Vibrating strings produce (more or less) harmonic overtones. If two strings are tuned in some simple frequency ratio such as 3/2, 4/3 or 5/3, then those harmonic overtones match up nicely and avoid roughness. But if the two strings are tuned in some haphazard fashion then the overtones of each string won’t match up, causing the overtones to clash with each other.
We can actually plot out a graph which shows the interval between two strings and the corresponding dissonance. This is called a dissonance curve, and for a normal string it looks something like this:
Well, imagine a weird kind of string that produces inharmonic overtones, such that the dissonance curve looks different to the one above. Because the dissonance curve is different, you couldn’t play Air on the G String and expect it to sound good. You could however write new music that would fit with the novel dissonance curve.
Today, such a string is more than just a mathematical curiosity. It exists in the physical world.
“Inharmonic Strings and the Hyperpiano” (by Kevin Hobby and William Sethares) is a paper published in Applied Acoustics. The strings in their hyperpiano have a stretched out dissonance curve where the double-octave sounds most consonant and the octave becomes dissonant. Okay so maybe it’s not going to be used on every new pop record, but this kind of freaky instrument can produce game-changing new tonalities.
Since the dissonance curve is stretched out to the double-octave or “hyperoctave”, Kevin Hobby suggests we might try tuning a hyperpiano instrument to 12 equal divisions of the hyperoctave. Wait, isn’t that just 6-EDO – a whole tone scale? Actually, it isn’t! They may be identical tunings, but the octave is considered a dissonant interval on the hyperpiano, analogous to the tritone on a normal piano. So it makes a lot more sense to describe this tuning as 12 equal divisions of the hyperoctave. Really.
The ringing of the strange hyperpiano sounds like a death bell for the unwavering cult-like belief in pure ratios and true frequencies. Tuning and timbre are deeply linked. If we’re willing to experiment with new timbres then we can uncover new musical vocabulary for the future to come.
The next step is to explore all this for yourself – download the sampled hyperpiano and give it a play.