16th century counterpoint rules

I was musing today about the discouraged parallel 5ths and octaves,
today from the standpoint of the actual 16th century instruments.

I imagine that the temperaments were usually bad enough to show up
particularly in these intervals, either because of the player/tuner or
the instability of instruments of such light construction and stringing
(I'm thinking of polyphonic instruments other than the organ - which
makes itself go out of tune). Even with a nicely tuned group/consort,
one (Boulliau in Jorgensen, Owen. Tuning) or some of the fifths would
have sounded different.

...all of which makes it even more interesting that this got
demonstrated in my classes on awful sounding, out of tune 12-tet console
pianos.

Clark!
From what I remember in Zarlino's Art of Counterpoint, the rule
against parallel were intervals of the same ratio. Thirds were allowed
only when their ratios were different. So ET would have had more
parallels to avoid. Just as Debussy Broke through the parallel 5th rule
he likewise broke through the parallel M3rd in his use of them in Whole
tone scales. It seems that hearing indonesian Music at the worlds fair
inspired him to use this scale. I can only guess that it was a Slendro
tuning he heard as Pelog wouldn't make sense. BTW this case with Debussy
illustrate how this exposure caused his music to become wider as opposed
to it being an evolution out of the european Continuum.
-- Kraig Grady
North American Embassy of Anaphoria Island
www.anaphoria.com

On Wed, 10 Mar 1999, Clark wrote:

> I was musing today about the discouraged parallel 5ths and octaves,
> today from the standpoint of the actual 16th century instruments.
>
> I imagine that the temperaments were usually bad enough to show up
> particularly in these intervals, either because of the player/tuner or
> the instability of instruments of such light construction and stringing
> (I'm thinking of polyphonic instruments other than the organ - which

The rules against parallel fifths and octaves were for 'part writing',
which usually meant people singing or playing matched string or wind
instruments, one-to-a-part. Some organ music of the sixteenth century is
written that way, but it was pretty peripheral to what the rules were
intended for.

Judy

<<I was musing today about the discouraged parallel 5ths and
octaves, today from the standpoint of the actual 16th century
instruments. I imagine that the temperaments were usually bad
enough to show up particularly in these intervals>>. . .<<or some
of the fifths would have sounded different.>>

1/4 comma meantone temperament, which was the de-facto
temperament for keyboard instruments from the 16th century
onward, featured fifths that were 696 cents. Equal tempered fifth
are 700 cents (100 cents = 1 semitone in 12-tone equal). The pure
fifth in just intonation (also the basis for Pythagorean tuning), the
third overtone in the overtone series which registerally transposes
into an octave with the ratio 3:2, is 701.9 cents. In most cases,
the ear cannot distinguish anything smaller than 5 cents.

In Medieval times when Pythagorean tuning reigned supreme,
parallel fifths were the rage. They sound great! After 12-tone equal-
temperament became the de-facto keyboard tuning throughout
Europe (circa 1850), parallel fifths were suddenly O.K. again. (e.g.
they sound great when Debussy uses them!) Parallel mean-tone
fifths sound awful because they call attention to the fact that the
interval is out-of-tune by a teeny bit over 5 cents. (701.9 - 696 = 5.9
cents)

Similarly, major thirds were considered dissonant intervals because
they were based on cumulative perfect fifths (3:2) rather than the
fifth partial of the overtone series.

(That is to say C to E was based on C-G-D-A-E, which registerally
transposes into the octave as 81:64, rather than the registerally
transposed fifth overtone which is 5:4. The difference between
these two "major thirds", the syntonic comma (81:80) is almost an
eighth of a tone and is very audible.

81:64 equals 407 cents

5:4 equals 386 cents

the major third in 12ET is somewhere in between at 400 cents)

Thirds didn't become O.K. until Pythagorean tuning was
supplanted. However, the just intonation of vocal music in the
Renaissance didn't work for instrumental music (esp. keyboard
music) which requires a limited set of pitches to draw from in order
to be practical, hence the compromise of 1/4 comma mean-tone
which preserved the pure major third (5:4) at the expense of the
pure perfect fifth (3:2) by subtracting each perfect fifth (3:2) by 1/4
of the syntonic comma (81:80) such that with

C-G-D-A-E

C-E equals 5:4 therefore each fifth (C-G, G-D, D-A and A-E) are
downsized equally.

In the Baroque, parallel thirds are everythere and they sound great.
But, no parallel fifths.

The evolution of temperament is the real reason for these
counterpoint rules.

Hope this makes sense. . .

Frank J. Oteri

Frank J. Oteri
Editor and Publisher
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NO! Keyboard tunings were not determining preferred harmony in the 14th
through 17th centuries. Keyboard tunings were devised to match as closely
as possible the ideals of harmony prevalent. Pythagorean -- perfect
fifths. Meantone -- the tyranny of the perfect third. Much keyboard
music exploited the excitements and tensions in meantone, but
keyboard music was not the center of the musical world. I doubt that
anybody much before the seventeenth century composed vocal music 'at
the keyboard'. Maybe with the discovery of circulating temperaments
composers started looking for harmonic inspiration from what their
harpsichord sounded like. By the nineteenth century, keyboards were so
important that large numbers of people lost the ability to hear perfect
intervals at all. But don't try to extrapolate that back too far. Before
the industrial revolution, the world was a lot quieter, everyone heard
more -- and everybody sang, and sang unaccompanied very regularly.

Judith Conrad, Clavichord Player (jconrad@tiac.net)
Music Minister, Calvary Baptist Church, Providence, RI
Director of Fall River Fipple Fluters
Piano and Harpsichord Tuner-Technician

Message text written by INTERNET:tuning@onelist.com
>Just as Debussy Broke through the parallel 5th rule
he likewise broke through the parallel M3rd in his use of them in Whole
tone scales. It seems that hearing indonesian Music at the worlds fair
inspired him to use this scale. I can only guess that it was a Slendro
tuning he heard as Pelog wouldn't make sense. BTW this case with Debussy
illustrate how this exposure caused his music to become wider as opposed
to it being an evolution out of the european Continuum.
-- Kraig Grady<

This was a point of long discussion on the Gamelan list in the Fall. What
Debussy heard in the 'Javanese Village' exhibition at the exposition was a
group of Sundanese plantation workers playing Sundanese and possibly some
Javanese repertoire (Javanese dances were performed; the kind of music used
to accompany them was unclear) and possibly arrangements of western tunes.
The instrument they played was tuned in the seven-toned 'madenda' scale,
which is esesentially a natural minor diatonic, neither slendro nor pelog,
of which there is no evidence Debussy ever encountered.

Debussy apparently visited the pavillion for coffee and entertainments
several times and later would write:

lettre de Claude Debussy
Claude Debussy's letter
A Pierre Lou�s 22 janvier 1895

Mais mon pauvre vieux ! rappelle-toi la
musique javanaise qui contenait toutes les
nuances, m�me celles qu'on ne peut plus
nommer, o� la tonique et la dominante n'�taient
plus que de vains fant�mes � l'usage des petits
enfants pas sages.
[...]

To Pierre Lou�s 22 january 1895

But old fellow ! Remember the javanese
music which contained all shades of sound,
even the ones that are beyond naming,
compared to which tonic and dominant where
nothing but vain fantoms to frighten naughty
little children.
[...]

It appears impossible to locate a concrete example of gamelan influence on
Debussy in his scores. No scales or modes are imitated, no instrumental
techniques imitated with any degree of recognizeablitiy and no known
gamelan melodies are cited. (In contrast, the impact upon Debussy of
American, Spanish and Russian folk or entertainment musics was quite
explicit).

I think that what can be much more concretely established is the fact that
the very _idea_ of Debussy being influenced by gamelan has captured the
imagination of musicians in later generations. Many of these, would
actually be so inspired by the idea to undertake a deeper study of the
music.

To the best of my knowlege it was Henry Cowell, who studied gamelan in
Berlin in the early 1930 who was the first western composer to gain a
working knowledge of gamelan music.

Daniel Wolf wrote:

> It appears impossible to locate a concrete example of gamelan influence on
> Debussy in his scores. No scales or modes are imitated, no instrumental
> techniques imitated with any degree of recognizeablitiy and no known
> gamelan melodies are cited. (In contrast, the impact upon Debussy of
> American, Spanish and Russian folk or entertainment musics was quite
> explicit).
>
> I think that what can be much more concretely established is the fact that
> the very _idea_ of Debussy being influenced by gamelan has captured the
> imagination of musicians in later generations. Many of these, would
> actually be so inspired by the idea to undertake a deeper study of the
> music.

Dan!
First, Thanks for clearing up the scale! It could well be that the
influence on Debussy was more of a way of hearing. There is his use of
Pentatonic scales as especially his use of Pentatonic chords. There are
passages where he rocks between two chords mush like you have in passages of
the Wayang. Would not these type of passages possibly be common in pieces with
Dance?

-- Kraig Grady
North American Embassy of Anaphoria Island
www.anaphoria.com

> >Just as Debussy Broke through the parallel 5th rule
> he likewise broke through the parallel M3rd in his use of them in Whole
> tone scales.

Perhaps this isn't very relevant since we're discussing 16th-century
part-writing in particular, but as far as the four-part writing taught in
typical freshman and sophomore Harmony classes are concerned, there's
nothing "wrong" with writing parallel thirds or sixths of the same type.
It's certainly not difficult to find plenty of examples of parallel thirds
and sixths of the same type in the examples in Harmony texts like Walter
Piston's.

Gary Morrison wrote:

>
> Perhaps this isn't very relevant since we're discussing 16th-century
> part-writing in particular, but as far as the four-part writing taught in
> typical freshman and sophomore Harmony classes are concerned, there's
> nothing "wrong" with writing parallel thirds or sixths of the same type.
> It's certainly not difficult to find plenty of examples of parallel thirds
> and sixths of the same type in the examples in Harmony texts like Walter
> Piston's.

I was just pointing out how Zarlino would have objected to parallel thirds.
In his book he states it is best to avoid parallel intervals of the same
ratio. In the diatonic the thirds alternate between major and minor except in
one place. I was using Debussy as an example of parallel thirds of the same
ratio in the whole tone scale!
-- Kraig Grady
North American Embassy of Anaphoria Island
www.anaphoria.com

Kraig Grady wrote:

>In the diatonic the thirds alternate between major and minor except in
>one place

???

c-e: major
d-f: minor
e-g: minor
f-a: major
g-b: major
a-c: minor
b-d: minor

Really, now, Kraig!

Message text written by Paul Erlich
<>Kraig Grady wrote:
<
<>In the diatonic the thirds alternate between major and minor except in
<>one place
<
<???
<
<c-e: major
<d-f: minor
<e-g: minor
<f-a: major
<g-b: major
<a-c: minor
<b-d: minor
<
<Really, now, Kraig!<

Although it doesn't directly support his point, Kraig was probably making
reference to the M-m alternations in a diatonic chain of thirds:

f-a M
a-c m
c-e M
e-g m
g-b M
b-d m
d-f m

The main point about the rule of successive thirds in the same ratio is the
avoidance of a tritone cross relation, as in b/d to f/d or from a/f to b/g.

>Message text written by Paul Erlich
><>Kraig Grady wrote:
><
><>In the diatonic the thirds alternate between major and minor except
in
><>one place
><
><???
><
><c-e: major
><d-f: minor
><e-g: minor
><f-a: major
><g-b: major
><a-c: minor
><b-d: minor
><
><Really, now, Kraig!<

Daniel Wolf wrote,

>Although it doesn't directly support his point, Kraig was probably
making
>reference to the M-m alternations in a diatonic chain of thirds:

>f-a M
>a-c m
>c-e M
>e-g m
>g-b M
>b-d m
>d-f m

Sorry, Kraig! Of course! But parallel thirds would occur most commonly
with both voices moving by step, so my list is more relevant to his
point.

>The main point about the rule of successive thirds in the same ratio is
the
>avoidance of a tritone cross relation, as in b/d to f/d or from a/f to
b/g.

That's right! So d/f to e/g or a/c to b/d would be very common instances
of allowed parallel minor thirds.

Message text written by INTERNET:tuning@onelist.com
>That's right! So d/f to e/g or a/c to b/d would be very common instances
of allowed parallel minor thirds.<

But these two sets of parallel minor thirds are -- in 5-limit just --
succession of different ratios 32/27 to 6/5. So Zarlino's rule stands.