4:5:6:7

My favorite recent quotes from the tuning list
regarding 7-limit from

Bob Valentine:
...
Why is 7-limit tuning any less legitimate than playing
a meantone
piece in 12-et, as a matter of principle?
-----------
JdL
...
Why are past masters relegated to some kind of holy
shrine, in which their works must never be touched, in
some people's
eyes? IMHO, the best way to honor someone is to take
bits of their
work and reconstitute them in new ways. When old
works become museum
pieces, they become brittle and eventually lost. This
is not honoring,
this is killing.

I do hope that faithful renditions of old works remain
in our ears, as
a point of comparison if nothing else.
-----------

With that great intro, now my 2.5 cents...

I became a real partisan for the use of 4:5:6:7
dominant sevenths about as soon as I could tune them
up with my Kurzweil and Clavette some 8 years ago.

We should remember the context in which past revered
musical theorists didn't find the harmonic 7th useful.
Most of them did not live at a time in which the
chromatically available harmonies and melodies in the
commonly used tunings had all been well-explored (as
is now the case with 12-ET), and they could not often
easily build instruments (or train choirs) for
reasonably easy >12-ET performance--practicality was
certainly a big factor

While it's fair to say that one can't easily
substitute this sonority for the dominant seventh
chords in most common practice music without
adjustments, this DOES NOT mean that we can't make NEW
pieces that sound as euphonious as music that period
using JIs or >12-ETs that represent them well.

As suggested by JdL, those of us on this list with
strong common practice harmony skills should also
consider 'desecrating' the 'holy writ of the musical
Masters' by taking some of those works, whether by
Monteverdi or Wagner or whomever else, moving 'em to
say 22-ET, and making musically appropriate
adjustments and corrections to create an aesthetically
satisfying transcription of the original into another
tuning domain.

Amongst the adjustments I make in musical context with
22-ET:

Descending major scales: from major scale degree 3,
the 5:4 match (7/22), I continue with 10:9 (3/22), not
9:8 (4/22).
Ascending: reverse the rule: 9:8 in place of 10:9
(the major scale here can be conceived of as "melodic
major")

My ears have no problem with melodic motion in 22-ET
that puts the minor 7th above the dominant, followed
by the harmonic 7th. You can even resolve from the
harmonic 7th with further hyperchromatic voice-leading
through the 9/7 (8/22) to the 5/4 (7/22).

We can also distinguish the top tone of the
minor-minor 7th chord from the top tone of the
4:5:6:7--in 22-ET these are 1/22 apart. Rich grounds
for investigation with jazzy styles.

-------------
Some recent quotes of Paul E. that deserve response:

>>...No one even conceived of music as a
set of "chord progressions" like we do today. Listen
to Victoria. What's the "chord progression"?

One way or the other, Victoria must have carefully
chosen his harmonies, even if German 19-century
harmonic theory was not known. We can hear 'chord
progression' because the music can fairly be heard
that way--just as we might label Martin Luther's
theology as Protestantism although perhaps no one in
1525 would understand that concept. Most Western music
is inextricably harmonic-melodic, or
melodic-harmonic--something like the way light can be
seen today by physicists as waves, or photons--but it
really is something of both, as well as being the kind
of brightness that we know as physical creatures with
sense organs.

>>...The meaning of the V7 chord is primarily
_melodic_ ("linear"), rather
than harmonic. The notes of the diminished fifth
always resolved in
contrary motion to a tonic third.

Even in common practice music the V7 frequently
resolves to a vi, and if reinterpreted as an augmented
7th it obviously resolves outward. (The moment of
reinterpretation obviously being as one hears the
resolution of what was first heard as a V7.)

Of course the "dominant seventh" chord is also the
basic harmony of the blues, and is generally the
'triad' of swing and later jazz. Although of course in
most of those functions, it's not a dominant seventh,
but a major-minor 7th chord.

I think you've taken too seriously the Schenkerian
ideology handed down in most US college music
departments today. If these analyses really revealed
so much about the structure of the masterworks from
which they're derived, why aren't we hearing new works
of brilliant tonal music from such theorists who after
all have unveiled 'everything' about, say, Beethoven's
5th? There is some value to Schenkerian theory, but
there is insufficient consideration of the interaction
of short and large-scale rhythm, orchestration,
dynamics, melodic shapes, the dramatic development of
tonal music: the surprises vs. the 'continuing', etc.
I found it quite interesting to look at 16th & 20th
century pieces in a Schenkerian way--music which
supposedly shouldn't be analyzed with his concepts.

-------------
Also: I don't find the conception of n-limit useful.
I'm not very interested in 7-denominator intervals
like say 10/7 or 25/49, while I find 7:4, 7:5, 7:6
really intriguing for the extension of common practice
harmony into >12 ETs.
==============
I look forward to all thoughtful critiques, and hope
to show you the fruits of my theorizations with more
music live and on the web in the near future.

Soundly yours,
Harold

__________________________________________________
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I very much appreciate your interesting contributions here, Harold. I
agree that the appeal of 4:5:6:7 is not and should not be dependent
on WHAT WE THINK WE KNOW about historical practice. On the other
hand, neither is it conditioned by modern common practice.
Additionally, I do not go even as far as agreeing with the apparently
fairly general concensus here that the low 7ths of 7-limit in
dominant 7th chords are always, even in a cappella vocal contexts,
"inauthentic" in, let us say Renaissance music or early baroque.

I do NOT believe that what composers wrote about and did consciously
in their tuning and tuning preferences with keyboards always and
inevitably reflects accurately the practices in performing a cappella
vocal works or other ensembles not tied to some temperament or fixed
tuning; not any more than it does today!

I have observed that innocent, not terribly talented or even musical
ears can be trained to prefer the simple just intervals, namely
fifths, fourths, and major thirds. Then quite without any training in
this new harmonic context those same ears will spontaneously
gravitate, given a sustained chord with plenty of time, toward the
low 7-limit version of the 7th in V7.

I believe this is because, given sufficient opportunity, the human
ear seeks out the simplest overall pattern of relationships rather
the simplest ratios between any two specific tones in triads and in
the more complex chords. I don't have any reason to believe this is a
peculiarity of the 21st or late 20th centuries, since whatever
previous exposure my subjects (members of my choir) have had to
tunings has been 12-tET and the horrible distortions of it made
available by entropy and lengthy periods of time between tunings.

However, even I do not pretend that such a seventh appearing as a
passing tone of brief duration over a dominant triad would suddenly
and reliably veer off the beaten track of its normal diatonic
position pitchwise to comply with the 7-limit version. Melodic habit
bids heavily against this.

--- In tuning@y..., Harold Fortuin <harold_fortuin@y...> wrote:
> My favorite recent quotes from the tuning list
> regarding 7-limit from
>
> Bob Valentine:
> ...
> Why is 7-limit tuning any less legitimate than playing
> a meantone
> piece in 12-et, as a matter of principle?
> -----------
> JdL
> ...
> Why are past masters relegated to some kind of holy
> shrine, in which their works must never be touched, in
> some people's
> eyes? IMHO, the best way to honor someone is to take
> bits of their
> work and reconstitute them in new ways. When old
> works become museum
> pieces, they become brittle and eventually lost. This
> is not honoring,
> this is killing.
>
> I do hope that faithful renditions of old works remain
> in our ears, as
> a point of comparison if nothing else.
> -----------
>
> With that great intro, now my 2.5 cents...
>
> I became a real partisan for the use of 4:5:6:7
> dominant sevenths about as soon as I could tune them
> up with my Kurzweil and Clavette some 8 years ago.
>
> We should remember the context in which past revered
> musical theorists didn't find the harmonic 7th useful.
> Most of them did not live at a time in which the
> chromatically available harmonies and melodies in the
> commonly used tunings had all been well-explored (as
> is now the case with 12-ET), and they could not often
> easily build instruments (or train choirs) for
> reasonably easy >12-ET performance--practicality was
> certainly a big factor
>
> While it's fair to say that one can't easily
> substitute this sonority for the dominant seventh
> chords in most common practice music without
> adjustments, this DOES NOT mean that we can't make NEW
> pieces that sound as euphonious as music that period
> using JIs or >12-ETs that represent them well.
>
> As suggested by JdL, those of us on this list with
> strong common practice harmony skills should also
> consider 'desecrating' the 'holy writ of the musical
> Masters' by taking some of those works, whether by
> Monteverdi or Wagner or whomever else, moving 'em to
> say 22-ET, and making musically appropriate
> adjustments and corrections to create an aesthetically
> satisfying transcription of the original into another
> tuning domain.
>
> Amongst the adjustments I make in musical context with
> 22-ET:
>
> Descending major scales: from major scale degree 3,
> the 5:4 match (7/22), I continue with 10:9 (3/22), not
> 9:8 (4/22).
> Ascending: reverse the rule: 9:8 in place of 10:9
> (the major scale here can be conceived of as "melodic
> major")
>
> My ears have no problem with melodic motion in 22-ET
> that puts the minor 7th above the dominant, followed
> by the harmonic 7th. You can even resolve from the
> harmonic 7th with further hyperchromatic voice-leading
> through the 9/7 (8/22) to the 5/4 (7/22).
>
> We can also distinguish the top tone of the
> minor-minor 7th chord from the top tone of the
> 4:5:6:7--in 22-ET these are 1/22 apart. Rich grounds
> for investigation with jazzy styles.
>
> -------------
> Some recent quotes of Paul E. that deserve response:
>
> >>...No one even conceived of music as a
> set of "chord progressions" like we do today. Listen
> to Victoria. What's the "chord progression"?
>
> One way or the other, Victoria must have carefully
> chosen his harmonies, even if German 19-century
> harmonic theory was not known. We can hear 'chord
> progression' because the music can fairly be heard
> that way--just as we might label Martin Luther's
> theology as Protestantism although perhaps no one in
> 1525 would understand that concept. Most Western music
> is inextricably harmonic-melodic, or
> melodic-harmonic--something like the way light can be
> seen today by physicists as waves, or photons--but it
> really is something of both, as well as being the kind
> of brightness that we know as physical creatures with
> sense organs.
>
> >>...The meaning of the V7 chord is primarily
> _melodic_ ("linear"), rather
> than harmonic. The notes of the diminished fifth
> always resolved in
> contrary motion to a tonic third.
>
> Even in common practice music the V7 frequently
> resolves to a vi, and if reinterpreted as an augmented
> 7th it obviously resolves outward. (The moment of
> reinterpretation obviously being as one hears the
> resolution of what was first heard as a V7.)
>
> Of course the "dominant seventh" chord is also the
> basic harmony of the blues, and is generally the
> 'triad' of swing and later jazz. Although of course in
> most of those functions, it's not a dominant seventh,
> but a major-minor 7th chord.
>
> I think you've taken too seriously the Schenkerian
> ideology handed down in most US college music
> departments today. If these analyses really revealed
> so much about the structure of the masterworks from
> which they're derived, why aren't we hearing new works
> of brilliant tonal music from such theorists who after
> all have unveiled 'everything' about, say, Beethoven's
> 5th? There is some value to Schenkerian theory, but
> there is insufficient consideration of the interaction
> of short and large-scale rhythm, orchestration,
> dynamics, melodic shapes, the dramatic development of
> tonal music: the surprises vs. the 'continuing', etc.
> I found it quite interesting to look at 16th & 20th
> century pieces in a Schenkerian way--music which
> supposedly shouldn't be analyzed with his concepts.
>
> -------------
> Also: I don't find the conception of n-limit useful.
> I'm not very interested in 7-denominator intervals
> like say 10/7 or 25/49, while I find 7:4, 7:5, 7:6
> really intriguing for the extension of common practice
> harmony into >12 ETs.
> ==============
> I look forward to all thoughtful critiques, and hope
> to show you the fruits of my theorizations with more
> music live and on the web in the near future.
>
> Soundly yours,
> Harold
>
>
> __________________________________________________
> Terrorist Attacks on U.S. - How can you help?
> Donate cash, emergency relief information
> http://dailynews.yahoo.com/fc/US/Emergency_Information/

--- In tuning@y..., Harold Fortuin <harold_fortuin@y...> wrote:

> As suggested by JdL, those of us on this list with
> strong common practice harmony skills should also
> consider 'desecrating' the 'holy writ of the musical
> Masters' by taking some of those works, whether by
> Monteverdi or Wagner or whomever else, moving 'em to
> say 22-ET, and making musically appropriate
> adjustments and corrections to create an aesthetically
> satisfying transcription of the original into another
> tuning domain.

That's fun, but to me the comma problems can never be fully resolved,
especially when the comma is inflated to a full 54.5 cents.
>
> Amongst the adjustments I make in musical context with
> 22-ET:
>
> Descending major scales: from major scale degree 3,
> the 5:4 match (7/22), I continue with 10:9 (3/22), not
> 9:8 (4/22).
> Ascending: reverse the rule: 9:8 in place of 10:9
> (the major scale here can be conceived of as "melodic
> major")

This is fine for you if you like it. My tastes are different.
>
> We can also distinguish the top tone of the
> minor-minor 7th chord from the top tone of the
> 4:5:6:7--in 22-ET these are 1/22 apart. Rich grounds
> for investigation with jazzy styles.

I do these sorts of things in my 22-tET compositions . . . the idea
is to make the 1/22-oct step a _motivic feature_ rather than an
awkward "correction".
>
> -------------
> Some recent quotes of Paul E. that deserve response:
>
> >>...No one even conceived of music as a
> set of "chord progressions" like we do today. Listen
> to Victoria. What's the "chord progression"?
>
> One way or the other, Victoria must have carefully
> chosen his harmonies, even if German 19-century
> harmonic theory was not known. We can hear 'chord
> progression' because the music can fairly be heard
> that way

I don't really hear chord progressions in Victoria. Do you?
>
> >>...The meaning of the V7 chord is primarily
> _melodic_ ("linear"), rather
> than harmonic. The notes of the diminished fifth
> always resolved in
> contrary motion to a tonic third.
>
> Even in common practice music the V7 frequently
> resolves to a vi,

Here the notes of the diminished fifth are resolved in contrary
motion to a third that normally is a subset of the tonic triad, but
here used in the other triad that it is a subset of. This is called a
deceptive cadence. It's almost identical to a viio/vi resolving to
vi, which would be a regular cadence on the relative minor.

> and if reinterpreted as an augmented
> 7th

Augmented sixth?

> it obviously resolves outward.

This kind of reintepretation had to wait until well after the advent
of closed 12-tone tunings. In the meantone era (through the Baroque
at least), the augmented sixth and dominant seventh sounded
different, were spelled differently, and resolved in different ways.

> I found it quite interesting to look at 16th & 20th
> century pieces in a Schenkerian way--music which
> supposedly shouldn't be analyzed with his concepts.

There was some discussion of this on this list about a year ago . . .
>
> -------------
> Also: I don't find the conception of n-limit useful.
> I'm not very interested in 7-denominator intervals
> like say 10/7 or 25/49,

25/49 isn't 7-limit according to the "odd" definition of limit, which
I normally emphasize.

> while I find 7:4, 7:5, 7:6
> really intriguing for the extension of common practice
> harmony into >12 ETs.

12:7 and 10:7 and 8:7 are simply octave-inversions of the above. I
agree that the ratios with smaller numbers (7:4, 7:5, 7:6) are more
clear and stable than these, but when considering questions of
designing tuning systems, when octave-equivalence is assumed in
advance, one can profitably consider ALL 7-limit intervals within the
octave: 8:7, 7:6, 6:5, 5:4, 4:3, 7:5, and their inversions. That's
all. You're not finding the conception n-limit useful because (a)
you're misunderstaning it, and (b) you're not considering the types
of problems where it is useful.

--- In tuning@y..., BobWendell@t... wrote:

> I believe this is because, given sufficient opportunity, the human
> ear seeks out the simplest overall pattern of relationships rather
> the simplest ratios between any two specific tones in triads and in
> the more complex chords.

Even in chords like CEGAD?

Even in chords that are _supposed_ to be moments of high drama and
instability?
>
> However, even I do not pretend that such a seventh appearing as a
> passing tone of brief duration over a dominant triad would suddenly
> and reliably veer off the beaten track of its normal diatonic
> position pitchwise to comply with the 7-limit version. Melodic
habit
> bids heavily against this.

Well, I'm glad you can see somewhat where I'm coming from.

Bob had said:
I believe this is because, given sufficient opportunity, the human
ear seeks out the simplest overall pattern of relationships rather
the simplest ratios between any two specific tones in triads and in
> the more complex chords.
>
Paul replied:
> Even in chords like CEGAD?
>
Bob answers:
Yes. Here you have the notorious syntonic comma problem built in,
forcing some kind of tradeoff between perfect fourths and fifths, and
the thirds. You have no choice. They can't all be just.

So 1/4-comma meantone gives perfect thirds, but fifths compromised by
-5.4 cents. 12-tET gives almost perfect fifths (-2.0 cents) and
heavily compromised thirds (M3 +13.7 cents). We have a range of
choices between these two extremes.

So the point here is that the human ear will seek an optimum
compromise that represents maximum tonal coherence. I would like to
posit here that the first principle behind the appeal of harmony to
the human ear and psyche is that they seek and savor maximum tonal
coherence. In the case of CEGAD, the compromise will be located
somewhere along a continuum that trades off thirds and fifths against
each other.

We can productively view all the variants on 1/4-comma meantone as
modifications of it that only partially rather than fully distribute
the comma on the major third to the fifths. As the distribution
becomes increasingly partial (e.g., 1/6-comma instead of 1/4), less
of the comma is distributed to the fifths, the major third going
increasingly sharp and the fifths becoming less compromised on the
flat side.

If we continue far enough in this direction, we will eventually end
up at 12-tET and a closed cycle of fifths instead of the open cycle
of all the meantone variants (excluding the 31-tET closed cycle of 31
fifths if we regard this temperament as equivalent to 1/4-comma
meantone). There should be some optimimum compromise along the
continuum between these two extremes (representing maximum harmonic
coherence = minimum harmonic entropy) that the human ear will tend to
prefer when executing CEGAD.

--- In tuning@y..., BobWendell@t... wrote:
> Bob had said:
> I believe this is because, given sufficient opportunity, the human
> ear seeks out the simplest overall pattern of relationships rather
> the simplest ratios between any two specific tones in triads and in
> > the more complex chords.
> >
> Paul replied:
> > Even in chords like CEGAD?
> >
> Bob answers:
> Yes. Here you have the notorious syntonic comma problem built in,
> forcing some kind of tradeoff between perfect fourths and fifths,
and
> the thirds. You have no choice. They can't all be just.

Hi Bob,

I thought you were implying that any chord would have to be
interpreted in terms of some set of harmonics over some implied
fundamental -- because that would be an alternative to seeking "the
simplest ratios between any two specific tones" -- see your first
paragraph above. However, in your reply here, and the rest of the
message (omitted here), it seems you _are_ seeking to approach "the
simplest ratios between any two specific tones" -- no?

Hi there :)

I have some questions about our efforts in general...
The vertical perfection do must be even respected ?
And if any temperament is not valide for all of
harmonies , is he helpful?
Is it good to have one temperament for play CEGAD, and
one different for play ...C#E#G#A#D# ?
Paul had say that between C# and Db we have diminushed
second...I want ask any thing about-when we play
false-what happen ? Hmmm...the same ! We play not in
tunning ...simply :) And all of divisions is the
result of "harmonic illusion" and attempting to play
even every ton accomoding him with the harmonie ...Why
?
I dont joke :) For me the just intonation is like when
you love one woman ! The name of this woman is "tonic"
or the tonality principal :)
If you love so so much, you will never play wrong !
What's the perfection ? The JI ? Only the himeres...
Ok, I agree that the universal temperament dont exist
like i thing, but...where we going now ?
Nowhere..because hmm, ok ! The compositions ...
How many years for undestand the base ?
What base ? I would be sure for respondre...
I had try some ET variants, but...
The third's are not commode for ....

Will stop now....
More? Later...

Dimitrov

--- BobWendell@technet-inc.com a �crit�: > Bob had
said:
> I believe this is because, given sufficient
> opportunity, the human
> ear seeks out the simplest overall pattern of
> relationships rather
> the simplest ratios between any two specific tones
> in triads and in
> > the more complex chords.
> >
> Paul replied:
> > Even in chords like CEGAD?
> >
> Bob answers:
> Yes. Here you have the notorious syntonic comma
> problem built in,
> forcing some kind of tradeoff between perfect
> fourths and fifths, and
> the thirds. You have no choice. They can't all be
> just.
>
> So 1/4-comma meantone gives perfect thirds, but
> fifths compromised by
> -5.4 cents. 12-tET gives almost perfect fifths (-2.0
> cents) and
> heavily compromised thirds (M3 +13.7 cents). We have
> a range of
> choices between these two extremes.
>
> So the point here is that the human ear will seek an
> optimum
> compromise that represents maximum tonal coherence.
> I would like to
> posit here that the first principle behind the
> appeal of harmony to
> the human ear and psyche is that they seek and savor
> maximum tonal
> coherence. In the case of CEGAD, the compromise will
> be located
> somewhere along a continuum that trades off thirds
> and fifths against
> each other.
>
> We can productively view all the variants on
> 1/4-comma meantone as
> modifications of it that only partially rather than
> fully distribute
> the comma on the major third to the fifths. As the
> distribution
> becomes increasingly partial (e.g., 1/6-comma
> instead of 1/4), less
> of the comma is distributed to the fifths, the major
> third going
> increasingly sharp and the fifths becoming less
> compromised on the
> flat side.
>
> If we continue far enough in this direction, we will
> eventually end
> up at 12-tET and a closed cycle of fifths instead of
> the open cycle
> of all the meantone variants (excluding the 31-tET
> closed cycle of 31
> fifths if we regard this temperament as equivalent
> to 1/4-comma
> meantone). There should be some optimimum compromise
> along the
> continuum between these two extremes (representing
> maximum harmonic
> coherence = minimum harmonic entropy) that the human
> ear will tend to
> prefer when executing CEGAD.
>
>
>
>

___________________________________________________________
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--- In tuning@y..., Latchezar Dimitrov <latchezar_d@y...> wrote:
> Hi there :)
>
> I have some questions about our efforts in general...
> The vertical perfection do must be even respected ?

I don't understand this question.

> And if any temperament is not valide for all of
> harmonies , is he helpful?

Hmm . . . different musics were written with different temperaments
in mind . . . the great majority of Western music from 1480-1780 came
from a meantone conception . . .

> Is it good to have one temperament for play CEGAD, and
> one different for play ...C#E#G#A#D# ?

In a regular meantone these would be the same. Of course you would
need more than 12 distinct pitches per octave if you also wanted to
use flats. This was not uncommon . . . for example, of the organs
Handel played on, one was capable of producing 14 pitches from the
meantone system, while another was reported to be able to produce 16.

> Paul had say that between C# and Db we have diminushed
> second...I want ask any thing about-when we play
> false-what happen ? Hmmm...the same ! We play not in
> tunning ...simply :)

But C# and Db are each respectively _in tune_, in their scalar
environments . . . one cannot substitute one for the other (until the
era of Beethoven, Schubert, etc., when enharmonic equivalency became
a fact of life.

> And all of divisions is the
> result of "harmonic illusion" and attempting to play
> even every ton accomoding him with the harmonie ...Why
> ?

Are you aware of the vast history and literature of the development
and usage of tuning systems in Western music? Even 12-tone equal
temperament came out of this history, with many painful changes to,
and harsh debates within, the musical culture in the 18th
century . . .

> I dont joke :) For me the just intonation is like when
> you love one woman ! The name of this woman is "tonic"
> or the tonality principal :)

Hmm . . . there is a big difference between meantone temperament and
JI.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., BobWendell@t... wrote:
> > Bob had said:
> > I believe this is because, given sufficient opportunity, the
human
> > ear seeks out the simplest overall pattern of relationships
rather
> > the simplest ratios between any two specific tones in triads and
in
> > > the more complex chords.
> > >
> > Paul replied:
> > > Even in chords like CEGAD?
> > >
> > Bob answers:
> > Yes. Here you have the notorious syntonic comma problem built in,
> > forcing some kind of tradeoff between perfect fourths and fifths,
> and
> > the thirds. You have no choice. They can't all be just.
>
> Hi Bob,
>
> I thought you were implying that any chord would have to be
> interpreted in terms of some set of harmonics over some implied
> fundamental -- because that would be an alternative to seeking "the
> simplest ratios between any two specific tones" -- see your first
> paragraph above. However, in your reply here, and the rest of the
> message (omitted here), it seems you _are_ seeking to approach "the
> simplest ratios between any two specific tones" -- no?

Wow! OK. No. I was proposing only that the ear tends to like the
simplest, most coherent OVERALL set of relationships among ALL the
elements of whatever harmonic pattern we call a chord RATHER than
seeking the simplest relationship between each set of two tones
within the structure. The tradeoffs in this case (CEGAD) between
thirds and perfect fifths (and by implication their inversions,
perfect fourths) are clearly NOT between two tones, but between two
SETS of relationships among multiple tones.

By the way, I found by experimentation that my ear has no problem
with tuning CEGAD justly as long as the A is raised to be a just
perfect fourth from D. The syntonic comma resulting between A
and E from this tuning is apparently overidden by the context of the
pure E in the basic CEG triad and the A perfectly coherent with the
3rd harmonic of the 4:9 D.

I also surmise that the CEG component of the structure predominates
powerfully enough so that the syntonic comma between A and E is much
more tolerable than if the A were left to directly challenge the 3rd
harmonic of the D, since the D has a more distant and therefore weak
relationship to the CEG structure than that of the A and D's 3rd
harmonic.

This clearly differs from the solution I offered previously, although
I don't have the means to easily compare the two approaches and
decide what my ear deems to be most euphonious.

--- In tuning@y..., BobWendell@t... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> > --- In tuning@y..., BobWendell@t... wrote:
> > > Bob had said:
> > > I believe this is because, given sufficient opportunity, the
> human
> > > ear seeks out the simplest overall pattern of relationships
> rather
> > > the simplest ratios between any two specific tones in triads
and
> in
> > > > the more complex chords.
> > > >
> > > Paul replied:
> > > > Even in chords like CEGAD?
> > > >
> > > Bob answers:
> > > Yes. Here you have the notorious syntonic comma problem built
in,
> > > forcing some kind of tradeoff between perfect fourths and
fifths,
> > and
> > > the thirds. You have no choice. They can't all be just.
> >
> > Hi Bob,
> >
> > I thought you were implying that any chord would have to be
> > interpreted in terms of some set of harmonics over some implied
> > fundamental -- because that would be an alternative to
seeking "the
> > simplest ratios between any two specific tones" -- see your first
> > paragraph above. However, in your reply here, and the rest of the
> > message (omitted here), it seems you _are_ seeking to
approach "the
> > simplest ratios between any two specific tones" -- no?
>
> Wow! OK. No. I was proposing only that the ear tends to like the
> simplest, most coherent OVERALL set of relationships among ALL the
> elements of whatever harmonic pattern we call a chord RATHER than
> seeking the simplest relationship between each set of two tones
> within the structure. The tradeoffs in this case (CEGAD) between
> thirds and perfect fifths (and by implication their inversions,
> perfect fourths) are clearly NOT between two tones, but between two
> SETS of relationships among multiple tones.

Thirds and perfect fifths and their inversions . . . each of these is
a set of two tones . . . that's what you considered in your previous
message on this topic . . . so isn't it true that you _were_ "seeking
the simplest relationship between each set of two tones within the
structure"?

In this message, though, you did bring in some larger (more OVERALL)
considerations, such as the strength of the CEG component. That's
good. I think somewhere between meantone, and having the full comma
between A and E, is where the best tuning lies, at least for some
voicing of the chord.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., BobWendell@t... wrote:
> > --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> > > --- In tuning@y..., BobWendell@t... wrote:
> > > > Bob had said:
> > > > I believe this is because, given sufficient opportunity, the
> > human
> > > > ear seeks out the simplest overall pattern of relationships
> > rather
> > > > the simplest ratios between any two specific tones in triads
> and
> > in
> > > > > the more complex chords.
> > > > >
> > > > Paul replied:
> > > > > Even in chords like CEGAD?
> > > > >
> > > > Bob answers:
> > > > Yes. Here you have the notorious syntonic comma problem built
> in,
> > > > forcing some kind of tradeoff between perfect fourths and
> fifths,
> > > and
> > > > the thirds. You have no choice. They can't all be just.
> > >
> > > Hi Bob,
> > >
> > > I thought you were implying that any chord would have to be
> > > interpreted in terms of some set of harmonics over some implied
> > > fundamental -- because that would be an alternative to
> seeking "the
> > > simplest ratios between any two specific tones" -- see your
first
> > > paragraph above. However, in your reply here, and the rest of
the
> > > message (omitted here), it seems you _are_ seeking to
> approach "the
> > > simplest ratios between any two specific tones" -- no?
> >
> > Wow! OK. No. I was proposing only that the ear tends to like the
> > simplest, most coherent OVERALL set of relationships among ALL
the
> > elements of whatever harmonic pattern we call a chord RATHER than
> > seeking the simplest relationship between each set of two tones
> > within the structure. The tradeoffs in this case (CEGAD) between
> > thirds and perfect fifths (and by implication their inversions,
> > perfect fourths) are clearly NOT between two tones, but between
two
> > SETS of relationships among multiple tones.
>
> Thirds and perfect fifths and their inversions . . . each of these
is
> a set of two tones . . . that's what you considered in your
previous
> message on this topic . . . so isn't it true that you _were_
"seeking
> the simplest relationship between each set of two tones within the
> structure"?
>
> In this message, though, you did bring in some larger (more
OVERALL)
> considerations, such as the strength of the CEG component. That's
> good. I think somewhere between meantone, and having the full comma
> between A and E, is where the best tuning lies, at least for some
> voicing of the chord.

You got it, Paul! That's where I've been heading all along. THE sets
of two are not sets of two. C-G-D are not two and are related by
fifths. D and A are two, but E forms a third with C and G. More
complex than you have represented here. I used the terms OVERALL and
WHOLE PATTERN very advisedly.

--- In tuning@y..., Latchezar Dimitrov <latchezar_d@y...> wrote:

/tuning/topicId_28308.html#28389

> ?
> I dont joke :) For me the just intonation is like when
> you love one woman ! The name of this woman is "tonic"
> or the tonality principal :)

And then "serialism" would be...?? Well, perhaps we shouldn't get
into it...

_______ _______ ______ ___
Joseph Pehrson

Joseph...

Do you think to respond, or... ?
What's "your" serialism ?
What do you mean with ?

Dimitrov

--- jpehrson@rcn.com a �crit�: > --- In tuning@y...,
Latchezar Dimitrov
> <latchezar_d@y...> wrote:
>
> /tuning/topicId_28308.html#28389
>
> > ?
> > I dont joke :) For me the just intonation is like
> when
> > you love one woman ! The name of this woman is
> "tonic"
> > or the tonality principal :)
>
>
> And then "serialism" would be...?? Well, perhaps we
> shouldn't get
> into it...
>
> _______ _______ ______ ___
> Joseph Pehrson
>
>
>

___________________________________________________________
Do You Yahoo!? -- Un e-mail gratuit @yahoo.fr !
Yahoo! Courrier : http://fr.mail.yahoo.com

--- In tuning@y..., Latchezar Dimitrov <latchezar_d@y...> wrote:

/tuning/topicId_28308.html#28503

> Joseph...
>
> Do you think to respond, or... ?
> What's "your" serialism ?
> What do you mean with ?
>
>
> Dimitrov
>

This was only a little joke, Latch... :)

It didn't translate well into French, so forget about it... :)

_______ ________ _________
Joseph Pehrson

Hi-
Could someone explain to me the meaning of "4:5:6:7
chords"? I'm pretty lost in most of these
discussions.

NTHL

> ----- Original Message -----
> From: "Robert C Valentine" <BVAL@IIL.INTEL.COM>
> To: <tuning@yahoogroups.com>
> Sent: Sunday, February 24, 2002 9:15 AM
> Subject: [tuning] First Impressions : 31ED2 G&L
> arrives
>
> >
> > Whats good : 4:5:6:7 chords everywhere (who cares
> if I use F and
> > E# in the same measure), small leading tones (who
> cares if its
> > the opposite of meantone), scale 4455445 (I sound
> like a
> > local now)... 5265256 and modes... blues (with
> real flat sevens
> > on the chords and neutral thirds and sevenths for
> the melodys)...
> > all the nifty new chromatic-stuff (minor third
> divisible by 4,
> > major third by 5... five whole tones is a real
> 7/4)...
> >

__________________________________________________
Do You Yahoo!?
Yahoo! Sports - Coverage of the 2002 Olympic Games
http://sports.yahoo.com

----- Original Message -----
From: "Nathaniel Braddock" <nbraddo@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: Monday, February 25, 2002 3:13 PM
Subject: [tuning] 4:5:6:7

> Hi-
> Could someone explain to me the meaning of "4:5:6:7
> chords"? I'm pretty lost in most of these
> discussions.

The numbers are harmonics and represent a chord
with these ratios:

4 is the fundamental, so 4 = 1/1
5 is the fifth harmonic, so = 5/4
6 is an octave above 3/2, so 6 = 6/4 or really 3/2
7 is the 7th harmonic, 7 = 7/4

1/1, 5/4, 3/2, 7/4 = a dominant 7th chord.

How's that?

* David Beardsley
* http://biink.com
* http://mp3.com/davidbeardsley

--- In tuning@y..., Nathaniel Braddock <nbraddo@y...> wrote:
> Hi-
> Could someone explain to me the meaning of "4:5:6:7
> chords"? I'm pretty lost in most of these
> discussions.

It refers to any chord of four notes where the frequencies of the
notes (in hertz or cycles-per-second (Hz)) are in those ratios. e.g.
if the lowest note was 440 Hz (an A) then the others would be
(reasonably close to) 550 Hz, 660 Hz and 770 Hz. I'd call it a
harmonic seventh chord or a major subminor seventh chord since it
sounds quite different from a dominant seventh (major minor seventh)
chord in the usual 12 tone equal temperament. It really "sings". We
say it is in just intonation

If you want to work out the frequencies in hertz of the notes in
12-equal, start with A at 440 Hz and multiply by the 12th root of 2
(about 1.059) each time you go up a semitone.

> From: Nathaniel Braddock <nbraddo@yahoo.com>
> Subject: 4:5:6:7
>
> Hi-
> Could someone explain to me the meaning of "4:5:6:7
> chords"? I'm pretty lost in most of these
> discussions.
>
> NTHL

Hi Nathaniel,

As David pointed out, I was referring to having those
harmonics very closely approximated on my 31 tone per
octave guitar and that this is also pretty musch like
a "dominant seventh". Except that that "7" is a very
different note than the one you hear on a 12 tone guitar
as is it is much closer to the harmonic pitch. So is
the "5".

4:5:6:7 in cents is about 0 386 702 969.
The 12et approximateion is 0 400 700 1000.
My 31et approximation is 0 387 697 968.

By all means ask quesions, I've been lost here for years
now and thats the only way to find ones way.

Bob Valentine

--- In tuning@y..., Robert C Valentine <BVAL@I...> wrote:
>
> > From: Nathaniel Braddock <nbraddo@y...>
> > Subject: 4:5:6:7
> >
> > Hi-
> > Could someone explain to me the meaning of "4:5:6:7
> > chords"? I'm pretty lost in most of these
> > discussions.
> >
> > NTHL

best is to hear them!

> 4:5:6:7 in cents is about 0 386 702 969.

that's the second example at
http://artists.mp3s.com/artists/140/tuning_lab.html

> The 12et approximateion is 0 400 700 1000.

that's the fourth example at
http://artists.mp3s.com/artists/140/tuning_lab.html

On 2/26/02 7:41 PM, "tuning@yahoogroups.com" <tuning@yahoogroups.com> wrote:

> Message: 4
> Date: Tue, 26 Feb 2002 21:33:47 -0000
> From: "paulerlich" <paul@stretch-music.com>
> Subject: Re: 4:5:6:7
>
> --- In tuning@y..., Robert C Valentine <BVAL@I...> wrote:
>>
>>> From: Nathaniel Braddock <nbraddo@y...>
>>> Subject: 4:5:6:7
>>>
>>> Hi-
>>> Could someone explain to me the meaning of "4:5:6:7
>>> chords"? I'm pretty lost in most of these
>>> discussions.
>>>
>>> NTHL
>
> best is to hear them!
>
>> 4:5:6:7 in cents is about 0 386 702 969.
>
> that's the second example at
> http://artists.mp3s.com/artists/140/tuning_lab.html
>
>> The 12et approximateion is 0 400 700 1000.
>
> that's the fourth example at
> http://artists.mp3s.com/artists/140/tuning_lab.html

The 4:5:6:7 example sounds terrible, Paul. I can't hear the "seventh" at
all. If this is intended to show what "partials" four through seven sounds
like, I'm missing something.

In contrast, the 22-tET sounds *wonderful* to me. It's one of the "best"
things I've heard in all of our messing around with tuning examples. (Any
clues here for our "quest"?)

The 12-tET sounds awful. Why, do you think?

BTW, why do you say that "it's best to hear them" in order to know what
4:5:6:7 means? No reference to partials? Is that fair?

Jerry

--- In tuning@y..., Gerald Eskelin <stg3music@e...> wrote:
> On 2/26/02 7:41 PM, "tuning@y..." <tuning@y...> wrote:
>
> > Message: 4
> > Date: Tue, 26 Feb 2002 21:33:47 -0000
> > From: "paulerlich" <paul@s...>
> > Subject: Re: 4:5:6:7
> >
> > --- In tuning@y..., Robert C Valentine <BVAL@I...> wrote:
> >>
> >>> From: Nathaniel Braddock <nbraddo@y...>
> >>> Subject: 4:5:6:7
> >>>
> >>> Hi-
> >>> Could someone explain to me the meaning of "4:5:6:7
> >>> chords"? I'm pretty lost in most of these
> >>> discussions.
> >>>
> >>> NTHL
> >
> > best is to hear them!
> >
> >> 4:5:6:7 in cents is about 0 386 702 969.
> >
> > that's the second example at
> > http://artists.mp3s.com/artists/140/tuning_lab.html
> >
> >> The 12et approximateion is 0 400 700 1000.
> >
> > that's the fourth example at
> > http://artists.mp3s.com/artists/140/tuning_lab.html
>
> The 4:5:6:7 example sounds terrible, Paul. I can't hear
the "seventh" at
> all. If this is intended to show what "partials" four through seven
sounds
> like, I'm missing something.

i don't know what you mean, jerry. all this is is a chord, just like
the others, but with the pitches tuned in the ratios 4:5:6:7. it's
what a lot of people seem to think the dominant seventh
chord 'should' be.

> In contrast, the 22-tET sounds *wonderful* to me. It's one of
the "best"
> things I've heard in all of our messing around with tuning
examples. (Any
> clues here for our "quest"?)

hey, welcome to the 22-equal fan club (please don't use it for
triadic diatonic music, though).

> The 12-tET sounds awful. Why, do you think?

'cause you haven't played a piano for a while? :)

> BTW, why do you say that "it's best to hear them" in order to know
what
> 4:5:6:7 means? No reference to partials? Is that fair?

the other explanations were already sufficient as far as basic theory
goes (if you want to get into psychoacoustics, that's another
matter). but surely it's better to know what these chords actually
sound like before going on theoretical flights of fancy, isn't it?

--- In tuning@y..., "paulerlich" <paul@s...> wrote:

/tuning/topicId_28308.html#34967

>
> the other explanations were already sufficient as far as basic
theory
> goes (if you want to get into psychoacoustics, that's another
> matter). but surely it's better to know what these chords actually
> sound like before going on theoretical flights of fancy, isn't it?

***Did I miss something, or was there never a total recap of the
various "jerry" major thirds that Paul posted? I don't believe I
read Jerry's ultimate opinions on them or what size, finally, they
were...

??

jp

--- In tuning@y..., Gerald Eskelin <stg3music@e...> wrote:

> > best is to hear them!
> >
> >> 4:5:6:7 in cents is about 0 386 702 969.
> >
> > that's the second example at
> > http://artists.mp3s.com/artists/140/tuning_lab.html
>
> The 4:5:6:7 example sounds terrible, Paul.

i would like to hear *joseph* and others chime in with their opinions
on 4:5:6:7 at this point.

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:

> ***Did I miss something, or was there never a total recap of the
> various "jerry" major thirds that Paul posted? I don't believe I
> read Jerry's ultimate opinions on them or what size, finally, they
> were...

he requested versions where the major third enters after a few
seconds, and then departs again . . . i'll work on it when i get a
chance . . .

----- Original Message -----
From: "paulerlich" <paul@stretch-music.com>

> --- In tuning@y..., Gerald Eskelin <stg3music@e...> wrote:
>
> > > best is to hear them!
> > >
> > >> 4:5:6:7 in cents is about 0 386 702 969.
> > >
> > > that's the second example at
> > > http://artists.mp3s.com/artists/140/tuning_lab.html
> >
> > The 4:5:6:7 example sounds terrible, Paul.
>
> i would like to hear *joseph* and others chime in with their opinions
> on 4:5:6:7 at this point.

Sounds fine to me. Kiind of short @ 10 seconds.

* David Beardsley
* http://biink.com
* http://mp3.com/davidbeardsley

----- Original Message -----
From: "dkeenanuqnetau" <d.keenan@uq.net.au>

> --- In tuning@y..., Nathaniel Braddock <nbraddo@y...> wrote:
> > Hi-
> > Could someone explain to me the meaning of "4:5:6:7
> > chords"? I'm pretty lost in most of these
> > discussions.
>
> It refers to any chord of four notes where the frequencies of the
> notes (in hertz or cycles-per-second (Hz)) are in those ratios. e.g.
> if the lowest note was 440 Hz (an A) then the others would be
> (reasonably close to) 550 Hz, 660 Hz and 770 Hz. I'd call it a
> harmonic seventh chord or a major subminor seventh chord since it
> sounds quite different from a dominant seventh (major minor seventh)
> chord in the usual 12 tone equal temperament. It really "sings". We
> say it is in just intonation
>
> If you want to work out the frequencies in hertz of the notes in
> 12-equal, start with A at 440 Hz and multiply by the 12th root of 2
> (about 1.059) each time you go up a semitone.

I thought my explanation was fine. What's the point in dragging frequencies
in?
You're just making it more complicated than an explanation should be.

* David Beardsley
* http://biink.com
* http://mp3.com/davidbeardsley

--- In tuning@y..., "paulerlich" <paul@s...> wrote:

/tuning/topicId_28308.html#34972

> --- In tuning@y..., Gerald Eskelin <stg3music@e...> wrote:
>
> > > best is to hear them!
> > >
> > >> 4:5:6:7 in cents is about 0 386 702 969.
> > >
> > > that's the second example at
> > > http://artists.mp3s.com/artists/140/tuning_lab.html
> >
> > The 4:5:6:7 example sounds terrible, Paul.
>
> i would like to hear *joseph* and others chime in with their
opinions on 4:5:6:7 at this point.

***Well, it was fun listening to the Tuning Lab page again, since, on
the overall, I know more about "Tuning" than when it was set up! :)

However, my basic responses to the chords remain pretty much the same.

My "favorites" are the virtually "beatless" ones:

4:5:6:7

1/7:1/6:1/5:1/4 the utonal

and the corresponding otonal: 5:6:7:9

I have no problem hearing the 7th in the 4:5:6:7 (??)

The difference between the utonal 5:6:7:9 and the utonal above is
still fascinating. Not a difference in "beating" per se but some
kind of strange "warbling" in the utonal chord. It's "going against
nature" buddies... :)

And, the 22-tET and 12-tET examples get further and further "out" in
terms of more "chorusing" and beating. Most for the 12-tET, of
course...

jp

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
>
> /tuning/topicId_28308.html#34972
>
> > --- In tuning@y..., Gerald Eskelin <stg3music@e...> wrote:
> >
> > > > best is to hear them!
> > > >
> > > >> 4:5:6:7 in cents is about 0 386 702 969.
> > > >
> > > > that's the second example at
> > > > http://artists.mp3s.com/artists/140/tuning_lab.html
> > >
> > > The 4:5:6:7 example sounds terrible, Paul.
> >
> > i would like to hear *joseph* and others chime in with their
> opinions on 4:5:6:7 at this point.
>
>
>
> ***Well, it was fun listening to the Tuning Lab page again, since,
on
> the overall, I know more about "Tuning" than when it was set up! :)
>
> However, my basic responses to the chords remain pretty much the
same.
>
> My "favorites" are the virtually "beatless" ones:
>
> 4:5:6:7
>
> 1/7:1/6:1/5:1/4 the utonal
>
> and the corresponding otonal: 5:6:7:9
>
> I have no problem hearing the 7th in the 4:5:6:7 (??)
>
> The difference between the utonal 5:6:7:9 and the utonal above is
> still fascinating. Not a difference in "beating" per se but some
> kind of strange "warbling" in the utonal chord. It's "going
against
> nature" buddies... :)
>
> And, the 22-tET and 12-tET examples get further and further "out"
in
> terms of more "chorusing" and beating. Most for the 12-tET, of
> course...

well, we all seem to agree on that last point . . . but . . .

ironic, isn't it, that the big champion of 'acoustic tuning' thinks
the just 4:5:6:7 chord sounds 'terrible'? i mean, what could be
more 'locked in' than that?

i think this may support my contention that 4:5:6:7 is *not* what
most people like to hear in the context of common-practice, western,
diatonic music. since that's the context that jerry works in, more so
than joseph pehrson or david beardsley, at least . . .

note also that jerry really liked the 22-equal chord, where the
tritone is, strangely enough for jerry, exactly 600 cents . . .

--- In tuning@y..., "paulerlich" <paul@s...> wrote:

/tuning/topicId_28308.html#34985

>
> ironic, isn't it, that the big champion of 'acoustic tuning' thinks
> the just 4:5:6:7 chord sounds 'terrible'? i mean, what could be
> more 'locked in' than that?
>
> i think this may support my contention that 4:5:6:7 is *not* what
> most people like to hear in the context of common-practice,
western, diatonic music. since that's the context that jerry works
in, more so than joseph pehrson or david beardsley, at least . . .
>

****I agree, Paul, that this seems to support your contention...

jp

On 2/27/02 10:21 AM, "tuning@yahoogroups.com" <tuning@yahoogroups.com>
wrote:

> Message: 17
> Date: Wed, 27 Feb 2002 17:23:50 -0000
> From: "jpehrson2" <jpehrson@rcn.com>
> Subject: the "jerries?"
>
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
>
> /tuning/topicId_28308.html#34967
>
>>
>> the other explanations were already sufficient as far as basic
> theory
>> goes (if you want to get into psychoacoustics, that's another
>> matter). but surely it's better to know what these chords actually
>> sound like before going on theoretical flights of fancy, isn't it?
>
> ***Did I miss something, or was there never a total recap of the
> various "jerry" major thirds that Paul posted? I don't believe I
> read Jerry's ultimate opinions on them or what size, finally, they
> were...
>
> ??

I posted a prelim response last Friday (I think) but intended to do a more
detailed one over the weekend. I got distracted with a publishing thing and
didn't got back to it. My apology.

I'll try to do it today or tomorrow. Thanks for the prod, Joe.

Jerry

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
>
> /tuning/topicId_28308.html#34985
>
> >
> > ironic, isn't it, that the big champion of 'acoustic tuning'
thinks
> > the just 4:5:6:7 chord sounds 'terrible'? i mean, what could be
> > more 'locked in' than that?
> >
> > i think this may support my contention that 4:5:6:7 is *not* what
> > most people like to hear in the context of common-practice,
> western, diatonic music. since that's the context that jerry works
> in, more so than joseph pehrson or david beardsley, at least . . .
> >
>
> ****I agree, Paul, that this seems to support your contention...

although we must admit, joseph, that dave keenan's first I-IV-V7-I
calls this into some doubt, doesn't it? since there the V7 *is*
4:5:6:7 . . .

i really think, as i have all along (how convenient for me to say
this now), that it's really a *scalar* phenomenon rather than a
*vertical* one (perhaps i go a bit brainwashed by forte's _tonal
harmony_? well, it sure is convincing). the *vertical* phenomena are
the triads, but the *scalar* template seems to be the more important
phenomenon (just about every culture in the world uses *some* scalar
template for any given segment of music, usually with four to nine
tones per octave). then the dominant seventh chord invokes the
*characterstic interval* within the diatonic scalar template, namely
the tritone, which then sets up a powerful drive toward resolution
(in contrary motion via semitones to notes of the tonic triad)
*regardless of fine tuning*.

so in dave keenan's example, none of the *scale pitches* moves around
by more than 9 cents, so the scalar template is fairly secure.

however, in the 'just 7-limit' example, the fourth scale degree moves
by 27 cents from the IV chord to the V7 chord. this is a large enough
step to disturb the scalar template, it seems, and to disturb joseph
and me when we listen to this progression.

jerry, though, likes this latter progression (though strangely he
*dislikes* the 4:5:6:7 chord in isolation) . . . perhaps he had
already decided he *should* like it in advance once he knew *what* he
was going to be listening to . . . ????

On 2/27/02 10:21 AM, "tuning@yahoogroups.com" <tuning@yahoogroups.com>
wrote:

> Message: 13
> Date: Wed, 27 Feb 2002 17:05:39 -0000
> From: "paulerlich" <paul@stretch-music.com>
> Subject: Re: 4:5:6:7
>
I said:
>>
>> The 4:5:6:7 example sounds terrible, Paul. I can't hear
>> the "seventh" at
>> all. If this is intended to show what "partials" four through seven
>> sounds
>> like, I'm missing something.
>
> i don't know what you mean, jerry. all this is is a chord, just like
> the others, but with the pitches tuned in the ratios 4:5:6:7. it's
> what a lot of people seem to think the dominant seventh
> chord 'should' be.

Yes. I'm one of them (almost). I think the recording just doesn't play well
for some reason. Oh, well.
>
>> In contrast, the 22-tET sounds *wonderful* to me. It's one of
>> the "best"
>> things I've heard in all of our messing around with tuning
>> examples. (Any
>> clues here for our "quest"?)
>
> hey, welcome to the 22-equal fan club (please don't use it for
> triadic diatonic music, though).

I'd ask why but I probably wouldn't understand the answer. I'll just let it
go at that. :-)
>
>> The 12-tET sounds awful. Why, do you think?
>
> 'cause you haven't played a piano for a while? :)

True. But then this recording doesn't sound much like a piano.
>
>> BTW, why do you say that "it's best to hear them" in order to know
> what
>> 4:5:6:7 means? No reference to partials? Is that fair?
>
> the other explanations were already sufficient as far as basic theory
> goes (if you want to get into psychoacoustics, that's another
> matter). but surely it's better to know what these chords actually
> sound like before going on theoretical flights of fancy, isn't it?
>
I probably shouldn't have responded as I did here. I didn't read the earlier
entries in this thread. I agree.

Jerry

Actually, I appreciated frequency-based explanation in
conjuction with the others.

Paul-
Thanks for having these examples posted out there. I
don't currently have a set-up to start trying to
create some of this myself, which I think inhibits my
understanding at times, so having some basic examples
is great.

-Nathaniel

>
> Message: 23
> Date: Wed, 27 Feb 2002 13:03:19 -0500
> From: "David Beardsley"
> <davidbeardsley@biink.com>
> Subject: Re: Re: 4:5:6:7
>
> ----- Original Message -----
> From: "dkeenanuqnetau" <d.keenan@uq.net.au>
>
> > --- In tuning@y..., Nathaniel Braddock
> <nbraddo@y...> wrote:
> > > Hi-
> > > Could someone explain to me the meaning of
> "4:5:6:7
> > > chords"? I'm pretty lost in most of these
> > > discussions.
> >
> > It refers to any chord of four notes where the
> frequencies of the
> > notes (in hertz or cycles-per-second (Hz)) are in
> those ratios. e.g.
> > if the lowest note was 440 Hz (an A) then the
> others would be
> > (reasonably close to) 550 Hz, 660 Hz and 770 Hz.
> I'd call it a
> > harmonic seventh chord or a major subminor seventh
> chord since it
> > sounds quite different from a dominant seventh
> (major minor seventh)
> > chord in the usual 12 tone equal temperament. It
> really "sings". We
> > say it is in just intonation
> >
> > If you want to work out the frequencies in hertz
> of the notes in
> > 12-equal, start with A at 440 Hz and multiply by
> the 12th root of 2
> > (about 1.059) each time you go up a semitone.
>
> I thought my explanation was fine. What's the point
> in dragging frequencies
> in?
> You're just making it more complicated than an
> explanation should be.
>

__________________________________________________
Do You Yahoo!?
Yahoo! Greetings - Send FREE e-cards for every occasion!
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--- In tuning@y..., Nathaniel Braddock <nbraddo@y...> wrote:

> Actually, I appreciated frequency-based explanation in
> conjuction with the others.

yeah, i didn't see what was wrong with that as an addendum.

> Paul-
> Thanks for having these examples posted out there. I
> don't currently have a set-up to start trying to
> create some of this myself, which I think inhibits my
> understanding at times, so having some basic examples
> is great.

you're welcome! hope you'll keep asking questions!

----- Original Message -----
From: "paulerlich" <paul@stretch-music.com>
To: <tuning@yahoogroups.com>
Sent: Wednesday, February 27, 2002 4:04 PM
Subject: [tuning] Re: 4:5:6:7

> --- In tuning@y..., Nathaniel Braddock <nbraddo@y...> wrote:
>
> > Actually, I appreciated frequency-based explanation in
> > conjuction with the others.
>
> yeah, i didn't see what was wrong with that as an addendum.

I don't think of frequencies when I look at the neck of my guitar,
I think about ratios.

* David Beardsley
* http://biink.com
* http://mp3.com/davidbeardsley

--- In tuning@y..., "David Beardsley" <davidbeardsley@b...> wrote:
>
> ----- Original Message -----
> From: "paulerlich" <paul@s...>
> To: <tuning@y...>
> Sent: Wednesday, February 27, 2002 4:04 PM
> Subject: [tuning] Re: 4:5:6:7
>
>
> > --- In tuning@y..., Nathaniel Braddock <nbraddo@y...> wrote:
> >
> > > Actually, I appreciated frequency-based explanation in
> > > conjuction with the others.
> >
> > yeah, i didn't see what was wrong with that as an addendum.
>
> I don't think of frequencies when I look at the neck of my guitar,
> I think about ratios.

fair enough, but i'm guessing a few more musicians out there know
what A-440 means, than would know what these ratios are supposed to
mean. it never hurts to try to answer a question from a few different
angles, to try to get the questioner over the initial 'hump'.
different answers only complement one another, they're
not 'competing'.

----- Original Message -----
From: "paulerlich" <paul@stretch-music.com>

> --- In tuning@y..., "David Beardsley" <davidbeardsley@b...> wrote:
> >
> > ----- Original Message -----
> > From: "paulerlich" <paul@s...>
> > > --- In tuning@y..., Nathaniel Braddock <nbraddo@y...> wrote:
> > >
> > > > Actually, I appreciated frequency-based explanation in
> > > > conjuction with the others.
> > >
> > > yeah, i didn't see what was wrong with that as an addendum.
> >
> > I don't think of frequencies when I look at the neck of my guitar,
> > I think about ratios.
>
> fair enough, but i'm guessing a few more musicians out there know
> what A-440 means, than would know what these ratios are supposed to
> mean.

Not everybody tunes to A-440 anyways - I tune my JI guitar (and synths)
to A=426.7. After it's tuned, I have no idea or interest in knowing what
freq.
13/8 or 7/4 is.

dB

On 2/27/02 3:51 PM, "tuning@yahoogroups.com" <tuning@yahoogroups.com> wrote:

> Message: 6
> Date: Wed, 27 Feb 2002 19:47:53 -0000
> From: "paulerlich" <paul@stretch-music.com>
> Subject: Re: 4:5:6:7
>
> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
>>
>> /tuning/topicId_28308.html#34972
>>
>>> Gerald Eskelin <stg3music@e...> wrote:
>>>
>>> The 4:5:6:7 example sounds terrible, Paul.

>> i would like to hear *joseph* and others chime in with their
>> opinions on 4:5:6:7 at this point.

> ***Well, it was fun listening to the Tuning Lab page again, since,
> on
> the overall, I know more about "Tuning" than when it was set up! :)
>
> However, my basic responses to the chords remain pretty much the
> same.
>
> My "favorites" are the virtually "beatless" ones:
>
> 4:5:6:7
>
> 1/7:1/6:1/5:1/4 the utonal
>
> and the corresponding otonal: 5:6:7:9
>
> I have no problem hearing the 7th in the 4:5:6:7 (??)
>
> The difference between the utonal 5:6:7:9 and the utonal above is
> still fascinating. Not a difference in "beating" per se but some
> kind of strange "warbling" in the utonal chord. It's "going
> against
> nature" buddies... :)
>
> And, the 22-tET and 12-tET examples get further and further "out"
> in
> terms of more "chorusing" and beating. Most for the 12-tET, of
> course...

This leads me to believe that there was some corruption going on with my
download. The 4:5:6:7 example consisted of a raucous and raspy root, a light
fifth, a nearly inaudible third and there wasn't a seventh within earshot.
Clearly, Joe and I were hearing different sounds--and I don't mean
subjectively.

(5 minute pause to re-download the example.)

Just as I suspected. It sounds lovely, Paul. All 4 pitches are expressing
themselves in balance, just as a music lover would expect. :-)
>
> well, we all seem to agree on that last point . . . but . . .
>
> ironic, isn't it, that the big champion of 'acoustic tuning' thinks
> the just 4:5:6:7 chord sounds 'terrible'? i mean, what could be
> more 'locked in' than that?

First of all, I'm no "champion"--not in the sense of "in support of" nor in
the sense of "better than anyone." What I said was the *example* sounds
terrible--not that 4:5:6:7 sounds terrible. If you remember, I expressed
much enthusiasm for your Jerry0 (which I now believe is JI). Believe me, the
example I listened to wasn't anything close to that.
>
> i think this may support my contention that 4:5:6:7 is *not* what
> most people like to hear in the context of common-practice, western,
> diatonic music.

Does this mean you are "championing" that point of view, Paul? (Just
kidding.)

> since that's the context that jerry works in, more so
> than joseph pehrson or david beardsley, at least . . .

That's assuming Jerry *knows* what he's working in. :-) Remember, that's why
he showed up here in the first place--because he had doubts. Come to think
of it, he left that way, too. What I'm trying to figure out is why did he
come back here anyway?
>
> note also that jerry really liked the 22-equal chord, where the
> tritone is, strangely enough for jerry, exactly 600 cents . . .

So? I liked it. Maybe it was the low seventh that seduced me.

Jerry

PS: I listened again to the first round of Jerries and have little to add to
my "preliminary" report. I hope there were some clues there. Looking forward
to the next set, Paul.

On 2/27/02 3:51 PM, "tuning@yahoogroups.com" <tuning@yahoogroups.com> wrote:

> Message: 10
> Date: Wed, 27 Feb 2002 20:25:55 -0000
> From: "paulerlich" <paul@stretch-music.com>
> Subject: Re: 4:5:6:7
>
> --- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
>> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
>>
>> /tuning/topicId_28308.html#34985
>>
>>>
>>> ironic, isn't it, that the big champion of 'acoustic tuning'
> thinks
>>> the just 4:5:6:7 chord sounds 'terrible'? i mean, what could be
>>> more 'locked in' than that?
>>>
>>> i think this may support my contention that 4:5:6:7 is *not* what
>>> most people like to hear in the context of common-practice,
>> western, diatonic music. since that's the context that jerry works
>> in, more so than joseph pehrson or david beardsley, at least . . .
>>>
>>
>> ****I agree, Paul, that this seems to support your contention...
>
> although we must admit, joseph, that dave keenan's first I-IV-V7-I
> calls this into some doubt, doesn't it? since there the V7 *is*
> 4:5:6:7 . . .

Thanks for remembering, Paul. I think you would agree (had you been able to
hear what I was hearing) that there was little in common between this V7 and
the 4:5:6:7 example I was listening to.
>
> i really think, as i have all along (how convenient for me to say
> this now), that it's really a *scalar* phenomenon rather than a
> *vertical* one (perhaps i go a bit brainwashed by forte's _tonal
> harmony_?

I taught from that book back in 1970. I don¹t remember any discussion of
flexible tuning. (But then, 32 years is 32 years.)

> well, it sure is convincing). the *vertical* phenomena are
> the triads, but the *scalar* template seems to be the more important
> phenomenon (just about every culture in the world uses *some* scalar
> template for any given segment of music, usually with four to nine
> tones per octave). then the dominant seventh chord invokes the
> *characterstic interval* within the diatonic scalar template, namely
> the tritone, which then sets up a powerful drive toward resolution
> (in contrary motion via semitones to notes of the tonic triad)
> *regardless of fine tuning*.

My god, Paul. You must have read my book! No? Then it must be you've been
listening to actual music composed and performed in the major/minor system.
Yeah. That must be it.
>
> so in dave keenan's example, none of the *scale pitches* moves around
> by more than 9 cents, so the scalar template is fairly secure.
>
> however, in the 'just 7-limit' example, the fourth scale degree moves
> by 27 cents from the IV chord to the V7 chord. this is a large enough
> step to disturb the scalar template, it seems, and to disturb joseph
> and me when we listen to this progression.

I'll just have to find some hot a cappella sounds with "flat" sevenths in
the melody line. Then we'll have something specific we can "like" or
"dislike."

I just flashed on a recording of an Indian folk song (alternately solo and
unison group) sung over a tonic drone. I used it as an audio example in my
book. It's melodic sevenths are so low my teachers would have "corrected"
them for being flat. Not exactly the same as a V7 chord, but indicative that
melody can and probably often does follow the leading of an acoustically
sensitive ear.
>
> jerry, though, likes this latter progression (though strangely he
> *dislikes* the 4:5:6:7 chord in isolation) . . . perhaps he had
> already decided he *should* like it in advance once he knew *what* he
> was going to be listening to . . . ????

I think we can forget this nonsense now. Okay? Incidentally, I'm no longer
(assuming I might have been in the past) married to any particular outcome
as we explore tuning preferences. I'm just as curious as the next ear
regarding what it is I've been listening to in more than a half century of
choral singing.

Jerry

--- In tuning@y..., "paulerlich" <paul@s...> wrote:

/tuning/topicId_28308.html#34989

> so in dave keenan's example, none of the *scale pitches* moves
around by more than 9 cents, so the scalar template is fairly secure.
>
> however, in the 'just 7-limit' example, the fourth scale degree
moves by 27 cents from the IV chord to the V7 chord. this is a large
enough step to disturb the scalar template, it seems, and to disturb
joseph and me when we listen to this progression.
>

***This "scalar template" is an interesting idea. It does seem
rather "peculiar" that I find the 7-limit progression with the
seventh at 21/16 so annoying, when I like the *isolated* 4:5:6:7...

jp

--- In tuning@y..., Gerald Eskelin <stg3music@e...> wrote:

> > i really think, as i have all along (how convenient for me to say
> > this now), that it's really a *scalar* phenomenon rather than a
> > *vertical* one (perhaps i go a bit brainwashed by forte's _tonal
> > harmony_?
>
> I taught from that book back in 1970. I don¹t remember any
discussion of
> flexible tuning.

exactly.

--- In tuning@y..., Gerald Eskelin <stg3music@e...> wrote:

> > jerry, though, likes this latter progression (though strangely he
> > *dislikes* the 4:5:6:7 chord in isolation) . . . perhaps he had
> > already decided he *should* like it in advance once he knew
*what* he
> > was going to be listening to . . . ????
>
> I think we can forget this nonsense now. Okay?

yup. i do regret writing it, and hope it wasn't taken too seriously
(those were four 'smiley' question marks).

> Incidentally, I'm no longer
> (assuming I might have been in the past) married to any particular
outcome
> as we explore tuning preferences. I'm just as curious as the next
ear
> regarding what it is I've been listening to in more than a half
century of
> choral singing.

and i'm extremely curious too, since i admire your renowned talent
(not because it's renowned, but because it's talent), and since it
seems we're on the verge of classifying, if not truly understanding,
an important phenomenon (or several) in one style of musical practice.

it's now impossible to upload examples to the files section of
tuning2. you'll have to pick another group to join :(

tuning-math or
harmonic_entropy or
miracle_tuning or perhaps
metatuning

?

pick one and i'll post the files you requested there.

--- In tuning@y..., "paulerlich" <paul@s...> wrote:

/tuning/topicId_28308.html#35071

>
> it's now impossible to upload examples to the files section of
> tuning2. you'll have to pick another group to join :(
>

***Why did Robert Walker close this off, again? I was never quite
clear on it...

jp

On 3/1/02 3:12 AM, "tuning@yahoogroups.com" <tuning@yahoogroups.com> wrote:

>
> Message: 24
> Date: Fri, 01 Mar 2002 11:04:25 -0000
> From: "paulerlich" <paul@stretch-music.com>
> Subject: Re: 4:5:6:7
>
> --- In tuning@y..., Gerald Eskelin <stg3music@e...> wrote:
>
>>> jerry, though, likes this latter progression (though strangely he
>>> *dislikes* the 4:5:6:7 chord in isolation) . . . perhaps he had
>>> already decided he *should* like it in advance once he knew
>>> *what* he
>>> was going to be listening to . . . ????
>>
>> I think we can forget this nonsense now. Okay?
>
> yup. i do regret writing it, and hope it wasn't taken too seriously
> (those were four 'smiley' question marks).
>
Paul, I think we know each other well enough now that these "jabs" are taken
with a certain affection.

>> Incidentally, I'm no longer
>> (assuming I might have been in the past) married to any particular
>> outcome
>> as we explore tuning preferences. I'm just as curious as the next
>> ear
>> regarding what it is I've been listening to in more than a half
>> century of
>> choral singing.
>
> and i'm extremely curious too, since i admire your renowned talent
> (not because it's renowned, but because it's talent),

And we can knock this stuff off, too. We are what we are. Let's get to it.

> and since it
> seems we're on the verge of classifying, if not truly understanding,
> an important phenomenon (or several) in one style of musical practice.

Yes. I think that's pretty exciting. So, when all is said and done...we
*need* each other. :-)
>
> it's now impossible to upload examples to the files section of
> tuning2. you'll have to pick another group to join :(
>
> tuning-math or
> harmonic_entropy or
> miracle_tuning or perhaps
> metatuning
>
> pick one and i'll post the files you requested there.

My god, what a choice! I have no idea what the last three are. I smother in
the numbers strewn over *this* list; I would drown in a purely math
environment. Since it matters not, why don't you just pick one and tell us
where you put them.

Jerry

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:

/tuning/topicId_28308.html#35094

> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
>
> /tuning/topicId_28308.html#35071
>
> >
> > it's now impossible to upload examples to the files section of
> > tuning2. you'll have to pick another group to join :(
> >
>
> ***Why did Robert Walker close this off, again? I was never quite
> clear on it...
>
> jp

***Yeah, well, I notice he never bothered to answer this, either...

JP

Joe and Paul,

--- In tuning@y..., "Joseph Pehrson" <jpehrson@r...> wrote:
> ***Yeah, well, I notice he never bothered to answer this, either...

C'mon you guys, Robert is one of the least histrionic people to ever frequent the lists, and the amount of time he spent posting stuff and trying to find ways to help out (remember the FAQ tree? remember the archive postings?), I have to think this is a misunderstanding.

He just posted on MMM about an improvisation, so he's around. Why doesn't one of you write him privately and clear this up, or at least get to the bottom of it?

Cheers,
Jon

--- In tuning@y..., "Jon Szanto" <JSZANTO@A...> wrote:

/tuning/topicId_28308.html#40500

> Joe and Paul,
>
> --- In tuning@y..., "Joseph Pehrson" <jpehrson@r...> wrote:
> > ***Yeah, well, I notice he never bothered to answer this,
either...
>
> C'mon you guys, Robert is one of the least histrionic people to
ever frequent the lists, and the amount of time he spent posting
stuff and trying to find ways to help out (remember the FAQ tree?
remember the archive postings?), I have to think this is a
misunderstanding.
>
> He just posted on MMM about an improvisation, so he's around. Why
doesn't one of you write him privately and clear this up, or at least
get to the bottom of it?
>
> Cheers,
> Jon

***You're right, Jon. Maybe there is some "hidden" reason for
this.... dunno. I just wrote to him.

He's pretty even-tempered... just like you and Partch, Jon... :)

Joe

--- In tuning@y..., "Joseph Pehrson" <jpehrson@r...> wrote:

/tuning/topicId_28308.html#40501

> --- In tuning@y..., "Jon Szanto" <JSZANTO@A...> wrote:
>
> /tuning/topicId_28308.html#40500
>
> > Joe and Paul,
> >
> > --- In tuning@y..., "Joseph Pehrson" <jpehrson@r...> wrote:
> > > ***Yeah, well, I notice he never bothered to answer this,
> either...
> >
> > C'mon you guys, Robert is one of the least histrionic people to
> ever frequent the lists, and the amount of time he spent posting
> stuff and trying to find ways to help out (remember the FAQ tree?
> remember the archive postings?), I have to think this is a
> misunderstanding.
> >
> > He just posted on MMM about an improvisation, so he's around. Why
> doesn't one of you write him privately and clear this up, or at
least
> get to the bottom of it?
> >
> > Cheers,
> > Jon
>

***Well this mini-mystery is solved. Robert wrote right back.
Apparently he just wants to keep that site as a list, that's all, and
doesn't want to confuse the issue.

So, we'll have to make a new site to store files if we so desire...
not very hard to do...

JP

--- In tuning@y..., "Joseph Pehrson" <jpehrson@r...> wrote:
> So, we'll have to make a new site to store files if we so desire...
> not very hard to do...

Sounds like tuning-files to me!

As for being Partch and I being mild-mannered, I've had a week with a conductor that has been... 'challenging'. My wife just came home with "Tension Tamer" tea, so I hope I don't fly off the handle before the weekend is out!

Cheers,
Jon (who swears that doing the 1911 version of "Petrouchka" is enough to send many people into histrionics...)

--- In tuning@y..., "Jon Szanto" <JSZANTO@A...> wrote:

/tuning/topicId_28308.html#40503

> --- In tuning@y..., "Joseph Pehrson" <jpehrson@r...> wrote:
> > So, we'll have to make a new site to store files if we so
desire...
> > not very hard to do...
>
> Sounds like tuning-files to me!
>
> As for being Partch and I being mild-mannered, I've had a week with
a conductor that has been... 'challenging'. My wife just came home
with "Tension Tamer" tea, so I hope I don't fly off the handle before
the weekend is out!
>
> Cheers,
> Jon (who swears that doing the 1911 version of "Petrouchka" is
enough to send many people into histrionics...)

***Well, that sounds pretty "exciting" to *me* Jon...! So, I guess
it's either that or rust away...

JP