[mrob]

Two bass notes a semitone apart won't necessarily sound bad; it depends on the timbre. Try it with sine waves and it will sound like a slow tremolo. Try it with sawtooth waves and it will sound dissonant.

Perception of consonance and dissonance is related to the phenomenon of "beats"[0]. If you add two sine waves of similar frequency, you get alternating constructive and destructive interference, sounding like tremolo. As you increase the difference in frequency, the beat becomes faster, until it's no longer heard as tremolo, and becomes a single dissonant tone. Increase it further still and the dissonance vanishes as it's heard as two separate tones.

Importantly, beats depend on absolute difference in frequency, not relative difference. Musical intervals are relative differences, e.g. a semitone higher in equal temperament is 2^(1/12) times higher frequency, not some fixed number of cycles per second. The higher in the musical scale, the bigger the absolute difference per semitone. This means low frequency sine waves a semitone apart will sound consonant, medium frequency will sound dissonant, and at high enough frequencies the dissonance diminishes.

However, this effect applies to all the harmonics/partials of the notes, not just the fundamentals. A smooth bass note will have mostly fundamental, so the pairs of harmonics with frequency differences that cause dissonance will be quiet and unnoticeable. A bright or distorted bass note will have much louder harmonics, so the dissonance will be obvious.

[0] https://en.wikipedia.org/wiki/Beat_(acoustics)

[uniqueid]

  Two bass notes a semitone apart won't necessarily 
  sound bad; it depends on the timbre.

Another factor is that the ear wants to makes repetition, in and of itself, work. That likely allows drums to sound good despite their fundamental tones often being 'wrong'. To pick an example at random: the triangle bells in this pop song sound pleasing, despite their key being 'wrong', simply because they repeat https://youtu.be/ZWmrfgj0MZI

[posterboy]

That's not how I understand the musical scale, if I even understood you correctly.

By relative interval I understand the interval within an octave, so C-D is a second regardless of the octave. The frequencies (notwithstanding fine tuning), double each octave. Of course the absolute difference is proportional to the power of two, depending on the octave.

The picture is different when counting the proportion relative a fundamental frequency of your choice. That's how dezibell is generally defined, arbitrarily over some reference point. This has two interesting consequences. When counting keys not modulo 8 but continuously, the ratio D5 over C5 is much lower than D4 over C4. Second, if you want integer multiples of the fundamental's wave length, the first multiple spans an octave, and only the fourth or fifth octave has a full scale--this chromatic scale worked reasonably well tested on AVR with a buzzer, except that F needed adjustment taken from a frequency table.

This means there can be no second in the lowest register unless you invert the programm and scale the higher octaves down linearly. In that case, the interference from the second (ca. 9/8'th of the fundamental's wave length) sounds extremely grating when played as a chord; the attenuation where the maxima of both waves meet forms the actual fundamental and your notes lie 9 to 8 above it, canceling each other out half the time; this is easier illustrated with a sixth that would be 1.5 of the base key. It is not a good illustration of music theory though, more like information theory while the signal chain is computationally intractable.

Jazz musicians, huh

[bradrn]

> By relative interval I understand the interval within an octave, so C-D is a second regardless of the octave.

I don’t think GP is denying this. They are simply saying that an interval at a lower frequency is generally more dissonant than the same interval at a higher frequency.

[posterboy]

I was conceeding to make sure I understood them correctly.

The problem is, if you have only two tones, the lower one is essentially the base frequency in my address. But I'm assuming you have somewhat of a natural buzz, or resonant frequencies from the environment that command the base frequency for you, so you can't take any two intervals and compare them as if they were relatively same. This should be relevant especially if you play them one after another to compare, no?

[mrob]

I think it's likely to be less dissonant at lower frequencies. Try a 51.913Hz sine wave (G#1) played with a 55.000Hz sine wave (A1), at low enough volume that they don't clip when added together. This does not sound dissonant to me. Then speed them up by 16x (increasing the pitch four octaves). This does sound dissonant to me, although not extremely so, because timbre makes a huge difference, and sine waves produce the least dissonance of all timbres.

I don't have a bass guitar, but if somebody does they might want to try playing those G# and A notes together, and check how consonant they sound with the tone knob turned all the way up and all the way down. I predict that the brighter tone will sound more dissonant.