Re: Pythagorean theory and practice & the octave

On 25 Apr 99, at 17:48, monz@juno.com wrote:

[snip]

> It is not until after the Romans conquered Greece
> that theorists such as Nicomachus and Ptolemy (c. 100 AD)
> specifically utilized the 'octave' in their descriptions
> of scales.

Did not Pythagoras do so, expanding on the work of Terpandros of
Antissa?

>Before that it was all tetrachords,
> and in many cases the systems used two *conjunct* tetrachords
> which only filled the space of a 'minor 7th'.

Nicomachos does not claim this for himself, but attributes it to
Pythagoras.

>
> I think there are two possible reasons for this
> recognition of the 'octave': the use of the organ
> (a Greek invention) by the Romans,

Why would it take Roman use of a Greek instrument for the Greeks
to employ the octave?

and the introduction
> of 'oriental' musical tendencies after the Roman Empire
> expanded into Egypt and Mesopotamia, altho evidence
> seems to go against the latter.

Again, why would 'oriental' musical tendencies (whatever that
means) have to do with the octave. Moreover, it is not clear that
these cultures had any tuning that was unusual to Greeks. And
certainly the Roman conquest had nothing to do with it. The City of
Alexandria was known as that "Greek city, not far from Egypt."

>
> But acceptance and use of the organ as a musical instrument
> certainly played a (if not *the*) major role in the
> development of harmony/polyphony as it happened in Europe.

That wasn't till about 800 AD or so (when the Romaioi bequeathed
an organ to Pepin the Short, I believe, or maybe his son). Anyway,
it was waaaaaaay after these theoretical discussions on the scale
by the ancients.

[snip]

> This was also during the time of the Crusades, when
> soldiers returning to Italy and France brought back
> with them from 'the Holy Land' the ancient Greek theory
> texts (such as Ptolemy's) which described all sorts of
> non-Pythagorean ratios.

I really don't know a great deal about the spread of Greek
knowledge to the Latins and environs, but I thought it actually
occurred through the intermediary Arabic translations, as a
consequence of the invading Arab hordes who learnt music from
the intellectual step-children of the Greeks, the Persians. (Who, in
turn, received an intellectual catalyst through the closing and exile
of the Athenian Academy by, was it, Theodosios I? Anyway,
many of the faculty fled, and were given refuge, in Persia.

Polychroni
Ypsilanti, MIchigan

I'll apologize in advance for the fact that this posting
is somewhat off-topic as it's mostly history and only
tangentially tuning. If not interested, skip it.

[Polychroni Moniodis, TD 157.10]
> On 25 Apr 99, at 17:48, monz@juno.com wrote:
>
> [snip]
>
>> It is not until after the Romans conquered Greece
>> that theorists such as Nicomachus and Ptolemy (c. 100 AD)
>> specifically utilized the 'octave' in their descriptions
>> of scales.
>
> Did not Pythagoras do so, expanding on the work of Terpandros
> of Antissa?

No actual works by Pythagoras survive. Everything we know of
what is purported to be his theory comes to us second-hand,
and much of that must be read with caution because there was
a huge neo-Pythagorean revival around 100 AD (600 years after
Pythagoras lived), and many of those writers slanted quotations
from ancient teachings to suit their beliefs.

>> Before that it was all tetrachords,
>> and in many cases the systems used two *conjunct* tetrachords
>> which only filled the space of a 'minor 7th'.
>
> Nicomachos does not claim this for himself, but attributes it
> to Pythagoras.

But there is no reference in the ancient Greek literature
*before* Nicomachus which uses scale constructions which
specifically embody the 'octave'. (Nicomachus was in the
forefront of the previously mentioned Pythagorean revival.)

Altho the descriptions of Aristoxenus take the 'octave' into
account, it is not seen as an 'essential' element of the
scale, but is noted rather because it is the second-strongest
consonance after the unison; i.e., the emphasis on it is as
an interval per se, and not as a meaningful boundary to a scale.

>> I think there are two possible reasons for this
>> recognition of the 'octave': the use of the organ
>> (a Greek invention) by the Romans,
>
> Why would it take Roman use of a Greek instrument for the
> Greeks to employ the octave?

All I can say is, again, the Greeks did not employ the 'octave'
in scale constructions until *after* Greece became part of
the Roman Empire.

It may have nothing at all to do with the Romans - I was
just speculating. But my knowledge of classical history
compels me to believe that it was the result of a Graeco-Roman
interaction.

>> and the introduction of 'oriental' musical tendencies after
>> the Roman Empire expanded into Egypt and Mesopotamia, altho
>> evidence seems to go against the latter.
>
> Again, why would 'oriental' musical tendencies (whatever that
> means) have to do with the octave. Moreover, it is not clear
> that these cultures had any tuning that was unusual to Greeks.

That's why I back-tracked at the end. Ancient Greek and Roman
music is only very fuzzily understood, and will probably remain
largely so, because very little remains in terms of actual
physical records.

My guess, based on my study of ancient Greek music theory
texts, is that it had a *lot* in common with 'oriental' music.

'Oriental musical tendencies' simply refers to the fact that
Egyptian and Mesopotamian music was no doubt quite different
from indigenous Roman music, and it's been documented
(see Grove's Dictionary, 'Roman' entry) that the Romans
gleefully absorbed and enjoyed this 'oriental' music
after those lands were incorporated into the Empire.

> And certainly the Roman conquest had nothing to do with it.
> The City of Alexandria was known as that "Greek city, not far
> from Egypt."

But Greece and Egypt were both part of the Roman Empire by
the time of Ptolemy/Nicomachus, so Alexandria was simultaneously
Egyptian, Greek, and Roman (but mostly Greek). Then, as now,
it was a very cosmopolitan city.

>> But acceptance and use of the organ as a musical instrument
>> certainly played a (if not *the*) major role in the
>> development of harmony/polyphony as it happened in Europe.
>
> That wasn't till about 800 AD or so (when the Romaioi bequeathed
> an organ to Pepin the Short, I believe, or maybe his son).
> Anyway, it was waaaaaaay after these theoretical discussions on
> the scale by the ancients.

That was the introduction of the organ into 'modern' (i.e.,
post-Germanic-invasion) music theory.

It has been documented that the Romans of classical times
played and enjoyed the organ very much. (See Grove's Dictionary,
'organ' entry).

> [snip]
>
>> This was also during the time of the Crusades, when
>> soldiers returning to Italy and France brought back
>> with them from 'the Holy Land' the ancient Greek theory
>> texts (such as Ptolemy's) which described all sorts of
>> non-Pythagorean ratios.
>
> I really don't know a great deal about the spread of Greek
> knowledge to the Latins and environs, but I thought it actually
> occurred through the intermediary Arabic translations, as a
> consequence of the invading Arab hordes who learnt music from
> the intellectual step-children of the Greeks, the Persians.
> (Who, in turn, received an intellectual catalyst through the
> closing and exile of the Athenian Academy by, was it, Theodosios
> I?

There was some leeching of ancient Greek knowledge into
western Europe thru the Arabs via their conquest of mainly
Spain, but also Sicily and other parts along the Mediterranean.

But this period is not called the 'dark ages' for nothing.
For at least two centuries immediately following the
large-scale Germanic invasions of the former Roman Empire,
nearly everyone in Europe was illiterate (see Gregory of Tours's _History
of the Franks_ for contemporary documentation of this
fact).

It was not until Charlemagne became Holy Roman Emperor
(at the court which had that organ) in 800, and established
good diplomatic ties with both the Byzantine Empire and the
Baghdad Caliphate, that Arab and Greek learning began to spread
into Europe in earnest. And that stopped almost immediately
after Charlemagne's death.

The large-scale movement of European soldiers into the
'Holy Land', beginning around 1100, and their theft and
exportation of Greek books from there and into Europe (mainly
Venice and Florence), is what started the Renaissance.

It really kicked into high gear after 1453, when Constantinople
was sacked by the Arabs, and...

> many of the faculty fled, and were given refuge, in Persia.

Now *that's* music I know very little about.

(But anyway, to the point, many of the faculty also fled to Italy.)

-monz

Joseph L. Monzo....................monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
--------------------------------------------------

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