hi all

I am new in this areal (acoustical) but i want to ask you what are your
view point abut "atraction's law" which are invocation in byzantine
music from Greece. sorry my english but i hope you understand my
question.

Thanks,

Constantin

On Fri, Feb 4, 2011 at 2:26 AM, anton_pann <anton_pann@...> wrote:
>
> I am new in this areal (acoustical) but i want to ask you what are your view point abut "atraction's law" which are invocation in byzantine music from Greece. sorry my english but i hope you understand my question.

Hi Anton,

I haven't heard of it. Can you link me to something that discusses it?
Perhaps it's a term I'm unfamiliar with.

Welcome to the list,
Mike

Good question! I recently came across "the unknown" in Byzantine psalmodic chant... Read about attraction's law here - go to page 123: http://www.byzantinechant.org/Resources/guide_to_music_of_eoa.pdf http://www.byzantinechant.org/Resources/guide_to_music_of_eoa.pdf
- Bogdan

Dear Bogdan and all,

The "Law of Attraction" in Byzantine music has its counterparts in other
modal traditions: for example, the concept of _cazibe_ or "gravity" in
Turkish maqam music (which Chrysanthos of Madytos writes about as closely
related to Byzantine music), the dint-s and dunt-s of Arab maqam, and the
various accidental inflections of medieval and Renaissance European music.

This "Law of Attraction," and similar patterns of modal inflection, can
function differently depending on local or regional tastes, the preferences of a given performer or ensemble, and also on a taste for
flexibility or variation which may lead the same performer to interpret
the same passage differently depending on the mood at a given moment.

The basic idea is that, for example, a note moving upward (e.g. toward
a cadence) may be inflected upward, while a descending note may be
inflected downward. Chrysanthos of Madytos, for example, gives an example
of the Fourth Mode in its papadic or diatonic form which resembles a
conjunct Maqam Rast -- e.g. 200-166-133-200-166-133-200 cents if the
tuning is expressed in terms of the Committee of 1881 (based on 36-ed2).
This form, uninflected, as in an example by Chrysanthos, would have a
9:8 or regular tone leading up to the final, e.g. F-G in one possible
transcription. However, as I recall Chrysanthos himself documents, some
performers back then -- and many now -- prefer a "law of attraction"
where F in F-G would be raised to F+ or F-half-sharp, as it would be
written in Arab notation -- in Byzantine terms, a "minimal tone" below
G, or around 133 cents under the Committee of 1881's recommendations.

This kind of alteration is also documented in the era of Chrysanthos
by Mikhail Mashaqa, a Syrian theorist, in Arab music under some
circumstances.

And it can be observed in Arab and Turkish performances of Maqam
Rast, for example, where an ascending form like C D Ed F G A Bd C
has a Zalzalian or middle third and seventh (e.g. at 27/22 and 81/44,
or 355 and 1057 cents if al-Farabi's tuning is followed), but with
a minor seventh in descent, C D Ed F G A Bb C (with Bb around 16/9,
or closer to 7/4 in some Turkish practice).

The Arabic terms dint and dunt refer to raising or lowering a note
(often in modern practice by a semitone) to emphasize an important
note such as the ghammaz (confinal or dominant where two genera
are joined), for example, and seem parallel to Byzantine "attraction."

Similar patterns happen in medieval and Renaissance European music,
often described by theorists in terms of polyphonic practices
(e.g. a preference for a vertical or harmonic major third before
a resolution to a fifth, or major sixth before an octave), but also
reported in plainsong, which is more parallel in its mainly melodic
focus to maqam music or the Byzantine tradition.

For example, writers near the end of the 15th century in Europe
report the use of semitones which are _subintellectum_ or
"understood" by performers of Gregorian chant, e.g. a passage
with the figure A A G A which is sung A A G# A.

Of course, the element of the ison or moveable pedal point in
Byzantine music does add a certain polyphonic aspect, and I
have seen some modern Byzantine settings that resemble the
two-voice polyphony of Guido d'Arezzo in the 11th century,
for example, with an emphasis on the consonance of the fourth
(which also defines a melodic tetrachord, and so can underscore
the patterns of a chant), and sustained notes which resemble
the Byzantine ison.

Both in whether to use an inflection in a given passage, and
how to tune that inflection, various local and personal customs
may vary: Byzantine intonation is a topic for lively dialogue
and debate, on the Web today as well as elsewhere. But the
"attractions" are themselves a point of consensus, even if
people differ on when, where, and how.

With many thanks,

Margo Schulter
mschulter@...

Thank you Margo! It seems like Byzantine intonations lack an extended and in-depth classification, because there has been no study of them, like those by Alain Daniélou or Erv Wilson on Hindu music for example. But given the oral tradition of it, I wonder how accurate are the 22 ratios we generally consider to define Indian music.

This is also true for Arabic, Turkish, Persian & so on musical cultures. Although there have been numerous classifications, my knowledge is limited in this area. Eric Ederer has a doctoral dissertation on the subject, I'll ask him for a copy. What do you think about this resource? Does anyone know about other classifications that won't require going through mountains of historical heritage?

Many thanks,
Bogdan

Dear Bogdan,

Please let me indeed recommend Eric Ederer's dissertation as an excellent
source on lots of aspects of the Turkish maqamat. What I'd say is that
tunings can be highly variable in Turkish, Byzantine, Arab, or Persian
music -- and likely in Kurdish music also, I suspect.

There's actually a lot out there, both in terms of measured modern
tunings and performances (sometimes involving flexible-pitch performances
as well as fixed frettings and the like), and in terms of traditional
tuning theory going back to al-Farabi in the 10th century, who reports
the practice of Mansur Zalzal, an `oudist in 8th-century Baghdad.

What I'd emphasize is that lots of modal concepts, as in Ederer's dissertation, can usefully be applied to a range of tunings, with
relative adjustments of notes or intervals often being more important
than the precise absolute values, which might vary with performers or
from region to region.

For example, in conventional 20th-century Turkish theory, and indeed
for many practical musicians including Eric Ederer himself on his
nautilauta (a custom-designed fretted JI instrument), a rast tetrachord
would be 1/1-9/8-5/4-4/3. There's an understanding that in descending
to a final cadence -- one manifestation of _cazibe_ or "gravity,"
synonymous with the Byzantine "attraction" principle -- the third is
lowered a bit, maybe to 26/21 or 16/13, for example.

As it happens, I often play an "Ottoman Rast" at 1/1-9/8-26/21-4/3,
a lower interpretation. So, in order to follow the ideal of cazibe
or attraction, I lower the third step to 16/13, or maybe 11/9 -- the
same kind of relative shift, although both the usual and lowered forms
are a bit narrower thirds than 5/4 and 26/21, say.

For some measurements of modern frettings and performances, Jean During
and Amine Beyhom are good sources, and also a study on recordings of
Turkish music done by Boris Bozkurt, Can Akkoc, Ozan Yarman, and others.
Some of these are available on the web. And the historical tunings of
al-Farabi, Ibn Sina, Safi al-Din al-Urmawi, and Qutb al-Din al-Shirazi
are quite beautiful, showing the diversity of 10th-14th century practice.

With Byzantine tuning practice, you'll find some differing approaches
and sometimes heated controversies on the web and elsewhere. It helps
to know that the Byzantine Diatonic is actually a Zalzalian diatonic,
with a tetrachord formed from a tone at around 9:8 (or sometimes a bit
larger), and two middle steps sometimes called the "minor tone" and
"minimal tone," at 12:11 and 88:81 (151 and 143 cents) in the tuning
of Chrysanthos of Madytos in the early 19th century which follows
that of al-Farabi about 900 years earlier -- or 167 and 133 cents
according to the Committee on Music of 1881. In practice, there will
be various shadings.

Byzantine practice has been expressed theoretically in 36-ed2 (as in
1881), 68-ed2 (as in Chrysanthos and followers as one model), or in
some 20th-century accounts in 72-ed2 (at times bringing into play
intervals not present in 36-ed2, as with approximations of ratios
of 5).

An important thing for people like Eric and me who like JI tunings
to acknowledge is that lots of tunings are variable -- Iranian
musicians are not necessarily going for precise ratios, for fifths
and fourths or other types of intervals, but for a pleasing variety,
for example in 17-note frettings on the tar or setar. Ratios like
12:11 and 13:12 are elegant and often influential, but not definitive
of how people fret or play in practice, although some measured tunings
come quite close.

As some of the Turkish studies have shown, often flexible-pitch
performers are aiming not so much for a single pitch in order to
represent a given step like "the third step of Rast," but a "cluster"
or region which could cover 20 cents or more. Some performers actually
speak of "glissando zones" between a regular minor third and a regular
major third (at 32/27 and 81/64, say), thus underscoring this
flexibility.

Again, During (carrying further some of the researches of Nelly Caron
and Dariush Safvate in the mid-20th-century), Beyhom, and the recent
Turkish studies are one good source -- with various discussions of
Byzantine intonation another.

Above all, thank you for asking an important question, and giving
me an opportunity to comment both on some beautiful traditional
tunings and on the considerable scope for flexibility,

In peace and love,

Margo

Dear Margo,

Thank you for the reading list, and most of all for the sunshine you bring along every time you share knowledge.

It is the relative adjustments that interest me - not so much the exact ratios used by different performers in different regions, but the complete range of movement. To use your example, this would be "between 11/9 and 5/4: not higher than 5/4 in ascent, not lower than 11/9 in descent; ratios included: 16/13 (descent) & 26/21 (ascent/descent)". This range, when extended to around a doubling in acoustic space - mostly in the lower part, covers the large "glissando zone" between 32/27 and 81/64.

I have this crazy theory about the "gravity" or "attraction" principle, according to which the ascent follows overtone tonal patterns, while the descent is naturally attracted to "step on" undertones. To use the same example, 1/1 9/8 5/4 4/3 refers to harmonics 24 27 30 32 from the ascending harmonic series. When descending, the 4/3 becomes 1/1 and the closest approximation to 26/21 would be harmonic 29 in the range (feel free to read from right to left) 36 32 29 27 of the descending harmonic series. If we wish to stay inside the same (mirrored) numbers 24-32 32-24, then the ascending 9/8 won't have a counterpart and it too will have to move. The problem is - and that's why all this is still a speculative adventure - this tone will be attracted to a higher place at subharmonic 28, thus (right to left again): 32 28 26 24. In this version 16/13 corresponds precisely with subharmonic 26, and the 9/8 becomes 8/7, when 1/1 is taken as the first tone on the left. That would explain why sometimes the 9/8 is a bit larger; also there is no reason for staying inside this double, because the same numbers can be reduced to 16 14 13 12. Incidentally, this corresponds with the right half ("tetrachord") of Kathleen Schlesinger's Phrygian or Venus Mode.

In harmony,
Bogdan

Dear Bogdan,

This is a very quick reply for the moment, with my apologies for not
visiting and checking the group more often! Thank you for your
patience.

Your hypothesis is fascinating, and of course might most apply to
flexible pitch performances. But whatever may hold there, you
have cited two tunings or ratios that I think merit special
attention.

The first is 16:14:13:12, Ibn Sina's "most noble genus" which for
me is a kind of "septimal Rast" that I consider a related maqam
in its own right, but also sometimes an inflected variation on
Rast. And, of course, it does fit with the harmoniai of Kathleen
Schlesinger and Elsie Hamilton.

Boris Bozkurt, Ozan Yarman, Can Akkoc, and colleagues
have described one kind of cazibe or attraction that can bring
this tuning about in Arab music: the Sikah (from Persian or Turkish
Segah) family maqamat. Here we might have a usual Rast tetrachord of something like 1/1-9/8-16/13-4/3, with an emphasis on the third
step, named sikah (from Persian segah, "third" step or location).
To get a smaller leading-tone below this step, the 9/8 step tends
to be raised by around a comma, to 8/7 -- giving us a compact
8/7-16/13 or 14:13 step, which I find delightful.

On keyboard, I might play the usual 16/13 Rast D*-E*-F#-G* (showing
the upper chain of fifths with an * sign), and this nuance as
D*-F-F#-G* (1/1-8/7-16/13-4/3).

Here the third step itself, or actually the final or resting note
of Sikah, doesn't necessarily change in an Arab context, but the
leading tone gets raised for a more definitive cadence. It's a
neat use for a comma nuance -- and for two keys a comma apart
in a keyboard tuning.

But your example raises a question. In the Turkish setting we
were addressing, how about ascending
1/1-9/8-26/21-4/3-3/2-27/16-13/7-2/1
or D*-E*-Gb*-G*-A*-B*-Db*-D*, but then descending
1/1-8/7-16/13-4/3-3/2-27/16-39/22-2/1
or D*-F-Gb*-G*-A*-B*-C*-D?

That would be a combination of segah or the third step
falling a bit from 26/21 to 16/13, and dugah or the
step at the tone rising a bit to meet it, so to speak.
As a result, the middle step of the tetrachord gets
compressed from 208:189 or 165.8 cents to 14:13 or
128.3 cents -- a difference of 1352/1323 or 37.5 cents!

This is interesting, because 208:189 and 14:13 both
occur in Ibn Sina, and represent what we might call
his largest and smallest Zalzalian steps.

Again, I love 16:14:13:12 and design my favorite
tunings to support either in JI (as here) or in near-just
form. Whether it fits with this particular idiom, I'm
not sure, and maybe Arab or Turkish musicians could give
a valuable perspective. But the Sikah idiom is something
I use often, as well as 16;14:13:12 as a "septimal Rast"
in its own right.

Also, your 36:29 at 374.3 cents is indeed only a bit
wide of 26:21, and it turns out that in one location
I have an odd interval of 704:567, which differs from
36:29 by only 5104/5103 or 0.339 cents!

What's happening is that 704:567 is a variation on
26:21, at 352:351 higher -- almost identical to the
378:377 difference between your 36:29 and 26/21!

Anyway, this could get into a whole world of possible
distinctions between ascending and descending motion --
everything from harmonic and arithmetic or subharmonic
series in relation to fine intonation, to rules of
melody or counterpoint (e.g. in 16th-century Western
European styles) that make distinctions depending on
the direction on motion, such as the ordering of
skips and steps, or larger and smaller skips.

I want to ponder your post more, but do want to give
it a fair reply in a timely way.

With warmest thanks,

Margo