I’ve read that a major chord is composed of the two most audible overtones of any one note, i.e, the third and the fifth. What I don’t understand is why the fourth isn’t more audible than the third. At first I thought that it might be because the fourth would be harder to distinguish than the third because it’s more consonant to the root, but if that theory were correct then the fifth would be harder still. Can anyone explain this to me?
I whipped up a spreadsheet with harmonic series for A-440, and I would say that the most audible overtone is the octave, but I guess that was set aside for purposes of discussing chords. The third (plus an octave) is 5 times the root frequency and the fifth (plus an octave) is 3, so they are the first multiples in the harmonic series other than the octaves. I suppose that makes them the most audible but that is dependent on what is generating the note. I’m not sure the fourth is anywhere significant in the harmonic series, but you’ll note* that the root is in the harmonic series of the fourth. In any case I’m not sure what you mean by, “the fourth would be harder to distinguish than the third because it’s more consonant to the root.” This chart gives some idea.
*No pun intended
IANA audio engineer, but the fifth is the third harmonic. If you pluck a string with your finger gently touching at the fifth, then you will produce a note that is one octave above the fifth. When plucked open, I assume that the string will at lest have some vibration about the 3f nodes (i.e., at one third points, whetever they’re called.) I have no idea about the third.
Let me give this a shot:
When you pluck or bow a string or blow air into an open pipe, you will in general excite a certain number of frequencies in the string/air. These frequencies are integer multiples of the fundamental frequency, i.e., the harmonic series. So, for example, if the fundamental tone of the string is 220 Hz (A below middle C), the other tones that will be excited in the series will be:[ul][li]440 Hz (A above middle C)[]660 Hz (the E above that)[]880 Hz (the A above that)[]1100 Hz (the C# above that)[]1320 Hz (the E above that)[]1540 Hz (a really flat G natural above that)[]1760 Hz (the A above that)[/ul][/li]And so forth. Notice what’s not on the list? D, the note a perfect fourth above our fundamental (in any octave.) In fact, if you consult the Wiki article I linked to, we see that you have to go up to the 21st tone in the harmonic series to get a D, and even then it’s really flat. Such high harmonics are generally not significantly excited relative to the fundamental, so you don’t generally hear them.
I think the best answer, then, is to say that third and the fifth are present in the lower parts of the harmonic series (albeit in higher octaves), while the fourth is not. I may be thinking about this all wrong, though — any acousticians or musicians want to chime in on this one?
PhD in Music checking in here.
MikeS has explained it well. In fact, back in the day, the perfect 4th above the bass was considered a dissonance. (However, perfect 4ths formed with notes other than the bass were considered consonant.)
So, in western tonal music (say Bach to Beethoven), in C major if you had a chord consisting of G, C, E (in that order from the lowest note) it would resolve to G, B, D (the dominant) which in turn would resolve to C, E, G (the tonic). (Note for the music theory types reading, I’m omitting consideration of parallel fifths for purposes of simplification.)
For those of us with 20th-century ears, it takes a lot of training to hear the G, C, E as a dissonance, but once you do, you’ll hear 18th century music very differently!