I was surprised recently to hear an advertisement offering vinyl records of modern music for audio enthusiasts. In case you were born in recent decades, music used to be stored on these round black discs called “records” in an analog format. This means that the discs were inscribed with grooves that directly represent the continuous sound waves of the music. In contrast, the vast majority of the music we listen to these days is digital: the sounds have been boiled down to a bunch of numbers, which are then decoded by our iPods or other devices to reproduce the original music. I’ve never noticed a problem with this, but certain hobbyists claim that there is no way a digital reproduction of music can be as faithful as an analog one. Do they have a point?
The key issue here is the “sampling rate”. As you would probably guess, there is no way a series of numbers can represent a truly continuous music wave— they are representing sounds at a bunch of discrete points in time, which are played quickly right after each other to produce the illusion of continuity. These rates are too fast for most of us to discern: the compact disc standard, for example, is a sampling rate of 44.1 KHz, or about 44,100 samples per second. This is far more than generally accepted estimates of what our ears can perceive. It also meets the criteria calculated by Swedish-American engineer Harry Nyquist in the early 20th century, showing that this sampling rate is more than sufficient to faithfully reproduce all sounds within the range of human hearing. But the small group of audiophiles who insist on listening to vinyl claim they can hear the difference.
These analog boosters of vinyl seem to be relatively vocal in online communities. They claim that there are subtle effects that make analog-reproduced music seem “brighter”, that digital has a “hard edge”, or other vague criticisms. There are also claims that the analog method provides an “emotional connection” to the original artist that is destroyed by digital. The most overwrought of them claim they are saving the world, with statements like, “future generations will be sad to realize that we didn’t preserve the majority of our music, we just made approximate digital records of it.” Some of them do admit that part of their enthusiasm comes from the rituals of analog music: leafing through records in a store, carefully pulling it out of the sleeve and placing the needle, etc.
You can think of audio sampling rates kind of like pixels in computer graphics, the small blocks that make up the images we see on any modern computer screen. in old computers from the 1980s, you could clearly see the pixels, since computer memory was expensive and the resolution, or density of the pixels, rather poor. But these days, even professional photographers use digital equipment to capture and edit photos. If you have purchased wedding pictures or something similar from a digitally-equipped professional, I doubt you have looked at the pictures and noticed anything missing. I’ve seen this lead to a few arguments with some of my snobbier friends about the need for art museums: since we can see high-resolution digital reproductions of just about any classic art online, why do we need to walk to an old building and stare at the painstakingly preserved original canvases? I think the “museum ritual” is kind of similar to the vinyl ritual: it evokes emotional memories and nostalgia for a past history, but isn’t really necessary if you think it through.
Getting back to the audio question, what we would really like to see are double-blind studies challenging audiophiles to distinguish analog vs digital music without knowing its source. I was surprised not to see any online— perhaps the logistics of such a study would be challenging, since you would have to use completely non-digital means to transmit the sound from both sources to the listening room, and avoid telltale giveaways like the need to flip records after a while. But in 2007 the Boston Audio Society did something pretty close, asking a bunch of volunteer audiophiles in a bunch of genres to try to distinguish recordings played at a standard CD sampling rate, 44.1 KHz, vs high-resolution formats recorded in formats like SACD, which sample at around 50 times higher rates. They would take the high-resolution recordings, and transfer them back to CD format for the experiment, so they were comparing the exact same music at the two sampling rates. Surely if sounds lost at the standards CD sampling mattered, these improved formats should give much better sound, right?
As you have probably guessed, their results showed that the massively higher sampling rate made essentially no difference— the volunteer audiophiles could not distinguish the high-resolution and CD-quality recordings any better than chance would predict, at 49.82%. So, it looks like the human ear really can’t distinguish sampling rates beyond what a CD provides, which after all is not a surprise in relation to the Nyquist calculations we mentioned earlier. Of course, some New Age types will continue to claim a mystical emotional connection that can only be transmitted through analog, and I’ll have to let them debate that with their spirit guides. But if you look at the science, you don’t need to comb the garage sales for old record players and unscratched vinyl—digital music should work just fine.
And this has been your math mutation for today.