Difference tones
Phil Robbins
discussion about difference tones. Difference tones being those tones which,
although not played, nonetheless sound when two instruments are playing in
tune. When a pure third is played, the difference tone (with a buzzing
quality) is the fundamental sounding two octaves lower or when a pure fifth
is played, one octave lower. I would please like to hear from other
recorder players and/or other musicians about this phenomenon.
Thanks,
Phil Robbins
BREWERPAUL
******************************
Got wood?
Check out my exotic hardwood pennywhistles at fair
prices...http://www.Busmanwhistle.com
rv
But aren't these just a figment of the cochlea of ones inner ear?
(Unless you're Hindemith, of course).;--o)
rob
Alain Naigeon
001501c2f40b$fc43e200$0e65a2cd@youryk5cbmeeo8...
Hi Phil,
I think you've just explained the main features of these difference tones.
I'm personnally not sure to hear them clearly, though I know reliable
persons who say they are - I believe them! However I can hear them
in some indirect way, when they are used for tuning : at some point,
a just chord has a suddendly richer sound that seems to fill the room
in which you're playing - I guess this is because of this lower difference
tone.
Another striking detail I've learnt recently : in some small churches, in
which big organ pipes can't be used, some low notes are got which
2 pipes according to the procedure you've described !
BTW, a difference tone is just a consequence of harmonic production
(or the reverse process, one might say) : the first harmonic of a
(difference)
tone is just at 1 octave + fifth, the second one at 2 octaves + major third,
as you've said.
--
Français *==> "Musique renaissance" <==* English
midi - facsimiles - ligatures - mensuration
http://anaigeon.free.fr | http://www.medieval.org/emfaq/anaigeon/
Alain Naigeon - anai...@free.fr - Strasbourg, France
>
> Thanks,
> Phil Robbins
>
>
>
>
rv
>>Sometimes called combination tones.
>>But aren't these just a figment of the cochlea of ones inner ear?
>>(Unless you're Hindemith, of course).;--o)
I should have added that Hindemith used combination tones to "prove" that a fourth is a consonant interval in his treatise on musical composition. Forget the title (Craft of Musical Composition?). Traditionally the fourth is, of course, a dissonance
in standard harmony and counterpoint, and that didn't fit with PH's system.
>>rob
On 27 Mar 2003 11:46:37 +0200, philr...@midtown.net (Phil Robbins) wrote:
>Last week, I was playing recorder duets with a friend and we had a
>discussion about difference tones. Difference tones being those tones which,
<<snip>>
Alain Naigeon
3e8323c0...@news.compuserve.com...
> Sometimes called combination tones.
> But aren't these just a figment of the cochlea of ones inner ear?
I don't think so!
The difference tone between two frequencies at f1 and f2
is just, of course : f2-f1
If f1 = 440 and f2 = 441, you hear a change in amplitude
at 1 Hz.
if f1 = 440 and f2 = 550 (that is, a major third of ratio 5/4)
then the difference is 110, which is 2 octaves lower.
and, in general : 5/4 - 1 = 1/4 = 2 octaves lower
Thus it is a real physical phenomenon; of course, inner hear
is sensible to changes in air pressure, but it just records them,
it doesn't create them (if anything like that would happen,
it would be caused by the brain, not by the ear IMHO).
BTW, difference tones are known as a standard tuning
method for a recorder ensemble, for example.
Owk28
>BTW, difference tones are known as a standard tuning
>method for a recorder ensemble, for example.
>
Yes, and string players use them to tune double stops. I believe they were
described in some detail by Tartini.
Oliver Webber
Rodney Myrvaagnes
>Sometimes called combination tones.
>But aren't these just a figment of the cochlea of ones inner ear?
>(Unless you're Hindemith, of course).;--o)
>
"Figment" makes it sound imaginary. Sum and difference tones result
from nonlinearity in the transmission of the signal somewhere after
the two come together.
Nonlinearity means the instantaneous amplitude of the output is not
proportional to the instantaneous amplitude of the input, for any
stage, or series of stages, of a signal path.
Since mixing of sounds in air is linear, at least for amplitudes a
recorder can geerate, the first nonliearity is that of the ear and its
associated stuff. But, once the effect is generated, it is real.
The nonliearity of the ear may not be identical for all listeners, but
it is always there, so everyone will hear the results in some way.
Rodney Myrvaagnes J36 Gjo/a
MOM CASTS TOT IN CEMENT
Most experts voice cautious optimism
Yvonne & Norman Rowe
to play one note, sing another, and do it so well in tune that it creates
both a subtone and an overtone, thereby producing a four-note chord. Few
hornists can pull it off!
Norm
"Owk28" <ow...@aol.com> wrote in message
news:20030327145149...@mb-fk.aol.com...
Martin Davids
ow...@aol.com (Owk28) wrote:
> Yes, and string players use them to tune double stops. I believe they were
> described in some detail by Tartini.
They are also known as "Tartini Tones" 'cause he was the first one to
publish anything about them. He talked about them as a way to know when
your double stops are in tune as Oliver pointed out. Of course lots of
vibrato ruins the effect...
Phil Robbins
Your response is excellent! So far, it's the one I like best and it's not a
dumb question, at all! Yes, two people can indeed "play consistently in tune
to reliably create... difference tones." However, I think it takes skill and
better quality instruments for best "results." In fact, I've played the
recorder for many years but it's only recently that I became aware of
difference tones. I was playing duets with a friend (a virtuoso; something
I'm not), and the difference tones were so pronounced, that I had to comment
on them. My friend, being knowledgeable, explained them to me in detail.
I think many advanced recorder players simply consider difference tones a
nuisance or at best, something of no real concern. I have always been aware
of the beats produced by bad intonation. However, I never thought that
playing perfectly in tune with recorders might actually be possible but it
is and difference tones are the result.
Most replies, so far, have been about technical explanations of hertz,
mathematics, physics and the psychology of tone production. Only two touched
on artistic considerations. I'm not surprised at the many replies discussing
the science and mathematics of intervals. There has always been a close
connection between math and music. In fact, although, personally, I have no
real understanding nor skill at math or arithmetic, I suspect there is
something in the human psyche which makes mathematics and music entirely
compatible. Mathematicians are often musicians. There is also a connection
which I don't understand between visual artistic creativity and music. The
great photographer, Ansel Adams, began his career as a concert pianist.
Another connection, at least for me, is the ability to write in a clear,
expository style and music. But I digress.
My real interest is in musical sensibility. Technical skill is, of course,
desirable, and we each attain our level. Some people can move their fingers
with great speed and accuracy. Other less so (that's me). But musicianship
is more than just technical skill; artistic sensibility seems more important
to me. Music is about interpretation and creativity. As musicians, we should
strive to do more than just play the notes on the printed page. Style and
interpretation will vary, musician to musician, but one thing we all have in
common is the requirement to play in tune. I used to think that recorders,
because of their inherent qualities, could not play in tune. Turns out I'm
wrong.
Phil Robbins
----- Original Message -----
From: <ma...@mss.tzo.com>
To: <reco...@stars.health.ufl.edu>
Cc: <reco...@stars.health.ufl.edu>
Sent: Thursday, March 27, 2003 8:51 AM
Subject: Re: Difference tones
> I'm a beginner so forgive me if this is a dumb question...
>
> Can two people play consistantly in tune to reliably create these
> desired difference tones?
>
> Marty Sasaki
>
BREWERPAUL
>>BTW, difference tones are known as a standard tuning
>>method for a recorder ensemble, for example.
You mean, an ensemble is supposed to be in TUNE? What a concept! :-)
Suzanne van der Helm
But musicianship
> is more than just technical skill; artistic sensibility seems more
important
> to me. Music is about interpretation and creativity. As musicians, we
should
> strive to do more than just play the notes on the printed page. Style and
> interpretation will vary, musician to musician, but one thing we all have
in
> common is the requirement to play in tune. I used to think that recorders,
> because of their inherent qualities, could not play in tune. Turns out I'm
> wrong.
The point is that the person in question has to be a musician, which is not
always the same as a recorderplayer. I am a professional recorderplayer and
singer of early music myself and I have experienced that many players (and
singers as well) tend to be only technical and a kind of emotional in their
playing, though they are not one with their instrument and therefore can not
communicate their real music towards others. With communication I mean that
they reach further with their playing, just because it is completely natural
for them, to tell what the music means to them on to the listeners. And with
that I mean that it is often very audible that the player in question
exposes his/her own struggle with the instrument, music, inner
feelings/opinions instead of transmitting the music itself. Often it becomes
a struggle about 'being right' or being afraid of making mistakes/being
wrong. I think music itself is not at all like that, but it becomes worse
because we are too much busy with ourselves nowadays. Real musicians don' t
talk or even quarrel about tuning: they listen to eachother and adjust
naturally, because they are in one with their instrument and the music. And
if they are technically not far enough they are not afraid of asking someone
else's advise to improve the music, not their ego.
I think playing the recorder in tune is more a matter of mentality: don't
try 'to be right' all the time, it is like life itself: give and take. That
is different from doing your best, by the way. Of course you need to keep on
working on your technique, but the music should always be the goal, not the
opinion of one person that has to be squeezed into the music. Often I think
that people nowadays lost a certain purity, which makes it more difficult to
play in tune on the recorder, although it is such a direct instrument! But
maybe that is simply the reason why it can be so difficult for some people:
it asks from the player a kind of directness and openness as well, then it
works almost by itself......
If you consider the instruments that are left from early times and if you
consider how they were tuned, you will realize that those people could
adjust their playing very well. Every instrument requires different
fingerings for instance, which was no problem at all for the players then.
This has changed a lot. I think we can learn a lot from that still. Not only
by reading all those books and treatises, but by listening to the instrument
itself and adapting our playing to every single instrument in our hands.
I think that has also to do with the fact that almost everybody could sing.
Singing (in the old way) gives a very physical awareness of being in tune.
Once you know this feeling you strive for it with your instrument as well:
you want to sing on your instrument.
In the end I think we should try to serve the music instead of 'making' her
and having quarrels about being 'right' or 'wrong'. We can only use maths to
prove what we already sense, and become therefore more aware, but we can not
use it in the opposite way. Indeed were music and maths always together, but
they interact, they don't substitute eachother. They improve eachother.
Funny though, that music often is considered to be a language as well.....
Music is more than a brain thing, it touches our hearts and therefore the
brain and the heart get connected. So it makes us more whole, ain't that
nice and worth living for?
Suzanne
meeso
> I should have added that Hindemith used combination tones to "prove"
> that a fourth is a consonant interval in his treatise on musical
> composition. Forget the title (Craft of Musical Composition?).
> Traditionally the fourth is, of course, a dissonance in standard harmony
> and counterpoint, and that didn't fit with PH's system.
consonance & dissonance - in practice - have never been of a scientific
foundation. it have been rather & through the ages of an artistic one.
there is no essential difference between a 5th & a 4th except of the
number - the physical measurement. one cannot "prove" that an interval is
consonant or dissonant, because consonance & dissonance themselves, cannot
be described scientifically, they are the same as good & bad, right &
wrong, & so on. but rather she could *believe* that some intervals are
*different* in some certain way than another intervals.
further more, someone like Hindemith should have been more enlightened
about that issue; it was in his own time when composers & theorist stopped
talking about what's consonant & what's dissonant & dealt with them as
different *tools* what ever names they got. much like the Renaissance
although, Renaissance theorists had a very restricted *table* of what's
consonant & what's dissonant. but in my opinion, & in the general usage of
dissonance in the polyphonic vocal practice, they used dissonance as a
tool that produces a specific impression - they thought.
let me quote this part regarding the suspension dissonance in the words of
Zarlino, the great theorist of the 16th century:
"Not only in such a dissonance not displeasing but, on the contrary, it
arouses great pleasure through the increased mildness and sweetness which
it lends to the succeeding consonance. And this for the reason that
everything comes out much more clearly as soon as it is placed in
contrast with its opposite."
& that's indeed one of the most obvious characteristics of Renaissance
art. they were very fond of the idea of opposites.
Thanks a lot
Maysara
Jerry Kohl
> On Thu, 27 Mar 2003 17:12:13 +0000, rv wrote:
>
> > I should have added that Hindemith used combination tones to "prove"
> > that a fourth is a consonant interval in his treatise on musical
> > composition. Forget the title (Craft of Musical Composition?).
> > Traditionally the fourth is, of course, a dissonance in standard harmony
> > and counterpoint, and that didn't fit with PH's system.
>
> consonance & dissonance - in practice - have never been of a scientific
> foundation.
This is not quite true. Helmholtz established a measurement of what he
called the "roughness factor" in simultaneous tones, and although his
means of measurement have been criticised as insufficiently rigorous,
a recent study by Douglas Keislar, "Psychoacoustic Factors in Musical
Intonation: Beats, Interval Tuning, and Inharmonicity", PhD. diss.,
Stanford University, 1991, has validated Helmholtz's basic conclusions,
while extending the reach of scientific measurement in this area. It is,
however, still true to say that such measurable "acoustical consonance
and dissonance" is not the whole story and the criteria have, as you say,
> have been rather & through the ages of an artistic one.
Jerry Kohl
Ken Moore
<philr...@midtown.net> writes
>Mathematicians are often musicians. There is also a connection
>which I don't understand between visual artistic creativity and music. The
>great photographer, Ansel Adams, began his career as a concert pianist.
>Another connection, at least for me, is the ability to write in a clear,
>expository style and music. But I digress.
Music and mathematics were associated in the Middle Ages, since the
quadrivium, the "more exalted" (Britannica) division of the seven
liberal arts, consisted of geometry, arithmetic, music, and astronomy.
The close association between mathematics and composition persists:
species counterpoint, still taught at some universities, has obvious
similarities to formal (programming) language theory, taught to computer
scientists.
Since Helmholtz, you can apply a lot of mathematics to analytical (what
makes sounds different) and perceptual (how you hear them) acoustics.
IMO, this ought to be the foundation of musical analysis, since some
results of acoustic investigations by perceptual psychologists during
the last 40 years invalidate what some branches of analysis take as
their foundations. I certainly find perceptual acoustics useful in
composition, since it gives detailed support to such recommendations as
wider spacing in the lower parts.
I am not so sure about connections between music and the visual arts.
At the highest level, concepts such as the authority of the artist and
his relationship with society clearly have similarities in the two
fields. Having just returned from visiting a show of paintings by a
friend of mine I am very conscious of the differences between her art
and mine: she produces unique objects; I produce easily reproducible
computer files, which can be printed as many times as you like and the
resulting parts and scores used for performance as many times as you
like. If you try to compare music with performance art (I mean
publicised unusual actions by an artist, like kicking a take-away carton
along the high street), differences abound. Perhaps the nearest
parallel would be between the production of CDs from a single
performance on the one hand and printing from etchings or photographic
negatives on the other.
As regards the sources of creativity and the technical capabilities that
are needed to allow them to be expressed, I can see no reasons why they
either should or should not occur in the same person, other than the
time that it takes most people to assimilate each of them.
If anyone is interested in continuing this thread, perhaps we should
find a more appropriate news group. Any suggestions?
--
Ken Moore
K.C....@reading.ac.uk
pg composition student, University of Reading
Pan
wrote:
>Last week, I was playing recorder duets with a friend and we had a
I play the (transverse) flute, and I deal with difference tones a
great deal. I use them as a teaching tool to help my students tune
their perfect fifths (more than any other interval, but sometimes
major and minor thirds and other intervals). I also explain the way
the acoustical phenomenon works as the lower note in fact being equal
to the difference in Hertz between the two higher notes.
As for my own performance, when I play in orchestras and chamber
groups, I do things like trying to get a difference tone of an E
rather than the easier-to-obtain F if I'm playing a C as Principal
Flutist and the Second Flutist is playing an A, if it's an A minor
chord. I also love to play just (very small) minor 7ths but usually
cannot do so in orchestras.
Michael
Pan
>I should have added that Hindemith used combination tones to "prove" that a fourth is a consonant interval in his treatise on musical composition. Forget the title (Craft of Musical Composition?). Traditionally the fourth is, of course, a dissonance
>in standard harmony and counterpoint, and that didn't fit with PH's system.
It's my opinion that the perfect fourth is a very consonant interval,
but the dissonance is when the 4th of a chord is played along with the
5th. In common-practice harmony, a naked 4th implies this 7th or 2nd,
and that's what makes it dissonant. When it's played as part of a
tonic chord and the 3rd of the chord is also used, or/and if there is
also a P5 below (forming what Margaret Schulter calls the Medieval
trine, a term I have adopted), no-one considers it a dissonance, so if
there is nothing inherent in the interval that makes it dissonant, its
"dissonance" must be solely a function of context. Right?
Michael
Pan
wrote:
>Marty,
>
>Your response is excellent! So far, it's the one I like best and it's not a
>dumb question, at all! Yes, two people can indeed "play consistently in tune
>to reliably create... difference tones." However, I think it takes skill and
>better quality instruments for best "results."
[snip]
It also takes a good ear and requires that the players care. I played
a concert as part of a 4-flute quartet in which we pretty consistently
nailed the tunings. Of course, once in a while something was just a
bit off, but it was mostly all there. That's what happens when you
have the chance to play with good professionals who listen and
concentrate. It was a lot of fun. :-)
Michael
Ken Moore
<jerom...@attbi.com> writes
>meeso wrote:
>
>>[...]
>> consonance & dissonance - in practice - have never been of a scientific
>> foundation.
>
>This is not quite true. Helmholtz established a measurement of what he
>called the "roughness factor" in simultaneous tones, and although his
>means of measurement have been criticised as insufficiently rigorous,
>a recent study by Douglas Keislar, "Psychoacoustic Factors in Musical
>Intonation: Beats, Interval Tuning, and Inharmonicity", PhD. diss.,
>Stanford University, 1991, has validated Helmholtz's basic conclusions,
>while extending the reach of scientific measurement in this area.
There has been a large body of work following up on Helmholtz, mostly
confirming it but refining and giving more detail. See Sethares,
"Tuning, Timbre, Spectrum, Scale (ISBN 3-540-76173-X, Springer-Verlag,
1998) for an exposition and a large bibliography (over 150 entries).
>It is,
>however, still true to say that such measurable "acoustical consonance
>and dissonance" is not the whole story and the criteria have, as you say,
>
>> have been rather & through the ages of an artistic one.
It is still the case that most performers are ignorant of this work,
which probably doesn't matter much, and that many analysts are, which
does.
Jerry Kohl
Bingo! And thanks for that reference, Ken, I did not know of it.
Jerry
Musicmajor
Math plays an important role in music theory. I think a mathematician
could easily learn music theory. Which would at least let you
harmonize with ease.
rw
On 24 Apr 2003 10:24:23 -0700, nice_te...@yahoo.com (Musicmajor) wrote:
<<snip>>
Ken Moore
<nice_te...@yahoo.com> writes
>Math plays an important role in music theory. I think a mathematician
>could easily learn music theory. Which would at least let you
>harmonize with ease.
I was a mathematician before I became a composer, but I didn't use any
of the mathematics I had learnt beforehand when I came to learning
counterpoint, and nowadays my attitude to harmony is "If it sounds
right, it is right".
Sybrand Bakker
Every interval can be expressed as a ratio of 2 overtones. Before the
Enlightment the degree of consonance or dissonance was partly derived
from those ratio's ie a fifth (ratio 3:2) is more 'perfect' than a
third (ratio 4:5). A major second (ratio 8:9) is dissonant because of
the ratio.
Sybrand Bakker
anti-spam maatregel
om te antwoorden verwijder '-verwijderdit' uit mijn e-mail adres
arthur ness
about the mathematical basis of the overtone series, and how one can classicfy intervals from the
most consonant (unison) to the most dissonant (tritone) Didn't we cover this already?
The Schillinger System, about which I am not fully conversant, uses mathematics, mainly as a means
for weak composers to construct melodies and chords. It uses permutations of notes, inter alia.
But otherwise, I don't see how being a mathematician wouold asslst one in writing a decent
harmonization of a scale. What's "mathematical" about a fugue?
rodney
Greg M. Silverman
>The problem is that music theory is a lot more than acoustics, to which you refer. Everyone knows
>about the mathematical basis of the overtone series, and how one can classicfy intervals from the
>most consonant (unison) to the most dissonant (tritone) Didn't we cover this already?
>
>The Schillinger System, about which I am not fully conversant, uses mathematics, mainly as a means
>for weak composers to construct melodies and chords. It uses permutations of notes, inter alia.
>
Arthur,
I certainly wouldn't say Gershwin was a weak composer. He used this
method to complete problematic pats of "Porgy and Bess," which is IMHO a
true masterpiece...
Then there is Schillenger's now infamous quote regarding his methods
(quoted from Stuckenschmidt's classic "20th Century Music"): "For
example, by comparing the music of J.S. Bach with the following
illustrations, the full range of what he could have done by using the
method of geometrical inversion becomes clear."
>But otherwise, I don't see how being a mathematician wouold asslst one in writing a decent
>harmonization of a scale. What's "mathematical" about a fugue?
>
The only help is that music is a symbolic language, of sorts, and as
such mathematicians (as well as logicians, linguists, etc.) may be able
to grasp the concepts of music theory more easily. Of course, being a
talented mathematician does not guarantee by necessity proficiency in
harmony, let alone the ability to create good music.
gms--
Pan
ness) wrote:
>The problem is that music theory is a lot more than acoustics, to which you refer. Everyone knows
>about the mathematical basis of the overtone series, and how one can classicfy intervals from the
>most consonant (unison) to the most dissonant (tritone) Didn't we cover this already?
[snip]
I don't know, but who thinks the tritone is more dissonant than the
minor 2nd?
Michael
ajn
the relative dissonance of the two intervals can be calculated. It is surely the ugliest interval
in music. The very Devil in music.<g> You could end a piece with a minor second or major seventh,
and many composers have done so, but could you use a tritone to end a composition?
ajn
Ken Moore
<gooid...@sybrandb.demon.nl> writes
>Every interval can be expressed as a ratio of 2 overtones. Before the
>Enlightment the degree of consonance or dissonance was partly derived
>from those ratio's ie a fifth (ratio 3:2) is more 'perfect' than a
>third (ratio 4:5). A major second (ratio 8:9) is dissonant because of
>the ratio.
Do you still believe this? I agree that it is what was believed in
Classical Greece and in the rest of Europe from the Middle Ages onward,
but Helmholtz gave some evidence that it applied only to the timbres of
forced vibrations, and his views have been confirmed, refined and
elaborated over the last 50 years. Amongst other things, the new theory
is consistent with the practice of piano tuners, and predicts the
greater perceived dissonance of nominal consonances, such as thirds, in
low registers.
an--boston
Musician, a monthly magazione issued by the national office of the American Federation of Musicians,
which I started reading and clipping for future reference long ago when I was still a teenager. I
emphasize this because the Schillinger Method was devised as an aid for composers of commercial
music, and most members of the musicians' union are involved directly with commercial music. It was
probably a very popular column.
I know that Gershwin, Benny Goodman, Vernon Duke and ?Glen Miller? studied the Method, but it was
presented as a method of creating ideas using permutations and various mathematical tricks Gershwin
studied with Dr. Schillinger, a mathematician and a distinguished composer in his own right.
I recall the claim being made that it could be used if a composer had run out of ideas. Which
seems, according to Greg's witness, the way in which Gershwin himself used it. It could also be
used by a composer faced with the unpleasant task of having to write a singing commercial for a new
dish detergent before noon.
And many ideas in "Porgy and Bess" would seem to follow upon the Schillinger techniques. If they are
worthwhile, that is because Gershwin created them in spite of whatever method he used. "Summertime"
seems a good example of Schillinger creation, especially the introductory vamp. And there is use of
rhythmical permutations as well as meloidic ones in a piece like "I got Rhythm.". If Gershwin used
it to complete "problematical parts" that confirms what I was trying to say about weak composers
using the system.
What Greg is confused about, is that the Schillinger Method did not compose Gershwin's music, it was
simply one of the many techiques that he used while composing. That;'s why composers study such
things as harmony, counterpoint, orchestration, musical form, 20th-century techniques of
composition, etc. In Gershwin's case, the Schillinger was just another technique he had studied.
When Gershwin had a problem, he solved it with the mechanical proscriptions of Schillinger. In
other words, he used it in his own "weak" moments. If anything, the Schillinger system was an
ancillary system to his own traditional training in jazz. Gershwin also attempted to take lessons
with Ravel, and techniques from Impressionist music can also be traced in "Porgy."
I haven't the slightest idea how your training as a mathematician would assist you with music
theory, Greg.
I had a very thorough training in math (incluiding trigonometry) before I went to college, but in
music it came in handy only when I took the acoustics course, not the music theory and composition,
I studied music theory and compostion wth Walter Piston. No math there, either.
I'm not going to touch your assertion that music is a symbolic language. What does a chromatic
appoggiatura symbolize? I think you should first learn how the notes themselves fit together to
make a piece of music. That book by Stuekenschmidt is not very good, either.
ajn
Greg M. Silverman
>
> My only acquaintance with the Schillinger system was a series of columns in the International
> Musician, a monthly magazione issued by the national office of the American Federation of Musicians,
> which I started reading and clipping for future reference long ago when I was still a teenager. I
> emphasize this because the Schillinger Method was devised as an aid for composers of commercial
> music, and most members of the musicians' union are involved directly with commercial music. It was
> probably a very popular column.
>
> I know that Gershwin, Benny Goodman, Vernon Duke and ?Glen Miller? studied the Method, but it was
> presented as a method of creating ideas using permutations and various mathematical tricks Gershwin
> studied with Dr. Schillinger, a mathematician and a distinguished composer in his own right.
>
> I recall the claim being made that it could be used if a composer had run out of ideas. Which
> seems, according to Greg's witness, the way in which Gershwin himself used it. It could also be
> used by a composer faced with the unpleasant task of having to write a singing commercial for a new
> dish detergent before noon.
>
> And many ideas in "Porgy and Bess" would seem to follow upon the Schillinger techniques. If they are
> worthwhile, that is because Gershwin created them in spite of whatever method he used. "Summertime"
> seems a good example of Schillinger creation, especially the introductory vamp. And there is use of
> rhythmical permutations as well as meloidic ones in a piece like "I got Rhythm.". If Gershwin used
> it to complete "problematical parts" that confirms what I was trying to say about weak composers
> using the system.
>
> What Greg is confused about, is that the Schillinger Method did not compose Gershwin's music, it was
> simply one of the many techiques that he used while composing. That;'s why composers study such
> things as harmony, counterpoint, orchestration, musical form, 20th-century techniques of
> composition, etc. In Gershwin's case, the Schillinger was just another technique he had studied.
>
Hi Arthur,
I agree... I never claimed it composed the music for him, the method
just helped him as another compositional tool.
> When Gershwin had a problem, he solved it with the mechanical proscriptions of Schillinger. In
> other words, he used it in his own "weak" moments. If anything, the Schillinger system was an
> ancillary system to his own traditional training in jazz. Gershwin also attempted to take lessons
> with Ravel, and techniques from Impressionist music can also be traced in "Porgy."
>
> I haven't the slightest idea how your training as a mathematician would assist you with music
> theory, Greg.
>
It was just a random thought, nothing more. For me music theory was
easy, just as mathethmatics was too (I have had some graduate
mathematics and statistics in my training). Mind you, I am still and
always learning more (like chromatic appoggiaturas in the Sarabandes of
in the 'cello suites of Bach ;-) )
> I had a very thorough training in math (incluiding trigonometry) before I went to college, but in
> music it came in handy only when I took the acoustics course, not the music theory and composition,
> I studied music theory and compostion wth Walter Piston. No math there, either.
>
I fully agree. Perhaps the problem is more cognitive: hypothesis being,
people who are good at mathematics or logic (etc) may be likley to
easily understand the theory of music, more so than some who is not good
at any of these.
But, I am NOT claiming this is true, just asserting there MAY be
something there. Nothing more.
> I'm not going to touch your assertion that music is a symbolic language. What does a chromatic
> appoggiatura symbolize? I think you should first learn how the notes themselves fit together to
> make a piece of music.
Agreed, but still there is a symbolic way of notating the actual
phenomenon, yes (good example BTW ;-))?
I may have been making a stretch, but what the heck. :-)
> That book by Stuekenschmidt is not very good, either.
>
it was interesting all the same, albeit rather cursory and randomly
thrown together bits and pieces... any recommendations on good books on
20th C music would be most appreciated.
Best Regards,
gms--
--
Greg Silverman
g...@umn.edu
EOH Health Studies
UofMN
arthur ness
important Norton series (books by Einstein, Reese, Sachs, Heartz) is probably the "standard text."
There is a "blow your mind" book by Joan Peyser. It just made me angry, though. I do not remember
who did the one in the Prentice-Hall series. If it is any good, it is the kind of thing to be used
in a junior college.
arthur ness
teacher Gustave Reese was trained as an attorney, and his two books read like legal documents. But
are they PACKED with information.
On Sat, 26 Apr 2003 20:26:44 GMT, 7116...@compuserve.com (arthur ness) wrote:
>It's been a while since I surveyed music history textbooks. But the one by William Austin in the
>important Norton series (books by Einstein, Reese, Sachs, Heartz) is probably the "standard text."
>
<<snip>>
Jerry Kohl
> It's been a while since I surveyed music history textbooks. But the one by William Austin in the
> important Norton series (books by Einstein, Reese, Sachs, Heartz) is probably the "standard text."
>
> There is a "blow your mind" book by Joan Peyser. It just made me angry, though. I do not remember
> who did the one in the Prentice-Hall series.
Eric Salzman, "Twentieth-Century Music: An Introduction". The latest
edition is 1988, twenty-two years more up to date than Austin.
> If it is any good, it is the kind of thing to be used
> in a junior college.
Salzman *is* good, particulary so in treating music of
the second half of the century. He is himself a composer,
and so he is more knowledgeable about recent trends than
most other writers on the subject. As an introductory book
I prefer it to the more recent "Music of the Twentieth Century:
Style and Structure" by Bryan R. Simms (1986; 2d ed. 199?).
Simms is more technically oriented, but that tends to make
him more uneven, since he is obviously more familiar with
some composers than with others. (For example, he's a bit
of a whizz with Schoenberg, but is almost clueless where
Stockhausen is concerned.) There is a separate anthology
of score examples for Simms's book, which makes it
attractive for classroom use, but is of less value, perhaps,
for someone just wanting to read up a bit on music from
the past hundred years.
--
Jerry Kohl <jerom...@attbi.com>
"Légpárnás hajóm tele van angolnakat."
Todd Michel McComb
arthur ness <7116...@compuserve.com> wrote:
>My teacher Gustave Reese was trained as an attorney, and his two
>books read like legal documents. But are they PACKED with
>information.
His Music of the Renaissance is a great book. It made a big
impression on me. His medieval book is too dated to be very useful,
although it can be worth reading.
Todd McComb
mcc...@medieval.org
R.A.G. Seely
news:b8ek3s$mki$1...@machaut.medieval.org:
Certainly those two books got me started in music before 1600 - and still
have a place on my bookshelf. Not surprising that after nearly half a
century they (esp the medieval one) are beginning to get dated!
-= rags =-
--
To reply by email, use "@" not "__A@T__"
<rags AT math . mcgill . ca>
<http://www.math.mcgill.ca/rags>
Entia non sunt multiplicanda praeter necessitatem.
arthur ness
with useful information and references, much of which will not be outdated in the near future.
I was also Reese's research assistant and helped hom revise the chapter on pre-Notre Dame polyphony,
in the Middle Ages book. It was still manageable at that time, and the new material augmented what
he had already written. I will not forget the first sentence, though. It said that the Moors had
never penetrated the north eastern corner of Spain where the Compostella cathedral was located. He
asked me if I had any corrections to the first sentence. And I told him that the Moors had burned
down the cathedral in 1230 (or whenever it was). He glared at me, took out his pen and added above
a caret, "except fleetingl;y." I was a bit more careful after that. He was a fine New York
gentleman, and I admired him very much. His and his wife's families were fifth-generation New
Yorkers.
But Reese was unable to finish the revisions before he died in the 1970s. One of Reese's NYU
colleagues was commissioned to revise the medieval history (or write an entirely new one), but it
has still not appeared, and I suspect he has given up.
There is such a tremendous amount of material now, that I think the "one-person" histories of music
are no longer possible, unless they become multi-volume giants. Daniel Heartz appears to have given
up in doing the classical period volume in the Norton series, and he had been working on it for 30
years. He just published a history of the music of Mozart and Haydn, instead.
I recently purchased Tom Mathiesen's history of ancient Greek music and music theory (_Apollo's
Lyre_), his life's work, and it is over 800 pages long. It has received several awards.
ajn
Sybrand Bakker
Whether I believe this or not doesn't matter. 17th and 18th century
composers believed this and used the theory abundantly.
Alain Naigeon
Xt68JVAC...@mooremusic.org.uk...
Hi Ken,
Would you have a book reference about this, including the
last refinements you mention, if possible?
--
Français *==> "Musique renaissance" <==* English
midi - facsimiles - ligatures - mensuration
http://anaigeon.free.fr | http://www.medieval.org/emfaq/anaigeon/
Alain Naigeon - anai...@free.fr - Strasbourg, France
Alain Naigeon
3eab2199...@news.compuserve.com...
>
> There is such a tremendous amount of material now, that I think the
"one-person" histories of music
> are no longer possible, unless they become multi-volume giants. Daniel
Heartz appears to have given
> up in doing the classical period volume in the Norton series, and he had
been working on it for 30
> years. He just published a history of the music of Mozart and Haydn,
instead.
>
> I recently purchased Tom Mathiesen's history of ancient Greek music and
music theory (_Apollo's
> Lyre_), his life's work, and it is over 800 pages long. It has received
several awards.
I've just got "Medieval music" by Richard Hoppin, advised by a student
in Valencia, she told me they use this book at the departement of
musicology.
The historical introduction is quite interesting - generally I hate
introductions
and read them quickly :-)
I'd be interested to know what people think of this book...
(I've only had quick glances at the musical part, yet)
Pan
wrote:
>You should be able to discover that by using your ears.
The way I phrased the question ought to be enough to suggest that I
think that statement is bunk, no?
> Acoutically it is also more dissonant, and
>the relative dissonance of the two intervals can be calculated.
Exactly. The tritone, in the form of a diminished 5th, in just
intonation, is a 7:5 ratio. The minor 2nd in just intonation is a
17:16 ratio, so it's more dissonant than the tritone-as-d5.
> It is surely the ugliest interval
>in music. The very Devil in music.<g>
Ugly? Nope.
> You could end a piece with a minor second or major seventh,
>and many composers have done so, but could you use a tritone to end a composition?
Listen to some blues and get back to us.
Michael
Todd Michel McComb
Alain Naigeon <anai...@free.fr> wrote:
>I'd be interested to know what people think of this book... [Hoppin]
It is the standard student text today. It could be improved upon,
but hasn't been yet to my knowledge.
Todd McComb
mcc...@medieval.org
Alain Naigeon
b8fbdv$n2v$1...@machaut.medieval.org...
> In article <3eab0a5d$0$30132$626a...@news.free.fr>,
> Alain Naigeon <anai...@free.fr> wrote:
> >I'd be interested to know what people think of this book... [Hoppin]
>
> It is the standard student text today. It could be improved upon,
> but hasn't been yet to my knowledge.
Thanks!
arthur ness
ajn
Ken Moore
<anai...@free.fr> writes
>I wrote:
>Helmholtz gave some evidence that it applied only to the timbres of
>> forced vibrations, and his views have been confirmed, refined and
>> elaborated over the last 50 years. Amongst other things, the new theory
>> is consistent with the practice of piano tuners, and predicts the
>> greater perceived dissonance of nominal consonances, such as thirds, in
>> low registers.
>
>Hi Ken,
>
>Would you have a book reference about this, including the
>last refinements you mention, if possible?
Sethares, William A., Tuning, Timbre, Spectrum, Scale, (Springer-Verlag,
1997, ISBN 3-540-76173-X)
Pierce, J.R., The science of musical sound (New York: W.H.Freeman and
Company, 1983, ISBN 0-7167-1508-2).
These both have good bibliographies. Much of the original work was
reported in the Journal of the Acoustical Society of America.
Alain Naigeon
> I am familiar with the first edition, and would agree with Todd's
assessment.
Thanks! If it's not too much, would you mind pointing out,
in a few words, which improvements are you expecting?
Is it just a question of design or presentation, or are they
some controversial points in the book?
Akrata
"Sybrand Bakker" <gooid...@sybrandb.demon.nl> escribió en el mensaje
news:shvlav0f2ap0fpvo3...@4ax.com...
> Whether I believe this or not doesn't matter. 17th and 18th century
> composers believed this and used the theory abundantly.
I don't know whether this statement is true. Ages ago I wanted to become a
musician, and went through all the training up to a couple postgraduate
courses (Early Music and Advanced Soloistic Studies in Recorder, both at the
Guildhall School of Music & Drama, London). I just lacked talent, so after
seven years of professional activitie, I had to quit.
I read a lot about the "consonance perfection" or simplicity of ratios, and
repeated it many times to my students, and theoricized on it, but *never*
used it for any practical purpose. Nor do I recall any practical treatise
describing any usage of this thory for practical purposes.
Given perfect sinusoidal sound waves, consonant intervals have a greater
number of coincidences in peaks and bottoms that dissonant intervals, or
inversely, have a lesser ratio of "interference", therefore producing a
"smoother" or "more blended" sensation to the listener. Dissonances are more
"tense", or "harsh". The ratios theory explains why some intervals are
"terser" than others. Even now, I do not see any practical usage for it.
Regards
Alain Naigeon
> >
> >Would you have a book reference about this, including the
> >last refinements you mention, if possible?
>
> Sethares, William A., Tuning, Timbre, Spectrum, Scale, (Springer-Verlag,
> 1997, ISBN 3-540-76173-X)
>
> Pierce, J.R., The science of musical sound (New York: W.H.Freeman and
> Company, 1983, ISBN 0-7167-1508-2).
>
> These both have good bibliographies. Much of the original work was
> reported in the Journal of the Acoustical Society of America.
Thank you very much !
Alain
arthur ness
way, it also has a volume of scores, which is surely a plus. My recollection is that I found it
uneven. That is, some areas that I would consider important are slighted, while others that I would
consider minor, get too much coverage.
This is a problem in many music histores, in which the author stresses those areas of interest to
him/her, or areas in which the author has special expertise. I no longer have the Hoppin books, so
I cannot refresh my memory with specifics.
We have not mentioned another important series in English, and that isThe New Oxford History of
Music. There are some ten volumes. In this there are essays by leading scholars in their area of
expertise. This approach of having each volume a group publication suffers because some authorities
will go into great depth on their subject, while others feel they should stress the high points.
Hope this answers your question, Alain. It is always nice to hear from you. If you happen to pass
Meyer's, please stop in and have a pastery on me.<g>
Todd Michel McComb
arthur ness <7116...@compuserve.com> wrote:
>This is a problem in many music histores, in which the author
>stresses those areas of interest to him/her, or areas in which the
>author has special expertise. I no longer have the Hoppin books,
>so I cannot refresh my memory with specifics.
In Hoppin's case, I don't think the idiosyncracy really came from
personal vanity (if you will), but more a conscious desire not to
follow the crowd in general. So he chose somewhat unusual examples
to illustrate standard points. The idea, I think, is to make sure
the book holds some interest even after it really is outdated.
I don't have the book either, so can't turn to specifics. I don't
know if Hoppin treats tuning at all, but knowledge there would've
improved tremendously in the interim. Rhythmic interpretation of
chant has progressed quite a bit, and with it the earliest polyphony.
The way lower voices worked, sustaining issues, vocalization, use
of instruments....
The basic "sweep" of his book is still pretty good, in terms of
outlining history and repertory developments. One area which has
really come into focus only recently (at least for me) is the way
English developments in the later 1300s bridged Ars Antiqua per se
and Dunstaple-style music. Since I have Hoppin's list of examples,
I can see that he does not illustrate this. I'm sure I could find
some other points of this nature.
Todd McComb
mcc...@medieval.org
ajn
Thank you for expanding on what we have both been discussing.
In dealing with music of the middle ages, there are often new and startling discoveries, more so
than those in other periods. For that reason, histories of that period will become out-dated sooner
than histories of other periods, as you have shown us.
In some cases what you describe as
>a conscious desire not to
>follow the crowd in general.
can be taken to an extreme.
I once encountered a single-volume music history intended to compete as an undergrad text with
Grout/Palisca History of Western Music (still the standard text?). It had some interesting
features, including some coverage of world musics. It was also filled with rather obscure
information. I recall in the baroque section, there was no mention whatsoever of basso continuo!!!
The author felt that the common materials would be covered in the lectures, so the obscure
information should be given in the textbook. Honest.
The author even said so in the preface. Sorry. I cannot remember the author's name or the title.
It had a purple-ish blue dust jacket, that I haven't forgotten..
arthur ness
Mark K. Ehlert
news:3eac5c58...@news.compuserve.com:
> I once encountered a single-volume music history intended to compete
> as an undergrad text with Grout/Palisca History of Western Music
> (still the standard text?). It had some interesting features,
> including some coverage of world musics. It was also filled with
> rather obscure information. I recall in the baroque section, there
> was no mention whatsoever of basso continuo!!!
>
> The author felt that the common materials would be covered in the
> lectures, so the obscure information should be given in the
> textbook. Honest.
>
> The author even said so in the preface. Sorry. I cannot remember
> the author's name or the title. It had a purple-ish blue dust
> jacket, that I haven't forgotten..
It wasn't by chance Stolba, was it? It's got a blue cover as I recall,
and quite a bit of information (historical) world music and women
composers through history, in addition to some obscure details that I
think may be a bit too much for the undergraduate student to take in.
This was my text in music history class some 10 years ago.
--
Mark K. Ehlert
To reply via e-mail, X = 3
Alain Naigeon
I have the second book too, with the examples;
it would have been still better with the original
facsimiles!
The word tuning doesn't appear in the index (but
that's not a 100% reliable proof, we've all seen
incomplete indexes).
[Todd McComb]
> The basic "sweep" of his book is still pretty good, in terms of
> outlining history and repertory developments. One area which has
> really come into focus only recently (at least for me) is the way
> English developments in the later 1300s bridged Ars Antiqua per se
> and Dunstaple-style music. Since I have Hoppin's list of examples,
> I can see that he does not illustrate this. I'm sure I could find
> some other points of this nature.
Indeed the last chapter of the main book is "An English epilogue",
where this point seems to be more or less commented, but at this
time I haven't read it. The first sentence is nevertheless interesting :
"Nothing in the history of European music before the fifteenth century
suggest that by 1475 Tinctoris would regard English composers as
the "fount and origin" of a new art." The three last examples are by
Senlenches, Ciconia and Cooke (whom I hadn't heard about till
the previous minute :-) ).
Thanks for the reference to the Oxford publication, but, as an
amateur, I'm always glad to find more compact (though as
wide range as possible) and more affordable books ;-)
[I'll certainly have this pastry with great pleasure, but a small
one, since I'm just in the process of loosing a few pounds ;-)]
arthur ness
Thanks for the additional information about Hoppin. I must take a look the next time I am in the
library.
You wrote about the New Oxford History
>Thanks for the reference to the Oxford publication, but, as an
>amateur, I'm always glad to find more compact (though as
>wide range as possible) and more affordable books ;-)
It would be expensive, and not my choice for a basic history. I guess still the best single volume
history in Engish is Donald Jay Grout and Claude Pailsca, _A History of Western Music_ unteenth
edition NY: Norton It also has anthologoes of scores and CDs of the Scores. Of course, a very
"readable" history is the one by Paul Henry Lang, _Music in Western Civilization (Norton, 1941).
But it's old.
Alain also wrote:
>[I'll certainly have this pastry with great pleasure, but a small
> one, since I'm just in the process of loosing a few pounds ;-)]
And we should let the rest of you in on the comment. Alain is from Strassbourg, and at the Uni
Strassbourg is an on-line index in progress of the manuscript sources of lute music
(www-bnus.u-strasbg.fr/smt/perc.html), being administrated by Christian Meyer (and others). When I
asked Alain if he knew the muscologict, he replied that he only knew of the pastry baker of the same
name.
Arthur,
arthur ness
library catalogue. I'm surprised that someone else has come up with the same scheme. I think
undergraduates (esepcially music majors) should have a history that takes them, hopefully by a
different path, through the same materials as the lectures.
arthur.
Greg M. Silverman
>No, it was not Stolba. I' recognize the name if I saw it. I even tried to find it in an on-line
>library catalogue. I'm surprised that someone else has come up with the same scheme. I think
>undergraduates (esepcially music majors) should have a history that takes them, hopefully by a
>different path, through the same materials as the lectures.
>
>arthur.
>
Hey all,
I must definitely thank you for the recommendations for books on music
history... plenty to go on now.
Danke Schoen!
gms--
John Howell
>You should be able to discover that by using your ears. Acoutically
>it is also more dissonant, and
>the relative dissonance of the two intervals can be calculated. It
>is surely the ugliest interval
>in music. The very Devil in music.<g> You could end a piece with a
>minor second or major seventh,
>and many composers have done so, but could you use a tritone to end
>a composition?
The short answer is yes, of course you can. The tritone is implicit
in a dominant 7th or 9th chord, and it is stylistically quite normal
to end a jazz piece with such a chord on the tonic. You simply can't
promulgate "rules" which apply to any, every, and all types of music.
The "music" in the quadrivium of medieval universities was the study
of proportions, not of actual sound in the sense of "making" music.
That distinction still holds true in a number of European
universities, which do not include practical music making in their
curricula. If you want to be a performing musician you go to
conservatory, not to university. American universities began the
same way, but during the 20th century most shed that distinction and
incorporated music making, often in a conservatory-like environment,
into their curricula.
From what I have read, the relationship between mathematics and music
is related to the fact (?) that the same parts of the brain are
involved in each. I believe that it has proven true that there is a
much closer relationship between computer programming and music,
probably for much the same reason. No one-to-one relationship
appears to exist, although many scientists and engineers are also
good musicians. But music theory is NOT mathematics in the sense
that most of us think of mathematics.
For whatever it's worth.
John
--
John & Susie Howell
Virginia Tech Department of Music
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
V.A. Austin
> The "music" in the quadrivium of medieval universities was the study
> of proportions, not of actual sound in the sense of "making" music.
> That distinction still holds true in a number of European
> universities, which do not include practical music making in their
> curricula. If you want to be a performing musician you go to
> conservatory, not to university. American universities began the same
> way, but during the 20th century most shed that distinction and
> incorporated music making, often in a conservatory-like environment,
> into their curricula.
Excellent points, John!
The study of music was also linked to advanced learning in ancient
Greece (think of Pythagoras) and Rome, which is how it came to be
included in the medieval quadrivium. Music in the ancient world, up to
the 1200s, was considered a science, more than an art. The study of
music, e.g. proportions and intervals, etc..., was, like the related
mathematical fields, supposed to bring one closer to an understanding of
God, and of those mathematical building blocks with which the Universe
was created. Understanding this mindset also helps with an appreciation
of early music and the way in which it was created, for example the use
of consonant intervals in cadences, and form-generating devices such as
isorhythm.
As for the relationship between maths and music, there is a good bit of
evidence to support improved mathematical abilities in those children
who study piano and/or violin. I haven't seen studies on computer
programming and its relationship to music, but do know of a recent study
which showed a significant increase in classroom grades in students who
had extra music, while another group of students with extra computer
lessons showed much less gain than did the music students. I believe
the current thought has to do with spatial concepts and the brain, and
that music helps develop the ability to internalize spatial ideas. The
other area of brain growth occurs as students must use both sides of the
brain at once, coordinating left and right, reading, listening, and
intepreting, all at the same time.
V. Austin
Alain Naigeon
> Alain,
>
> Thanks for the additional information about Hoppin. I must take a look
the next time I am in the
> library.
>
> You wrote about the New Oxford History
And thanks for the added bibliography!
Alain
Margo Schulter
this thread: I was especially fascinated by the material on Gustave
Reese.
One important point I would make about tuning, indeed a topic on which
much more information is now widely available as Todd commented, is
that choices of ratios for different categories depend a great deal on
style.
For a medieval style of polyphony in Continental Europe around
1200-1400, the theoretically specified value for a major third, for
example, is 81:64 (~407.82 cents), a third formed from a chain of four
pure 3:2 fifths. In practice, the size might somewhat vary, with
14th-century French music, for example, sometimes inviting a larger
size somewhere near 14:11 (~417.51 cents) or 9:7 (~435.08 cents),
although these specific ratios are not, to my knowledge, mentioned in
the literature. Marchettus of Padua (1318) does seem to describe
cadential major thirds larger than 81:64, so that the interval more
"closely approaches" the 3:2 fifth toward which it expands, and this
information could be useful for the early Ars Nova style which he
describes.
The main point is that here the third is an _active_ interval,
imperfectly consonant but unstable and "striving" toward a stable
resolution. In Renaissance music, something at or near the simplest
ratio of 5:4 (~386.31 cents) is the ideal, and the prevaling tuning
systems reflect this preference.
How about the tritone? It can seem very "dissonant" if it arises
unexpectedly in a texture where a smooth flow of fifths and fourths is
the norm, but less dissonant than a minor second or major seventh in a
16th-century context (as Zarlino, for example, recognizes in
permitting some freer treatments), and indeed stably concordant in a
modern style based on 4:5:6:7 as a complete harmony.
A quick comment on Hoppin's book, which I find very valuable 25 years
later: the discussion on Perotin does, in my view, reflect some
elements of an 18th-19th century view on what is expected in
harmony. He notes that a "triad" sometimes occurs, but is unstable --
meaning what Jacobus of Liege describes as the _quinta fissa_
(c. 1325) or "split fifth," a three-voice sonority with an outer fifth
"split" by the middle voice into a major third below and a minor third
above, or vice versa. I prefer the historically authentic term of
Jacobus, which accurately fits with the role of thirds as _unstable_
although relatively blending intervals.
Also, there are lots of unstable three-voice and four-voice sonorities
in Perotin other than the _quinta fissa_, some relatively concordant
(e.g. a fifth and fourth together above the lowest voice, or a ninth
"split" into two concordant fifths, the latter highly recommended by
Jacobus), and others very effective as directed points of cadential
tension.
It's curious that the influence of the 20th century hasn't played a
more prominent role in such analyses: other authors do draw this
connection, introducing a different set of expectations. As it
happens, both 13th-century and 20th-century styles often favor a
pluralistic choice of vertical intervals and combinations with lots of
flexibility and room for "liberties," but, of course, 13th-century
style should also be analyzed in terms of Gothic theory.
If a late 16th-century composer concludes a piece with a sonority of
fifth and octave above the lowest part, we might call this
"conservative," since the complete _harmonia perfetta_ of Zarlino
(third and fifth, or octave equivalents) is clearly the ideal and norm
of "harmonic richness."
If a 13th-century composer concludes with the same sonority, we have a
usual closing on a complete trine, the richest and most harmonious
stable sonority possible, and equivalent to Zarlino's complete
_harmonia perfetta_. To describe such a conclusion as "conservative"
is anachronistic -- Hoppin doesn't do this, but an article on the 13th
century in another history which has much valuable information
actually does.
Any good history should leave room for improvement, and indeed
encourage people to take up residence there -- so this isn't meant as
negative criticism, only as indication of what I seem as some issues
one can find in treatments of medieval music.
Most appreciatively,
Margo Schulter
msch...@value.net