Not one music lover needs to have the tension in a dominant chord pointed out to them, nor do they need to have the difference between a major key and a minor key explained to them. These are some of the many aspects of music that even the untrained ear can identify, even if the listener does not posses the vocabulary to label them. But what is it about these pitches, intervals and sequences that make them constant? Why is a fifth always a fifth, an octave still an octave? Why are tritones, for the most part, avoided? What is it about the relationship between notes that gives them the strength to withstand the test of time? For all of modern day’s advanced technology and extensive research and experimentation in every field of expression, why do so many of the tenets of music remain unfaltering? While these questions remain hard to answer – and maybe it is in that unanswerability that music gains some of its magic – I would like to attempt to draw similarities and parallels between a number of different tuning systems and theories, dating from BCE times to today.
First let us visit the ancient Greeks. Much of their work in music has inspired musicians and theorists throughout the time, up to and including composers of the present day. While the documentation we currently have of Greek music is not as extensive as their discussions on philosophy, politics, mathematics and sciences, a great deal of their work in music can be cross-referenced in these other arts.
Take, for example, pitch. A Greek invention credited to Pythagoras is the instrument known as the monochord. The name itself gives a clue that this instrument has only a single string. This string was placed over two fixed bridges with a moveable bridge then placed under the string, dividing it into two sections. Monochords were used well into the 19th century for teaching, experimentation and tuning.
Pitches on a monochord were found through proportions, and string length. A musician didn’t have to know what a fifth or a major second sounded like to know that he was playing the correct interval as long as he knew the correct proportions for the pitches and how to apply them to his specific instrument. Pythagoras’ system of tuning included what we know as the octave (2/1) , the fifth (3/2), the fourth (4/3) and the major second (9/8). Aristotle and Euclid agreed on these intervals as well, and interest in ancient music grew in the Middle Ages, Theon of Smyrna, Ptolemy, Bacchius and others wrote of this system as well. [Adkins]
Simple math and our own collective ears have been saying that these intervals are aesthetically pleasing to listen to for millenia, however, it is only until recent years with the advent of modern technology that we can actually measure the ratios of string vibration that Pythagoras discovered all those years ago. It is true that, when two strings are vibrating and one is tuned to exactly an octave above the other, the first string is vibrating twice as fast as the second. As with the fifth, the higher note is vibrating three times every time the lower note vibrates twice, and so on for the other intervals.
It is my own speculation that a system that involves perfect intervals such as Pythagoras’ octave, fifth, fourth and second would inherently be a microtonal system, as specific pitches would be chosen in relation to the notes that surround them. A tone that fits into one group of pitches may need to be adjusted by just a few cents to fit into the next.
However, it is this slight adjustment that has fallen by the wayside with the advent of equally tempered systems of tuning, developed in the mid to late 1500s and still in wide use today. [Lindley] Still, it is these original intervals, especially the fourth and the fifth, whose special relationship to the root has maintained their importance through the years.
Even before the Greeks, the ancient Babylonians, it has been discovered, had a system of tuning based on perfect fourths and fifths that, it is believed, dates back to the 18th century BC. [West, 162] The tuning was applied to a lyre-like instrument that may have had up to 9 strings. Strings 8 and 9 on this instrument, it is believed, were tuned to an octave above strings 1 and 2, respectively. This instrument had a number of different tunings, each approached by fifths and fourths skipping up and down the instrument until all the strings have been tuned. Each of the tunings starts on a different string and follows what we would consider in modern musical notation the following pattern: B – E – A – D – G – C – F. The difference between these tunings however, is how the pattern is applied to the strings. In one tuning, the kitmum tuning, B is on string 6, E is on string 3, A is on string 7, D is on string 4, G is on string 1, C is on string 5 and F is on string 2 (remember that string 8 doubles 1 and string 9 doubles 2). This, then, gives us a tuning that starts on F and ascends to G1. [West, 168]
Since these intervals are based on the sound and not a fixed pitch arrived at with the help of an electronic tuner as is the way instruments can be tuned presently, the pitches, presumably then, are slightly different in each tuning. Tuning an E a perfect fourth up from B and then tuning A a perfect fourth up from E in one tuning will arrive at an A that is not related by an octave to an A arrived by tuning up a fourth from B and then down a fifth to A. It can be gathered, then, that each tuning had a distinct sound to it, even more distinct than the 24 different major and minor keys we have today. While our 24 keys each have their own personalities and intricacies that many of our greatest composers have explored in detail – Chopin’s Preludes for the piano, for example, or Bach’s Preludes and Fugues for the Well Tempered Clavier – they are probably much more generic in their overall sound when compared to the temperaments of old.
The tunings of keyboard instruments in particular, went through an interesting time in the 1300s – 1600s, as notes which today we consider enharmonic spellings of one another, were considered separate pitches. Many keyboard instruments were tuned to a regular mean tone temperament and many of the late church modes during the Renaissance used this system. Most notably, G sharp and A flat, more often than other current enharmonics, were considered two completely different notes. In mean tone systems, however, not all of the pitches accessed are “pure” intervals and pitches, and while the intervals found in our modern day 12 tone equal temperament system are also not always “pure,” mean tone temperament’s popularity diminished while 12 tone equal temperament has become the standard.
Interestingly, today’s method of temperament, while much more accessible, is much more complex for the ear to comprehend and for the modern musician to accomplish than the ancient Greek, Babylonian, or even the Greek influenced Renaissance and Baroque theories of tuning and musicality. Other influences of the Greek sense of music can be felt elsewhere, if only subtly.
Madrigal writers of the Renaissance period composed their music in such a way that the melody mimicked the text they were setting to music. Greek composers also believed in this kind of musical setting of music, though in a slightly different manner. Instead of accenting the thoughts put forth by the words (accenting text about heaven with high pitches and text about mountains and rocks with uneven melodies and rhythms, for example), Greek compositions seem to have accented the words themselves. A syllable with an acute accent, for example, would have a higher note than the following syllable. In this way, the pitch accented the grammatical form of the text and not the ideological meanings the text represented. [Williams, 131]
Modern day composer Harry Partch takes this one step further. Partch’s theories on text setting shift the focus from the actual words being said to how those words are being said. Partch’s treatment of pitch more closely follows the way a human being would speak naturally and while his work is a step away from the vocal pieces of later classical composers, it is also a simultaneous step closer towards the work of the ancient Greeks.
Partch also took the Greeks’ ideas on tuning and developed his own scale. Over the years, this scale had a different number of tones involved within the confines of one octave, ranging from 29 to 55, before he finally settled on a 43 tone octave. The names of all these notes are, in fact, ratios, exactly like the ancient Greeks’ work.
Partch’s use of inventive time signatures also seems to mimic the Greek’s penchant for uneven meters (the most favored seeming to be 5), which is a practice overlooked by most composers of Western music [Williams, 130]. In fact, the only widespread use of five beats in any grouping in a creative endeavor is not in music at all – but in poetry’s iambic pentameter.
Further delving into the topic of ancient music theories’ influence on music of the modern era would probably reveal even further subtleties that carry through to today’s world. Music has always reflected its creators and the world around them. The Babylonians, Greeks, and Western composers all knew what they liked to hear and set their texts accordingly, and so too, will composers of the future rely on the simple logic of the perfect intervals, cultivated millenia ago, on a planet they may no longer even inhabit.
please note: this article was originally a research paper I wrote in college. while the article itself is intact, my works cited list seems to have disappeared. I left the references in for you to do your own google searches if you are interested, but also, in the event that someday soon, I do, in fact, find the works cited page.