Distortion of intervals

Question

I'm wondering if this is a common phenomenon and if so how does it actually affect music:

When I play harmonic min2nd's the actual pitches I hear are not completely the individual pitches of the two notes but something in the middle. My ear averages the notes. The top note sounds slightly flat(probably around 10-20 cents) and the bottom note slightly sharp(probably less so). Of course, I do not hear the two pitches as if they were played melodically, there is inter modulation distortion going on which seems to act like the average of the two but I can force myself to hear the other pitches, but when I do so I always hear the top one a little flat (say I release the bottom note).

If this is a common phenomenon of the ears, which I believe it is although some individuals may be better trained or have better ears to distinguish min2nds and, of course, context matters (I'm assuming a synthetic piano), then how does this affect the harmonic aspects of theory? If one plays a closed voicing Cmaj7/B the C and B notes then, by this phenomenon, would produce sort of C|B(notation for note in between C and B) and this would throw off the entire harmonic expression of a Maj7 chord, out of context, at least, it would probably make the other notes sound sharp. Also, then it would affect voice leading and all that.

Maybe such things do actually go on in music and theory has not advanced enough to take them in to account? That is, in some sense we are actually dealing with something like 24-tet and harmonic m2nd's would be accessing notes in the extend divisions. It may not be 24-tet but whatever. The idea, though, is that it could dictate voice leading and resolutions. E.g., a closed Cmaj7/B would sound quite dissonant and suggest resolving probably to a G/B while a closed Cmaj7 would not have such a strong dissonance. Of course, then one would have to take into account the overtone series and compare any harmonic m2nd's as they too could inflect resolutions.

Trills seem to take advantage of this, typically trills on a m2nd are going to slightly alter the perceived pitch slightly below the principal tone (the subordinate tone pulls down the principal tone's pitch slightly allowing it to act sort of as a leading tone).

I've only heard this phenomenon talked about in one context in a book on blues where it suggested that this phenomenon existed and it was blues players trying to get at tones that 12-tet could not use. Guitar players would bend the notes microtonally to express them.

I'm not all that familiar with high note divisions of the octave which could possibly shine light on this besides being able to bend/slide notes on some stringed instruments. That is, has anyone explored higher order harmonic theory that can understand this phenomenon?

Answer 1

Two very nearby pitches combined can indeed result in a perceived single “average pitch”, albeit with different tone character from the individual notes.

However, this generally requires the pitches to be really nearby, like ⅓ of a semitone. For a minor second, the tones normally won't blend together in this way but always be noticeable as a distinct dissonances – though I suppose it varies between listeners.

Regardless, minor seconds are such a strong, concentrated dissonance that they're avoided in most situations. maj7 chords are almost always voiced so as to not have a root note right above the j7 one. If the j7 note is in the bass, then it's actually hardly perceived as a maj7 chord at all, but rather as a _sus4^♭6_♭9 kind of situation.

Trills are a bit of a different pair of shoes. In particular when playing fast trill on a string or wind instrument, then the waveform just continues through the trill. In the extreme case – trill on bass – this means the result is indeed almost indistinguishable from a single vibrato note of a pitch in the middle. Even in higher registers and ensemble playing, where a trill definitely does result in both individual pitches sounding seperately but simultaneously, the choppy nature means the effect is different from two instruments each playing a sustained note a semitone apart. This is a special case of the general phenomenon that for sufficiently short notes the pitch becomes more indistinct. There is in fact a fundemental physics reason for this (https://en.wikipedia.org/wiki/Uncertainty_principle#Harmonic_analysis), combined with human perception in particular.

Answer 2

The mathematical relation

sin(a + b) + sin(a - b) = 2sin(a)cos(b)

shows that the sum of two sound waves with different pitch is also the product of the average pitch with a changing volume.

This is more than just a perception; it is a physical fact. The same combination of sounds can be expressed in two different ways. It can also be measured and perceived in two different ways.

We are more likely to perceive the average when the pitches are close together. The volume changes are then known as 'beats', and we can tune instruments by listening to the beats and adjusting until they slow enough to be undetectable. When the pitches are far apart we are more likely to perceive the two separate parts of the sum.

Your ability to perceive the same sound combination as two different things reminds me of the pictures which can be seen in two different ways, even though it is still the same picture.

Most variations in perceived pitch arising from related effects are usually taken as part of what a particular chord sounds like, without specifically trying to use the effect to get a quarter- tone sound. I am not a blues player, and it is interesting that blues players may be using the effect in this less usual way.