Confusion with Sharps (Διέσεις) and Flats (Υφέσεις)

frephraim

Παλαιό Μέλος
#1
According to page 92 of the 1947 Byzantine Music Theory book by Demetrios Panagiotopoulos (a book held in high regard by many), a sharp without a crossbar raises the pitch of a note by a half step: i.e., 6 units (μόρια) which is 100 cents, whereas a sharp with a crossbar raises the pitch by only 3 units (μόρια) which is 50 cents. He also writes that a sharp with two crossbars raises the pitch by 9 units, which is 150 cents.

Other respectable theory books, however, state something entirely different. For example, the 1958 theory book by Margaziotis states on page 32 that a sharp without a crossbar raises the pitch of a note only by 2 units, which is 33 cents, whereas a sharp with a crossbar raises the pitch of a note by 4 units, which is 67 cents. He also shows that a sharp with two crossbars raises the pitch by 6 units, and a sharp with three crossbars raises the pitch by 8 units. Margaziotis also mentions that these numbers are based on the Patriarchal Musical Committee of 1881.

Can someone please explain to me why this disagreement exists, and which of the two is correct?
 

apostolos

Απόστολος Κομπίτσης
#2
According to page 92 of the 1947 Byzantine Music Theory book by Demetrios Panagiotopoulos (a book held in high regard by many), a sharp without a crossbar raises the pitch of a note by a half step: i.e., 6 units (μόρια) which is 100 cents, whereas a sharp with a crossbar raises the pitch by only 3 units (μόρια) which is 50 cents. He also writes that a sharp with two crossbars raises the pitch by 9 units, which is 150 cents.

Other respectable theory books, however, state something entirely different. For example, the 1958 theory book by Margaziotis states on page 32 that a sharp without a crossbar raises the pitch of a note only by 2 units, which is 33 cents, whereas a sharp with a crossbar raises the pitch of a note by 4 units, which is 67 cents. He also shows that a sharp with two crossbars raises the pitch by 6 units, and a sharp with three crossbars raises the pitch by 8 units. Margaziotis also mentions that these numbers are based on the Patriarchal Musical Committee of 1881.

Can someone please explain to me why this disagreement exists, and which of the two is correct?
Papa Ephraim,

In that same book (Panagiotopoulos) there are two important footnotes that should be mentioned: #2 at the bogttom of p. 92, and #4 at the bottom of p. 94, the latter of which explains the Margaziotis interpretion of the yfeseis/dieseis.

Apostolos
 

Shota

Παλαιό Μέλος
#3
According to page 92 of the 1947 Byzantine Music Theory book by Demetrios Panagiotopoulos (a book held in high regard by many), a sharp without a crossbar raises the pitch of a note by a half step: i.e., 6 units (μόρια) which is 100 cents, whereas a sharp with a crossbar raises the pitch by only 3 units (μόρια) which is 50 cents. He also writes that a sharp with two crossbars raises the pitch by 9 units, which is 150 cents.

Other respectable theory books, however, state something entirely different. For example, the 1958 theory book by Margaziotis states on page 32 that a sharp without a crossbar raises the pitch of a note only by 2 units, which is 33 cents, whereas a sharp with a crossbar raises the pitch of a note by 4 units, which is 67 cents. He also shows that a sharp with two crossbars raises the pitch by 6 units, and a sharp with three crossbars raises the pitch by 8 units. Margaziotis also mentions that these numbers are based on the Patriarchal Musical Committee of 1881.

Can someone please explain to me why this disagreement exists, and which of the two is correct?
Father,

In the proceedings of the 1st psaltic conference in Athens there is an article by Dimitri Giannelos, one of the prominent topics of which is exactly this, i.e. differences between definitions of sharps and flats in various books and the reasons of their existence.
 

frephraim

Παλαιό Μέλος
#4
In that same book (Panagiotopoulos) there are two important footnotes...
Thanks for pointing that out. I hadn't noticed those footnotes. The footnote by Panagiotopoulos on p. 94 does recognize the way that the Patriarchal Committee of 1881 defines those sharps and flats, but it still seems as if he is not interested in following those definitions, since he merely puts them in a footnote while presenting his own intervals in the body of his text.
So my basic question is this: When we see a sharp (or flat) written, how can we know how much of a change of pitch is meant?

In the proceedings of the 1st psaltic conference in Athens there is an article by Dimitri Giannelos...
Oh, yes. I remember reading that a few years ago, but now I've forgotten what he said, and I no longer have that book.
If someone has it, could you please give us a brief summary or post a scan of it?
Thank you.
 

Shota

Παλαιό Μέλος
#5
Oh, yes. I remember reading that a few years ago, but now I've forgotten what he said, and I no longer have that book.
If someone has it, could you please give us a brief summary or post a scan of it? Thank you.
I'll scan the relevant part when I find time.
 

Nikolaos Giannoukakis

Παλαιό Μέλος
#6
Dear Fr. Ephraim,

Also, please have a look at this section (appended pdf files) from Avraam Eythymiadis.

In many cases, the human ear cannot perceive miniscule intervals, nor can the human voice perform them. They are of theoretical and mostly INSTRUMENTAL relevance. I challenge anyone on this forum to perform CLEAN tritimoria and CLEAN yfesh/diesh homologues of an ELAXISTOS interval that the HUMAN EAR (and not a computer) can perceive or perform :)

In Christ,

NG.
 

frephraim

Παλαιό Μέλος
#8
Dear Nick,

Those comparative charts clearly show the differences I was trying to explain.
I agree with you that many of those differences in pitch are extremely subtle. For example, the difference between the two different systems for a sharp with a single crossbeam is the difference between 1/4 and 4/12, which is a mere 1/12 ! (=17 cents). But other differences between the two systems are quite audible. For example, a sharp without any crossbeams is 1/2 in one system (100 cents) but only 1/6 (33 cents) in the other system. A difference of 67 cents is clearly audible.

So what I'm asking is this: how can we know which of these two systems to follow when we see, for example, a sharp without any crossbeams? Should we just rely on context, i.e., should the alteration in pitch depend on what note it is on?
 
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antonios

Αετόπουλος Αντώνιος
#9
Dear Nick,
So what I'm asking is this: how can we know which of these two systems to follow when we see, for example, a sharp without any crossbeams? Should we just rely on context, i.e., should the alteration in pitch depend on what note it is on?
Who wrote it, when, where (in which note in which mode)...

For example Avraam Eythimiadis uses a simple sharp (or flat) meaning a number of different things explained in detail in his theory. (In brief. I have no time now. Mabe tommorow, with more...)
 

Nikolaos Giannoukakis

Παλαιό Μέλος
#10
Dear Fr. Ephraim,

It's purely contextual.

Even if one executes successive sharps and flats (simple or tritimoria) of an interval representing a MEIZON tonos in time, on an x-y graph (pitch in Hz vs. "try"), I guarantee you that the number of times each try will be identical to the previous or next one withing 20% of the value will be ZERO. Try it. Or get a world-class opera singer (not to mention someone like Hatzichronoglou) to try it.....

I agree that divisions of tritimorion, tetartimorion or simple yfesis/diesis of a WHOLE tone (MEIZON TONOS) are executable and audible.

When we try these divisions on ELLASONES AND ELIXISTOI tones, we need a computer to execute and to perceive.

In Christ,

NG
 

apostolos

Απόστολος Κομπίτσης
#11
Dear Fr. Ephraim,

It's purely contextual.

Even if one executes successive sharps and flats (simple or tritimoria) of an interval representing a MEIZON tonos in time, on an x-y graph (pitch in Hz vs. "try"), I guarantee you that the number of times each try will be identical to the previous or next one withing 20% of the value will be ZERO. Try it. Or get a world-class opera singer (not to mention someone like Hatzichronoglou) to try it.....

I agree that divisions of tritimorion, tetartimorion or simple yfesis/diesis of a WHOLE tone (MEIZON TONOS) are executable and audible.

When we try these divisions on ELLASONES AND ELIXISTOI tones, we need a computer to execute and to perceive.

In Christ,

NG
I agree with Mr. Giannoukakis. I believe that even in the classical tomes, you would be hard-pressed to find anything above a single-bar yfesis or diesis. And I'm being a tad liberal here, because in all of the books I've seen, I think I could count the instances of single-bar neumes on one hand. I think attempting to actually executes those sharps/flats with any degree of precision can tend to make one incredibly nasal. Maybe on a "sliding scale" exercise you can hit 2-, 4-, 6-, etc. -moria, but to hit such a note "dead on" in actual practice, hmmmmm... I question that.

Of course, there are some "experts" who insist on using computers and spectrascopes to sit and analyze recordings of chanters to determine their accuracy, but I find those contraptions a bit too bulky for the analogion. :D:D

Apostolos
 

Nikolaos Giannoukakis

Παλαιό Μέλος
#12
One day, in the interest of purity, we may end up substituting human beings with computers or robots who will fulfill the fetish of the "purists" to be dead on the precise interval.....even if the human ear cannot perceive it....

Common sense trumps any theoretical treatise or consideration, or it should...

NG
 

Nikolaos Giannoukakis

Παλαιό Μέλος
#15
Perhaps this issue can be raised under a new thread:

What use are myriads of theoretical manuals, treatises, documents, exegeses if a student HAS NOT LISTENED TO A TRADITIONAL MASTER AND STUDIED THE ORAL TRANSMISSION????

These days, universities (largely in Greece) have tasked individuals who NEVER LEARNED TO CHANT FROM A TEACHER to teach ......CHANT (!!!!)

Starting from a theoretical manual (name your favorite here), they begin....self-taught.....on a journey of revisionism and arbitrary pseudoscience to justify untenable hypotheses which they present as "tradition" at the analogion.

We should be very careful to not make theory superior to 60 years of oral tradition which, unless some aural evidence points to the contrary, has few outliers among individual chanters.

Theory, according to the old masters helps to understand and perhaps sharpen knowledge.

It does not take over what the oral tradition passes on.

That is why at the Patriarchate, music books were SELDOM used in practice, but hymns were passed on ORALLY.

I am not advocating that theory be dismissed, but I am advocating that theory be used judiciously, with common sense and with an aim to supplant the oral tradition and NOT confuse and lay the foundation for arbitrary heresies.

NG
 

frephraim

Παλαιό Μέλος
#16
After reading that informative article by Giannelos, I wrote the comments pasted below that I intend to include in an article for beginners I am working on. If I am mistaken in anything I wrote, someone please correct me.

Here are my comments:

...Unfortunately, some confusion currently prevails regarding the exact meaning of some sharps and flats. When Chrysanthos devised the "New Method" of Byzantine Music notation in the early 19th century, he decided to use five different symbols for sharps and five for flats. The amount that each of those symbols changes the pitch is proportional to the interval between it and the next note. Thus, a plain sharp (i.e., a sharp without a hook or crossbeams) raises the pitch halfway to the next note in the scale. If that interval is a whole step (12 units—or 200 cents), that sharp will raise the pitch by 6 units (100 cents). But if that interval is only 10 units (167 cents), it will raise the pitch by only 5 units (83 cents).

In order to make Byzantine Music notation more definitive, the Patriarchal Committee of 1881 decided to change the meaning of sharps and flats. They eliminated sharps and flats that have a hook, and they used sharps and flats with 0, 1, 2, 3, or 4 crossbeams. The meaning they assigned to these symbols was as follows: A plain sharp (i.e., without any crossbeams) adds 2 units (33 cents) to the pitch of a note, and each additional crossbeam added to that sharp adds another 2 units to the pitch. Thus, a sharp with one crossbeam adds 4 units (67 cents), a sharp with two crossbeams adds 6 units (100 cents), a sharp with three crossbeams adds 8 units (133 cents), and a sharp with four crossbeams adds 10 units (167 cents).

The problem is that many books printed after 1881 continued using a plain sharp (i.e., without any crossbeams) not with the new meaning assigned to this symbol by the 1881 Committee (which stated that it adds two units or 33 cents to the pitch), but with the meaning given to it by Chrysanthos (who stated that it increases the note's pitch halfway to the next higher note).
 

Nikolaos Giannoukakis

Παλαιό Μέλος
#17
Dear Fr. Ephraim:

you should EMPHATICALLY emphasise the following point in your tutorial, because if not, it will confuse and lead to problems:

"The problem is that many books printed after 1881 continued using a plain sharp (i.e., without any crossbeams) not with the new meaning assigned to this symbol by the 1881 Committee (which stated that it adds two units or 33 cents to the pitch), but with the meaning given to it by Chrysanthos (who stated that it increases the note's pitch halfway to the next higher note)."

Now, on the practical aspect, you may wish to discuss human physiology, especially what the human ear can discern and what the human voice can accomplish. Specifically, you should qualify the following:

"......A plain sharp (i.e., without any crossbeams) adds 2 units (33 cents) to the pitch of a note, and each additional crossbeam added to that sharp adds another 2 units to the pitch. Thus, a sharp with one crossbeam adds 4 units (67 cents), a sharp with two crossbeams adds 6 units (100 cents), a sharp with three crossbeams adds 8 units (133 cents), and a sharp with four crossbeams adds 10 units (167 cents)."

I would add something to the following:

"While these intervals can be discerned by an electronic sensor (computer), the human ear is not always sensitive to minute changes where two distinct pitches are separated by less than 45 cents. Furthermore, the human voice is not always capable of reproducibly performing discrete jumps between successive pitches separated by less than 45 cents. "

Yours in Christ,

NG
 

frephraim

Παλαιό Μέλος
#18
I would add:
"While these intervals can be discerned by an electronic sensor (computer), the human ear is not always sensitive to minute changes where two distinct pitches are separated by less than 45 cents. Furthermore, the human voice is not always capable of reproducibly performing discrete jumps between successive pitches separated by less than 45 cents. "
Thank you very much for the suggestion, Nick. But are you sure that 45 cents is the cutoff level? I would like to know what made you choose that particular value.
John Boyer once told me that when he was singing in an ensemble of Western music, the conductor commented that he was singing his major thirds too low. This was because John was accustomed to chanting the interval Nee-Vou as 22 units (μόρια), whereas a major third is 24 units. The difference between these two pitches is only 33 cents. Of course, it is safe to assume that such a conductor would have an exceptional talent for hearing proper pitches, but I'm not so sure it's such a rare talent. After all, even I can hear the difference between my own Westernized intervals and real chanters doing their Vou properly at 22 units above Nee. I must admit, though, that it's one thing to detect this difference, and quite another thing to fix it!
 

Nikolaos Giannoukakis

Παλαιό Μέλος
#19
Dear Fr. Ephraim,

Take a synthesiser (softsynth or a hardsynth) and assign an interval difference of 40 cents between C and D. Can you repeat the notes successively (set the metronome at 130 bpm) and discern this difference?

I have an old Korg M1 at home and I play often microtonal music (Arabic, Turkish) and the interval that is discernible is 40 cents. Anything smaller, I have to pay really close attention to.

As for accurate performance by voice that;s another matter altogether and it would indicate a true MIRACLE performer!

In Christ,

NG
 

Nikolaos Giannoukakis

Παλαιό Μέλος
#20
Dear Fr. Ephraim,

From my old Korg M1 synthesiser:

Appended is a sound file that has a C-D up-down sequence where the intervals between C and D are:

33 cents, 67 cents, 100 cents, 133 cents, 167 cents.

As you can hear, the 33 cents interval is **barely** discernible. If the human voice were to actually hit this interval RIGHT ON, 50% of the time AUTONOMOUSLY and without any synthesiser in the background or as a guide, I would be astounded...

N.
 

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