Parallel fifths discussion

And now the parallel fifths email...

On Fri, Dec 7, 2012 at 2:26 AM, Margo Schulter <mschulter@...> wrote:
>>
> So various people, including Joseph Yasser if I recall, have
> suggested that parallel fifths in a medieval setting are like
> parallel thirds or sixths in a 16th-century setting. As the
> favorite stable concords, they are acceptable as parallels -- but
> limited in serious counterpoint by the general preference for a
> variety of motions (especially contrary) and intervals.

This is an interesting thought; I've never come across this idea
before. But I guess my question is, why do the parallel thirds and
sixths have to come -at the cost- of parallel fifths then? Why didn't
16th-century harmony just adopt full parallel triads, with parallel
thirds and parallel fifths and everything?

Also, do you know if the status of parallel octaves changed from the
medieval era to the 16th century?

> >> And even in the 16th century, it's not the _sound_ of parallel
> >> fifths in textures for three or more voices that's the issue, but
> >> the relative loss of independence of parts where 3/2 is no longer
> >> the standard of rich stability, but less ideally euphonious than
> >> a third, sixth, or tenth. If the two voices cross which form the
> >> fifths, there's no violation of the rule. Some anachronistic
> >> criticism of 16th-century compositions treats this as a flaw; but
> >> it's a flaw in the eyes of the beholder, not of 16th-century
> >> practice or theory.
>
> > Not sure I understand; do you mean that they're treating 3/2 as
> > dissonant in general? As in, it's not as "stable"?
>
> A good question that helps me communicate more clearly! There's
> no question that 3/2 or 2:3:4 is still stable in the 16th
> century, but it's increasingly felt as "stable but incomplete."

OK, so after your examples, I know what you mean. So if I understand
correctly, you're saying that a tradeoff is involved: in the medieval
era, having parallel fifths gives you a loss of independence of parts,
but now given the added advantage of having lots of nice rich trines
around, this trade-off is worth it. But in the 16th century, trines
weren't such a big deal, as you demonstrated with your Emaj -> A5
resolution, so now you're only getting the loss of independence of
parts without any of the "functional" advantage. Right?

I also note that a similar situation happens in extended harmony,
particularly in things like jazz standards where every dominant 7
chord has tons of extensions on it and so on. Playing a raw dominant 7
tetrad in closed position is pretty much the kiss of death in that
setting; it's rather "conservative," as you described the resolution
to A5 in Zarlino's time.

> And Don Randel has suggested that the prohibition against
> parallel fifths, as it became more consistently observed by
> around 1450, played a large role in shaping 16th-century and
> later progressions by a process of exclusion. As someone most
> often following a medieval style, with countless cadences and the
> like routinely involving parallel fifths, I can appreciate his
> point.

Do you mean here because the "rules" prohibiting parallel fifths
started to pigeonhole composers into newer and different directions
when they'd invent chord progressions?

> The interesting thing is that, if one assumes our 20/11 or
> whatever is stable and ideally euphonious, analogous to 5/4 in a
> 16th-century style, then applying both factors might lead to
> tentative rules we could try out like these:
>
> (1) Avoid parallel 3/2's in "serious" 16th-century-like
> writing;
>
> (2) Use parallel 20/11's or 51/28's or whatever in a
> restrained way, especially in two-part writing, because
> they're ideally rich and euphonious, but a row of more
> than two or three creates something more like a textural
> effect than the development of two independent voices.
>
> (3) With three or more voices, we might loosen up a bit on
> rule (2), since two voices moving in parallel 20/11's or
> whatever can be balanced by other voices in oblique or
> better yet contrary motion.

I think these rules are a great starting point! As for number 2: Do
you expect that the generator, aka this 20/11 or 9/5 or 11/6, will be
acting in some sort of "rich and euphonious" way, in analogy to the
role of the fifth in medieval music, by virtue of its generating the
scale? Or is it simple ratios that you expect will be rich and
euphonious, such as 3/2 and 5/4? Or both? I do expect that 3/2 and 5/4
will be more concordant from a purely psychoacoustic perspective, but
I think we're talking about something different here.

> No problem, and taking some time led you to some really helpful
> questions which I saw shortly after getting back online. And
> thanks for your patience in waiting for my reply!

No problem, and thanks for taking the time to write these rules out!
Can I repost these on the Facebook Xenharmonic Alliance group?

Thanks,
Mike

Mike wrote:

> No problem, and thanks for taking the time to write these rules
> out! Can I repost these on the Facebook Xenharmonic Alliance
> group?

Please let me very quickly reply to say, "Yes, and thank you for reposting!" while I read more carefully over your two great posts.

I might just add that I was assuming a style where ~20/11 or
whatever is regarded as consonant and richly stable, like Paul
Erlich's 4:5:6:7 in his decatonic system. And I'd say that the
generator of a given linear system is often, but not necessarily
always, regarded as a consonance of one sort or another.

Since I can't access Facebook with my available browsers, I would
also be glad by e-mail to respond to any comments of questions
people may have for me in that group.

With many thanks,

Margo

an overlooked tonal strength of parallel fifths, such as in the progression dflat-f-aflat ---> c-e-g, is that you have semitone movement in each voice, displaying the "semitone force" which notable psychoacousticians (I think it was Richard Parncutt; I can't find the reference) have discussed. The six-four version (aflat-dflat-f ---> g-c-e) is perhaps even stronger, as it retains the semitone force and has, instead, parallel P4s and M6s.

--- In tuning@yahoogroups.com, Margo Schulter <mschulter@...> wrote:
>
> Mike wrote:
>
> > No problem, and thanks for taking the time to write these rules
> > out! Can I repost these on the Facebook Xenharmonic Alliance
> > group?
>
> Please let me very quickly reply to say, "Yes, and thank you for
> reposting!" while I read more carefully over your two great posts.
>
> I might just add that I was assuming a style where ~20/11 or
> whatever is regarded as consonant and richly stable, like Paul
> Erlich's 4:5:6:7 in his decatonic system. And I'd say that the
> generator of a given linear system is often, but not necessarily
> always, regarded as a consonance of one sort or another.
>
> Since I can't access Facebook with my available browsers, I would
> also be glad by e-mail to respond to any comments of questions
> people may have for me in that group.
>
> With many thanks,
>
> Margo
>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
>
> > >> And even in the 16th century, it's not the _sound_ of parallel
> > >> fifths in textures for three or more voices that's the issue, but
> > >> the relative loss of independence of parts where 3/2 is no longer
> > >> the standard of rich stability, but less ideally euphonious than
> > >> a third, sixth, or tenth. If the two voices cross which form the
> > >> fifths, there's no violation of the rule. Some anachronistic
> > >> criticism of 16th-century compositions treats this as a flaw; but
> > >> it's a flaw in the eyes of the beholder, not of 16th-century
> > >> practice or theory.
> >
> > > Not sure I understand; do you mean that they're treating 3/2 as
> > > dissonant in general? As in, it's not as "stable"?
> >
> > A good question that helps me communicate more clearly! There's
> > no question that 3/2 or 2:3:4 is still stable in the 16th
> > century, but it's increasingly felt as "stable but incomplete."
>
> OK, so after your examples, I know what you mean. So if I understand
> correctly, you're saying that a tradeoff is involved: in the medieval
> era, having parallel fifths gives you a loss of independence of parts,
> but now given the added advantage of having lots of nice rich trines
> around, this trade-off is worth it. But in the 16th century, trines
> weren't such a big deal, as you demonstrated with your Emaj -> A5
> resolution, so now you're only getting the loss of independence of
> parts without any of the "functional" advantage. Right?
>
> I also note that a similar situation happens in extended harmony,
> particularly in things like jazz standards where every dominant 7
> chord has tons of extensions on it and so on. Playing a raw dominant 7
> tetrad in closed position is pretty much the kiss of death in that
> setting; it's rather "conservative," as you described the resolution
> to A5 in Zarlino's time.
>

For the 16th century, part of my understanding behind the prohibition on parallel fifths was meantone temperament, where the interval of a fifth is not, in fact, 3/2. Parallel intervals of whatever sort do tend to draw the listener's attention, so minimizing the impact of a dissonant interval would involve avoiding parallel motion in that interval. For sure, having interesting counterpoint is also very important - I'm sure that the avoid-the-parallel-fifth rule from this period did not have just one reason behind it.

Also, a dominant 7 tetrad in closed position is extremely common in jazz. The parallel motion that happens in sequences of closed position chords is one of the most powerful ways to harmonize a melody. Every voice has similar motion to the melody, making the melody that much clearer. Even for non-melodic material, closed position harmonies are still pretty common, if for no better reason than that most pianist's left hand isn't big enough to play more spread than that while the right hand covers (for example) bebop melodies.

On Mon, Dec 10, 2012 at 4:25 PM, bigAndrewM <bigandrewm@...> wrote:
>
> For the 16th century, part of my understanding behind the prohibition on
> parallel fifths was meantone temperament, where the interval of a fifth is
> not, in fact, 3/2. Parallel intervals of whatever sort do tend to draw the
> listener's attention, so minimizing the impact of a dissonant interval would
> involve avoiding parallel motion in that interval. For sure, having
> interesting counterpoint is also very important - I'm sure that the
> avoid-the-parallel-fifth rule from this period did not have just one reason
> behind it.

I'm not sure I agree with this. I think that even a 696 cent 3/2, for
instance, is a bit more consonant than something like 8/5, for
instance. Plus, if we're talking about four voices, the voices aren't
required to sing exactly 696 cents for every fifth; they're free to
dynamically sing the fifth a bit higher to improve the intonation.

> Also, a dominant 7 tetrad in closed position is extremely common in jazz.
> The parallel motion that happens in sequences of closed position chords is
> one of the most powerful ways to harmonize a melody. Every voice has similar
> motion to the melody, making the melody that much clearer.

Yes, that's true. In a big band setting, where there'll be something
like 5 voices all harmonizing the melody, that will happen. I was
thinking more from the perspective of a pianist playing pads.

> Even for
> non-melodic material, closed position harmonies are still pretty common, if
> for no better reason than that most pianist's left hand isn't big enough to
> play more spread than that while the right hand covers (for example) bebop
> melodies.

Closed-position harmonies are common, but closed-position dominant 7
tetrads with no extensions whatsoever are not common. I guess I might
play one as a quick jab here and there during a solo, where my right
hand is free to imply whatever extensions I want, but I'd probably be
more likely to play third-seventh or third-seventh-ninth or something
like that. And if I'm -not- soloing, but I'm just comping behind a
horn player on a tune like Conception or whatever, you can bet I'd
almost never actually decide to play closed-position dominant 7
tetrads behind those ii-V's.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Mon, Dec 10, 2012 at 4:25 PM, bigAndrewM <bigandrewm@...> wrote:
> >
> > For the 16th century, part of my understanding behind the prohibition on
> > parallel fifths was meantone temperament, where the interval of a fifth is
> > not, in fact, 3/2. Parallel intervals of whatever sort do tend to draw the
> > listener's attention, so minimizing the impact of a dissonant interval would
> > involve avoiding parallel motion in that interval. For sure, having
> > interesting counterpoint is also very important - I'm sure that the
> > avoid-the-parallel-fifth rule from this period did not have just one reason
> > behind it.
>
> I'm not sure I agree with this. I think that even a 696 cent 3/2, for
> instance, is a bit more consonant than something like 8/5, for
> instance. Plus, if we're talking about four voices, the voices aren't
> required to sing exactly 696 cents for every fifth; they're free to
> dynamically sing the fifth a bit higher to improve the intonation.
>

Well, yes, I'm assuming that keyboards drove the development of theory in this period with the meantone reference; of course choirs would have no such restriction, whether or not a 696 cent fifth sounds better than an 8/5 or not.

To rephrase the other point, might it be that if the focus is to maintain the greater integrity of independent lines, parallel thirds might be more allowable because they are higher on the overtone series than fifths, thus are more distinguishable by the ear? By that logic, if we extend harmony to higher harmonics than the third, say perhaps the ninth, then would it not follow that such harmony would best preserve independent lines if parallel fifths and thirds are avoided, but parallel ninths and seconds are encouraged?

--- In tuning@yahoogroups.com, "kellyjohnson5001" <kellyjohnson5001@...> wrote:
>
> an overlooked tonal strength of parallel fifths, such as in the progression dflat-f-aflat ---> c-e-g, is that you have semitone movement in each voice, displaying the "semitone force" which notable psychoacousticians (I think it was Richard Parncutt; I can't find the reference) have discussed.

Can anyone provide a reference on "semitone force"?

I'm pretty sure I saw it in Richard Parncutt's book "Harmony: a Psychoacoustical approach". The context was the semitone and voiceleading. I don't have the book handy now.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "kellyjohnson5001" <kellyjohnson5001@> wrote:
> >
> > an overlooked tonal strength of parallel fifths, such as in the progression dflat-f-aflat ---> c-e-g, is that you have semitone movement in each voice, displaying the "semitone force" which notable psychoacousticians (I think it was Richard Parncutt; I can't find the reference) have discussed.
>
> Can anyone provide a reference on "semitone force"?
>

Dear Mike and all,

There are some historical points I would like
to offer, apologizing for length, but seeking
to present a balanced picture.

Whether the introduction and general adoption of
meantone contributed to the strict enforcement of
the rule against parallel fifths in multivoice
textures is an open question. It isn't the answer
I would have given, but that doesn't mean that it
isn't at least part of the picture.

The rule itself -- understood at first to apply
only in two voices moving note against note, as
opposed to ornamental counterpoint or multivoice
composition -- appears in the early 14th century,
and seems associated with the Ars Nova "moderns."
These "moderns" also call for a stricter treatment
of intervals such as major seconds (9:8), major
ninths (9:4), and minor sevenths (16:9) as clearly
dissonant, and reserved for ornamental contexts.

In contrast, 13th-century perspectives do not
prohibit any specific parallels (including octaves,
which frequently occur), but simply call for a
variety of intervals and motions, with contrary
motion generally preferred. Parallel fifths are
common in the best writing, e.g. Perotin, and in
two-voice, note-against-note, textures as well
as others. Also, 9:8, 16:9, and 9:4 are often
held to be relatively dissonant but with some
"compatibility" (a common 20th-century European
view also), and Jacobus Liege regards them as
"imperfect concords," likewise meaning rather
tense but not acutely so, with 9:4 actually
an "intermediate concord" comparable to 81:64
or 32:27.

The rule against parallel fifths, as well as
octaves, in simple two-voice writing could
thus be seen, like the treatment of major
seconds and ninths as well as minor sevenths,
as a shift toward a more privileged role for
thirds -- and also major and eventually minor
sixths, still unstable but likely more often
to be used under the new rules simply because
lots of other traditional possibilities would
be excluded -- if these rules were actually
followed.

In 13th-century theory and practice, the contrast
was between stable 2:1, 3:2, and 4:3 concords,
and a range of unstable intervals, with thirds
and sixths very important, but seconds and sevenths
also used frequently and often boldly. Even
"perfect discords" about which theorists had
mixed feelings, such as minor seconds (256:243)
and major sevenths (243:128), occur prominently
in practice, as Perotin's music will bear out.

Despite the new 14th-century rules, a composer
such as Machaut favors traditional 13th-century
liberties with seconds, sevenths, and ninths,
while also following the modern taste for an
increased focus on thirds and sixths.

For traditionalists, moderns, and artists such
as Machaut choosing the most appealing traits
of both the old and new approaches, however,
parallel fifths are an accepted reality in
writing for three or more voices. Standard
cadences would be impossible if the modern
rule -- however observed or otherwise in
two-voice writing -- were applied here.
And this remains true, at times, even in
the earlier 15th century. Consider, for
example, this wonderful cadence:

G# A
C# D
E D

Here the unstable sonority of major sixth and
tenth could be 32:54:81 (1/1-27/16-81/32) in
the standard Pythagorean tuning, or possibly
something like 7:12:18 in an accentuated
cadential style of the kind described by
Marchettus of Padua. The resolution to a
stable 1:2:3, with the wide 12th typical of
the wider range often favored in this era,
is most memorable. And the parallel fifths
between the two upper voices are a routine
aspect of this cadence.

A four-voice version, perhaps most famously
used in Machaut's _Mass_, shows that parallel
octaves are also permissible in this context:

G# A
C# D
G# A
E D

At the opening of the 15th century, Prosdocimus
de Beldemandis, also an advocate of a 17-note
Pythagorean tuning (Gb-A#) to make regular
Pythagorean intervals available at more locations,
explains that parallel fifths and octaves are
excluded because the point of counterpoint is
for the singers to produce a variety of intervals,
not to have them sing the same thing. This is a
common argument in later literature, also.

Prosdocimus definitely takes a Pythagorean
viewpoint on intonation, specifically preferring
to avoid the near-5-limit schismatic thirds which
around 1400 are coming into vogue, with the
tuning chain altered to move this altered thirds
into more prominent locations. So a general
rule of avoiding parallel fifths in two-voice
writing clearly developed well before the era
where meantone is presumed to have come into
vogue, around 1450-1480.

One date suggested as the point where the rule
against parallel fifths becomes generally observed
in multivoice writing is around 1450. The advent
of meantone, which some have seen as implied by
the style of Conrad Paumann's keyboard compositions,
likely dates to about this time also.

Other changes are also taking place. For example,
the beautiful 14th-century cadence with major
third and sixth expanding to fifth and octave,
with some variants with an expansion from major
tenth to twelfth as shown above, is being largely
replaced by other forms. Restrictions on seconds
and sevenths are being more strictly observed --
with these intervals, however, being harnessed
in the special idiom of the suspension dissonance.

What is new is not the prominent use of thirds and
sixths -- important intervals through the 13th-14th
century era -- but the increasing feeling for these
intervals as not only pleasant and euphonious but
restful and "firm." It is this "firmness" which
meantone or 5-limit JI supports.

Both the increasing stylistic and intonational
stability of thirds and sixths, and the general
desire for a refined art of counterpoint where
all elements are in a delicate balance, may have
led to the feeling that any two voices moving
in parallel fifths somehow introduced an element
of disproportion.

Yet there are sometimes exceptions made in the
later 15th century for certain situations
involving canon or imitation for example --
loopholes generally closed in 16th-century theory.

The rule against parallel fifths between any two
voices of a multivoice texture thus seems to
correlate with a number of changes around the
mid-15th century, with meantone temperament
being one of those changes. However, the causal
relationships remain open to debate: correlation
sometimes, but not always, involves causality.

However, the idea that a desire to avoid parallel
fifths was related specifically to meantone might
invite a consideration of some factors on either
side of the argument.

Certainly parallel fifths _were_ favored in vocal
genres such as the villanella, and also used for
less "serious" instrumental music, including much
dance music for keyboards, which would very likely
have been tempered in meantone. In Italy, where
such dance music was common, the tempering may
have been often at 1/4-comma or 2/7-comma, making
any meantone-related distaste for these fifths
more pronounced; but there seems to have been
no problem for performers or listeners.

Especially interesting are the statements of
early composers and theorists of basso continuo
or thoroughbass such as Viadana and Praetorius,
who advise that the extemporized _organ_ continuo
part is not obliged to avoid parallel fifths.
Around 1600, organs would have generally been
tempered in meantone, with Praetorius specifically
favoring 1/4-comma, which in the German literature
(e.g. Werckmeister) sometimes became known as the
"Praetorian temperament." So formally correct
written counterpoint versus a more flexibly realized
continuo seems to have been the relevant distinction
for at least these writers, rather than the impurity
of fifths in meantone.

The views of Vicenzo Galilei might be cited to support
either side of the argument here. He regards the
application of the rule against parallel fifths to
multivoice writing as wrong and pedantic, as he also
holds of many of the conventional rules restricting the
use of dissonance.

Interestingly, although proposing a possible scenario
for the adoption and evolution of the rule rather
than citing actual medieval developments (not so well
known in this era), he suggests that the rule
originally applied only to two-part counterpoint,
where a series of fifths might seem not to have
enough variety. With three or more voices, however,
the rule did not make sense to him.

Galilei was a noted advocate of 12-EDO, which he saw
as a "perfection" of the lute in its standard fretting,
and wanted to apply to harpsichord as well, although
he admitted that, having tried it, he preferred 2/7-comma
meantone, the tuning of his former teacher and major
opponent Zarlino. One might argue either a correlation
between his tolerant attitude toward parallel fifths and
advocacy of 12-EDO with its near-pure fifths; or note his
willingness to have these fifths played on a harpsichord
in 2/7-comma meantone, whose imperfections he evidently
saw not so much in terms of the greater temperament
of the fifths, but the absence within a usual 12-note
tuning of free transposibility.

Someone might also argue that the general adoption
around 1900 of 12-EDO as a standard for keyboards
correlates with the trend toward new styles favoring
fourths and fifths, in a neomedieval manner or
otherwise, with the free use of parallel fifths as
a trademark of Debussy and others. The argument
might run that standard tunings with pure or near-pure
fifths correlate with the two eras, the 9th-14th
centuries and the 20th-21st centuries, when parallel
fifths have been permissible and even relished.

One reason I am inclined from experience to the view
that tempering in itself may not be the main factor
is experience with parallel fifths in systems where
the tempering is in the _wide_ direction, but
comparable to that of 15th-17th century meantone.

For example, 17-EDO with fifths almost 4 cents wide
(705.88 cents) is comparable in impurity to a more
moderate shading of 16th-century meantone at
around 1/5-1/6 comma. George Secor's 17-WT has its
nine nearer fifths at 707.22 cents, very close to
the impurity of 1/4-comma meantone. And 22-EDO
at 709.09 cents is almost identical in its degree
of impurity to 1/3-comma meantone or 19-EDO.

While my own experience may say little about
how European composers and theorists heard things
around 1450, I can say that parallel fifths pose
no problems for me in any of these wide-fifth
tunings: if they did, I would have problems,
since such fifths are absolutely routine in
standard medieval or neomedieval cadences.

While not deciding the matter, the views
of period theorists may also be of interest
on this point: it is sometimes explained that
those who developed the rule against these
parallels did so because "they did not wish
to repeat perfection many times." Such fifths
are disfavored in a Renaissance style not
because they are too dissonant, but because
they are felt as too completely blending,
too "simple," even when offset by the varied
motions of other voices.

My apologies for possibly being detailed to
a fault; and I would emphasize that exploring
this kind of hypothesis can be very productive,
wherever the inquiry leads, both in understanding
history and getting ideas for the creation of
new music.

Also, recent scholarship could have things to
say that might make my suggestions a bit
obsolete or even incorrect -- this happens!
My initial caution doesn't mean the hypothesis
is wrong, and I'm very open to persuasion in
either or any direction.

With many thanks,

Margo

As always, I am amazed at the expertise and clarity of how people discuss here.

Thank you!