which the content is a time-based art form?
Well, we need to decide whether we’re discussing a problem of mathematics or a problem of description. In mathematics or physics, linearity is easy to measure, because we have an equation defining exactly what it is and what it is not, and the robustness of that equation means we can represent the relationship between two variables graphically and get a straight line, right?There are countless examples, none of which need to be listed here, as I’m sure you covered this in grade school. So far, it doesn’t appear we have a mathematics problem.
A time-based art form like music, if it is to be recorded, needs to capture two variables (pitch and amplitude) against one constant (time). That is, music is a relationship between three entities in which two are modulating and one is constant, and can be graphically represented as a waveform or literally represented as a groove in a record. But wait! Didn’t Einstein’s theory of relativity argue time is not constant? He did indeed, and James Chin-wen Chou managed to illustrate this when two atomic clocks separated in height by 33 centimetres showed time dilation at the National Institute of Standards and Technology in 2010.
Ruh roh! We have a problem then, don’t we? If time is not constant, then we have three variables not two, and this is before we even get to our playback chain, which is required to play back pitch and amplitude over time from a source component that, whether it be digital or analogue, must be constant in the time domain if it is not to affect the pitch and amplitude of the signal. What do we do? Well, we could say Einstein’s theory of relativity is just, y’know, a theory, and one experiment by a lab in Boulder, Colorado hardly makes for definitive and conclusive evidence (they could be making this up, right?). But still, we should probably at least consider whether it’s worth asking, just how accurate should our source components be in the time domain to be considered accurate?
Hmm. We need a real-world example. How about the Antelope Isochrone 10M Master Clock? That has an Atomic oscillator with stability of 1 second in 1,000 years - “a staggering 100,000 times more accurate than the quartz oscillators used in most equipment” (according to their website) - that’s pretty accurate, right? Well, kinda. But quite a bit less accurate than the atomic clocks used at the National Institute of Standards and Technology, which are able to keep time to within 1 second in 3.7
billion years. (That makes the Antelope 3.7 million times less accurate than the ones at the NIST, but they're probably unlikely to include that copy in their future marketing.)
Oh. So really, all we have is “relative” time-domain accuracy - we don’t have a perfectly precise measure of time? Einstein is still right and we should cut James Chin-wen Chou some slack? Mathematically speaking, wouldn’t this mean we can never categorically state the mechanism involved in recording and playing back music can be linear if one of the three entities is not a constant? Are we simply introducing a qualifier - approximation - in order to call something what it is not? Are the only things we’re left with simply components that in-and-of-themselves are and can only ever approximately approach linearity but never achieve it?
Again, I’m not really interested in belief, only what I think I know and holding that which I think I know lightly. And what I think I know is that no component is linear, or for than matter, can be linear, because a component that cannot be precisely stable in time cannot therefore perfectly recreate a time-based art form - it will only ever interpret it. (Sorry if this is offending anyone’s grasp of the bleeding obvious, but I am, afterall, an indie and alternative rock musician who moved from the music industry which has been decribed as “a cruel and shallow money trench, a long plastic hallway where thieves and pimps run free, and good men die like dogs,” (1), into advertising, “which may be described as the science of arresting human intelligence long enough to get money from it”. (2))
The general formula for a sine wave is written as - *y(t) = Asin(?t +*?) - where A is the amplitude, ? the frequency and ? - the phase. Here of course, we can contrast the sine wave with the the musical waveform, which contains all the above, but with
constant modulation of the frequency
and its occurence in time. A sine wave is neither modulating its frequency, amplitude, nor its occurence in time. We can stack as many sine waves on top of each other as we like, to produce a lot of graphs and numbers, but they still do not represent the constant modulation of frequency (and related harmonics) and amplitude and their occurence in time that are the inherent and defining features of a musical waveform .
So now, I’m back to thinking about the transfer funtion of an ideal amplifier. But I don’t see anyone outside of a few people on this forum (and possibly, other forums, I guess) arguing that the ideal amplifier actually exists, and that it can be linear in the real world. Groucho said:
Groucho said:
I don't accept the point about audio systems not being linear from one end to the other. Of course, in practice, they're not literally linear - there are distortions - but there's no reason for a system not to be very close:
- good mics are close to linear;
- digital audio is linear to any arbitrary degree we choose, by definition;
- a solid state amp is linear to all intents and purposes;
- a good speaker transducer is close to linear especially if not driven beyond its limits (so it pays to be clever in how we use them).
As jkeny answered, this still remains the sticking point. Platonic idealism vs Aristotelan realism. One the one hand Groucho isn’t willing to accept an audio system isn’t linear from one end to the other, but introduces a qualifier of approximation in order to hold onto the concept of linearity, even as he admits they can’t literally be linear in the real world, like for instance when we connect our “ideal” solid state amplifier to an actual speaker and play music through it.
So, it seems reasonable for me to think that I know a component that cannot be precisely stable in time cannot therefore perfectly recreate a time-based art form - it will only ever interpret it (or, if you prefer more prosaic language, distort it). Futhermore, it appears to me that when describing audio systems we are using a very strictly-defined mathematical and scientific term - “linear” - in the context of approximation, such as when we state a component offers “superb measured performance”
within the context of what is likely to be considered audible. That is still a qualifier, and neither mathematics nor science seems to need to use those when considering what is linear and what is not.
Just sayin’.
You asked:
Phelonious Ponk said:
If the "accuracy" of an audio component is not "high fidelity," if it's not the ability of that component to put out the signal it receives with the least amount of distortion of that signal possible, what is it?
My answer is: Er, to attain market share?
I don’t know, Tim. I don’t design, manufacture or market audio components. I’m an end-user who’s fairly agnostic in regard to format, transistors, thermionic devices, stats, planars, dynamics and horns. I try not to make sweeping generalisations in regard to anything, so I think it’s a question best asked of those in the business of making and marketing them.
(1)Hunter S. Thompson’s full quote is: “The music business is a cruel and shallow money trench, a long plastic hallway where thieves and pimps run free, and good men die like dogs. There's also a negative side.”
(2) Stephen Butler Leacock