Questions on chords

I have yet read in encyclopedia that Dominant Seventh chord (G B D F in C
major) and "Pseudo-sensible" Seventh chord (B D F A in A minor) were
introduced without preparation 50 years before other seventh chords.

[Questions]

Is this fact well established ?

Is it possible that this fact may proceed only of theoritical ideas on
dualism that would have been present at this epoch ?

[Comments]

If the fact proceeds only of dual considerations, it's less interessant.
But if it results of pure musical appreciation, it seems to me more
important. If compositors have accepted these two seventh chords as
autonomous consonant entities (without preparation need), very long before
other seventh chords, this simple fact command a serious study of chord
perception, for the simplest 4-tones chords in both dual forms would have
been perceived as such.

[Thougts from which I question] (I'm not musician)

In counterpoint period of occidental polyphony there were instant complex
vertical cumulation of notes. We can't appreciate musical pertinence
isolating them without context. Tonal music has introduced perception of
vertical entities as autonomous objects with the two triads (major and
minor) as foundation. It were so much important that modes were reduced to
major and minor (in which those triads are most implicated) for intensive
usage. Tonal modulation was perhaps largely used to add variations without
loss of clearness in simple chords consciouness.

Early theory of chords (Rameau) has tried to explain them as part of
harmonic series but has failed to really give a clear explanation of minor
triad's equality status. In spite of (or because) this blank, a great
importance was gived at rooted perception. Subsequent developpement of
tonal language relies on treatment of fundamental bass. Chords were
sophisticated later by thirds superposition on the two triads without
possible explanation in term of harmonic series. But it seems that most
tempered chords, in a long list of those currently used in jazz, have a
dual equivalent in the list.

First questions I ask concern distinction between perception levels. Have
acoustical and tonal perceptions to be distinguished ? Have concordance in
context and pure sonance to be distinguished ? Is usual root perception the
only possible ?

[On dualism]

Generally, superposition of subharmonics can't be like superposition of
harmonics. The first appears like an external amplitude modulation of wave
at high frequency and the second like an internal form modulation of wave
at low frequency.

With just finite chords constructed with little rationnal numbers, chords
may be seen abstractly as harmonics or subharmonics superposition. One of
these two reduced possible forms (common multiplicator or divisor) is
generally simpler than other, but there are also mixed chords like (1 5 3
15) or (1 21 3 7). Questions are the following. If subharmonic reduced form
is simpler than harmonic form, has mind capacity to perceive rationality in
the simpler way ? If yes, is this perception possibly pertinent for using
in musical works ?

Pierre Lamothe

--- In tuning@egroups.com, Pierre Lamothe <plamothe@a...> wrote:
>

> If compositors have accepted these two seventh chords as
> autonomous consonant entities (without preparation need), very long
before
> other seventh chords, this simple fact command a serious study of
chord
> perception, for the simplest 4-tones chords in both dual forms
would have
> been perceived as such.

Pierre, if these two seventh chords were regarded as consonant, they
would not have need for resolution. You say, rather, that they had no
need for preparation. That is quite different.

Which era of music are you talking about? Do you have a date? If you
mean around 1600-1650, then I would suggest that they didn't need
preparation because they, containing the tritone, were clear tonal
signifiers that would resolve in a key-defining way. Other seventh
chords (major and minor seventh chords) tended to arise as a result
of
sequences and so typically can be analyzed in terms of suspensions,
anticipations, etc.
>
> [Thougts from which I question] (I'm not musician)
>
> In counterpoint period of occidental polyphony there were instant
complex
> vertical cumulation of notes. We can't appreciate musical pertinence
> isolating them without context. Tonal music has introduced
perception of
> vertical entities as autonomous objects with the two triads (major
and
> minor) as foundation. It were so much important that modes were
reduced to
> major and minor (in which those triads are most implicated) for
intensive
> usage.

I see the situation quite differently (see my paper for my view).

> Tonal modulation was perhaps largely used to add variations without
> loss of clearness in simple chords consciouness.
>
> Early theory of chords (Rameau) has tried to explain them as part of
> harmonic series but has failed to really give a clear explanation
of minor
> triad's equality status. In spite of (or because) this blank, a
great
> importance was gived at rooted perception. Subsequent developpement
of
> tonal language relies on treatment of fundamental bass. Chords were
> sophisticated later by thirds superposition on the two triads
without
> possible explanation in term of harmonic series. But it seems that
most
> tempered chords, in a long list of those currently used in jazz,
have a
> dual equivalent in the list.
>
> First questions I ask concern distinction between perception
levels. Have
> acoustical and tonal perceptions to be distinguished ? Have
concordance in
> context and pure sonance to be distinguished ?

Yes, absolutely.

> Is usual root perception the
> only possible ?
>
> [On dualism]
>
> Generally, superposition of subharmonics can't be like
superposition of
> harmonics. The first appears like an external amplitude modulation
of wave
> at high frequency and the second like an internal form modulation
of wave
> at low frequency.
>
> With just finite chords constructed with little rationnal numbers,
chords
> may be seen abstractly as harmonics or subharmonics superposition.
One of
> these two reduced possible forms (common multiplicator or divisor)
is
> generally simpler than other, but there are also mixed chords like
(1 5 3
> 15) or (1 21 3 7). Questions are the following. If subharmonic
reduced form
> is simpler than harmonic form, has mind capacity to perceive
rationality in
> the simpler way ? If yes, is this perception possibly pertinent for
using
> in musical works ?

I know George Kahrimanis will disagree with me, but I believe that
chords which are expressed most simply as subharmonic series are only
consonant insofar as the individual intervals are consonant, and
there
is no perception of unity through an octave-shifted common overtone
or
a Partchian "Numerary Nexus" or any such phenomenon. What is well-
established in psychoacoustical science, however, is our nervous
system's ability to process and simplify the sensation of chords
which
are expressed most simply as harmonic series -- the brain is able to
supply a missing fundamental (we know it is the brain at work since
the harmonics can be separated dichoically), and nonlinear
combination
tones will only reinforce whatever harmonic series is already
implied.

Note, however, that the shape of the wave has very little to do with
how we hear, and should not be used as a guide.

Paul

"À cause de mon anglais" I'll take only one remark in the same post.

You wrote :

<< Pierre, if these two seventh chords were regarded as consonant, they
would not have need for resolution. You say, rather, that they had no
need for preparation. That is quite different. >>

Yes. Perhaps term "consonant" is not appropriate but what is a question for
me is the anterior need for preparation of these chords and gap of 50 years
before other seventh chords were not prepared. I don't understand very well
the problem at musical level. I seek only for sign to direct my attention.

Need for resolution is another topic for which distinction between
dissonance and discordance seems important. The term "dissonance" has
always been used to qualify what has to be resolved. I note that macrotonal
standpoint shows a new approach in term of "discordance". But I can't begin
discussion on that in english. There are too much aspects to call together.
When I'll write a text, in french, on that question, maybe I'll put topic
in dicussion.

For the next paragraph :

<< Which era of music are you talking about? Do you have a date? If you
mean around 1600-1650 ... >>

I'll try to find, first, the reference.

Pierre

[Paul Erlich, TD 738.6]
>
> I know George Kahrimanis will disagree with me, but I believe
> that chords which are expressed most simply as subharmonic series
> are only consonant insofar as the individual intervals are
> consonant, and there is no perception of unity through an
> octave-shifted common overtone or a Partchian "Numerary Nexus"
> or any such phenomenon. What is well-established in
> psychoacoustical science, however, is our nervous system's
> ability to process and simplify the sensation of chords
> which are expressed most simply as harmonic series -- the brain
> is able to supply a missing fundamental (we know it is the brain
> at work since the harmonics can be separated dichoically), and
> nonlinear combination tones will only reinforce whatever harmonic
> series is already implied.

Just for the record, I (mostly) agree with Paul.

I am willing to admit that perhaps *intellectually* our ear-brain
system is able to perceive a subharmonic construction to some
degree, probably chiefly because of the Numerary Nexus. That
is, perhaps we are willing to grant a subharmonic chord a
greater degree of consonance *because* we can analyze it
numerically as a subharmonic structure.

But other than that, I see the subharmonic idea useful in music
mainly in the analysis of contextual (i.e., time-dependent) cues;
for instance, the Riemannian transformations such as the mediant
relations. (As Pierre commented [TD 738.24]: 'static (or
paradigmatic) aspect of chords and scales' vs. 'dynamic (or
syntagmatic'.) This too is primarily an analysis of *intervals*
and not of complete chords, however.

I'm convinced (with Paul) that the psychoacoustical research done
so far points to an inherent human ability to recognize *harmonic*
constructions, and perhaps shows that we even try to to some extent
to 'force' what we hear to fit into this paradigm.

-monz

Joseph L. Monzo San Diego monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
| 'I had broken thru the lattice barrier...' |
| -Erv Wilson |
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[Paul Erlich, TD 738.6:]
>Pierre, if these two seventh chords were regarded as consonant, they
>would not have need for resolution.

I very much disagree! I'm taking this statement out of context, and
haven't heard Pierre's work, but to my ear, a well-tuned 7-limit
dominant 7th (4:5:6:7, or some inversion thereof) is both beautifully
consonant AND in pressing need of resolution. This combination of
qualities gives it, and the transition, irresistible beauty (again, to
my ear).

JdL

[Paul Erlich wrote:]
>>>Pierre, if these two seventh chords were regarded as consonant, they
>>>would not have need for resolution.

[I wrote:]
>>I very much disagree! I'm taking this statement out of context, and
>>haven't heard Pierre's work, but to my ear, a well-tuned 7-limit
>>dominant 7th (4:5:6:7, or some inversion thereof) is both beautifully
>>consonant AND in pressing need of resolution. This combination of
>>qualities gives it, and the transition, irresistible beauty (again, to
>>my ear).

[Paul:]
>John, if you read Blackwood, you would know that a better word for
>describing your pure 4:5:6:7 dominant seventh would be _concordant_.
>Consonance, in the analysis of Western tonal music, does imply a lack
>of need for resolution, which the seventh and tritone in the dominant
>seventh chord could never possess, however well-tuned.

So, you're saying that the word consonance == "doesn't need resolution".
What word ("non-consonance?") is the opposite? I've always thought
that consonance and dissonance were opposites, but dissonance implies
actual beating intervals, does it not?

[Paul:]
>Since you seem to agree with Blackwood in principle, it might be
>clearer, especially when conversing with those trained in the Western
>tradition, to use this terminological distinction.

Well, I have no problem adjusting my use of words for the purpose of
clear communication. But, the more I read of your post, the more
confused things seem to get:

[Paul:]
>_However_, I part with both you an Blackwood in that I see some
>fluidity in what constitutes consonance, depending on musical style. In
>Gothic music, for example, a triad was felt to be dissonant, and had to
>resolve to a 3-limit dyad. In blues and rock the dominant seventh can
>be used for all the chords in the I-IV-I-V-IV-I progression, and it has
>no need to resolve to a triad. Similarly, much latin jazz in a
>mixed-minor mode ends on a minor chord with added major sixth. In this
>spirit, my paper (http://www-math.cudenver.edu/~jstarret/22ALL.pdf)
>proposes a new type of "tonal" music where approximations to 4:5:6:7
>and 1/7:1/6:1/5:1/4 tetrads can, with enough exposure, become
>recognized as the canonical "consonances", to which other chords would
>resolve, and compared to which, triads would sound incomplete.

I fact I agree at both ends; I like sparse music that resolves to open
fifths ("a 3-limit dyads"), and can get my ear around music heavily
laden with tetrads, even on the final tonic. For the music I listen to
most, my original statement holds, as the 4:5:6:7 chord, while
wonderfully, uhhh, non-beating, contains a longing quality that begs for
resolution.

Your proposed definition for the word "consonant", Blackwood
notwithstanding, seems to rob it of almost all substance; it is reduced
to a subjective feeling fluid with context and the listener's ear. This
is inconsistent with my past exposure to the word. I'd be curious to
know how other list members feel. Again, it is not my purpose to argue
over words; we are allies in wanting to communicate clearly.

JdL

Regarding the words "consonant" and "concordant", and which word better
describes a 7-limit dom 7th (pure tones, but longing for resolution),
I just consulted Monzo's tuning dictionary at

http://www.ixpres.com/interval/dict/index.htm

His definition largely agrees with Paul's, equating consonance with a
feeling of being 'at rest'.

Monz doesn't have entries for concordance or discordance. However,
under sonance he writes:

I recommend we distinguish between "sensory consonance" (aka
roughness, sonance etc.) and "contextual consonance" as Tenney does
in his History of Consonance and Dissonance

So, it would seem I was speaking of "sensory consonance", while Paul
is speaking of "contextual consonance". Monz (and others), do you
agree with equating the word concordance with sensory consonance? If
so, I have no objection.

JdL

John A. deLaubenfels wrote

<< Regarding the words "consonant" and "concordant", and which word better
describes a 7-limit dom 7th (pure tones, but longing for resolution) ... >>

I propose (with humility for I'm not musician and I don't understand all
the discussion) this distinction between 3 levels of concepts :

[1] ACOUSTICAL concept of (Softness)/ROUGHNESS = [Douceur/Rugosité in
French]

[2] MICROTONAL concept of Sonance as CONSONANCE/DISSONANCE field

[3] MACROTONAL concept of CONCORDANCE/DISCORDANCE dichotomy

The following descriptions are very bad for I'm very limited here by
language barrier.

[1] ROUGHNESS of (an interval of) two notes is correlated to (small)
distance between witdh of interval and center of "cuvette de consonance".
(I don't know how to translate : "consonance basin" ??) When width is
centered on the "cuvette", roughness disapears. There is no beat between
harmonics of the two notes or there is no overlap of "bandes critiques" in
"ciliées" cells. At small distance of the center begin roughness which then
go up rapidly. As acoustical phenomenon, it depends of ("timbre" or
"spectre") i.e. presence or absence of harmonics (for possible interaction).

[2] CONSONANCE/DISSONANCE as microtonal perception don't depend of timbre.
It's not a local information like roughness but a global infornation on
"cuvette" position as whole. This information gives not the possibility to
appreciate degree of fusion but to determine, when there are several notes,
which chord is formed, what is the approximative global structure.

[3] CONCORDANCE/DISCORDANCE dichotomy (partially described on my web pages)
is a macrotonal concept. On a very coherent set of tones with a
constitutive well-defined set of chords, introduction of extension tones in
chords for harmonic vertical completion, introduces discordance. It's not
forcely dissonant. But it's like a tourist visitor : he has to return for
he's not citizen of coherent set. This process is not incompatible with
parallele process of dissonance reduction. In Zarlino context F of G B D F
is discordant. With triton BF resolution process : B toward C is only
reduction of dissonance (15 - 1), but F toward E is not only reduction of
dissonance (21 - 5), it's also a formal return of the discordant 21/16.
What is the part of a such macrotonal factor in need for resolution ?

Pierre

[Johnny Reinhard wrote:]
>I am having difficulty with the notion that the 4567 needs to resolve.

When you hear a 4:5:6:7 chord, with approximately equal volumes in all
notes and some voice with harmonic overtones (a piano, say), do you
experience a sense of "rest", or the need to resolve? With some
possible exceptions when the ear is set up for very rich tetrads, I
experience the latter.

>If the stasis of the overtone series does does not need to resolve, why
>should a straight ordering with the root in the bass need to resolve?

A question of degree, perhaps. A single piano note is struck by the
hammer in such as way as to minimize, if not eliminate, the 7th
harmonic, so a chord deliberately tuned to 4:5:6:7 would seem to be a
completely different animal.

>There must be a rule of inertia involved.

Not sure what this means...

JdL

[I wrote:]
>>A single piano note is struck by the
>>hammer in such as way as to minimize, if not eliminate, the 7th
>>harmonic, so a chord deliberately tuned to 4:5:6:7 would seem to be a
>>completely different animal.

[Paul Erlich wrote:]
>That is a myth. It may have been true at one point -- hammers hitting
>the string 1/7 of the way along their length -- but today's piano
>hammers strike much closer to the end of the string.

No kidding! Can the piano tuners on this list confirm this?

[Paul:]
>Anyway, I still suggest your feeling of a need for resolution is based
>on excessive [:)] exposure to diatonic tonal music -- and perhaps most
>egregiously [:) :) :)], your 7-limit adaptive retunings of classical
>pieces, where dominant seventh chords are deliberately pulled toward
>4:5:6:7. Listen to the blues for a while and see if you still feel that
>4:5:6:7 needs to resolve.

I do listen to the blues, as it happens, but please tell me: where does
one find blues music with 7ths properly tuned? I'm sure I don't have to
tell you, Paul that a 12-tET dom 7th is very different from 4:5:6:7.

As for the source of my feeling of a need for resolution in a 4:5:6:7,
in truth I don't ask; I just experience. Speculation is interesting,
but ultimately secondary. I try to achieve the sounds I like, and don't
question where the desire comes from.

JdL

[I wrote:]
>>I do listen to the blues, as it happens, but please tell me: where
>>does one find blues music with 7ths properly tuned? I'm sure I don't
>>have to tell you, Paul that a 12-tET dom 7th is very different from
>>4:5:6:7.

[Paul Erlich wrote:]
>Exactly, but if the 12-tET dom 7th doesn't need to resolve, isn't it
>true that retuning to 4:5:6:7 makes it need _even less_ to resolve? At
>least that's my perception.

Well, that would seem to make sense, but it's not my perception. I
experience a well tuned 4:5:6:7 as more longing for resolution than the
12-tET version. There is a hunger in the sound, to my ear. Perhaps
this difference in our perceptions has a lot to do with your staying
away from 7-limit retunings where I embrace them.

JdL

John A. deLaubenfels wrote:

> [I] experience a well tuned 4:5:6:7 as more longing for resolution than the
> 12-tET version. There is a hunger in the sound, to my ear.

I've read with fascination this exchange about the musical and emotional effects of the 4:5:6:7 chord. I listen to a lot of what they call "early" music; that is, Western art (and sometimes folk) music
written during the medieval and Renaissance periods. (Yes, I know "they" include Baroque, too, but I don't. Baroque sounds modern to me.) Much of this music is customarily performed in purer tunings than
later Western art music usually is, especially if played on period instruments. That leaves lots of opportunities for the listener to fill in the harmonies with "missing" 3rds and 7ths. I've become quite
used to the increased satisfaction of ending a phrase, and especially the last phrase of a piece, as 4:5:6:7. It has come to feel more resolved to me than the technically more consonant 4:5:6, just as an
ending of 4:5:6 feels more resolved than an open 5th does to almost any modern Westerner.

Even so, I think I know exactly what John means by the terms "hunger" and "longing." The added 7th gives me the same sort of feeling, but I've come to know that feeling well enough to be comfortable with
it, to feel at home with it, even to not want to go home (so to speak) without it. It's a closely related feeling to the basis of the blues, IMO. It's bittersweet, and it's a taste that can grow on you
until _you_ begin to long for _it_. Try it with Concerto Italaliano's Monteverdi recordings, especially the Musica Sacra CD. Try whistling a 7th over a major tonic chord played by a good natural brass
ensemble - it'll blow your mind when it locks in tune. It shakes your being at a level that 5-limit music can't touch.

Another fun exercise, though not involving a final cadential chord, uses a recent hit song in the US: "Fly Away" by Lenny Kravitz. His triadic vocal harmonies on the words "yeah, yeah, yeah" in the chorus
are quite nicely tuned, close enough to get a good, buzzy 7th with many of them. The progression there is IIIb-VIIb-IV-(I), or C-G-D in the key of A. Try singing the 7th over all three chords, making each
as nearly pure 7:4 (octave invariance taken for granted) to the chord root as possible. Delicious!

--
David J. Finnamore
Nashville, TN, USA
http://members.xoom.com/dfinn.1
--

--- In tuning@egroups.com, "John A. deLaubenfels" <jdl@a...> wrote:
> [I wrote:]
> >>I do listen to the blues, as it happens, but please tell me:
where
> >>does one find blues music with 7ths properly tuned? I'm sure I
don't
> >>have to tell you, Paul that a 12-tET dom 7th is very different
from
> >>4:5:6:7.
>
> [Paul Erlich wrote:]
> >Exactly, but if the 12-tET dom 7th doesn't need to resolve, isn't
it
> >true that retuning to 4:5:6:7 makes it need _even less_ to
resolve? At
> >least that's my perception.
>
> Well, that would seem to make sense, but it's not my perception. I
> experience a well tuned 4:5:6:7 as more longing for resolution than
the
> 12-tET version. There is a hunger in the sound, to my ear. Perhaps
> this difference in our perceptions has a lot to do with your staying
> away from 7-limit retunings where I embrace them.

And perhaps due to my conscious attempts to create music where better
approximations to 4:5:6:7 and 1/6:1/5:1/4:2/7 are stable, final
consonances (which is what my paper is all about). But perhaps not .
.
.