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When I play to keys that form a dissonant interval (for example a major second using C and D) in the lower octave, I perceive the dissonance to be very strong. But, when I move up to higher C's and D's the dissonance intensity seems to diminish.

Am I correct with my observation? And, if so, why is that happening?

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This is on a piano? –  neilfein May 3 '12 at 22:14
    
@neilfein: yes, on piano –  hauptstadt May 7 '12 at 8:13
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4 Answers 4

up vote 9 down vote accepted

This may be due to the interferences that the tone combination generates. When you tune in a string to another, you can hear a vibration getting slower as you approach unison. This effect is known as kick and the resulting interference is the difference between the two frequencies.

According to wikipedia, differences above 15 Hz are not perceived as vibrations anymore, rather as a "roughness".

When the difference reaches the hearing span of frequencies, a tone can be heard instead.

If you play C3 and D3 together, the frequency difference is approximately 16 Hz. The chord sounds rough.

If you play C6 and D6 together, the tone difference is approximately 128 Hz. You hear a third tone (a quite low C3) instead of a vibration or a "roughness".

The higher the frequency of two tones that are a whole tone apart, the greater the frequency difference is between them. The higher the tones, the less "rough" their sound.

Note that I have no other sources than the wikipedia page I linked to earlier, but this answer makes sense to me.

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That's quite interesting, and I do believe you're right that the beat frequency can appear to be a third note. –  Matthew Read May 2 '12 at 14:54
    
@MatthewRead: yes, the third note is a combination tone. See en.wikipedia.org/wiki/Combination_tone or my answer to music.stackexchange.com/questions/5824/… . –  Ulf Åkerstedt May 4 '12 at 12:07
    
@Gauthier: the "roughness" is an effect of the construction of the ear. The two tones stimulate overlapping regions of the basilar membrane. The frequency bandwidth sensitive for overlap is increasingly greater at low frequencies (below 1000 Hz). I've written a longer explanation in another answer. :-) –  Ulf Åkerstedt May 4 '12 at 12:14
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Yes, you are correct!
At least there is a physiological explanation.
The construction of the human hearing apparatus causes a quality that is called critical bands.
A critical band represents a bandwidth in which a sounding frequency has to be alone for us to hear or perceive it clearly. This bandwidth is, relatively speaking, increasingly wider for lower frequencies (less than 1000 Hz) and thus close notes are more likely to be perceived as dissonant in low musical registers.


More detail

If two tone frequencies are close to each other they disturb overlapping regions of the basilar membrane - where the hair cells are located - within the cochlea in the inner ear; but if the frequencies are far apart they stimulate two separate regions. The range of frequencies, in relation to a base frequency, that have a stimuli overlap is called the critical band for that base frequency.
If two tones are close enough - within approximately 10 Hz - they are fused and perceived as one tone with a beating, i.e modulation of the amplitude. (Unless they have the exact same frequency which will only generate a louder single tone.)
Increasing the frequency difference of the two tones to more than 10 Hz, but still with overlapping critical bands you pretty much hear one tone but with an unpleasant roughness (constituted by very fast beating).
When approaching a separation of the two tones' critical bands they will be perceived as two separate tones.

For frequencies above cirka 1000 Hz the critical bandwidth (in Hz) is a fixed fraction of roughly 15% of the frequency, so for higher octaves there shouldn't be a physiological difference in the perception of dissonance for the same tones.
But for frequencies below this the critical bandwidth is constant at about 100 Hz. This means that the critical band of a musical scale tone will encompass more and more surrounding notes as the frequencies get low and the frequency differences become small. That is; an interval (or chord) that was quite consonant in a high register might become dissonant in a low register because the tones' critical bands overlap there.

The highest amount of roughness or dissonance is perceived when the frequency difference is about 30% of the appropriate critical bandwidth. Which means about 30 Hz apart for tones below 1000 Hz. Further, all of this applies to all overtone partials of a tone from a musical instrument.

Example

Lets look at an example with frequencies (in Hz) for C and D and their first set of overtone partials. First the C and D one octave below middle-C:

    Note    1st     2nd     3rd     4th     5th     6th
    C3    130.8   261.6   391.4   523.3   654.1   784.9
    D3    146.8   293.7   440.5   587.3   734.2   881.0

The first partials are 16 Hz apart which is within the critical band and yet more than 10 Hz apart, and thus will be perceived with roughness; i.e. as dissonance. The second partials are about 30 Hz apart, which here is 30% of the critical bandwidth and will therefor be perceived as rather much dissonant. The higher partials up to the sixth have increasing frequency differences, and since the critical bandwidth here is still (almost) constant they have decreasing roughness (with frequency differences representing about 50% to 80% of the critical bandwidth.) Also the higher partials are likely weaker for the tone on the instrument and therefor have a smaller impact on the dissonace perception.

Now let's look at the frequencies of the C and D one octave above middle-C:

    Note    1st     2nd     3rd     4th     5th     6th
    C5    523.3    1047    1570    2093    2616    3140
    D5    587.3    1175    1762    2349    2937    3524

The frequency difference of the first partials is at about 64% of the critical bandwidth. For the rest of the partials it's at about 82% of the critical bandwidth. This causes roughness or dissonance but not nearly as much as frequency differences at the roughness peak at 30% of the critical bandwidth such as was present in the C3-D3 chord.

Therefor the C3-D3 is perceived as more dissonant than the C5-D5!

I suppose different individuals might have different critical bands distribution over their hearing range, and of course the perception of dissonance is subjective (and cultural), but this is a general physiological explanation of why hauptstadt and others perceives greater dissonance for the same interval in lower registers than in high.

Sources:
1. Musical Acoustics s.e, by Donald E. Hall, Brooks/Cole Publishing Company, CA.
2. http://hep.physics.indiana.edu/~rickv/consonance_and_dissonance.html

I hope I got this right. It was a long time since I studied these kind of things.

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There is no "correct" when it comes to dissonance; it's a subjective phenomenon. If we're talking about a mathematical measure of dissonance, then the dissonance is the same in both cases since the ratio of the frequencies is the same. (See Is there a way to measure the consonance or dissonance of a chord?)

I can guess at why it seems this way to you though. The absolute frequency difference is greater for the higher pair of notes than the lower pair which may make the comparison "harder"; you perceive them less as nearby notes that are off from each other. Though I can't find a reference at the moment I believe that in general it's harder to distinguish high notes so there may be a sort of mental blending effect that lowers the dissonance.

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If the reference notes are on a piano, then one might take into account the 'bar' like timbre of the piano in the highest octaves vs the string like timbre in the lowest octaves. –  filzilla May 1 '12 at 23:28
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As Matthew has pointed out "dissonance" is quite subjective. One potential objective metric could be "frequency components that are very close together". For example some consider a flat-five interval (say E to Bb) to be somewhat dissonant. This could be because the third harmonic of the and he second harmonic of the F# are just a half step apart and create some tension. As you add more notes you get more and more frequency combinations and the few close ones matter less. So you can add a low C and G to the mix and you get yourself a nice C7 chord.

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You are absolutely correct about the flat-five. :-) –  Ulf Åkerstedt May 7 '12 at 20:19
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