So, you don't believe our analogy? Then, let's get technical. Play two pure sine wave tones together, one at 440 Hz (440 cycles per second), one at 441 Hz. The clash you will hear is the one sound beating against (alternately reinforcing and canceling) the other. The repetition of this beating occurs at the difference in frequency of the original tones (441 - 440), which is 1.0 Hz or once every second. This level of out-of-tuneness is already plenty noticeable, but we don't want to be accused of stacking the deck in our favor, so let's use these numbers.
How does this relate to cents scaling? Actually it is a little complicated because the cents difference of the tones depends not only on the difference in frequency but on the size of the frequencies themselves. For this example, at 440 Hz, the cents difference is about 3.9 cents.
So, any tuner that can get you 4 cent (actually ±2 cent) accuracy should be fine, right? Well there's more to it. First, even though almost any tuner these days can have an internal accuracy at this level or greater, what is important to you is the accuracy you can reliably and quickly see on the display. Other tuning display systems generally do not give good results-or usually any results-within about ±3 cents.
But there is still more! Remember, cents scaling changes with the size of the frequencies themselves. If you are so picky that you need your High A (at 880 Hz) to be in tune with everything else (good musicians are funny that way!), any beat frequencies produced must still be below the 1 Hz-once a second-level. This already requires twice the cent accuracy as before or ±1 cents!!
Will it ever end? Not just yet!! We don't generally spend our time listening to laboratory-perfect sine waves (well, we have to sometimes, but we don't recommend it). Real musical tones include a unique and often extended series of overtones (additional sine waves at multiples of the pitch frequency) that gives each sound its timbre or character. Even a flute, which is considered to be relatively pure, has five or more overtones which are significant enough that, if any were to be artificially removed, would leave the tone noticeably wanting. In instruments ranging from guitar-especially with even a touch of over-drive distortion-to woodwinds and brass, overtones at 10 or 15 times the pitch frequency can be significant. This has a huge impact on the human ability to detect tuning. |
