Pure fifths and "high" thirds?
Margaret Hasselman
Clearly, the style of the music is relevant to the kind of tuning you should
use. I was just at a wonderful vocal workshop where the acoustics of the
hall rendered the overtone series unusually audible. (In fact, one
participant performed "Taps" on a single fundamental). This demonstrated to
ALL the a capella singers present, many of whom were newbies, just how
different acoustic thirds sound from the ET piano!
By no coincidence, much of the chosen repertoire was from the Renaissance.
In medieval music, where thirds were considered unstable and needing a
resolution to a fifth, a less "sweet" tuning would be appropriate.
Likewise, in music clearly conceived for equal temperament, one would tune
accordingly. The choice is ESSENTIAL for keyboard tuning, of course, but
needs to be considered by singers (and other instrumentalists) as well.
Just think: is the interval stable or unstable?
Similarly for sevenths: are they resolving or are you sitting on them?
Cheers, and keep listening sensitively!
Margaret
John Howell
>
>By no coincidence, much of the chosen repertoire was from the Renaissance.
>In medieval music, where thirds were considered unstable and needing a
>resolution to a fifth, a less "sweet" tuning would be appropriate.
>Likewise, in music clearly conceived for equal temperament, one would tune
>accordingly. The choice is ESSENTIAL for keyboard tuning, of course, but
>needs to be considered by singers (and other instrumentalists) as well.
>Just think: is the interval stable or unstable?
I've known Margaret for a long time, and played and sung with her a
lot, so she knows how much I respect her musicianship and opinions.
Indeed, she told me about this List, the first I ever joined. Still,
she is a keyboardist and I am not. And she has also been attending
the sessions at Kalamazoo regularly, which I have not.
Here's my conceptual problem. Granted, I think the medieval
theorists did write about Pythagorean tuning (just as renaissance
theorists wrote about equal temperament, and I'm sure Margo or Todd
could provide the citations that I cannot). But does that mean that
they actually sang the extremely wide Pythagorean major 3rds? It
seems that fashion today accepts that they did. But I have to
question that, because I find it hard to believe that medieval
singers' ears would accept the harsh beats of those intervals,
especially in a reverberant hall, when a slight adjustment would make
them pure. Pythagorean intervals are, of course, a perversion of the
pure intervals of the natural harmonic series, which both Pythagorus
and his later disciples understood quite well, and Pythagorean is a
keyboard temperament.
Granted, the theorists also considered 3rds and 6ths "imperfect
consonances"--neither dissonant nor fully consonant--and that
continued into the early 16th century in the structure of renaissance
cadencial formulas, moving from dissonance (2nds or 7ths) to
imperfect consonances (3rds or 6ths) to perfect consonances (octaves,
5ths & 4ths). And of course this observation can be used on either
side of the argument: either medieval major 3rds WERE more dissonant
than later major 3rds, or their ears were more attuned to the perfect
consonances so that 3rds and 6ths just SEEMED more dissonant.
(To be fair, when I attempt to tune our small organetto, I do tune
perfect 5ths because they simply sound better, and let the 3rds fall
where they may!)
Adding to that the fact that all "theorists" were first and foremost
performing musicians, however, I have to wonder about those
Pythagorean major 3rds, when pure 3rds were so easy to hear and sing.
(At one point in history, when Bob Marvin was making sets of
recorders with Pythagorean tuning, I had the perfect opportunity to
ask him about it, but at that time I didn't even understand the
problem! Or how recorders could be in Pythagorean tuning in more
than a single key.)
John
--
John R. Howell, Assoc. Prof. of Music
Virginia Tech Department of Music
College of Liberal Arts & Human Sciences
Blacksburg, Virginia, U.S.A. 24061-0240
Vox (540) 231-8411 Fax (540) 231-5034
(mailto:John....@vt.edu)
http://www.music.vt.edu/faculty/howell/howell.html
"We never play anything the same way once." Shelly Manne's definition
of jazz musicians.
Todd Michel McComb
John Howell <John....@vt.edu> wrote:
>Granted, I think the medieval theorists did write about Pythagorean
>tuning (just as renaissance theorists wrote about equal temperament,
>and I'm sure Margo or Todd could provide the citations that I
>cannot). But does that mean that they actually sang the extremely
>wide Pythagorean major 3rds? It seems that fashion today accepts
>that they did. But I have to question that, because I find it hard
>to believe that medieval singers' ears would accept the harsh beats
>of those intervals, especially in a reverberant hall, when a slight
>adjustment would make them pure.
It's certainly my belief that singers did sing the wide thirds. My
aural intuition is the same. A lot of medieval music sounds
absolutely absurd to me in any other tuning; I can't even listen
to it.
Linear concerns and keeping the same notes sung at the same pitch
throughout a piece are very important to this music. I've heard
e.g. a Dufay mass sung with singers adjusting notes to have pure
vertical thirds in the middle of phrases, and it just sounds
ridiculous, making a total jumble of the musical logic. But then
that's to my ears.
Todd McComb
mcc...@medieval.org
pedrosousasilva
theorists did write about Equal Temperament. But does that mean that
they actually sang the extremely tasteless 3ds and 5ths? It
seems that fashion today accepts that they did. But I have to
singers' ears would accept the boredom of those intervals,
especially in a reverberant hall, when a slight adjustment would make
the
pure intervals of the natural harmonic series, which both Ellis
and his later disciples understood quite well, and Equal Temperament
is a keyboard temperament.
Pedro
Oliver Webber
> Here's my conceptual problem. �Granted, I think the 21st Century
> theorists did write about Equal Temperament. �But does that mean that
> they actually sang the extremely tasteless 3ds and 5ths?
This is the key: "tasteless"
This, of all words, has no absolute point of reference from century to
century! What is tasteless to one generation may be the height of
elegance in the next, and vice versa.
�It
> seems that fashion today accepts that they did. �But I have to
> question that, because I find it hard to believe that post-modern
> singers' ears would accept the boredom of those intervals,
> especially in a reverberant hall, when a slight adjustment would make
> them pure.
Sorry, what do you mean exactly? What post-modern singers? Which
intervals are "boring"? Why?
Equal temperament intervals are, of course, a perversion of
> the
> pure intervals of the natural harmonic series, which both Ellis
> and his later disciples understood quite well, and Equal Temperament
> is a keyboard temperament.
All temperaments are keyboard temperaments, (although I believe ET as
a theory was mentioned by lutenists more often than keyboardists, as
there seems to be no easy way to match mean-tone on a lute.)
All temperaments involve compromising the natural harmonic series -
mean tone prioritises thirds in home keys, Pythagorean prioritises
5ths, ET spreads the "problem" equally.
>
> Pedro
John Howell
I agree completely. You may now remove your tongue from your cheek!
(Makes it difficult to talk.)
pedrosousasilva
if some previous points are not made.
In every period, including ours, there is so much of empiricism as
reflective knowledge. Imagine for instance that one wants to
understand pop music without ever listening to any of it, only from
books, critics, interviews, scores, photos and cd covers. How further
in understanding or recreating pop could one go with this information
only?
As human beings, we all create our emotional-logical references that
guide our perception. This dictates greatly our conception of a given
repertory and help us to build a picture of how things "were", "are"
or "should be".
There is no right or wrong in such a matter as temperaments. My
inversion of John Howell's text was to demonstrate that the same words
and reasoning could apply to equal temperament and that the
conclusions could be equally true or false, according to who reads
them. That's why John is "convinced that" or Todd has an "aural
intuition". These expressions are true since they participate on their
perception of the phenomena but they might be false to someone else.
However, and this is a very big however, when we devote ourselves to
historical practices we have to consider greatly the factor "context".
Music from the the XIVth century is different from the one from the
XVIth, XVIIIth or somewhere else. We all know that, of course, but it
seems we easily forget it. Let me give you an example:
Everyone likes to quote Galillei when it comes to "defend" ET. Some
will remember that we have to consider that Vicenzo was a lutenist and
therefore we have to restrain his information from the lute world. But
a slightly younger lutenist, John Downland, also proposes a
temperament which is (suprise!) a slightly modified Pythagorean (not
meantone). So, two contemporary lutenist propose solutions which are
so opposite among them and that not comply to what to "should be" the
standard from the period, meantone. We have, however, to keep in mind
that the music from Galillei is very different from Downland's.
Galillei has pieces written in 24 keys, which cannot be separated from
the fact that he advocated ET; or in other words, Gallilei advocated
ET which cannot be separated from the fact that he wrote pieces in 24
keys (aka the chiken and the egg paradox).
Another example worth mentioning is Rameau, also considered to be a
defensor of ET. But in 1726 he proposes a temperament "pour avantager
les tonalités avec dièses" in which the keys with sharps will sound
exactly as 1/4 meantone. Evidently that taste changes, at least
Rameau's did.
Going back to middle age we fewer options. If in Renaissance and
Baroque we have many "solutions" to the "problem", in continental
middle ages all indicators point to a Pythagorean model. In
Marchetto's temperament, major 3ds are even bigger than in
Pythagorean. Temperament, harmony and counterpoint go hand in hand.
The same way that in continental music we cannot separate the tuning
of a major 3rd or 6th from the rule that states "all perfect
consonances should be approached by the nearest imperfect consonance",
we should not put in the lot English music which is related to
Anonymous 4's notion that "3ds are the best consonances". Some might
object that theory is one thing and practice is other, and that is
true since many treatises start stating that they write about what
musicians are doing already. But it will take an while until non-
Pythagorean solutions will start to spring, so it seems that
Pythagorean and medieval harmony are quite inseparable issues.
In short, there is no answer to this "problem". In fact, there isn't a
problem at all. There are options and contexts.
kind regards,
Pedro
P.S. I'm unfamiliar with the expression "remove your tongue from your
cheek".
howard posner
On Jul 16, 2009, at 9:11 AM, pedrosousasilva wrote:
> Some
> will remember that we have to consider that Vicenzo was a lutenist and
> therefore we have to restrain his information from the lute world.
You mean we have to limit what he says to the context of the lute?
> But
> a slightly younger lutenist, John Downland, also proposes a
> temperament which is (suprise!) a slightly modified Pythagorean (not
> meantone). So, two contemporary lutenist propose solutions which are
> so opposite among them and that not comply to what to "should be" the
> standard from the period, meantone. We have, however, to keep in mind
> that the music from Galillei is very different from Downland's.
> Galillei has pieces written in 24 keys, which cannot be separated from
> the fact that he advocated ET; or in other words, Gallilei advocated
> ET which cannot be separated from the fact that he wrote pieces in 24
> keys (aka the chiken and the egg paradox).
You make good points, but while it may be logical to assume that
Vicenzo Galilei's yen for ET went hand in hand with writing music
that needed ET, Vicenzo's music actually tends to be less tonally
adventurous than some of Dowland's, particularly the chromatic
fantasies. Galilei's 24-key pieces contain a good many pieces
obviously conceived in simple keys (by which I mean both simpler in
terms of sharps and flats as well more comfortable for the player's
hands -- for example, on a G lute, f minor is a fairly easy key and E
major clumsy and almost never used, though they have the same number
of accidentals) and then transposed into some more remote key to show
that it's possible to do it, even if hurts your hands and sounds
bad. I've been a lute player for 27 years and a listener longer than
that, and never heard anyone actually perform them, though a few
other Vicenzo Galilei pieces in conventional modes make an occasional
appearance (no one ever accused Vicenzo of being a great composer).
So I would class those works, unlike, say, the foreign-key excursions
of John Wilson, as theoretical exercises.
> P.S. I'm unfamiliar with the expression "remove your tongue from your
> cheek".
Something said with "tongue in cheek" is not meant to be taken
seriously, probably referring to the facial expression created by
sticking tongue in your cheek, perhaps to suppress laughter.
Sticking your tongue in your cheek tends to make you wink.
Oliver Webber
"tongue in cheek" post?
That's what comes of reading a thread in a hurry before having had my
first coffee of the day...
Mea culpa!
Oliver
pedrosousasilva
making decisions. But when it comes to decide, we must take the most
meaningful option for us, and that's personal, of course. Our opinions
reflect our lives (and vice-versa); this is true both for Downland,
Galillei or each one of us.
Historical information is, for me at least, the boundaries for this
research.
Pedro
P.S. I didn't take the expressions "tongue in cheek" seriously, I just
never had hear it before and got curious.
Neal Plotkin
"Margaret Hasselman" <mhas...@vt.edu> wrote:
> By no coincidence, much of the chosen repertoire was from the Renaissance.
> In medieval music, where thirds were considered unstable and needing a
> resolution to a fifth, a less "sweet" tuning would be appropriate.
> Likewise, in music clearly conceived for equal temperament, one would tune
> accordingly. The choice is ESSENTIAL for keyboard tuning, of course, but
> needs to be considered by singers (and other instrumentalists) as well.
> Just think: is the interval stable or unstable?
In article <h3g2ms$3044$1...@agricola.medieval.org>,
mcc...@medieval.org (Todd Michel McComb) wrote:
> It's certainly my belief that singers did sing the wide thirds. My
> aural intuition is the same. A lot of medieval music sounds
> absolutely absurd to me in any other tuning; I can't even listen
> to it.
>
> Linear concerns and keeping the same notes sung at the same pitch
> throughout a piece are very important to this music. I've heard
> e.g. a Dufay mass sung with singers adjusting notes to have pure
> vertical thirds in the middle of phrases, and it just sounds
> ridiculous, making a total jumble of the musical logic. But then
> that's to my ears.
Much of renaissance polyphony uses triads as stable consonances. But
performances may run into the comma-shift problem, first written about
by Benedetti (published in 1585): that if a vocal ensemble tries to
sing all chords pure, then, depending on the transitions between chords,
the ensemble may end up one or more (syntonic) commas away from where it
started.
Ross Duffin has an article about this issue in Music Theory Online
(http://mto.societymusictheory.org/issues/mto.06.12.3/mto.06.12.3.duffin_
frames.html). His thesis is that there are different ways to choose how
to do the transitions, and there are often (usually?) ways that make
musical sense, sound very good, and end up where they started.
Here's the abstract: "Just intonation has a reputation as a chimerical,
theoretical system that simply cannot work in practice. This is based on
the assessment of most modern authorities and supported by misgivings
expressed during the Renaissance when the practice was supposedly at its
height. Looming large among such misgivings are tuning puzzles printed
by the 16th-century mathematician, Giovanni Battista Benedetti. However,
Renaissance music theorists are so unanimous in advocating the simple
acoustical ratios of Just intonation that it seems clear that some
reconciliation must have occurred between the theory and practice of it.
This article explores the basic theory of Just intonation as well as
problematic passages used to deny its practicability, and proposes
solutions that attempt to satisfy both the theory and the ear.
Ultimately, a resource is offered to help modern performers approach
this valuable art."
The article has many sound clips, showing the problem, and what Duffin
considers bad and good ways to get around it. Obviously, his preferred
solutions are subjective. And my ears aren't good enough to hear many
of his distinctions. But I would be curious if Todd still finds
Duffin's solutions (or the included Hilliard Ensemble clip) ridiculous
and a jumble.
--
Neal Plotkin
my first name dot my last name at nyu dot edu
Todd Michel McComb
Neal Plotkin <m...@private.invalid> wrote:
>I would be curious if Todd still finds Duffin's solutions (or the
>included Hilliard Ensemble clip) ridiculous and a jumble.
I certainly do have to note that your post spoke exclusively about
Renaissance music, while I was discussing medieval. Admittedly, I
didn't help matters by naming an example on the border between the
two.
That said, I do think the approach that Rogers Covey-Crump outlines
(and the ensemble uses) in the Hilliard Live recording of Dufay's
Missa Se la face ay pale works well, but this is some of Dufay's
later music. I am guessing this is the source of the clip, but do
not really know.
That approach is/was a matter of choosing strategic note values
based on the piece, and not of retuning every chord. The latter
is something that occasionally seems to be implied here, and which
I think is a really bad idea. Luckily, ensembles hardly ever subject
medieval music to this kind of treatment.
Todd McComb
mcc...@medieval.org
Neal Plotkin
mcc...@medieval.org (Todd Michel McComb) wrote:
> In article <me-8618AD.15...@70-3-168-216.pools.spcsdns.net>,
> Neal Plotkin <m...@private.invalid> wrote:
> >I would be curious if Todd still finds Duffin's solutions (or the
> >included Hilliard Ensemble clip) ridiculous and a jumble.
>
> I certainly do have to note that your post spoke exclusively about
> Renaissance music, while I was discussing medieval. Admittedly, I
> didn't help matters by naming an example on the border between the
> two.
True, in both senses.... Although I think the actual distinction is
between music that uses triads as stable consonances (renaissance-like)
and music that doesn't (medieval-like). For the latter, Pythagorean
tuning is best.
> That said, I do think the approach that Rogers Covey-Crump outlines
> (and the ensemble uses) in the Hilliard Live recording of Dufay's
> Missa Se la face ay pale works well, but this is some of Dufay's
> later music. I am guessing this is the source of the clip, but do
> not really know.
Duffin's cite for the clip in the article is: Hilliard Ensemble (Thomas
Tallis: Lamentations of Jeremiah, ECM 1341 833 308-2 (1987).
> That approach is/was a matter of choosing strategic note values
> based on the piece, and not of retuning every chord. The latter
> is something that occasionally seems to be implied here, and which
> I think is a really bad idea. Luckily, ensembles hardly ever subject
> medieval music to this kind of treatment.
I agree. Retuning every chord may put the chords in tune, but it ruins
the transitions between chords. Duffin's goals are to have the chords
in tune, the transitions sound good, and the piece end where it began.
Duffin gave a class on his methods last week at summer early music camp
in Madison, WI. He also gave a public lecture based on the article. I
attended the lecture, but didn't take the class.
Todd Michel McComb
Neal Plotkin <m...@private.invalid> wrote:
>I think the actual distinction is between music that uses triads
>as stable consonances (renaissance-like) and music that doesn't
>(medieval-like).
I agree, although pinpointing this kind of thing can be difficult
over a few decades. Composers of the Josquin generation do final
cadences on open fifths, but do internal cadences in ways that sound
rather stable with thirds. If I were to briefly describe e.g. Dufay
in this regard, I'd say that he uses a lot of thirds, often in ways
that seem rather consonance-like, but there isn't a real stability
there.
>Duffin's cite for the clip in the article is: Hilliard Ensemble
>(Thomas Tallis: Lamentations of Jeremiah, ECM 1341 833 308-2 (1987).
Ah. I don't know what was said exactly, but I certainly agree that
the structural nature of the thirds in this piece are rather different
from Dufay, let alone earlier music.
>Duffin's goals are to have the chords in tune, the transitions
>sound good, and the piece end where it began.
It sounds like Duffin and I are mainly on the same page. Thanks for
bringing this up.
Todd McComb
mcc...@medieval.org