7
How scales work
This book has described and discussed a form of music most people have never heard. The development, culture, and philosophy of ancient Greek song is rich enough that much can be said about it even in the absence of first-hand experience. And indeed most people assume that no melodies can possibly have survived from so long ago. But in fact the ancient Greeks did have a system of music notation – a way of writing down the notes in a tune. There are sixty-one ‘documents’ – scraps of papyrus, inscriptions on stone, and in some cases manuscripts – which preserve written music from between as early the fifth century BC and the third century AD.
These are some of the most exciting things that survive from antiquity, and also some of the hardest to understand. It was in 1581 AD that the first known modern editions of Greek musical documents were published by Vincenzo Galilei (father of the famous astronomer). Ever since then, scholars have been trying to wrap their heads around the written music that comes down to us from ancient Greece. In the twentieth and twenty-first centuries, a burst of new research and discoveries helped experts to read Greek notation more accurately than ever before, meaning that with some careful effort we can now try – albeit without certainty – to hear snatches of music echoing across the centuries from the ancient world.
There’s a tremendous appeal in such a prospect, of course, but since the research is still quite new it can be very obscure and technical. These final two chapters, therefore, represent an effort to distil some of the basics that underlie Greek melodic and rhythmic notation in a way that doesn’t require a lifetime of study to understand. As such there is a world of detail left out here, but in outline and as a rough picture this will serve as an introduction to how Greek music was written down.
First, a little bit on how the Greek scale works. A ‘scale’ is a set of musical notes between two pitches that are an octave apart. Sing the first two notes of ‘some-where over the rainbow’: ‘some’ is an octave lower than ‘where.’ In the Americas and Europe, most songs will use a set of eight notes that can be written within the span of an octave. In addition to the two notes of ‘some’ and ‘where,’ there are six others in between, and together they make up a scale.
The distance between two notes is called an ‘interval’ – an octave is one type of interval, and another very important one is called the ‘fourth.’ A fourth is smaller than an octave, meaning that its top note is less high in pitch above its bottom note. So, now sing the first two notes of ‘here comes the bride’: ‘here’ is a fourth lower than ‘comes.’ There’s just one other, smaller interval that needs mentioning for now, and that’s the ‘whole step’ (or ‘major second’ or ‘whole tone’). It’s the gap between ‘happy’ and ‘birthday’ in the song ‘Happy Birthday.’
Here’s the next step: if you sing two fourths separated by a whole step, you get an octave. Try it:
1.Sing ‘here comes the bride,’ then
2.Start on the same note as comes to sing ‘happy birth’ from ‘Happy Birthday,’ then
3.Start on the same note as ‘birth’ and sing ‘here comes the bride’ again.
The last note you sing on comes in (3) will be an octave higher than the first note you sang on here in (1). Sing those two notes next to each other, and you’ll find they’re the same two notes as you would sing if you sang ‘some-where over the rainbow.’
Those two fourths are likely the skeleton of every scale most Westerners have ever heard, even if they don’t realize it. There are two basic kinds of scale in modern Western music, and they are called ‘major’ and ‘minor’ scales. Even those who have never studied music may know the major scale: often people sing through it using the syllables ‘do-re-mi-fa-sol-la-ti-do.’
The notes on the first ‘do’ and ‘fa’ are one fourth, and then from ‘so’ to the second ‘do’ are another fourth, just like the two ‘here comes the bride’s in (1) and (3) above. Those notes stay exactly the same when we switch from the major to the minor scale, too: only the notes on ‘mi,’ ‘la,’ and ‘ti’ change.
It’s important to remember here that one can begin a major and a minor scale on any note of the piano keyboard – or more precisely, on any ‘absolute’ pitch. The basic structure – the intervals between the notes that make up a major or minor scale – can be repeated starting from any note or pitch. So, a C major scale is what results when a musician starts on the note ‘C’ and then plays the eight major notes up to the next C an octave above, whereas an A minor scale starts on ‘A’ and then goes up to the next A, hitting the minor notes along the way. The word we use for the set of notes obtained by starting a scale on a particular note is a ‘key’: we say that a certain song is in the ‘key of G minor’ or the ‘key of C major’ depending on which notes it tends to use and gravitate towards. But no matter where the scale starts, and no matter whether it is major or minor, it will always have those two fourths separated by a whole step as its basis.
In its fundamentals, the ancient Greek scale worked in the very same way – in fact, one of the reasons our scales work the way they do is because Greek scales did so. The skeleton of any Greek scale may be outlined by starting on a given note and then going up a fourth.1 After that, the scale would either go up a whole step and another forth to make an octave, as in a modern Western scale, or leave out the whole step and just stack a second fourth directly on top of the first one. Skipping the whole step creates a ‘conjunct’ scale (because the two fourths are conjoined together), whereas the modern Western scale is called a ‘disjunct’ scale (because the two fourths are disjointed by a whole step). One of the earliest forms of modulation (transfer from one key to another) was to keep the lowest notes of the scale the same up to the central one, mesē, and then re-tune the higher notes to switch back and forth between the conjunct and disjunct forms of the same scale. The diagram on this page gives a bare-bones illustration of how this works.
Fig. 4 Diagram of disjunct and conjunct Greek scales compared to the modern Western scale. Spencer A. Klavan.
Things get still more complicated. Much of the music produced today only uses two types of scale: the major and the minor. The Greeks had at least three basic types: the diatonic, the chromatic, and the enharmonic. This seems strange to modern listeners. We are used to thinking in terms of the piano keyboard, which divides the whole octave up into twelve ‘half steps’ (or ‘semitones’ or ‘minor seconds’). This is the smallest available interval in modern Western music – the melody of the famous theme in the movie Jaws is simply two notes a semitone apart. But now try this: start by singing any note of your choosing, then slide all the way up to the note an octave above, without stopping. It’s a continuous slide, which means there are actually an infinite number of pitches between every note. We happen to stop at the half step, but we could just as easily keep dividing that into smaller intervals and sing a third or a quarter step.
Those smaller intervals aren’t playable on a keyboard – they would be ‘in between’ the white and black keys. But anyone with training and practice can sing them just fine. Greek musicians and audiences were used to them, which means quarter tones, though they sound unusual and out-of-tune to us, sounded quite acceptable to them. So starting with the standard two fourths, a Greek musician could then fill out the scale by putting different notes in between the fourths. If there was a quarter tone between each of the bottom, second, and third notes, that created what was typically called an enharmonic scale. A semitone between each of those same notes produced a chromatic scale, and one semitone between the first two notes followed by a whole tone between the second and third made another type of scale called the diatonic (when the first two intervals of the tetrachord collectively took up less than half of the whole tetrachord – as in the standard enharmonic and chromatic species – they were called a puknon, or ‘bunch’). In reality, there were many more ‘shades’ (chrōmata in Greek) than just these three species – musicians could subtly adjust their strings or finger their pipes in any number of ways. But in ancient Greek music as in modern Western music, those two fourths always stayed the same – they were rooted in place and then filled in with notes that could change depending on the type of scale.
The series of four notes (the two fixed notes of the fourth and the two moveable ones within them) that served as the basis for a scale was called a ‘tetrachord’ (systēma in Greek), and a particular type of tetrachord (diatonic, enharmonic, or chromatic) was called a ‘species’ (genos). Just like our major and minor, these enharmonic, chromatic, and diatonic tetrachord species could be played starting at any pitch.
How we got here
This basic series of harmonic practices (and others besides) gave rise to a huge diversity of musical forms and traditions. Over time, efforts were made to form a unifying theory of how those traditions fit together, principally by fixing the various scales into a coherent system of shared pitches and relating them to one another.
The simplified and smoothed-out version of things presented here was probably not widely accepted until at least the very end of the Classical period. Musicians in the ancient world, after all, didn’t have international conferences or universally standard textbooks. They met together to compete at different festivals around Greece, or collaborated in gatherings or guilds where they could share ideas and pass down traditional practices. That meant that different communities had different ways of doing things, and pockets of local custom would develop from place to place.
Much of the information I’ve been summarizing so far comes mostly from the work of Aristoxenus of Tarentum. Aristoxenus left behind a very complex treatize, made more complex because not all of it survives. The Elements of Harmony was meant to explain the principles behind all the different ways of writing and playing Greek melody – a kind of unified field theory explaining how all Greek scales worked. His system was quite successful and ended up being influential as musicians after him tried to standardize the way they played and wrote. But Aristoxenus was drawing together some of the major strands of thought that had gained traction before him, as well as rejecting some of the variations that didn’t fit into his theory.
Terpander, another early musician called Olympus, and Pythagoras were all important predecessors to Aristoxenus who laid the groundwork for Greek music theory. It’s not totally clear what each of them really invented themselves, and what their followers invented but then attributed to them. Terpander and Olympus were said to have tuned the strings on their lyres in a few simple ways which caught on and became the norm for professional musicians.2 If Terpander and Olympus fixated on a few ‘tunings’ for their lyres, it means they deliberately chose to use a particular set of scales – a few sets of seven notes, each probably spanning an octave (for disjunct scales) or the slightly smaller interval of a ‘seventh’ (for conjunct scales). What these stories suggest is that, by the sixth century BC, musicians had a set of scales they liked to use and that might even have been standard for competitions.
It’s worth noting that these early scales would have been fixed within the range of pitches that a lyre or an aulos can play. So instead of a series of modes in higher and lower pitch, there would have been a series of different note arrangements, all within the same pitch range but tuned differently. The most basic and common of these were called Dorian, Phrygian, and Lydian. But there were many others, and already by the fifth century (likely before), musicians were devoting themselves to finding ways of relating one pitch to another so as to modulate between them. Eventually theorists attempted to come up with a definitive model for these relationships using the ‘Greater Perfect System’ (the systēma teleion meizon). This was a standard sequence of intervals, originally developed to standardize the construction of auloi but – it turned out – useful much more generally as a tool for understanding the relationships between scales.
The Greater Perfect System spanned two octaves in relative, not absolute pitch (it could be mapped, that is, onto any series of pitches no matter how high or low). There was a bottom note (the proslambanomenos), followed by four tetrachords of which the first was conjunct with the second and the third was conjunct with the fourth. But the second and third were disjunct, separated by a whole tone, meaning that the centre of the system was a full disjunct scale spanning an octave. The tetrachords within this Greater Perfect System could be diatonic, chromatic, or enharmonic, depending on the species under discussion (see the diagram for further clarification).
Aristoxenus would argue that every important key could be obtained by starting on a different absolute pitch and progressing upward according to the sequence dictated by the Greater Perfect System. Technically, the sequence dictated by the System could start on any note. But it was most useful for modulation if a central scale was fixed in place as a standard to which users could refer. This centre of the system (whose core was a disjunct scale with the mesē fixed at about the pitch of our modern b natural above middle c) came eventually to be called Lydian. But if the musician wanted to shift to a lower key he could treat the note below the mesē of Lydian (the lichanos mesōn of the Lydian) as the mesē of a new key, called Phrygian. One note below that came the Dorian – each of these proceeded according to the interval sequence of the Greater Perfect System, transposed up and down the absolute pitch spectrum.
Fig. 5 Diagram of the Greater Perfect System with Greek scale degree names.
As will have become clear, Aristoxenus applied names like ‘Dorian’ and ‘Lydian’ to fixed keys (tonoi in Greek) whose pitches were set within the Greater Perfect System. But those names had previously referred in many cases to particular tunings (perhaps originating from the particular regional or ethnic groups whose names they bore) which were not pitch-fixed keys at all but modes (harmoniai): sequences of intervals that could be played starting on any pitch. That local colour and variation was lost in Aristoxenus’ system and the ones which followed it. But a major advantage of keeping all the keys mapped out onto one grid based on the Greater Perfect System was the ability to modulate (relatively) easily from one key to the next.
The motley crew: musicians, theorists, and everything in between at Athens
As Athens came into its own, it became a place where theoretical experimenters and practical performers alike tested new ways of developing and combining the ideas of older authorities like Pythagoras and Terpander. By the fifth century BC, musical scholars all over Greece were talking about Pythagorean theory and debating its finer points of detail. Some felt that numbers were the fundamental building blocks of the universe, and that Pythagoras’ ratios were at the heart of music’s beauty and power. Others thought that mathematical abstractions were too removed to capture the realities of live performance – they preferred to improvize based on their own feel for the music and go with what sounded good. Starting from traditional scales like the ones credited to Terpander, they played around with new ways of shifting between different keys in the middle of the song.
Others of a more Pythagorean bent were inclined to theorize and abstract music down to its essentials. Eventually these more mathematically inclined thinkers became known for experimenting with something called a ‘monochord,’ a simplified instrument with just one string that could be stopped at different lengths to produce different notes. With these and other techniques, they stripped the scale to its bare bones and attempted to describe its basic structure without reference to the messiness of live performance.
Some of the leading lights in Athens combined theory and philosophy with practical craftsmanship and performance experience. Lasus of Hermione was one of the earliest ones to do so: he was a music director and a composer in his own right, but also a writer and a theorist. Damon of Athens was another popular authority on music in the city – rich elites or up-and-comers who wanted the best for their sons would have sent them to the likes of Damon to receive the cutting edge of musical education. Celebrities like Damon and Lasus helped spur on the lively musical activity that continued throughout the fifth century.
That activity was particularly fervent in the second half of the 400s, as bold young artists made a series of changes to musical tradition and experimented with unorthodox styles. Timotheus of Miletus was said to have experimented with all sorts of new forms, ornamentations, and styles of modulation. Strict conservatives (like Plato) were against modulation and experimentation of this kind, because they threatened the purity of the more basic scales. These traditionalists accused performers like Timotheus of pandering to the public’s taste for novelty at the expense of the more stately forms and traditions which had gone before – these were pretty tunes designed to titillate, but not to edify. That’s probably pretty unfair, as Timotheus and his fellow innovators (people like Cinesias and Philoxenus of Cythera) were trained professionals who took meticulous care in constructing their melodies. They may have been radical, but they weren’t careless.
And they were certainly crowd favourites. The written melodies which survive show that modulation did catch on, and Timotheus’ songs, so shocking in their day, became old standards just a generation later. Think of rock stars like Elvis Presley and the Beatles, who appalled older listeners in their day, but who show up now on oldies stations as easy listening.3 One artist who probably helped to popularize the new musical style in the fifth century was Euripides. Of the three great tragedians whose work survives from the fifth century, Euripides was the most experimental, prone to creative risks. He seems to have incorporated some of the trendier musical fashions from the concert stage into his own plays, and there are rumours that he collaborated professionally with Timotheus.4
As the fifth century unfolded, artists fed off of one another’s energy with greater and greater enthusiasm, leading to an explosion in new tastes and forms. But they were still working from that basic harmonic structure – two fourths, each filled with two middle notes, to make a scale. Even as they went wild with ornamentation and experimentation, Greek musicians shared a few core theoretical elements with each other: no matter how new the music got, it was always rooted in that original scale structure.
Writing things down
It was because of this endless proliferation of new scalar forms and tunings that Aristoxenus did what he did. From the fixed set of early tunings that many early musicians used, Aristoxenus set out to develop a system in which one could transition easily from one key to another. That meant placing each tuning in a different pitch range and establishing the relationships between them, so that each one was distinctive, but related to the others, in the notes it used. That’s the origin of the complicated system described above.
This also meant that Greek artists could share a system for writing music down. They may have had more than one such system, but only one survives, written out and explained in a handbook by the scholar Alypius of Alexandria in the fourth or perhaps fifth century AD. The notation itself is much, much older than Alypius – in fact, it almost certainly goes all the way back to the fifth century BC. So its creation might have been part of the flurry of discovery and creativity that we have been discussing in this book.
‘Alypian’ music notation (as it is now called by scholars) works quite differently from the graphic systems that we now use to write music down. In modern sheet music, the most widespread form of written notation uses something called a ‘staff’ – a stack of horizontal lines onto which composers write dots to represent notes. The dots are interchangeable in terms of pitch – an ‘A’ doesn’t look any different in shape than a ‘C’. But how high or low they are placed on the lines of the staff determines how high or low they ought to be played or sung.
In Alypian notation, there is no staff. Instead, the notes are written out on top of the song’s words: each syllable has a symbol above it indicating the pitch that goes with that syllable. That means that every pitch has to have its own symbol. From the bottom of the lowest key to the top of the highest, every possible note in the scale is assigned a shape. There is one set of symbols for vocal music, and another for instrumentation – so a musician could tell by reading a piece of Alypian music whether he needed to sing the words on the notes indicated, or whether there needed to be accompaniment with a lyre or pipes.
The Alypian symbols basically correspond to the notes of the Greater Perfect System – that is, in their final form they were used to write music with the kind of orderly, coherent arrangement of keys that Aristoxenus put together. Aristoxenus was originally from the Pythagorean school, but he eventually studied under another philosopher, Aristotle, who emphasized experimentation and attention to real-life detail. So Aristoxenus made sure to devize a system that would describe as accurately as possible the real intervals and scales that sounded good to Greek audience members of his time.
But he also tried to find a theoretical scheme that would line up those scales in logical relationship to one another and create orderly routes to modulation in between them. That means he smoothed over some of the rough edges that come with live performance – the ad hoc techniques that expert performers devize in the moment. It’s important to be aware of that so that we keep in mind how limited our knowledge is: as wonderful as it is to have written music from the ancient world, we have to remember that standardized systems for writing music are always a little bit artificial.
It’s the same with music today: you can notate the melody of Taylor Swift’s Shake it Off, but how can you capture on paper the little scoops and flips that her voice makes when she raps the bridge? Or how can you write out the way Bob Dylan’s fingers grate against the strings of a guitar? The documents that survive give us a basic sense of some melodies which the ancient Greeks played and sang, and that’s a huge gift. But there is a lot which we can only imagine or guess at from descriptions – things like the particular vocal quality of a performer, or the dynamics that musicians would have used to make their pieces exciting. What we’re doing here is combining careful scholarly research with artistry and imagination to approximate something like what the Greeks might have heard.
An example will help show how it works. There is a scrap of papyrus in the Imperial Library of Vienna, Austria which was used as part of a mummy’s wrapping in Egypt. Since papyrus was expensive, it was often recycled and repurposed to do things like wrap up corpses for burial. Some of the most precious writing from antiquity was discovered by accident because it was re-used as scrap paper. This particular papyrus is invaluable: written on it are a few lines from a play by Euripides called Orestes. The lines are from a song sung by the chorus after the title character, Orestes, has murdered his mother and finds himself haunted by vengeful spirits called furies who drive him mad with guilt. Terrified, the chorus sing out a desperate prayer: ‘I beg you, I beg you,’ they sing, ‘let Agamemnon’s son [that is, Orestes] forget his wild whirling madness.’
What makes this papyrus special is that above the lines are written symbols in Alypian notation. Orestes débuted in 408 BC, and there’s a good chance that the notes written on this papyrus are from the original performance. That would make this the oldest melody preserved from ancient Greece. Let’s take a look at the papyrus.
The notes which are written above the words are from the Lydian mode, but they shift between the enharmonic and diatonic species – a kind of modulation, like shifting in the middle of a song between C major and C minor. That fits our idea of Euripides as someone who experimented with the new forms of music that emerged in the later fifth century. The change of species might also have given this melody an unsettling or unexpected twist, the way a song’s mood can take a sudden turn when it shifts keys in the middle. That would make sense for this song, which is sung during a moment of desperation and unease when things are increasingly uncertain for the characters onstage.
Let’s take a look now at part of a modern transcription of this papyrus by the Oxford scholar Armand D’Angour. D’Angour has written the notes which you see on the papyrus into modern sheet music, using staves and noteheads to write the same melody in symbols that any modern musician can understand. The notes with the unusual square heads are the ones we can see written on the papyrus, while the normal rounded ones are the missing notes which Dr. D’Angour has filled in using educated guesses based on the trajectory of the melody and some of the more advanced rules of Greek melodic composition (we can’t get into those rules here, but you’ll find resources for learning more about them at the end of the chapter). Notice the odd notes, though, with little ‘up’ and ‘down’ arrows next to them: those are the quarter tones mentioned earlier, the notes that are just a little higher or lower than they could be played on the piano keyboard.
Fig. 6 Vienna Papyrus (Pap. Vienna G 2315), containing words and musical notation for Euripides’ Orestes 338–44. Permalink from Austrian National Library: http://digital.onb.ac.at/rep/access/iiif/image/v2/5af078d39f1683785829f77db4be965359577f6dc708417941693fa76d99941b1a9c87bcbef81bd6fcadb7984bfcbb9b7471f8f9.
The repeated word kathiketeuomai, which means ‘I beg you’ or ‘I pray,’ is sung on a sequence of notes separated by very small intervals – this creates a creeping, ominous sort of sound which fits with the mood of the song. Altogether, the notes Euripides selected and the way he moves between them – the whole harmonic profile or ‘tonality’ of the piece – creates an auditory atmosphere which amplifies the meaning of the words and gives them powerful emotional impact which they wouldn’t have if they were simply spoken without melody.
What’s the point?
That fact helps answer one last important question with which we can close out this chapter: why bother doing this at all? There is so much that is uncertain in reading ancient music. We don’t know exactly how these words would have been pronounced, or what dynamic choices the actors might have made onstage. We have lost all the nuance of live performance and the tiny subtleties of feeling, impossible to capture in writing, which would have made the experience of Greek music what it is. Often it is even difficult to tell the exact tuning of a song, especially when we only have a few lines as in this papyrus.
So If we want to recover anything like the sound of these songs, we have to do some guesswork. We have to use our careful reading of theorists like Aristoxenus, as well as more descriptive writing which tells us how people reacted to this music in its day, to imagine how the gaps in our knowledge might have been filled in. But if it’s just guesswork, what’s the point?
Fig. 7 Modern transcription of the Vienna Papyrus by Dr. Armand D’Angour (Oxford University).
To start answering that question, consider this: when we write about the ancient world we are always, no matter what, filling in gaps. Hopefully our guesses get more and more educated as we go along, but there are vast oceans of information that we simply don’t have, even outside the realm of music: when we read Greek tragedy, for example, we only read a tiny fraction of the innumerable plays that were performed on the Athenian stage (let alone all the drama that went on outside Athens). Most of those plays are completely gone – not a single copy survives. Given that we live more than 2,000 years after the ancient Greeks, it is a small miracle that we have managed to preserve and unearth as many of their cultural achievements as we have. We have lost much more than we have saved, and we owe what does survive to a massive intergenerational feat of intellectual collaboration: for centuries these texts were copied down, hidden away, corrected, misplaced, and rediscovered. It took a lot of work and a lot of luck.
But it was worth it, because it’s worth knowing where we came from. For better or for worse – usually for better – we live today in a world filled with societies that have been inspired by ancient Greek writing and thought. By learning from authors like Plato and Aristotle, by arguing with them, even by misunderstanding them or misinterpreting them, modern cultures all over the world have formed their own ways of life and government in response to the Greeks. Whether we adore the results of that process, or despize them, or a little bit of both and everything in between, we will engage more effectively with the world around us if we know about the complicated story of how it came to be. The society of fifth-century Athens – in all its complexity and variegation, in all its inheritance from the other societies that lived around and before it – remains powerfully present with us. We retain foundational elements of Greek life today, right down to the basic structure of the scales we use in music.
And those scales are an important kind of cultural heritage, because they are a different kind than what we get from written words. Take an analogy from another genre: when we read a book, we learn information about what Greek writers, especially rich elites, thought. But when we look at a sculpture, then we actually see something that a Greek sculptor saw – it’s a visceral, sensory experience that brings the ancient world a little bit more to life. But not many people know that scientists have recently discovered traces of ink and paint on marble sculptures from antiquity. That is, the art which we usually think of as cold white marble was once painted in bright, living colour. When scholars analyse those traces of ink, they come up with careful, educated guesses about the way ancient art once looked – they are able to re-paint Greek sculptures in something like their original hues. The result may not be exactly accurate, but it is probably quite close to the truth. And it is a vivid, shocking way to experience antiquity – a new way to see the world as the Greeks did, as colourful and alive.
What painted sculptures do for the eyes, musical reconstructions do for the ears. Maybe these tunes aren’t exactly right; certainly there is lots about them we will never know. But they take us a small step closer, not just to knowing about ancient Athens, but to feeling and experiencing the ancient world in a visceral way. Music, as we’ll continue to see, was everywhere for the Greeks. It coloured their experience of every day and seeped into their subconscious minds. It made their experience of the world what it was. We will never be able to share that experience entirely, but making educated guesses at it is, in some sense, what the study of Classics is all about. Listening carefully for echoes of Greek music adds another dimension to our understanding of a culture which remains enduringly important and foundationally influential for the modern world. It is well worth a few guesses and a lot of work.
Some further reading
The known surviving documents of ancient Greek music can be found in a handsome edition from 2001, edited by two experts in the field, Egert Pöhlmann and Martin L. West (Documents of Ancient Greek Music, Oxford: Oxford University Press). Check out their introduction (pp. 5–7) for a very short history of the documents and their publication in modernity.
The introduction to Volume 2 of Andrew Barker’s Greek Musical Writings (Cambridge: Cambridge University Press, 1989, pp. 1–27) contains another helpful explanation of how Greek scales work.
Barker has also written a somewhat more challenging book, The Science of Harmonics in Classical Greece (Cambridge: Cambridge University Press, 2007), which explores the intellectual history presented in this chapter in much greater detail. Still more challenging, but also more cutting-edge, is Stefan Hagel’s Ancient Greek Music: A New Technical History (Cambridge: Cambridge University Press, 2009).
If you’d like to see a video of the song from Orestes being performed live, along with a number of other reconstructions from Greek antiquity, you can watch this YouTube video (which, I’m afraid, features the author of this book): https://www.youtube.com/watch?v=4hOK7bU0S1Y.