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Ancient Greek Music


leftybassman392
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First installment

Introductory remarks and basic ideas

1. Background

The Ancient Greek civilisation is an endless source of fascination for me. Modern Western civilisation owes more to the Greeks than to any other single source; Science, Mathematics, Art, Philosophy, Politics, Social structures – and, of course, Music. I don't think it's too much to say that they provided the blueprint from which modern western civilisation has developed.

Many aspects of Greek culture are well covered in the literature, but music – surprisingly – isn't one of them. When I studied the topic in the early 1980's there was very little by way of modern commentary on this important aspect of Greek life in the period. I remember having to wade through massive dusty tomes for small snippets of information, most of which had a Mathematical bias; there wasn't much that I found that dealt with music from a musician's perspective.

In the 20-odd years that have passed since then, more work has been done on the subject, so that music has become more widely accepted as having a key role in everyday life for the Ancient Greeks.

2. Sources and preparatory reading

A lot of people will no doubt be happy to follow this main text, and that's just fine as it saves me some work! However one or two of you have already indicated to me that you may want to investigate some of the material a bit more thoroughly for yourselves. As a general point, Wikipedia covers the Ancient Greeks in some detail, and is actually not bad at all for getting some background to a lot of what is said. Although quality is sometimes a bit patchy by academic standards, it will be plenty good enough for most people. (If you do a Wiki search on 'Ancient Greece' for example, you should find plenty to keep you busy.)

There's also quite a lot of Wiki articles that cover musical scales, intonation and other related subjects – again though, be careful because quality does vary, and a lot of it isn't written in a particularly reader-friendly way. When we get into the nitty gritty of the Greek approach to developing and using scales, it will definitely help if you have a comfortable working knowledge of intervals and scale structures – shouldn't be too much of a problem for members of this forum I would hope! (A knowledge of how to express musical intervals in cents wouldn't do any harm either, but I'll go through it when we get there).

For those of you prepared to do more digging, there are works of a more academic nature that will allow you to form your own opinion of the topics being discussed – be warned though that most of them are either academic studies by scholars mostly talking to other scholars and/or very advanced students; or else translations of works from original texts (either Ancient Greek or Latin in their original form). This really is doing it hard way, and is definitely not for the casual reader! I'll try to point things out as we go.

3. Language issues

Modern European languages are laced with words that have their origins in Ancient Greek culture. Words like Scale, Chromatic, Harmony, Chord and Diatonic are all direct descendents of Greek originals. However there is a problem here. Almost without exception, the Greek originals had substantially different meanings from their modern counterparts. Whenever these words come up in discussion (and they will!), you need to be very careful to resist putting a modern interpretation on them. Perhaps an example will help to make the point:

Let's take the phrase 'Ionian Mode'.

The standard modern take on this is 'a fancy name for the Major Scale'; forms the basis of a series of 7 interdependent patterns – once you have defined one of them you have in effect defined all of them.

However in Ancient Greece it would have meant something quite different. Ancient Greece was populated by a number of distinct tribes or regional groups. The music from a region was a reflection of the tribe's collective 'personality'. The scale devised to make this music was named after the tribe from whom it originated. The Ionian Mode or Ionian Scale was a scale devised by the Ionians. This scale would have been distinct from the scales from other regions, and not musically related to any of them beyond the most basic elements of its structure. More to the point, the Ionian scale of the Ancient world would have borne little resemblance to the modern Major scale – indeed the whole methodology of scale construction was different. More on this in a later article, of course.


In the next article I propose to start looking at the basic mechanics of scale construction. Don't forget to do your homework... :)

Edited by Dad3353
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Second Installment.

The Ancient Greek approach to scale construction

( Note: this whole topic is inevitably laced with lots of technical terms and words. Where necessary I will make a habit of explaining them 'in situ', but I try always to make sure I have checked several sources to make sure that more detailed explanations are available. For the most part, I have found Wikipedia very useful as a first-stop resource – I would recommend having a second window open on your browser, pointing at the Wiki homepage, when reading these articles. Wiki does get a well deserved bad press for the things it does badly, but it just so happens that the Greeks and Music Theory are on the whole covered pretty well – not that I agree with it all mind you! Like all such resources though, it's a good idea not to overuse it as it will make the main argument harder to follow, especially if you land yourself in the middle of a highly technical Wiki article. )


1. The way we do it.

In order to get a handle on the way the Greeks constructed their scales it wouldn't be a bad idea to briefly summarise the way we do it. (Apologies if you've heard this before a zillion times, but I'm going to get at the Greek approach by comparing it with contemporary practice – which will serve several useful purposes, so please bear with me.)

Contemporary music practice centres around the Octave as the standard unit for scale construction. The octave is then subdivided into 12 equally spaced semitones using a system called Equal Temperament. This is a system that makes it easy to move between registers and move between keys – accidentals, modulation and transposition would all be a lot weirder without it! (Note: The harmonic theory that sits behind the Equal Temperament system is actually quite awkward unless you have a good working knowledge of geometric series' and base 2 logarithms, but thankfully someone has come up with a brilliant idea that makes things a bit easier to follow – cents! Using this ingenious device we can talk about musical intervals using simple arithmetic. An octave is 1200 cents, and since there are 12 tones in the octave that means exactly 100 cents per semitone – it works best if you think about each note in the scale being at the centre of a 100 cent band, i.e. 50 either side. If you've never looked closely at the markings on your electronic tuner, now might be a good time... )

However, as with so many things in life there's a price to pay – in order to have this freedom of movement, we have to give up something called Sonic Purity. What this means in practice is that the only interval in the octave that maintains an absolutely pitch accurate relationship (in the sense of an exact ratio) is the octave itself. All the other interval relationships within the octave are something of a compromise (in simple terms, they're all slightly off-pitch, but close enough so that we can live with it). Actually, precise pitching of notes in relation to each other is a historically knotty problem for musicians, so much so that in recent years I believe there's been a number of attempts to ditch Equal Temperament and revert back to older tuning methods (the fearlessly curious amongst you might want to check out something called 'Just Intonation' – but you have been warned..). I'll need to talk about this a bit more when I get to the Greek approach, but for now suffice it to say that they did it a different way.

The other thing to say about western musical scales is that by convention we talk about them as starting at the lowest (root) note and ascending in interval increments up to the highest (octave) note. In fact we're so used to doing it that way that most people will likely be finding it hard to imagine doing it any other way – 'why would you want to?' may well have been uttered out loud by someone already... Tell you what – we'll come back to that one later.


2. The Ancient Greek approach.

( Note: before starting this section I should say that in this article I will stick to the basic concepts and avoid going into specific details about the scales as they were used by the Greeks in practice. This is for two reasons: firstly, once we get into that level of detail it is a very substantial topic on it's own – much too long to include as an add-on to this article; and secondly I feel it would be better at this stage to give people the basic idea and suggest some examples that people can try out for themselves at home, so that you get a chance to play around with the methodology. )

The Tetrachord.

Musical scales in Ancient Greece were organised around the concept of a Tetrachord, an interval equivalent to a modern Perfect Fourth. The Greeks certainly knew about octaves and used them routinely, but in situations that called for an octave note span they would simply stick two tetrachords together, along with a Major Second interval (in practice the process was of course somewhat more involved than this, but I've deliberately simplified so as to make the point about octaves).

Structurally a Tetrachord is a fixed interval of a perfect fourth (expressed as the ratio 4:3 – ratios are the key to understanding how Greek music works; and although we can usefully skirt around it for the time being, a proper explanation of how to construct the kind of scales that Greek musicians would actually have used will eventually require us to tackle it head on). The scale is then subdivided using (usually) two subdivision points, giving a four note scale equivalent to a perfect fourth. The placement of these subdivisions is another critically important factor in the process – although the two notes at either end of the Tetrachord were fixed relative to each other, the remaining notes could in principle be more or less anywhere. (Again, I've deliberately oversimplified the situation: this explanation makes it sound like a 'pin-the-tail-on-the-donkey' game - which of course it wasn't - but the technicalities governing placement of intermediate intervals will require a further article.)

There were three generic tetrachord types in common use. The best way I can describe them at this stage is to place the intervals using modern scale theory, but with the HUGE caveat that this is being done only to illustrate the general characteristics of the scales, and to allow you to have something you can play: the actual notes used – and hence the sounds you would hear – would be somewhat different from the ones you will hear when you try these out for yourselves. One final point – as you probably anticipated from earlier in the article, the Greeks thought downwards for their scales, i.e. the starting note (sometimes called the Principal note to distinguish it from the modern concept of a Tonic or Root note) was at the top.

The Diatonic scale genus consisted of (approximately) Tone, Tone, Semitone;

The Chromatic scale genus consisted of (approximately) Minor Third, Semitone, Semitone;

The Enharmonic scale genus consisted of (approximately) Double Tone, Quarter, Quarter.

( Notes: 1. Notice that I have used the word 'genus' in the descriptions; this is because each type permits many subtypes within its structure by making small alterations to the positioning of the subdivisions – the size of the first interval down from the Principal note is the determining factor. 2. As mentioned in an earlier article, we are seeing technical words that look as if they should be familiar, when in fact it is clear that they have different meanings to their modern counterparts – although by reversing the order of notes on the Greek Diatonic tetrachord and adding a whole tone followed by another diatonic tetrachord, it is possible to see how the modern diatonic major scale developed. 3. For those of a curious nature, the original source for this classification is Aristoxenus. Usual rules and warnings apply – doubly so in this case as this is an original Greek source: reading stuff like this, even after translation, is hard! )

This gives you something you can actually play! (Yay!!)

You may want to play around with these ideas – the quarter tones are gonna be fun! As a suggestion, you might want to play it on a stringed instrument, or a keyboard with a pitch wheel. Time to get your fretless or EUB out perhaps?

Hints & Tips

Don't forget to play downwards. Avoid open strings on fretted instruments – you'll understand why when you try to play a quarter tone for the first time. Use pitch bend or string bend to approximate quarter tones (less of a problem with fretless instruments of course). Music in Ancient Greece was commonly played in unison with notes sung by a singer (usually in the telling of epic tales using epic poetry), so for extra added effect you might like to try this out if you have an epic poem or two handy – can't wait!

Plenty to keep you busy again. Any questions please ask either through PM or on the other thread. Feel free to chime in with comments as well.

In the next article we'll begin looking at Rhythm. See you next time. :)



Andy

Edited by Dad3353
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Third Installment


Notation & Rhythm

Preliminaries

Most of the basic rhythmic concepts we take for granted in writing or reading music were well known to the Ancient Greeks. Note values, bars, time signatures, rhythmic phrasing, tempo and rests (but, importantly, not accents) all had their equivalents in the music of the period – albeit with different names. As always though, there are a number of key differences that we will need to discuss.


Bars and beats

On a bass players' forum it is reasonable to expect most people reading this topic to have a well developed sense of rhythm. However complex our rhythm playing gets though, it depends largely on one fundamental notion – the time signature. (Note: accenting and tempo are important considerations as well since since both have a significant bearing on the rhythmic feel of a piece, but for the time being I'm going to put them on the back burner so that we can focus on where the notes fall within the rhythm.) Once you have a time signature you have bars of a fixed length, and once you have bars you can then start subdividing them – and hence we get rhythm. By inserting a combination of notes and rests into the bar up to the total number of beats indicated by the time signature we give the bar it's rhythmic character. In this sense it has the status of an empty box into which the notes and rests are inserted. Contemporary music theory defines 7 note values (whole notes down to 64th notes), plus numerous variations (dotted notes, various odd beat subdivisions, etc.). The number of different ways these notes and rests can be organised into even a single bar of common time is staggeringly large. This in turn permits highly complex and intricate rhythms to be generated. In essence, the limits of what can be achieved in this regard have more to do with our ability to imagine the notes than with the capacity of the notation system to record them. (Note: Despite these facts, rhythms used in real music tend to be relatively straightforward and somewhat repetitive, which remains true almost independently of the style of music being written – the opening sequence of Beethoven's fifth symphony, for example, is a very simple and highly repetitive sequence of bars, as is the main riff to the Gary Moore tune 'Parisienne Walkways'. This is done at least partly to engage the listener – music would have little point if the people it was intended for were unable to fathom what was going on! In this respect typical modern rhythms have much in common with the rhythms used by the Greeks.)

Syllables and Foots (or is that Feet?)

Musicians in Ancient Greece had to work with different rules. For them, musical instruments had a subordinate role – the job of the musician was to reinforce and support poetic declamation, singing, dancing, or marching. (Note: there is evidence that there was a class of 'specialist' musicians even in Ancient Greece – virtuoso players known for their skill on their instruments; but such examples were relatively rare. Most musicians knew their place!) The notation system they developed is a reflection of this situation.

The best way to understand Greek music notation is to relate it to the many spoken or sung music forms that it was the player's job to support. Instead of beats and bars, Greek musicians thought in Syllables and Foots. The Greek language in the Ancient period was spoken using a very simple syllabic rhythm – simply put there were long syllables and short syllables, organised in such a way that the long syllable was generally around twice the length of the short one (in practice there were variations in this, but the basic point remains valid). It is possible to find this in the structure of the Greek alphabet, which contains the letters Omicron (literally, short o, as in 'hot') and Omega (literally, long o, roughly equivalent to the double-o sound in modern English, as in 'hoot') – vowel sounds, then as now, have a key role in syllabic structure.

A simple example will help I think. In what follows I am going to make the long syllable equivalent to a modern crochet, and a short syllable equivalent to a quaver. (Note: as happens from time to time, this scheme simplifies the situation somewhat in order to make the point.)

Let's take the first line of the well known Christmas carol 'Jingle Bells':-



As sung: Jin - gle bells, jin - gle bells, jin - gle all the way

Note values: quaver quaver crochet quaver quaver crochet quaver quaver quaver quaver minim

Greek notation: short short long short short long short short short short long pause


Notice particularly what happens at the end of the line – in modern notation the last note of this line would normally be rendered as either a minim or a tied crochet pair. In Greek notation there was no such thing as a tie, and neither was there a direct syllabic equivalent to the minim. The notation would have either contained a pause (only ever used at the end of a line – leaving pauses in the middle of a line of Greek verse would have interrupted the natural flow); or simply missed the last long syllable off altogether, leaving what we would see as a bar of 3:4 at the end of the line. (Because Greek musicians were often following the natural flow of speech or song in long and short syllables, variations of this kind were more common than they are in modern music writing – the notion of a fixed time signature that the musical information is subsequently slotted into is a more recent development in music notation, and would have seemed a bit strange to a musician from this period. Although the end result can look – and sound – very similar, the thought process behind it would have been somewhat different.)

The Greek equivalent of the bar was called a Foot, which referred quite literally to the rise and fall of the foot in counting time. A single sequence of raising and lowering the foot constituted the Greek equivalent of the modern bar or measure. However, the important difference between the two concepts is that counting time was for the Greeks a consequence of following speech or singing patterns, which in turn meant that it was the spoken or sung rhythm that the musician depended on to derive his or her playing sequence. The Foot was primarily a way of breaking up the pattern into convenient footfalls – in essence the music was there already; but since poets and singers did not normally feel the need to punctuate their work, the markings were developed as a form of punctuation for the benefit of the accompanists. (In effect it was the reverse of the way we do it today.)

(Note: In reading this account, it might help to bear in mind that accents of the type used as part of modern speech (and which are of course an essential element in modern rhythmic playing) were not used to anything like the same degree in Ancient Greece, certainly not in their music making. In trying to get your head round Ancient Greek rhythmic playing it might help to think about the way liturgical texts are 'sung' in many types of formal religious observance - each line of the liturgy is chanted rather than sung in the normal sense, with little or no rhythmic modulation.)


Rhythmic variations

All of the above makes it appear that all Greek music was played in the same monotonous 2:4 rhythm. Although something akin to a modern 2-time rhythm was very common in this music, there were many variations on the basic idea. I'll leave the details to a later article, but for now suffice it to say that despite being an activity designed to support and underpin other activities such as singing, dancing and poetic declamation, there were nevertheless plenty of opportunities to express oneself in different ways according to the nature of the activity the musician was involved in – for example music to be played at a sacred ceremony would have had to be very different from the music played at a drunken orgy!

As always, I hope this gives you food for thought, and if you have any questions please feel free to PM me or post into the other thread.


The next article will start to look more closely at how the Greeks developed and used scales.


See you next time. :)

Edited by Dad3353
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Fourth Installment

Scales, Intervals and Tuning

Preliminary Remarks

Having introduced the Greek approach to scales and intervals in an earlier article, we now need to begin to get down to the details of how these scales were constructed and used in making actual music. This immediately presents us with two issues:

1 In Ancient Greece, music theory was mostly studied as a branch of mathematics, and the mathematicians that carried out this study (primarily the Pythagorean sect) didn't really care what it sounded like as long as the maths looked good. Despite this fact it is important to have a look at their work, since it constitutes a significant contribution to our knowledge of music theory as known and used in Ancient Greece. In doing this we will need to do a bit of arithmetic using fractions & ratios. I'm aware that some people will find a detailed mathematical exposition tough to follow, so I'll keep the details to a minimum and will write a separate appendix-type article for the benefit of those with the necessary skills and inclination.

2. Much of what we know about the music of the period comes from a contemporary of Plato and Aristotle, called Aristoxenus of Tarentum. In contrast to the mathematical approach adopted by other scholars, Aristoxenus was more concerned with how the music sounded – so much so, indeed, that he was prepared to forego the niceties of mathematical rigour for the sake of a pleasing sound. As such, he was more in line with what the musicians of the day were doing. The downside of this is that the precise positioning of the internal intervals within a tetrachord was likely to have been a little more 'hit & miss', which makes it that little bit harder to pin them down precisely.


Tuning and Temperament

In common with the format of previous articles, I think this will make most sense if we approach it from a position that most people will be (hopefully!) familiar with, and work our way backwards from there.

Current practice – Equal Temperament

I have already mentioned the Equal Temperament (ET) method for constructing scales in a previous article. It has its origins in the late 16th Century, and in time became the standard system for generating notes in modern western music of all kinds; although numerous projects have been undertaken to recapture the perceived sonic purity of more traditional methods, ET remains overwhelmingly the tuning of choice for musicians working within the Western musical tradition.

Briefly, ET is constructed by specifying a reference point (concert A4 at 440Hz is the accepted standard), and then generating all the other notes in the audio spectrum in terms of intervals based on the semitone as a unit value, using a mathematical system based on powers of 2 (raising the pitch of a note by exactly an octave gives exactly x2 frequency; 2 octaves gives x4 frequency; 3 octaves gives x8; and so on). Although not difficult to do with a scientific calculator or spreadsheet, the calculations involved are a bit long-winded for everyday use. By taking advantage of a clever little mathematical device called Base-2 Logarithms, it can be reduced to a matter of simple addition and subtraction. Hence we have cents, so called because 1 semitone is defined as an interval of exactly 100 of them. Measuring musical intervals in cents is now pretty much universal as a way of specifying musical relationships, even to the extent that modern scholars of ancient music routinely use it in their work as well. ( Note: This is a shame in my opinion; although I follow the argument about making a difficult topic more accessible, it gives a somewhat misleading impression of how the Greeks processed the information – they were highly ingenious and creative thinkers, very good at spotting and exploiting connections across different areas of study. I have stated elsewhere in this series that one of the major problems in studying this material is to try as much as possible to get away from modern notions and methods, for the simple but hugely significant reason that the Greeks did it – and thought about it – differently. I'm aware that I'm likely to be in a fairly small minority on this one though, and so the mathematical work will use cents as well as ratios.)

The principal benefit of this approach is that it defines each semitone interval to be, in effect, musically identical to all other semitone intervals. (Exactly what that means in practice – not as obvious as it might seem - will be explained more fully in the appendix article, but for now suffice it to say that doing it this way provides great utility, making modulation and transposition in particular much simpler.) It is such an integral part of our everyday lives as musicians that many of us find it hard to conceive of doing it any other way. However, as will be demonstrated in the appendix article, this utility comes at a price – in order to have this convenience we need to forego the sonic purity that comes with the system it replaced, namely Just Intonation (JI). ( Note: I have deliberately simplified the situation here: the transition from Just Intonation to Equal Temperament went through numerous phases, with a variety of attempts being made to generate a compromise that would facilitate modulation without doing too much injustice to the purity of Just Intonation – e.g. J.S. Bach used a system called Well Temperament (widely acknowledged as the main forerunner of modern Equal Temperament) to write the 'Well Tempered Clavier'. However we won't be looking at any of these details - all of them were devised to overcome the same specific problem inherent in the Just Intonation approach. Equal Temperament, once it became the tuning method of choice, effectively rendered all other methods redundant for all practical purposes.)


The Western Ecclesiastical tradition – Just Intonation and Pythagorean tuning

Unlike ET, which is essentially an exercise in geometric progressions and Base-2 logarithms, Just Intonation works purely through ratios. The benefit of doing it this way is that the ratios used to create the intervals reflect the natural harmonic series, and as such the intervals have inherently better harmonic integrity than ET – simply put, they sound more 'in tune' when compared to intervals generated using clever but ultimately compromised Mathematics (although to be fair some of the pitch differences are very small and can be hard to spot even for the trained ear of a professional musician).

Just Intonation as used in the early Western musical tradition uses the Perfect Fifth (a ratio of 3:2) repeatedly to generate a series of intervals that eventually yields a chromatic scale (in the modern sense, that is) of 12 notes.

Without getting too far into the maths, here's how it works:

Let's start with Middle C at 256Hz; (not what you get for this note from Equal Temperament, but then again we're not using Equal Temperament...)

Applying our fifth ratio of 3:2 gives us a G at 384Hz, a fifth above the root;

Apply again to get (3/2) x 384 = 576Hz (which is a D). At this point we have gone above the octave (at 512Hz), so halve the result (i.e. drop an octave) to get 288Hz (which is a major second) ( Note: the octave as a ratio of 2:1 is universal and goes back well before the rise of the Greek civilisation);

And so on...

Modern musicians who are familiar with this process will most likely know it as 'cycle of fifths' tuning, but historically it is more correct to call it Pythagorean Tuning. As a tuning method it was definitely known to the early Pythagoreans as long ago as the 6th Century B.C. (and as a mathematical process it almost certainly predates even that ancient date).

The Pythagorean tuning method pretty much guarantees a series of sonically pure notes. There is a problem however: despite the acknowledged sonic purity of the intervals it generates, repeated use of the Pythagorean method eventually gives rise to a tuning error that manifests itself at the #4/b5 point as a Wolf Fifth (strictly speaking the phenomenon that arises through the mathematics is something called a Pythagorean Comma – it is the attempt to resolve the comma that creates the Wolf Fifth). In a key that doesn't require this note there isn't a problem; but as soon as you try to use or modulate to a key that does, it sounds catastrophically out of tune. This in turn places strict limitations on the range of keys that can be accessed from a single collection of 12 notes. (Interestingly though, all the standard ecclesiastical modes would still have been available since the modal system of the time was based on moving the start and end points of a single parent scale to create the modal variations, which could of course be achieved with a single set of diatonic intervals. Medieval music is a little outside my area, but I would speculate that this could help to explain the widespread use of modal writing in that period.) It is the need to be able to move between keys without having to deal with Wolf Fifths that led to the various compromise methods referred to above, leading ultimately to the Equal Temperament system that most of us use today.

None of this would have meant anything to early Greek musicians though. Although they would have been aware of the Pythagorean tuning method, the roots of their musical system originated in a different place.


Greek methods and scales – the Tetrachord.

'If they knew about Pythagorean tuning, why on earth didn't they use it?' On the face of it this seems like a perfectly fair question to ask. In fact there are several very good reasons why they didn't;

1. By the time the Pythagoreans worked this method out in the 6th century B.C., Greece already had a well established musical tradition that had been developing for several hundred years. Why would they want to ditch it for this? For one thing the basic concords of 4th, 5th and Octave were already widely known by the time the Pythagoreans got their hands on them (see below).

2. The Pythagoreans were mathematicians, and as such were not particularly bothered about music as a performance activity. This would not have endeared them to the musicians of the day, which in turn would have meant them having to work that much harder to disseminate their ideas.

3. The Pythagoreans were geographically remote from the rest of Greek civilisation, occupying an area of what is today part of southern Italy – many Greek musicians would have hardly heard of them until some time after the initial formation.

Note though that the Pythagorean comma would not have been one of these reasons. Being able to change key in the modern sense requires a sufficiently well developed sense of keys for it to make sense to do so, which in turn requires an understanding of and feel for Absolute pitch. Greek notions of pitch were not well developed enough for this to be an issue – so long as the music could be encompassed broadly speaking within the range of the human voice, that would have been enough. At best the Pythagorean comma would have had the status of a mathematical curiosity. ( Note: Again this is something of an oversimplification, but it does convey the main point.)

A brief recap on Tetracord basics:

A tetracord (literally 'four notes' or 'four strings' – which on some instruments effectively meant the same thing) is a type of scale spanning an interval of exactly a Perfect Fourth, expressed as the ratio 4:3 (= 498 cents against an ET value of 500).

The outer notes are fixed or 'standing', while the inner notes are moveable.

There are many combinations mathematically possible and quite a few variations in use during this period, but they are commonly classified into three broad types:-

Diatonic genus – 'through the tones', reading down from the top or Principal note we get (approximately) tone, tone, semitone

Chromatic genus – 'coloured' , giving minor 3rd, semi, semi

Enharmonic genus – 'in harmony' or 'in tune' giving major 3rd, quarter, quarter.

( Note: Ancient scholars offered a variety of further subdivisions, with as many as seven being suggested by later writers. However the 3 main genera are the basis for classification by all ancient authors. Of the three, the Enharmonic is widely accepted as the earliest and purest, followed in turn by the Chromatic and the Diatonic. Even at the height of their creativity during the Classical period - 5th and 4th centuries B.C. - both theoreticians and musicians alike held the Enharmonic as the purest and most technically demanding genus. It was only in the later period - probably partly under the influence of later Pythagorean scholars (the Pythagoreans had been adherents of the diatonic from an early stage in their existence) – that the Diatonic genus gained an ascendency that it subsequently never lost. Had things gone differently, modern Western music could have sounded very different!)

Technical elements

Tetracords could be joined together and an extra tone added (the tone was easy to generate by tuning up a fifth from a known pitch and then down a fourth, or vice versa) to give a total range equal to a modern octave. The extra tone could be inserted above, in between or below the tetracords. This was by no means universal however, and there is plenty of evidence indicating instruments that clearly only had the capacity to play four notes and were thus designed to be used for playing within the range of a single tetrachord (certain types of Phorminx, for instance), as well as several scale types known to have been used that differed from the octave as just described. As we shall see below in the paragraph dealing with the pitch range of early Greek music, the system was much less formalised than talk of tetracords and octaves as working units would lead a modern musician to believe - in the early period at least.

In accordance with the musical practice of the day, a distinction was made between concordant intervals – fourths(4:3), fifths(3:2) and octaves(2:1); and discordant intervals – pretty much everything else. Remember that harmony in the modern sense did not exist in any meaningful form. It was pairs of individual notes played sequentially that gave rise to these relationships.

The tetrachord system lay at the heart of Greek music, and was the standard scale format from an early date, well before the start of the Classical Period. Very early Greek music was a little simpler, dividing the Perfect Fourth into a 3-note form called the Tricord. In situations where tricords were joined as explained above, the resulting octave scale would have been Pentatonic in form. The fourth note would have been added over a period of time as musicians felt the need to have more expressive tools at their disposal.

As has been hinted above, the range of Greek music was very small – less than two octaves. The notion of an octave format that can be extended in both directions to the limits of human hearing (roughly 20 Hz – 20kHz) is a much more recent development, made even easier by the advent of Equal Temperament. To Greek musicians using instruments to support vocal expression the instruments themselves needed only the ability to match the range of the human voice as it was used at the time (modern human singing encompasses a somewhat larger range than would have been the case in ancient Greece). In effect the concordant notes form what could be described as a sort of primitive Absolute Pitch (although the precise pitching of notes would have been a little Hit-and-Miss across such a large geographical region since there was no way to guarantee accuracy). In practice this would have manifested itself as a central pitch (in some ways not unlike a modern Middle C or Concert A), with a range up and down whose precise extent was dictated by specific needs of the performance, but which was never more than an octave in either direction and usually somewhat less. In early forms the standard approach would be to specify a tetrachord plus a few notes at either end. Here are a few examples whose names will look familiar but whose note sequences will most definitely not! (For convenience they have been organised so that the main tetracord, where complete, runs from E to A – this should not be taken as indicating the actual notes used):

Ionian: E, E+, F, A, C, D
Dorian: D, E, E+, F, A, B, B+, C, E
Phrygian: D, E, E+, F, A, B, B+, C, D
Lydian: E+, F, A, B, B+, C, E, E+
Mixolydian: E, E+, F, G, A, A+, Bb, E

These scale types are attributed to a scholar by the name of Damon, and are reported as descriptions of scales of much earlier origin at the time he was writing (5th Century B.C.), and which would therefore predate by some way the formalised scales known to the Pythagoreans or to Aristoxenus. If you've been paying attention you will have noticed that they are all centred around the Enharmonic tetrachord E, E+, F, A, which ties in with the prevalence of that genus in Pre-Classical music of the period. There are several points worth making about these scales:

1. The actual pitch values of the individual notes used in this scheme are not known for certain: they are best thought of as being working scales that musicians would have actually used, and the precise pitching of the notes would almost certainly have been down to the musicians of the regions from which they originated;

2. Despite their very strange appearance to modern eyes they would have been surprisingly easy to replicate and tune accurately: if we take one of these scales more or less at random, and remind ourselves that musicians would have found it very easy to tune in fourths and fifths, we get the following as a possible method available to the musicians of the day (it can be done several ways but the following seems like a good candidate):-

Phrygian: Tune A (Principal note); Tune E (fourth down from A); Tune low D (fifth down from A); Tune E+ and F according to enharmonic genus; Tune C (fifth up from F); Tune high D (fourth up from A). (Note: Wherever possible later notes are tuned directly from the principal note so as to minimise cumulative tuning errors – this approach would have been known to the musicians of the day.)


3. The Mixolydian seems to be a kind of hybrid scale whose precise origins are unclear; it is also the only scale in this group that has a third internal note (G) in the main tetracord (strictly speaking this would need to be called a Pentacord to reflect the 5 notes, but there seems to be no evidence of that term being used).

4. These names will be well known to most modern musicians as Modes (which is actually where this entire series of articles started from). They were referred to by the Greeks as Harmonai, which translates as harmonies, atunements or tunings. The word Mode derives from Latin, which has 'mood' as one of its connotations. Although not a direct translation from any Greek word, it captures the notion (widely discussed amongst the Greeks themselves) that the different scale types could evoke differing emotional responses from the listener. ( Note: The modern equivalent of this is the way major and minor scale types are often identified with certain moods or states of mind...how many times have you heard a minor scale sound described as 'sad' or 'reflective'?)

5. One needs to emphasise the very early nature of this treatment – over time notions of scale evolved and changed, so that Pythagorean scholars such as Archytas (contemporary and friend of Plato) came to different conclusions, Aristoxenus put an altogether different interpretation on them; and Ptolemy (2nd century A.D.) revised the scheme yet again, attempting to reconcile the Aural tradition of Aristoxenus with the mathematical approach of the Pythagoreans. But we have to start somewhere, and the Damonian commentary is the first known use of these specific regionally-based names.

Reference has been made in an earlier article in the series to the identification of these modes with the native characteristics of the regional tribes from which they get their names. Objective evidence of this association is not always as clear as we might like – there are certainly references in the literature to individual tunings having geographical associations with the regions they get their names from; and there are numerous allusions to certain melodies evoking the 'spirit' of a particular region. In general though it is probably not a good idea to pursue the analogy too far, not least because the notion of a tribal or regional mood or temperament that can be reflected in its music is at best somewhat subjective, and at worst probably a little fanciful. Whilst undoubtedly present, the association is likely to be somewhat looser.


I think that'll do for now. There's plenty more to say on this subject – indeed part of the difficulty in writing this article involved deciding what to leave out so as to make it of a reasonable length. However that will need to wait for another article.

There will be an appendix article covering in greater detail some of the mathematical notions raised in this article, which will appear over the next few days.

The next main article will cover perhaps the most elusive aspect of this whole are of study, namely the notion of Melody. There is almost nothing that survives to tell us how these scales would have been used by the musicians of the day, and much of what we believe has the status of highly educated guesswork. Nevertheless we need to delve into this tricky subject.

There is a very substantial amount of detail in this article; as always, please feel free to ask questions.

All the best for now. :) Edited by Dad3353
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Appendix to Installment 4 – the mathematics of musical intervals

Equal Temperament tuning:

Notes in the Equal Temperament system are derived from a reference source (identified as a frequency in Hertz) using a calculation based on powers of 2. Intervals are defined in terms of cents, where an octave is 1200 cents and a semitone is 100 cents. In this sense the intervals are equally spaced by definition. In terms of relative frequencies the relationship is somewhat more complex, since the actual difference in frequency depends on the register – the higher the register the bigger the frequency range between corresponding notes.

In 12-tone Equal Temperament, pitch values are derived for the 12 notes of the western scale relative to a fixed reference frequency, F(ref), of 440 Hz (A4).

The algorithm is as follows:

F(t) = F(ref) x 2 (n/1200), where F(t) is the target frequency and n is the interval in cents

In this form it can be used to find the frequency of a note given its interval in cents above or below the reference.

Example: To find the frequency of the note E, a fifth (700 cents above concert A at 440Hz)

F(t) = 440 x 2(700/1200) = 659.26Hz


To find value of the interval in cents between the target frequency and the reference, it would be used in this form:

n = 1200 x Log2(F(t)/F(ref))

Example: To find the number of cents in the interval between A4 at 440Hz and E5 a fifth above it in Pythagorean Tuning (440 x 3/2 = 660)

n = 1200 x Log2(660/440) = 701.96 cents


Just Intonation.

Strictly speaking the term refers to any tuning system where the intervals are obtained using calculations based on whole-number ratios. The following results will be obtained using Pythagorean Tuning, based on repeated applications of a ratio of 3:2. This was the standard tuning method in the Western tradition up to the end of the Medieval era.

( Note 1: The following calculations are carried out using a starting note of 440 Hz for purposes of easy comparison with the same intervals derived using Equal Temperament. In reality this would not have happened in a Medieval tuning system, much less in Ancient Greece!)

( Note 2: Where a calculation takes the target note outside the octave A4 – A5, the resulting value is multiplied or divided by 2 as necessary in order to bring it within the range 440 – 880Hz. The octave as a 2:1 ratio is universal in all tuning systems.)

A = 440Hz


E = 440 x 3/2 = 660Hz (702 cents) - Perf 5th


B = 660 x 3/2 = 990 /2 = 495Hz (204 cents) - Maj 2nd


F# = 495 x 3/2 = 742.5Hz (906 cents) - Maj 6th


C# = 742.5 x 3/2 = 556.9Hz (408 cents) - Maj 3rd


G# = 556.9 x 3/2 = 835.3Hz (1110 cents) - Maj 7th


D# = 835.3 x 3/2 = 626.5Hz (612 cents) - #4th


At this point there are different routes for completing the procedure, but the convention is to obtain the remaining intervals by going downwards in 5ths, since doing so allows the perfect 4th to have a ratio of precisely 4:3 – an interval known to have been important to the Greeks.

(Procedural note – dividing by 3/2 is mathematically equivalent to multiplying by its inverse - 2/3)

A = 440Hz


D = 440 x 2/3 = 293.3 x 2 = 586.7Hz (498 cents ) - Perf 4th


G = 586.7 x 2/3 = 391.1 x 2 = 782.2Hz (996 cents) – b7th


C = 782.2 x 2/3 = 521.5Hz (294 cents) – b3rd


F = 521.5 x 2/3 = 347.7 x 2 = 695.3Hz (792 cents) – b6th


Bb = 695.3 x 2/3 = 463.5Hz (90 cents) – b2nd


Eb = 463.5 x 2/3 = 309 x 2 = 618Hz (588 cents) – b5th


At this point we have the 12 notes of the chromatic scale. Particular note should be made of the #4th and b5th intervals. In Equal Temperament these are defined to be the same note. Using Pythagorean Tuning, however, there is a noticeable difference:

D# = 626.5Hz (612 cents)

Eb = 618Hz (588 cents)



A trained musician can spot a discrepancy of around 5 cents. These values put the notes 12 cents either side of the Equal Temperament value of 600. More importantly, they are 24 cents apart. This discrepancy is called a Pythagorean comma, and is the reason that modulation is such an awkward proposition in Pythagorean Tuning.


Greek concordant and discordant intervals

Concordant intervals played a very important role in the music of Ancient Greece, since they were a prerequisite in defining the basic structure of Tetracords and Octaves, and were used by musicians to tune their instruments (as has been demonstrated in the main article). Octave (2:1), Perfect Fifth (3:2) and Perfect Fourth (4:3) were as important to the ancients as they are to us. The Major Third, however, (an important concord in modern music) was not. Although it was clearly known and used as an interval in both Diatonic (as two consecutive tones) and Enharmonic genera, it was one among numerous intervals possible in both forms.

The whole tone (9:8) was also well known, but in Greece was not used as a building block in scale construction the way it is today. It was, rather, seen as a consequence of putting two tetracords together to make up an octave. The following calculation makes the point:

Tetracord + tetracord = 4/3 x 4/3 = 16/9 (adding intervals means multiplying ratios)

Octave = 2/1 (= 2 of course)

Question: what interval is needed to fill the gap between the sum of two tetracords and the octave?

Answer: Octave – two tetracords = (2/1) / (16/9) = 2/1 x 9/16 = 18/16 = 9/8

(subtracting intervals means dividing ratios) Edited by Dad3353
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Brilliant!!!!
You got my attention and I'm going to have to read and take note of these things in detail! But Ancient history and cultures are a definite brownie point here. I've had a fascination with the culture, lifestyle and mythologies of the ancient mediterranean. Sumer, Babylonia, Mesopotamia, Greeks, Macedonians, Egyptians. The lot, when I finished my Archaeology A Level and moved into music for good I've since struggled to find ways to apply the knowledge I got from studying archaeology and the history of cultures such as these.

Wish I found this topic sooner, would have been my night sorted but I got to absorbed in the manga I was reading... whoops.
I'll read through this full on after college tomorrow/today and give some feedback that's actually useful, I've barely skim read it and such information deserves more!!

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Brilliant!!!!


You got my attention and I'm going to have to read and take note of these things in detail! But Ancient history and cultures are a definite brownie point here. I've had a fascination with the culture, lifestyle and mythologies of the ancient mediterranean. Sumer, Babylonia, Mesopotamia, Greeks, Macedonians, Egyptians. The lot, when I finished my Archaeology A Level and moved into music for good I've since struggled to find ways to apply the knowledge I got from studying archaeology and the history of cultures such as these.

Wish I found this topic sooner, would have been my night sorted but I got to absorbed in the manga I was reading... whoops.
I'll read through this full on after college tomorrow/today and give some feedback that's actually useful, I've barely skim read it and such information deserves more!!



Cheers. Nice to know people are finding it useful. :) Got a favour to ask though: I'm trying to keep this pinned thread just for posting the main articles if I can. There's a related thread in this forum that I'm encouraging people to use for comments/debate. I check both regularly so anything you post there will get a response. TBH I've been a bit taken aback by how many people do seem to be reading it. Thanks again for your support. Feel free to contribute! Edited by Dad3353
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  • 2 weeks later...

Hi Andy, thankyou so much for this brilliant and informative series of installments.



I have just read one and two and now I need to plug in my keyboard, as I don't own a fretless, for quarter notes.

Back to inst 3, speak soon
Steve.



No worries mate. Next one will be out in a few days. Edited by Dad3353
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Fifth Installment


Melody

Preliminary Remarks

Of all the elements of music from Ancient Greece, this aspect is by far the most difficult to get any sort of handle on. Whilst we have a relatively good idea about scale structures, phrasing and rhythmic devices (based on a fairly substantial body of source material from the period and the centuries following), there is almost nothing that survives of the music that was actually played and listened to. The body of surviving documents numbers just 51, which between them encompass the entire development of Greek musical culture from around the 11th century B.C. right through to the early church in the 4th century A.D. - a span of some 1500 years. Of those, barely a dozen have come down to us from the Greeks themselves, with most of the remainder being either Roman transcriptions of earlier works now lost, or else later compositions intended to be 'in the style of' earlier works or composers. Many of the 51 items are no more than fragments a few bars in duration. As if that wasn't hard enough, we have very little to go on beyond educated guesswork and a degree of commonsense as regards dynamics, tempi, and precise pitching of notes – remember that the Greeks had no real notion of either key signature or register in the sense that we think of such things today.... Hopefully you see the scale of the problem!

The reason this is such a big deal is that, of all the elements of music in any culture it is the melodic ideas that tell us most about them. Scales and rhythmic devices are the tools of the musician's trade – which was as true of the Ancient Greeks as it is for us. It is in the flow of their melodies that we find out what their music was like to listen to. To emphasise the point, I'm going to conduct a little experiment using somewhat more recent music:-

Here's a few short excerpts from some well-known lyrics...

1.The long and winding road, that leads to your door........
2.The hills are alive, with the sound of music.....
3.Rule Britannia, Britannia rules the waves.....
4.All of me, why not take all of me....
5.Spiderpig, spiderpig, does whatever spiderpig does...


O.k., hands up everyone who sang along at some point?

Frankly, I'd be a little surprised if there was anybody who didn't hum or sing at least one of them... which of course is the whole point of the experiment. Whether you actually like the tunes or not is essentially irrelevant – you know them (or some of them at least!), and as such you can use them to help explain to a visiting Martian how modern western music sounds.

The difficulty in trying to do the same with Ancient Greek music is that not only do we not have a great deal to go on in terms of content, but we're really not sure how the ones we do have might have sounded in performance. (Note: in this series of articles I have gone to some lengths to avoid the more technical elements of music theory in Ancient Greece, but the plain fact is that it is an enormously complex and confusing subject – so much so that many of the scholars of the period disagreed with each other about what was going on, where it was going on and when it was going on: in addition to which notions of scale construction, harmony and melodic expression shifted constantly throughout the period, to the point where it is actually impossible to make a categorical statement of the 'Ancient Greek music sounded like this..' variety – the best we can do is to say something like '...during that century in that part of the country we think it might have sounded something like this...')

Although it is not possible to recreate the exact sounds people would have listened to, it is nevertheless possible to form some sort of picture about how ancient tunes would probably have been written.

Tonic notes and tonal centres

As has been said in an earlier article, the basic building block for the Ancient Greeks was the Tetrachord, a sequence of 4 notes covering an interval of a Perfect Fourth. Scales were constructed from combinations of Tetrachords and additional notes. For example, the Dorian scale from the Damonian commentary (Installment 4) has the notes:

D, E, E+, F, A, B, B+, C, E

Structurally, this has 2 Enharmonic Tetrachords (E, E+, F, A and B, B+, C, E), separated (disjunct) by a whole tone interval (A->B ) and an extra note at the bottom (D).

I also discussed the notion of the Principal note that sits at the top of each tetrachord. As part of that discussion I was careful to distinguish it from the modern notion of a tonic note. In modern harmony the tonic is a critical component in melodic construction as it is the tonal centre from which all other notes in the scale get their identity, and is the thing that listeners home in on when making sense of the musical harmonies (which they do even if they're not aware that they're doing it). A change of tonic note denotes a change of key, which in turn entails a change in the combination of notes used in the scale.

For the Greeks, however, the tonal centre appears to have been a somewhat more flexible notion. There is evidence that it could be placed at any of a number of points in the scale, with positions near the top or near the bottom appearing as common options. This would have had consequences for the character of the music heard – by placing the tonal centre near the bottom, for example, the music would have had most of it's melodic content pitched above that tonal centre, and would also have contained a preponderance of notes from the lower part of the scale (the reason for this characteristic will be clarified shortly). Fixed notes from the tetrachords would have been used for this purpose, so that in the Dorian scale above, the low E would have been used as a tonal centre, as well as the top E (and perhaps the B as well). (Note: In this respect the scheme begins to look a little like modern modal scale theory, where a single set of notes is used with a shifting tonal centre to create the modal variations from a single parent scale.)


There are instances in the fragments of different tonal centres being used within the same piece. A modern musician would interpret this as a shift involving altered emphasis for the various notes within the scale:

Example – playing a passage in A Aeolian would have the root on A, with D as a fourth and E as a fifth, and a flat third at C – if the harmony then moves to G Mixolydian, the root changes to G, the fourth to C and the fifth to D, with a major third at B. If you want to hear it in action, Blues guitarist Robben Ford (for example) is a very skillful exponent of this technique.

A Greek musician would not have thought about it in this way: shifts of tonal centre appear to have been used to provide contrast between different sections of the piece. For example a piece might start with a low tonal centre and hence contain notes mainly from the lower range of the scale (perhaps to impart a sense of gravity); and then by shifting the tonal centre to the top for the next section, the music acquires a lightness that would provide a contrast to the darker tone of the previous section.

The effectiveness of this procedure has to do with the function of the tonal centre in Greek melodic writing. In the musical passages contained in the fragments, a melodic sequence tends to begin and end with the tonal centre note (although there are variations at the beginning in some passages, the vast majority end with either the tonal centre note or a note a fourth below it – where the end of the passage is available, of course...)


Melodic structure

Although the inner detail of Greek melodic writing is lost, there are some general patterns that can be discerned (Note: these are not hard and fast rules, but statistically common patterns that modern commentators have discerned, and which are thought to be indicative of a methodology in the melodic writing of the period – for such methods to have survived in musical writing over such a long period of time, there had to have been rules or standards that the composers would have assumed in their compositions.)

1. Greek composers tended to prefer melodic ideas to have a rising quality from the start, which subsequently falls back down towards the starting pitch. This would have entailed a tendency towards a low or lowish tonal centre at the start of the section.

2. There is a distinct preference for small intervals between successive notes. Whilst the surviving fragments show evidence of leaps as big as an octave on rare occasions, around 2/3 of all the note-to-note movements are either static (i.e. same note) or adjacent (i.e. nearest available note). This would have given the melodic sequence a sinuous, weaving quality. Where such large intervals were used, the general feeling is that it would have been done for a specific musical effect rather than simply as a continuation of the main melody: it may even be that some of these instances were conventions (and hence expectations by the listener) for indicating specific points in the music – the end of a section perhaps, indicated by a substantial drop in pitch.

3. There is some evidence, especially in later works, of scale changes within a piece (not modulation in the modern sense, but a clear alteration to the notes nevertheless). This could have been achieved in one of several ways – for instance a change of genus from, say, Diatonic to Enharmonic whilst keeping the fixed notes in their original positions; or perhaps an alteration to the positioning of the tetrachords from conjunct to disjunct or vice versa.

4. As to dynamics and tempo there is very little to go on. (Although Greek musicians and their audiences clearly had a well developed sense of the importance of such characteristics in conveying an appropriate character to the music so as to make it suitable for the occasion at which it was played, it is almost impossible to get anything more than a vague indication as to the music's dynamics and speed beyond wishy-washy terminology such as 'vigorous' or 'gentle' or 'grand'.)

5. Phrasing is another area that is hard to get much of a handle on, simply because the surviving fragments are too short to get much of an idea what the complete texts might have looked like in terms of phrasing. In general, however, Greek composers appear to have disliked melodic repetition – which puts them immediately at odds with modern compositional technique, where composers often take great delight in exploring what can be done with melodic ideas often no more than four or five notes long – not to mention the sort of techniques that are pretty much universal in popular songwriting. The likely exception to this is the accompaniment of epic verse, where the nature of the poetry more or less requires the musician to repeat lines, sometimes at great length.

6. Accents of the kind that appear in modern music were not used by the Ancient Greeks. They did have a resource for providing emphasis, however. Modern European languages (including modern Greek, by the way) use something called Stress to emphasise certain syllables in normal speech, in much the same way as we use accents to emphasis certain key points in music. Ancient Greek did not use this technique, and instead used a pitch-based method (in much the same way as many IndoChinese languages). When following recitation, they appear have developed a musical formalisation of this pitch-based speech method.


There are several other elements that have not been discussed here, such as chromaticism, grace notes, drone notes and vocal/instrumental harmonic interplay (all of which appear to have been encountered by ancient commentators). The thinking behind this is that these constitute somewhat more advanced elements. The main thrust of these articles (certainly at this stage) is to convey some impression of the basic elements of Ancient Greek music.




At this point we have gone about as far as we can go without getting into a more serious analysis of Greek musical Theory and Practice. At some point in the not-too-distant future I will prepare an article on the various instruments of the period (which actually turns out to be both more varied and more sophisticated than is immediately apparent, including for example a remarkable keyboard instrument whose basic operating principle is surprisingly similar to the modern church organ).

Unfortunately I cannot be specific about when it will appear, as my various business and teaching commitments are making it increasingly hard to produce these articles at anything like their earlier rate. (Each article requires a good deal of research, preparation and checking, and I'd rather get it right and let it take as long as it takes.)

Longer-term, I'm planning to continue to produce articles on an occasional basis over the coming months. I'd be happy to take suggestions as to which topics to pursue in greater depth.


See you next time. :) Edited by Dad3353
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