Were harmonic intervals invented by man, or were they merely discovered?
The truth is freeing and empowering. When we realize that the basic laws of harmony are built into God's creation, we are freed to use those basic building blocks to produce beautiful music. Rejection of the fundamental ideas embodied in the harmonic series leads to chaos and dissonance. It is no coincidence that the greatest musicians in history also had a great respect for musical rules that would help them express the greatest agreement with the harmonic series of music.
What we know as the major chord, which is foundational to knowledge of harmony, is not something made up by musicians. It didn't "evolve" into being, and it isn't something someone randomly thought up.
Actually, God invented the major triad, and man discovered it.
The major triad comes directly from what is found in nature, something known as the harmonic series or overtone series. The fundamental and its overtones are where the major chord originates.
Certainly by Genesis chapter 4, Jubal was working with the harmonic series. "....and his brother's name was Jubal: he was the father of all such a handle the harp and organ" (Genesis 4:21).
A taut string that is plucked will produce overtones. The harp, which refers to many stringed instruments, and the organ, which indicates pipe-based instruments, both can be used to produce music because of the overtone series.
Although the instruments we use to work with the harmonic series have changed since Genesis, the harmonic series has not changed.
What, then, is the "harmonic series"?
It is what we hear every time any musical instrument is played. It is what distinguishes between music and noise. When an orchestra plays, we hear many harmonic series at once. (One writer describes this as hearing series-es).
On the piano, we can understand the harmonic series as a mathematically consistent series of frequencies that sound all at once any time any note is played. For example, if we strike the string we know of as "C below middle C," in reality, that string produces a whole range of frequencies at once. "C below middle C" is the fundamental, or strongest, tone we hear. But at the same time, on the same string, middle C is also sounding.
These two tones are the first two tones of the harmonic series: 1. The fundamental, which is also called the tonic. (In this case, the C-below-middle-C), and 2. The fundamental repeated one octave above itself.
But the harmonic series of "C-below-middle-C" doesn't just include C! We can also hear G, E, more C's, and so on into the harmonic series that goes on into frequencies we can't hear.
What about the harmonic series of notes other than "C-below-middle-C"? The ratios will be exactly the same. This is where solfeggio does a great job of helping us understand the nature of the harmonic series as a relationship between the fundamental and its overtones.
Using just do-re-mi-fa-sol (or "so") as our example, we see that "do" always represents the fundamental. "Sol" exists in relationship to "do" and is an overtone (or "upper tone") of "do." What if we use C as our "do"? Then "sol" is G. What if we use F as our "do"? Then "sol" is C. What if we use D as "do"? Then "sol" is A. Although the pitch of the fundamental ("do") can change, the ratio or relationship between the fundamental and its overtones stays the same. This is built into God's creation.