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I post this as a new thread because I don’t want to pre-occupy anyone from Stephen's thread and composition of his variations on La Folia.

I have done years ago a set of variations for bouzouki on this Folia theme, but they're lost amongst my manuscripts.

The last two years I've been working on a big song cycle called "LIBYAN SEA TALE" where I thought of using modulations as instrumental interludes, and one of the themes that came first into my mind was La Folia again. I wanted something that could take me round the clock in terms of tone steps and as Handel is one of my favourite sets I started with his setting.

So my aim was to go quickly and smoothly from Dm to Em and imo this can be done as early as from the 1st or 2nd bar of Handel's setting, if you agree. Bars 17 - 18 in this pdf behave as if the 2nd triad in Dm is not diminished but Em itself. I marked the harmonic understanding with Roman numerals for both tonalities, and after bar 19 in the new tonality only. The change sounds fairly smooth to me.

What now remains is to write my own variation instead of repeating Handel's.  :-)


Perhaps what Stephen says about a competition on this theme could take ground and give all sorts of nice results.

Something like a "Composers Forum contribution to a Musical Cathedral", as the great cathedrals took centuries and many architects to be completed, so is Folia a cathedral still in progress.

How about it Gav? (After this summer preferably)

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I appreciate your efforts to find these three examples. I grew up with The Beatles. I watched both of their appearances on the Ed Sullivan Show. I say watched because there was so much screaming that it was hard to hear. I have never been a big fan. I know that to say that is tantamount to sacrilege. How dare I. Sure, I like some of their songs, but they were surely not gods. The things you mention about And  I love Her, are probably due more to Gorge Martin than anything else. Before too long, all they cared about was making money, and they made more of it than anyone before them by a long shot. 

As for the other two, I'm sorry you are offended by them. but they surely don't care. They were (are) in it for the money. I can't tell you how many young people I've been around who all they want to do is form a band, make a record and make money. No art is involved. It's all about the money.


I agree Bob, I tend to forget about G. Martin and his decision making and musical work on the songs. Do you think this was at his suggestion? Anyhow, it seems to work well musically for me. I don’t know how to explain it really, it sounds a lot less pretentious to my ears than the other two examples.

Yes, now a days, I think it is only about money in rock and pop, but it was not in the sixties with everyone, I'd like to think.

There were still alive some honest intentions. The catastrophe begun imo, when rock and pop were fused with disco.

No, I think Elvis was the beginning of the end. He was the first really big money maker. There were other big name singers in the late fifties and early sixties, of course. But Elvis over shadowed them all. So much so that The Beatles made a special trip to meat him. By all accounts, they were unimpressed with each other. By the time of their last tour of America, The Beatles were already millionaires. And that tour made everyone connected with it rich, even while the band only made a fraction of what the tour made overall. 

When a record company signs a band, the band get up front money and contract to produce so many albums in a certain length of time. The band has to pay all the production costs out of their up front money. It's not unusual for a band to have a popular album, but not make any profit because the recording studio took all the up front money and then some, just to make the album. The company gets their money no matter what. The band? Not so much. 

Dave, I don’t have a problem with being subjective, in some sense any opinion on abstract matters could be so.

This thread is about modulations in general with a hope that a few of us can provide an insight or reference of how they understand them and how that understanding can affect their own work or other people's work.

So, again I can only talk about myself in this line, in an effort to separate some things subjective from some others less so:

If it is not clear yet from what has preceded so far, to me whether a change of tonal centre by going there directly is in good taste or bad, , I think I made clear, the Beatles example is in good taste to me, the other two in bad taste for the subjective reasons I mentioned.

But you will observe that I don’t use the word modulation, only "change of tonal centre". I do this because I define all three as non-modulations. It would not be logical to define them as such if by the word "modulation" I define a different well-established compositional technique which achieves the change that I want in the way that I want, i.e. by technical but also inspirational musical work that takes me to the new tonal centre gradually, and which all three examples do not display (a change of mode added to the change of tonality, I consider a bonus, like in the Greek dance example above). To change key suddenly (in however a good or bad taste) is to me a decision of choice, not a technique as I have defined it, and that is objective, as there is not such technique involved in whatever abrupt change of tonality takes place.  You may like or dislike all three, but they are not the kind of thing I look for in this thread, and as far as modulation is concerned, I can still call it a lazy approach, but perhaps taking into account Bob's addition that it is a stylistic element, not a modulation as found in art songs, cause these are pop songs. I hope to deal with questions on style much later in this thread, 'cause we are still in the beginning, with definition of modes, rather than extended complicated instances of modulation.

So, starting from Bob's remark, that they do not display laziness but a stylistic element, I included them, as examples of what I like or dislike as "stylistic elements" only, not as technical modulations.

So, to make it clear beyond doubt to you, this thread is about technical, gradual modulation. Do you have anything to offer in that department? Either yours or an insight into someone else's work.

Dave Dexter said:

Exactly, different cultures and tastes and backgrounds lead to our different interpretations. As long as you're not stating objectively that these modulations are terrible we have no real disagreement.

Is that modulation an example of commercialism to impress the masses? It's surely a pretty esoteric one, if so!

The obvious Schoenberg interpretation is the difference between a jarring move and a more evolved, refined journey to the same destination. And the disagreement there simply lies in our subjective reactions to the same modulation. I didn't find it the musical equivalent of jumping from a building, but I'm happy to mess about with chords and modulations that are deliberately a bit jarring (not that I think the Please Release Me modulation is jarring!)

Socrates Arvanitakis said:

Dave, as I said, they give away my likes and dislikes. But as examples I think they still stand the way I describe them.

1 I am a life-long Beatles admirer-not trying to undersell anything.

2 We come from different cultures obviously, so what to you is "now or never" to me is the original "o sole mio" in its Neapolitan version which every mandolinist in the neighbourhood use to play when I was a kid. No transpositions up a semitone in those evenings. So, yes, it does make me sick to see how far commercialism is prepared to go to impress and sell to the crowds.

3 I refer you to the Schoenberg quotation above. Modulating abruptly from F to B is of course possible (everything is possible). But what did he mean do you think, (Schoenberg) by referring to your condition when you arrive there in the ground, if you have chosen to jump there instead of using the staircase or the elevator?

Hi Em,

I just came in wanting to post in another thread, but I saw your post first. I am pressed for time as I am preparing to travel, but very briefly I can say first, thanks for your interest in this thread which I hope will lead us somewhere in the way of discovery for the benefit of all of us, and secondly that (very briefly again) the primary sources for me in ancient theory are the writings of Aristoxenus and his resume done centuries later by Cleonides.

For how ancient theory developed and became the basis of modern day systems I study mainly from d' Erlager (in French) and other sources in Greek which are quite numerus. I think Aristoxenus' and Cleonides' writings have been translated into English, I will come back on that in future.

But referring specifically to modulations, I thing re-tuning one string (and having two or more instruments available)was the easiest way in practical music.

As to the enharmonic genre it was abandoned as indeed very difficult, especially for singers to perform correctly.

you see, its basic tetrachord was: Diesis-Major third-Diesis.

"Diesis" in modern Greek means "sharp" and it is used to raise by semitone one given pitch. But in ancient Greek when this term was invented it meant raising/lowering the pitch by quarter tone so a Lydian 4chord would be:

C - D 3 quarter tone flattened - E 1 quarter tone raised - F.

I hope you can see the difficulty involved and the decision of really able musicians to abandon this genre early.

In considering 4chords in general with regard to how they are still practiced/realised in all eastern systems you have to think of these concepts:

  1. They always cover the range of the perfect fourth (otherwise they are considered by different names as 3chords, 5chords, etc)
  2. they always contain 2 fixed pitches (estotes phtongoe) and two movable pitches.
  3. The pitches standing a perfect forth apart are the fixed ones. The movable pitches are between them and their movement or measured intervals can be of any possible value.


I hope we continue this discussion in the near future.


Hi Em,
Sorry for my rush reply a few days ago, I was in a hurry. At the moment I am not, but I already experience very gross problems in my internet connection, very slow indeed even to change or refresh a page or a screen, so it doesn't look good for me for the next few months.
Because of this I am not able at present to follow your links at present but I will do so if and when the situation improves a little. :-)

But since it looks at present that only we two are taking an interest in these matters and having in mind that this thread started with modulation as its main interest but developed into a general discussion of modality, I will probably change again its title to reflect the new development.

Anyway, in my opinion we should not be rushing in our discussion of modality, before clarifying some of its most basic tenets, and to that effect I have looked in some old notes of mine which I used years ago in my lessons to advanced students of theory or advanced players of an instrument. These notes are my original research into all types of modality and therefore under my copyright. The difficulty to present some of them in this thread is that most if not all of these notes are still in my manuscripts which I used to photocopy and distribute to pupils. To digitise all of them is out of the question for me at present, but I will try to digitise some of them for presentation and I started tonight with what I consider as very important.
I attach a PDF containing some notated examples and my theoretical exposition on some basic modal material and I will continue whenever possible in this routine.
If you are still interested and you have to make observations, contribution, ask for further clarification please do.
I will try to follow your links and other observations, as I said, later.

\uap>Attachment here

My second attached PDF continues with the exposition of the division of canon on its seven prescribed steps, before any negotiation on the sizes of intervals can begin meaningfully. I am still considering the Pythagorean diatonic scale in its hard version. I give in screen shots the content of this PDF, but also I attach it as a separate document for any who want to combine all PDFs in a book. The delay in continuing is due to my bad internet connection and to the fact that I am digitising my old manuscripts in Sibelius and translating them into English.




\uap>The first staff bellow shows the seventh step used in the division of canon (as given in my previous post) and the subsequent  arrival at the mode whose structure gives a further six modes created by this division using the intervals of octave and fifth.  It was shown that the second of these seven modes is the hard diatonic Pythagorean scale (hard Lydian diatonic mode).  Given the highly speculative nature of all Greek scientific and theoretical thought from the time of the Ionian philosophers down  to the time of Euclid, it is far more logical to assume that the division of canon did not stop there.  The question here is rather philosophical: Do divisions stop at any time? The answer is no, as far as mathematical science is concerned.  For musical purposes and as far as the only intervals allowed are the octave and the fifth, the division can repeat the seven steps  demonstrated already.  The last note arrived at was Gb. We make an enharmonic change to this and give it as F#, purely for practical purposes. 






\uap style="margin: 0in; font-family: Calibri; font-size: 11.0pt;">RESULTING SCALE AND OBSERVATIONS/CONCLUSIONS

\uap style="margin: 0in; font-family: Calibri; font-size: 11.0pt;"> 

\uaol style="margin-left: .375in; direction: ltr; unicode-bidi: embed; margin-top: 0in; margin-bottom: 0in; font-family: Calibri; font-size: 11.0pt; font-weight: normal; font-style: normal;" type="1"> \ua
  • The structured of the scale produced by repeating the seven steps of the previous procedure is exactly the same as in the first instance of the division, and also the same are the remaining six scales of the modes produced on the degrees 2 to 7.
  • \ua
  • The hard diatonic Pythagorean scale structure of [T-T-S-T-T-T-S] can again be found as before, starting on the second degree (the second mode of the division).
  • \ua/ol> \uap style="margin: 0in; font-family: Calibri; font-size: 11.0pt;"> 

    \uap style="margin: 0in; font-family: Calibri; font-size: 11.0pt;">From the above two observations we can safely conclude that the division of canon by Euclid refers always to the creation of a scale which in our present day understanding is the scale starting on the seventh note (leading note) of a major scale, otherwise the ancient Mixolydian mode. Therefore the major scale/Lydian mode is always the second mode of Mixolydian.

    \uap style="margin: 0in; font-family: Calibri; font-size: 11.0pt;"> 

    \uap style="margin: 0in; font-family: Calibri; font-size: 11.0pt;">The division of the canon can continue by using the same seven steps of the procedure and the intervals of octave and fifth, to take us into the complete cycle of fifths, and it is not far-fetched to conclude that this cycle was understood by practical musicians of the time of Euclid (c. 300 BC). The reason that this procedure did not express its self theoretically in terms of the cycle of fifths known and appreciated by us today for its tonal and harmonic implications and creation of a different musical civilization, is in my opinion a matter of choice (and of secondary importance at that). The Ancients were far more interested in their already established theory of the System Perfect Greater with its divisions into sub-units of conjunct and disjunct tetrachords which had already taken them into the pan-modality that all successive modal systems displayed later in time.

    \uap style="margin: 0in; font-family: Calibri; font-size: 11.0pt;">But more of that later.

    \uap style="margin: 0in; font-family: Calibri; font-size: 11.0pt;">

    \uap style="margin: 0in; font-family: Calibri; font-size: 11.0pt;">KATATOME%20KANONOS%201b.pdf

    hi Socrates,

    For geeks like me (and especially you...:-) this is a wonderful read. I don't often read much music theory these days because it is hard enough just writing the darned stuff but I am enjoying your posts and pdfs and finding them fascinating. As you know, I am ploughing through Greek and Greco/Roman philosophy up to present day at the moment and your work here is giving me an added insight into how music was considered and practiced at that time. I don't know what you bad Med boys where drinking in the BC period, but if you find out, I'll have a few bottles of it.

    As your thread is about modulation too perhaps I could post some thoughts on how modal manipulation can be used in a technical way to wander into different areas of modality/tonality,  albeit within the sterilised realm of equal temperament. However I have no desire to de-rail your flow so please, please keep it coming.

    Hi Mike and thanks. I am into two minds about this thread. It started off as an insight into modulations so yes, by all means feel free to publish your thoughts and insights on various aspects of the subject. It is about modality and modulation in fact. In the meanwhile, I will keep up translating my manuscript notes on ancient theory and eastern modality and we can discuss anything that takes our fancy.


    my two previous posts deleted as irrelevant (just my confusion). I have established now all Pythagorean intervals in terms of midi bend messages and I'll carry on with my research on tuning systems for compositional purposes. I may publish some results during the summer if I find time and internet fast connection. But I am glad to observe from Bob's thread that Dorico has already been moving in that direction.

    Hey Socrates. It's October now and I'm wondering when this thread will resume. 

    I also have a question I've been wondering about this summer that may make for  a good splinter topic:

    Are there any uniquely Greek approaches to rhythm and time signatures that are directly related to such modulation?  Your mention of thesis and arsis in another thread had brought this to mind.

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