# Minor Second Chord (or Microtonal) Dissonance Exploration

I have been fooling around with some minor second dyad chords and am coming up short on what to call the resulting sounds they produce. For instance on a piano/keyboard, a chord made of middle C and the B just below it. When a chord like that is played, it produces a sound that is almost like tremolo in that it shifts up and down slightly in volume. Its similar to the phenomenon produced when tuning a guitar using 5th and 7th fret harmonics on adjacent strings, where slightly out of tune harmonics produce an unstable tremolo-like effect, until they are in proper unison. Anyway, I just wanted to ask if anyone knows anything about what this unstable sound is called, or if it has been explored by any musical theoreticians, or if anyone here has done much fooling around with it. I have been toying around with using a loop pedal and a bass (lower notes seem to tremolo more slowly) to lay down a rudimentary tempo-keeping loop. Anyone have any thoughts or info?

As other answers have already said, the most likely explanation is some form of beats. Assuming your piano or keyboard is equal-tempered, the frequencies of middle C and the B below will be about 261.6 Hertz and 246.9 Hertz respectively. The primary beat frequency is calculated by subtracting the two numbers, i.e., 14.6 Hertz.

Which means that you'd hear a sort of fast buzzing that increases and decreases around 14-15 times per second. As notes get closer together, the difference in their frequencies decreases, which means fewer beats per second. To me, 14-15 cycles per second is quite fast for a "tremolo," so I wonder whether OP was actually hearing primary beats or something else. (As I said, at those pitches to me it's more like a fast buzzing.)

Lower pitches also have smaller differences in frequency. For example, the lowest C on the piano has frequency 32.7 Hz, and the lowest B has frequency 30.9 Hz, resulting in a beat frequency of 32.7-30.9 = 1.8 Hz, which would feel much more like a gradual oscillation/slow tremolo.

As Lawrence Payne noted, beats also occur among harmonics of pitches. I just tried playing C-B minor seconds on my keyboard with various timbres, and particularly for lower pitches, I could often hear beats quite strongly for harmonics. Many of the organ timbres, for example, had strong beats at the twelfth above the fundamentals (e.g., a C-B near the bottom of the keyboard would have a sort of oscillation also at the G-F♯ range an octave and a half higher).

In that case, I wasn't just hearing beats at the harmonics (as piano tuners would use). I also heard a slower oscillation almost like the harmonics were trilling back and forth between G and F♯, which I assume was an artifact of some element of the synthesis or sampling process used for my keyboard. Furthermore, I heard other oscillations occurring at various frequencies that were definitely produced by sampling artifacts, some of which didn't seem to be associated with specific frequencies at all, but which were more noticeable when played with dissonant intervals.

So, without knowing the specific equipment and timbres you were listening to, it's possible that you were hearing a lot of different things. Most likely, given the effect you noticed where lower frequencies slowed down the "tremolo," it's something related to beats, but I wouldn't rule out other phenomena depending on the equipment you're using.

• Organ sounds are perhaps not the best to use, as a lot of them contain various different harmonics which will mess up any basic pitches.
– Tim
Dec 26, 2019 at 17:33
• @Tim: I tried using a variety of sounds, as OP said he was using a "piano/keyboard," so I assumed a lot of possible timbres could have been used. I just gave an example here. I also tried various other sustained sounds too -- for example, some brass has the kind of effect I was mentioning at the double octave, some winds had a stronger oscillation at the double octave plus third, etc. The point I was trying to make is that timbral effects can produce all sorts of beating, and coupled with synthesis/sampling artifacts on an electronic keyboard, you might hear all sorts of cycling. Dec 26, 2019 at 17:38

Beats. When two notes are very nearly at the same pitch, the sound waves they make don't quite co-incide. So we hear a pusing in volume as the waves come together making the volume go up, and then try to cancel each other, making the volume go down.

It's the way a lot of players tune guitars - adjusting until the beats slow down and eventually disappear, at which point the two strings are at the same pitch - in tune with each other when matching harmonics are played.

If notes are a semitone apart, often they're too far away from each other to hear those beats.

Chorus pedal effects use a similar situation, where shimmering effects are made. Bass notes, because the wavelengths are longer, produce slower beats,

• It's perhaps more useful to consider the equivalent statement that "Bass notes, because the frequencies are lower, produce slower beats." And when the frequencies are father apart, the beats are sometimes audible as difference tones. Dec 26, 2019 at 16:59

Two close pitches played together will 'beat' at the difference between their frequencies. So a string at 440Hz (A) and 441Hz (a slightly sharp A) will produce a beat frequency of 1Hz. As you say, this phenomenon is useful when tuning one guitar string to match the pitch of another.

Beats also occur between the harmonics of a note. Piano tuners make great use of this, not only when setting unisons (aiming for zero beats) but when setting other intervals, which in a 'tempered' tuning scheme WILL 'beat'. For instance, a perfect 5th above middle C will be set... - oh I'm not going to even try to précis this complex topic, see if you can make head or tail of this article: https://en.wikipedia.org/wiki/Piano_tuning

Anyway. You're probably hearing 'beats' in some form.

• I think you meant 440Hz, not 44Hz. Dec 26, 2019 at 16:57
• Then the difference is 1 beat per second, with an envelop modulation of 1 beat every 2 sec. You are hearing beats.
– user50691
Dec 26, 2019 at 17:10