At its core, music is as much mathematics as art: The godfather of Western music—all Western music—is none other than Pythagoras, the Triangle King himself. In or around 500 BC, Pythagoras developed the modern scale by taking metal bars and dividing them sequentially by 2/3 to create successive notes. Pythagoras’ scale had 12 tones—you can see these on any modern-day keyboard, where there are 12 keys within each octave. These are not, however, Pythagoras’ original tones, but their modern counterparts. The basics of western music are organized around a series of “perfect” fifths—called perfect because they are easily tuned by ear. The math, for those interested, is explained here: https://pages.mtu.edu/~suits/fifths.html.
But Pythagoras’ scale had a problem—although his 12-tone scale replicated natural tones perfectly, the spacing between the notes was off and increasingly so as you went up the scale. So much so, in fact, that the octave note was considerably higher and thus “off”. Mathematically, this can be reduced to the basic premise that no power of two can equal any power of 3. Pythagoras’ solution to what became known as the Pythagorean Comma was to simply throw out all notes above 12 and 5 of the 12 tones he had discovered. The remaining seven form the bedrock of all Western music—they are literally the Do, Re, Me, Fa, So, La, and Ti that Julie Andrews sang about in the Sound of Music (bonus points to anyone who had that song as the first one I’d mention in this series). Again, the math stuff is here: https://pages.mtu.edu/~suits/pythagorean.html.
As a side note, there are far more tones possible than the 12 set out on a modern keyboard. This may be summarized in the adage that G# is not the same thing as Ab. Surely, our resident cellist, The Professor, can attest to that. While we consider semitone composition to be a 20th century phenomenon (influenced largely by Arabic music), experimentation with additional semitones goes back more than 500 years. Check out this video of an Archicembalo, which has 31 keys per octave, play an early experiment with 24-tone music:
But the bedrock for Western music is that familiar seven note scale and, with that established, it is time to start.
Not to endlessly quote Julie Andrews, but the beginning is indeed a very good place to start. Well, not really the beginning, since we know that music has existed pretty much as long as mankind has. Jazz musicians are known to lament all of the great music that disappeared, unrecorded, into the walls of jazz clubs—but that is nothing compared with the centuries, if not millennia, of music that have fallen silent, forever. There is a reason why a Greek chorus was given that name—its part was more than likely sung. It was the rise of what became modern staff notation in 11th century that allowed for modern musicians to replicate the music of the past (take a bow, Friar Guido of Arezzo—paying homage to Friar Guido is the second best reason to visit Arezzo, after the staggering Piero della Francesca fresco cycle depicting the Golden Legend, perhaps the greatest fresco cycle ever painted: http://www.travelingintuscany.com/art/pierodellafrancesca2.htm).
At the beginning, Western music was monophonic, that is a single line of melody only. Here is a classic example, and one we will return to in a few hundred years.
Anon., Crux fidelis:
I’d like to think it was the acoustics in churches that got composers thinking about harmony. Sound reverberates in a Gothic cathedral, producing direct and indirect sounds that overlap with each other. This is the primary reason why music composed for church performances should be heard in situ, and not in a sterile concert hall with its perfected acoustics. Regardless of the inspiration, late Gothic composers added a second line of music to their works. This was called organum.
Anon., Dies Irae:
Anon., Advocatam innocemus:
Commonly, that second line of melody was sung by a boys’ choir. In the Dies Irae selection, the two musical lines come together at around the 7:10 mark to produce the sound that is so characteristic of late Gothic music. Alternatively, composers created organum by having one voice sing a continuous unchanging note, around which the plainchant is sung. An example of this comes at the 1:30 mark of the second selection. This is, hilariously, called a drone and one of the more popular late Gothic instruments was called a drone organum, since it played only one note continuously.
Incidentally, the concept of a drone has endured through the centuries. The Velvet Underground used a drone extensively (and, no, I’m not talking about Lou Reed’s voice):
The Velvet Underground, Heroin:
Eventually, these new melodic lines would become independent on the main plainchant melody. Reflecting church hierarchy, the primary melody continued to be sung in the lower male voices (the cantus firmus), while the higher voices were given faster lines to decorate the basic plainchant. The invention of harmony, however, created a problem. While monophonic plainchant was easy enough to learn orally, multiple melodic lines needed to fit together precisely. Eventually, the unmeasured rhythm that characterizes early Western music gave way to measured rhythm—the allocation of precise time values to individual notes, allowing singers to remain both rhythmically and melodically together as the composer had intended. The need for measured rhythm gave rise to a need for written music. Enter Friar Guido and his neumes. (https://brianjump.net/2015/08/29/the-origin-of-notation/).
A Gertus History of Music 