MIDI files and tuning

I've heard that there is a MIDI specification for tuning, at www.midi.org/about-midi/tuning.htm
But it didn't work for me ( does it work with sombody here ? )
Also Bitch Bend message was not useful.
The only useful way was sending a fine tune message immediately after or before the note message.

Does anybody here have a simpler solve for tuning MIDI files or devices?

Rami Vitale

[Rami Vitale wrote:]
>I've heard that there is a MIDI specification for tuning, at
>www.midi.org/about-midi/tuning.htm But it didn't work for me (does it
>work with sombody here ? ) Also Bitch Bend message was not useful.
>The only useful way was sending a fine tune message immediately after
>or before the note message.

>Does anybody here have a simpler solve for tuning MIDI files or
>devices?

Manuel Op de Coul is more knowledgeable than I am on this, but I'm
pretty sure the methods referenced at that web site are not implemented
by very many modules.

Pitch bends should work for you, however, on any module which is GM
compliant and many that are not. Is this not what you mean by "fine
tune message"?

I use pitch bends for all my tuning work, and the resultant MIDI files
seem to be playable by many. There are some test sequences you might
want to try on my website,

http://www.adaptune.com

(change to Studio J and scroll about 3/4 of the way to the bottom of
the page).

JdL

Why use the sound card propriety to implant tunning
conceptions?
Do you think that any conseptor of a sound card knows
how to divide or give you a better to do it?!
To bend modification is not the right way to do it!
You must create your proper instrument to play your
own tunnings! There is no other way!

Dimitrov

--- "John A. deLaubenfels" <jdl@adaptune.com> a
�crit�: > [Rami Vitale wrote:]
> >I've heard that there is a MIDI specification for
> tuning, at
> >www.midi.org/about-midi/tuning.htm But it didn't
> work for me (does it
> >work with sombody here ? ) Also Bitch Bend message
> was not useful.
> >The only useful way was sending a fine tune message
> immediately after
> >or before the note message.
>
> >Does anybody here have a simpler solve for tuning
> MIDI files or
> >devices?
>
> Manuel Op de Coul is more knowledgeable than I am on
> this, but I'm
> pretty sure the methods referenced at that web site
> are not implemented
> by very many modules.
>
> Pitch bends should work for you, however, on any
> module which is GM
> compliant and many that are not. Is this not what
> you mean by "fine
> tune message"?
>
> I use pitch bends for all my tuning work, and the
> resultant MIDI files
> seem to be playable by many. There are some test
> sequences you might
> want to try on my website,
>
> http://www.adaptune.com
>
> (change to Studio J and scroll about 3/4 of the way
> to the bottom of
> the page).
>
> JdL
>
>

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It does not work and we all know that...

Dimitrov

--- Rami Vitale <alfred1@scs-net.org> a �crit�: >
I've heard that there is a MIDI specification for
> tuning, at www.midi.org/about-midi/tuning.htm
> But it didn't work for me ( does it work with
> sombody here ? )
> Also Bitch Bend message was not useful.
> The only useful way was sending a fine tune message
> immediately after or before the note message.
>
> Does anybody here have a simpler solve for tuning
> MIDI files or devices?
>
> Rami Vitale
>

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[Dimitrov wrote:]
>Why use the sound card propriety to implant tunning conceptions?
>Do you think that any conseptor of a sound card knows
>how to divide or give you a better to do it?!
>To bend modification is not the right way to do it!
>You must create your proper instrument to play your
>own tunnings! There is no other way!

Hi, Dimitrov! I'm with you in that I think that using pitch bends is
a _terrible_ way to tune. It just happens to be the only method I'm
aware of that works on a wide range of modules and sound cards, and it
works very well.

Its principle practical drawback is that each note of each voice must
be split onto a separate channel, which can quickly exhaust the list
of 15 available General MIDI channels (16 minus one percussion channel).
Yet, I have successfully tuned many multi-voice sequences, even while
failing to tune others because of channel exhaustion.

I'm not quite clear exactly what you're saying there is "no other way"
to. Actually, many modules that _do_ support (proprietary) tuning
tables do so in a limited way, in that a sounding note is not retuned on
the fly even if you want it to be. So, pitch bends are extremely
practical and effective for implementing whatever dynamic tuning one
wishes.

I wish I had the clout to insist that sound card manufacturers adhere to
my own ideas about what they should support! In the mean time, I see
no problem with making use of techniques that work, whether or not
they're pretty.

JdL

1) What temperament do we have in ANY sound card?
Is it the same for all sound cards?

2) How can we change a thing that is not determined
by condition ? And if dynamic correction is implanted
there?!

3) I have never argued about the precision of the
pitchbend (+1821 -1822 or something like that for one
tone deviation...).

4)One correction in this:
> >Do you think that any conseptor of a sound card
> DOES NOT knows
> >how to divide AND give you a better WAY to do it?!

5) The main question is not how to divide but what we
will do with the result :) Because I have listened
many samples here but I liked nothing...I'm sorry :)

Respectfully

Dimitrov

--- "John A. deLaubenfels" <jdl@adaptune.com> a
�crit�: > [Dimitrov wrote:]
> >Why use the sound card propriety to implant tunning
> conceptions?
> >Do you think that any conseptor of a sound card
> knows
> >how to divide or give you a better to do it?!
> >To bend modification is not the right way to do it!
> >You must create your proper instrument to play your
> >own tunnings! There is no other way!
>
> Hi, Dimitrov! I'm with you in that I think that
> using pitch bends is
> a _terrible_ way to tune. It just happens to be the
> only method I'm
> aware of that works on a wide range of modules and
> sound cards, and it
> works very well.
>
> Its principle practical drawback is that each note
> of each voice must
> be split onto a separate channel, which can quickly
> exhaust the list
> of 15 available General MIDI channels (16 minus one
> percussion channel).
> Yet, I have successfully tuned many multi-voice
> sequences, even while
> failing to tune others because of channel
> exhaustion.
>
> I'm not quite clear exactly what you're saying there
> is "no other way"
> to. Actually, many modules that _do_ support
> (proprietary) tuning
> tables do so in a limited way, in that a sounding
> note is not retuned on
> the fly even if you want it to be. So, pitch bends
> are extremely
> practical and effective for implementing whatever
> dynamic tuning one
> wishes.
>
> I wish I had the clout to insist that sound card
> manufacturers adhere to
> my own ideas about what they should support! In the
> mean time, I see
> no problem with making use of techniques that work,
> whether or not
> they're pretty.
>
> JdL
>
>

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>Why use the sound card propriety to implant tunning
>conceptions?
>Do you think that any conseptor of a sound card knows
>how to divide or give you a better to do it?!
>To bend modification is not the right way to do it!
>You must create your proper instrument to play your
>own tunnings! There is no other way!

I agree!What i want is an all software,integrated sequencer/synth system supporting different kind of pitch mappings for whatever tuning you program for it.Not at all based on 12 notes,not based on the MIDI standard,but proper piano rolls and event lists for equal tunings,perhaps some kind of 2-dimensional for just and more complex tunings.

I'm very experienced with trackers(all software sample players,not based on MIDI)and these could make a good basis for composing in different tunings if only modified to support it,and i have talked to several programmers working with trackers about this,but there have been no result due to lack of interest(i'm the only one who asks for it).

>Dimitrov

-=-=-=-=-=-=-
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http://www.angelfire.com/mo/oljare

_________________________________________________________________
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--- In tuning@y..., Latchezar Dimitrov <latchezar_d@y...> wrote:
> Why use the sound card propriety to implant tunning
> conceptions?

Implant tuning conceptions in what/whom?

> Do you think that any conseptor of a sound card knows
> how to divide or give you a better to do it?!

What does that mean?

> To bend modification is not the right way to do it!

Why not? Combined, we on this list have hundreds of years of
experience with this method. Its accuracy is easily tested by
listening to JI intervals.

> You must create your proper instrument to play your
> own tunnings! There is no other way!

The computer is the instrument of the future. I prefer acoustic
instruments today . . . but in 100 years?

--- In tuning@y..., Latchezar Dimitrov <latchezar_d@y...> wrote:
> It does not work and we all know that...
>
>
> Dimitrov
>
> --- Rami Vitale <alfred1@s...> a écrit : >
> I've heard that there is a MIDI specification for
> > tuning, at www.midi.org/about-midi/tuning.htm
> > But it didn't work for me ( does it work with
> > sombody here ? )
> > Also Bitch Bend message was not useful.
> > The only useful way was sending a fine tune message
> > immediately after or before the note message.
> >
> > Does anybody here have a simpler solve for tuning
> > MIDI files or devices?
> >
> > Rami Vitale
> >

Latchezar,

Whom do you refer to when you say "we all"? You just joined this list
very recently and you're the first person here expressing this
opinion. Many, many individuals, including Manuel Op de Coul, Herman
Miller, Joe Monzo, and John deLaubenfels, have been doing this for
years, with wonderful results. Sure, certain synths and soundcards
can have problems, but these problems are almost always surmountable
with a little thought and effort.

Where do you get off?

-Paul

--- paul@stretch-music.com a �crit�: > --- In
tuning@y..., Latchezar Dimitrov
> <latchezar_d@y...> wrote:
> > Why use the sound card propriety to implant
> tunning
> > conceptions?
>
> Implant tuning conceptions in what/whom?

I'm not sure how my sound card work !
If there is used real time matrice correction in
relation of tone(triad) before and tone after ?
I can't modify one thing who is not determined...

>
> > Do you think that any conseptor of a sound card
> knows
> > how to divide or give you a better to do it?!
>
> What does that mean?

That mean nothing, ok... It's my poor english...
I dont have frequency-meter to verify what temperament
is in use in my sound card...I think that the
constructor have use the best possible (for now) :))
I'm not sure if the constructor give me a better way
to use this card...

>
> > To bend modification is not the right way to do
> it!
>
> Why not? Combined, we on this list have hundreds of
> years of
> experience with this method. Its accuracy is easily
> tested by
> listening to JI intervals.
>
> > You must create your proper instrument to play
> your
> > own tunnings! There is no other way!
>
> The computer is the instrument of the future. I
> prefer acoustic
> instruments today . . . but in 100 years?
>
I prefer my violin, ok :))
But using Cool Edit Pro you can simulate your
instrument(if your sound card have a sample tables
like AWE32 or other and flash memory)
The way is different, no?
Because you can make one little wave for each 1/2 tone
and hear after the result. This wave can be very
precise(0.0001Hz)!
No ?

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[Dimitrov wrote:]
>The main question is not how to divide but what we
>will do with the result :) Because I have listened
>many samples here but I liked nothing...I'm sorry :)

That's ok; you're not required to like anyone's work! ;-> I do wonder,
though, whether what you're experiencing is

. A lousy sound card. It is a weakness of MIDI that the results vary
on every machine. An actual MP3 sound file gets around this
problem, but is very fat for my phone lines.

. Problems with pitch bend range. The diagnostic files on my web
page would answer this question.

. You just don't like [my?] tunings! If you've been listening to the
"wobbly" ones in the files area, I'm not surprised; those were
prepared at Paul E's request and are not what I would pick as
ideal.

I invite you to try listening to Herman Miller's tunings of Pachelbel's
Canon, at http://www.io.com/~hmiller/music/warped-canon.html . Most
especially, how bad does it sound in 12-tET? If lousy, that's a sound
card problem, and nothing will sound good on that card, I'm afraid.

JdL

Getting off what?
Do you thing that all sound cards have the same
tech-proprety ? And I would repeat my last
question-what's the actual division in almost of PC
sound cards?
Do you know that?
Who explate this question and where ?
Pls :)

--- Paul Erlich <paul@stretch-music.com> a �crit�: >
--- In tuning@y..., Latchezar Dimitrov
> <latchezar_d@y...> wrote:
> > It does not work and we all know that...
> >
> >
> > Dimitrov
> >
> > --- Rami Vitale <alfred1@s...> a �crit�: >
> > I've heard that there is a MIDI specification for
> > > tuning, at www.midi.org/about-midi/tuning.htm
> > > But it didn't work for me ( does it work with
> > > sombody here ? )
> > > Also Bitch Bend message was not useful.
> > > The only useful way was sending a fine tune
> message
> > > immediately after or before the note message.
> > >
> > > Does anybody here have a simpler solve for
> tuning
> > > MIDI files or devices?
> > >
> > > Rami Vitale
> > >
>
> Latchezar,
>
> Whom do you refer to when you say "we all"? You just
> joined this list
> very recently and you're the first person here
> expressing this
> opinion. Many, many individuals, including Manuel Op
> de Coul, Herman
> Miller, Joe Monzo, and John deLaubenfels, have been
> doing this for
> years, with wonderful results. Sure, certain synths
> and soundcards
> can have problems, but these problems are almost
> always surmountable
> with a little thought and effort.
>
> Where do you get off?
>
> -Paul
>
>

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--- "John A. deLaubenfels" <jdl@adaptune.com> a
�crit�: > [Dimitrov wrote:]
> >The main question is not how to divide but what we
> >will do with the result :) Because I have listened
> >many samples here but I liked nothing...I'm sorry
> :)
>
> That's ok; you're not required to like anyone's
> work! ;-> I do wonder,
> though, whether what you're experiencing is
>
> . A lousy sound card. It is a weakness of MIDI
> that the results vary
> on every machine. An actual MP3 sound file
> gets around this
> problem, but is very fat for my phone lines.
>

For info, my "lousy" sound card is simply Creative AWE
32 and have 2mb dyn.memory for create into...
BTW I use ADSL :)

> . Problems with pitch bend range. The diagnostic
> files on my web
> page would answer this question.

Are you sure ? Nowhere -any info about what
temperament is used in my sound card ...if no, my
pitch bend work good,np

>
> . You just don't like [my?] tunings! If you've
> been listening to the
> "wobbly" ones in the files area, I'm not
> surprised; those were
> prepared at Paul E's request and are not what I
> would pick as
> ideal.

Wobbly ones ? No , not so :) When I hear false sounds
I stop the sequence...Sometime it's horrible :))
See canon12 in 7 limit...But
1/7 comma meatone and 1/7 widened octave is not so bad
for me :)

>
> I invite you to try listening to Herman Miller's
> tunings of Pachelbel's
> Canon, at
> http://www.io.com/~hmiller/music/warped-canon.html .
> Most
> especially, how bad does it sound in 12-tET? If
> lousy, that's a sound
> card problem, and nothing will sound good on that
> card, I'm afraid.
>
> JdL

Ok, maybe my card is not perfect...
I invite you to try listening in my file folder nt1
sample or the same canon12 played by my card and with
my instrument in my temperament :))(canon12 retuned)
One question...why we have a vibrato in this midi
files ? It's strange bescause the frequency deviation
is too much important for listen the samples there !

Dimitrov

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[Dimitrov wrote:]
>Wobbly ones ? No , not so :) When I hear false sounds
>I stop the sequence...Sometime it's horrible :))
>See canon12 in 7 limit...But
>1/7 comma meatone and 1/7 widened octave is not so bad
>for me :)

Ah! So you're not ready for my radical 7-limit treatments! Not
surprising; that's entirely a matter of taste, and fewer than 50% of
list members like to go that way. Some of us who do are rather
passionate about our love for 7-limit harmony, even though imposed
"inauthentically" upon past works.

>I invite you to try listening in my file folder nt1
>sample or the same canon12 played by my card and with
>my instrument in my temperament :))(canon12 retuned)

Sorry, where is that?

>One question...why we have a vibrato in this midi
>files ? It's strange bescause the frequency deviation
>is too much important for listen the samples there !

Which pieces? I don't hear vibrato in the canon.

JdL

Hi again...

I try to think "tunning" like you just now...
It's strange, but, ok.
Dont have any words for the rest in english...

--- "John A. deLaubenfels" <jdl@adaptune.com> a
�crit�: > [Dimitrov wrote:]
> >Wobbly ones ? No , not so :) When I hear false
> sounds
> >I stop the sequence...Sometime it's horrible :))
> >See canon12 in 7 limit...But
> >1/7 comma meatone and 1/7 widened octave is not so
> bad
> >for me :)
>
> Ah! So you're not ready for my radical 7-limit
> treatments! Not
> surprising; that's entirely a matter of taste, and
> fewer than 50% of
> list members like to go that way. Some of us who do
> are rather
> passionate about our love for 7-limit harmony, even
> though imposed
> "inauthentically" upon past works.
>

Maybe my sound card dont play the supposed thing...
Can you explate me what's 7-limit ?
Thanks

> >I invite you to try listening in my file folder nt1
> >sample or the same canon12 played by my card and
> with
> >my instrument in my temperament :))(canon12
> retuned)
>
> Sorry, where is that?
>

Where ?! In the forum tunning Yahoo...hmm Do you not
know really where is it ?
Each forum have file areas for share...

> >One question...why we have a vibrato in this midi
> >files ? It's strange bescause the frequency
> deviation
> >is too much important for listen the samples there
> !
>
> Which pieces? I don't hear vibrato in the canon.
>
> JdL
>

Strange...I can prove you with one little mp3, but if
it's (for more one time) my sound card...I can remove
the vibrato, np

Thank you for your attention

Dimitrov

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[Dimitrov wrote:]
>I try to think "tunning" like you just now...
>It's strange, but, ok.
>Dont have any words for the rest in english...

I'm sorry that I'm unable to converse in any language but English! We
English speakers can easily fall into the habit of expecting the rest
of the world to come to us. Kind of unfair, really, and I wish I had
more knowledge of other languages.

[Dimitrov:]
>Maybe my sound card dont play the supposed thing...
>Can you explate me what's 7-limit ?
>Thanks

Well, I have details on my web site, http://www.adaptune.com . Change
to the "Studio J" directory, then follow the links at the top of the
page.

In brief, 5-limit music tries to tune four 12-tET semitones (i.e., a
major third) as the interval 5:4 (about 14 cents flatter than 12-tET)
and three 12-tET semitones (a minor third) as 6:5, about 16 cents
sharper than 12-tET. In 7-limit, dom 7th chords get mapped to 4:5:6:7,
and the top note (F if a G7 dom 7th resolves to tonic in C) is a full 31
cents flat of 12-tET! Most ears find this excessive, while a few of us
delight in it.

[Dimitrov:]
>>>I invite you to try listening in my file folder nt1
>>>sample or the same canon12 played by my card and with
>>>my instrument in my temperament :))(canon12 retuned)

[JdL:]
>>Sorry, where is that?

[Dimitrov:]
>Where ?! In the forum tunning Yahoo...hmm Do you not
>know really where is it ?
>Each forum have file areas for share...

Yes, thanks, I'm aware of the file area. Just didn't realize your file
was there! Sorry to say that with my slow dial-up connection, Yahoo
aborts file downloads of more then 100K to 200K, so I'm not able to
listen to your files. I envy you your DSL connection!

[Dimitrov:]
>>>One question...why we have a vibrato in this midi
>>>files ? It's strange bescause the frequency deviation
>>>is too much important for listen the samples there!

[JdL:]
>>Which pieces? I don't hear vibrato in the canon.

[Dimitrov:]
>Strange...I can prove you with one little mp3, but if
>it's (for more one time) my sound card...I can remove
>the vibrato, np

I've just looked Herman Miller's canon49.mid, and the only control
messages I find are of the form:

B0 07 78 (channel volume)
B0 0A 41 (pan position)

This should not cause vibrato. I suggest that you reset your sound
card before playing anything, if in doubt. Again, see my web page,
about 2/3 of the way down, for files to do this. Your AWE32 should be
a reasonably good card.

>Thank you for your attention

My pleasure!

JdL

--- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:
In 7-limit, dom 7th chords get mapped to 4:5:6:7,
> and the top note (F if a G7 dom 7th resolves to tonic in C) is a
full 31
> cents flat of 12-tET! Most ears find this excessive, while a few
of us
> delight in it.

What is the evidence most ears find the 7-limit excessive? The
dominant seventh in 12-et sounds out of tune to me, I would have
thought that was generally true.

[I wrote:]
>>In 7-limit, dom 7th chords get mapped to 4:5:6:7, and the top note (F
>>if a G7 dom 7th resolves to tonic in C) is a full 31 cents flat of
>>12-tET! Most ears find this excessive, while a few of us delight in
>>it.

[Gene wrote:]
>What is the evidence most ears find the 7-limit excessive? The
>dominant seventh in 12-et sounds out of tune to me, I would have
>thought that was generally true.

I'm basing my conclusion on the very unscientific small sampling of
people who've listened to my various treatments over the past two years.
About 40% to 50% like 7-limit, but many more like 5-limit. Some, for
example Paul E, think that 7-limit treatments of past works (19th
century and earlier) sound _terrible_.

I've actually gotten a taste recently for tuning a dom 7th chord with
two 6:5 minor thirds, putting the 7th degree very high, higher than
12-tET or even meantone, but I love 7-limit treatments, with that
wonderful sweet low 7th degree, even more.

JdL

--- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:

> I've actually gotten a taste recently for tuning a dom 7th chord
with
> two 6:5 minor thirds, putting the 7th degree very high, higher than
> 12-tET or even meantone, but I love 7-limit treatments, with that
> wonderful sweet low 7th degree, even more.

It sounds like the 19-et might be a good one for you. Of course in
the 12-et (3/2)*(9/10), (3/2)*(8/9) and (3/2)*(7/8) are all the same
note, but if we have any meantone system (where 9/10~8/9) then the
ordinary dominant seventh chord using (3/2)*(8/9) = 4/3 and your
version using (3/2)*(9/10) = 27/20 are the same, and the 19-et with
its pure 6/5's does this particularly well.

[I wrote:]
>>I've actually gotten a taste recently for tuning a dom 7th chord with
>>two 6:5 minor thirds, putting the 7th degree very high, higher than
>>12-tET or even meantone, but I love 7-limit treatments, with that
>>wonderful sweet low 7th degree, even more.

[Gene wrote:]
>It sounds like the 19-et might be a good one for you. Of course in
>the 12-et (3/2)*(9/10), (3/2)*(8/9) and (3/2)*(7/8) are all the same
>note, but if we have any meantone system (where 9/10~8/9) then the
>ordinary dominant seventh chord using (3/2)*(8/9) = 4/3 and your
>version using (3/2)*(9/10) = 27/20 are the same, and the 19-et with
>its pure 6/5's does this particularly well.

I'm spoiled with adaptive tuning: I don't have to accept 19-tET's narrow
fifths and major thirds; I can target chords as close to JI as I'm
willing to pay the price for (horizontally, largely).

I _do_ want to support taking 19-tET pieces as input, using those pitch
degrees for grounding, while adjusting the vertical intervals at least
part way toward JI.

JdL

Hi Dimitrov,

Just about all the midi voices on my soundcard have a _little_ residual
vibrato even when played with no modulation. That could be what you are
hearing. Varies from one voice to another.

You can get an alternative way of playing midi files for very little
cost using the Yamaha Soft synth. It's free trial for 3 months,
then you have to register if you want to keep it.

http://www.yamaha-xg.com/ssynth/index.html

It gives a pretty nice rendering of midi compared with the
most basic types of soundcard, especially older ones, and would
certainly give the idea. The tuning is pretty reasonable,
I think accurate to about 0.5 cents or so (while my SB Live!
is accurate to within 0.2 cents or so, with the absolute pitch
also varying depending on the voice). It also has a little residual
vibrato on its voices.

There are other soft synths too, a fair number; could be that others are better.
Seems to me that a soft synth should be able to do the tuning as
accurately as one likes, so I don't know why one would have as much
variation as 0.5 cents; I would be interested to know if there are
any that achieve a greater accuracy. But +-0.5 cents isn't bad for
many of the example midi clips. It's not that easy to keep a note
steady to the nearest cent while playing a real instrument.

The residual vibrato on some of the voices with modulation set to
zero amounts to +- several cents on my soundcard, while others
have hardly any, but a tiny amount that one can measure using
wave counting.

That I could understand as possibly being something to do with
the original sample that the waves are recorded with - perhaps
the notes were played with slight vibrato when recorded. Just
a guess.

(Some wave forms on my soundcard also have points
where the two ends of the wave meet at a sharp angle,
which one sees as a fluctuation in the frequency when wave
counting).

Robert

John, hi again :)

Will try to respond you with...my english :)
Excuse-me...

--- "John A. deLaubenfels" <jdl@adaptune.com> a
�crit�: > [Dimitrov wrote:]
> >I try to think "tunning" like you just now...
> >It's strange, but, ok.
> >Dont have any words for the rest in english...
>
> I'm sorry that I'm unable to converse in any
> language but English! We
> English speakers can easily fall into the habit of
> expecting the rest
> of the world to come to us. Kind of unfair, really,
> and I wish I had
> more knowledge of other languages.
>
> [Dimitrov:]
> >Maybe my sound card dont play the supposed thing...
> >Can you explate me what's 7-limit ?
> >Thanks
>
> Well, I have details on my web site,
> http://www.adaptune.com . Change
> to the "Studio J" directory, then follow the links
> at the top of the
> page.
>
> In brief, 5-limit music tries to tune four 12-tET
> semitones (i.e., a
> major third) as the interval 5:4 (about 14 cents
> flatter than 12-tET)
> and three 12-tET semitones (a minor third) as 6:5,
> about 16 cents
> sharper than 12-tET. In 7-limit, dom 7th chords get
> mapped to 4:5:6:7,
> and the top note (F if a G7 dom 7th resolves to
> tonic in C) is a full 31
> cents flat of 12-tET! Most ears find this
> excessive, while a few of us
> delight in it.
>
Ok, ok...In "my" temperament(NT1) "at less" the octave
is "respected" with no more 2-2.5 cents(wide of
course) and the fifth-0.8 cents !
I dont take care with the rest of intervals, ok...
But my conception of tunning is the folow:
I work ONLY with a K's... My "K" reference of Bach is
naturally 12's "square" of 2 and for Mr Cordier's
theory(fifth juste)
the "K" is the 7's of 1.5, ok ? K= "multiplicator"
only for the semi-tone frequency ...for up of A=440 I
multiplicate... if not-for lower= I divide by "K"...
all of that's logic... The question is about the
value of this "K" between the two "extremities" of
possibles...(hmm no time for reading if the word
existe:) ) More and more sorry !

Hmm, now I have send the mail with ...Enter :)
I would terminate before...

> [Dimitrov:]
> >>>I invite you to try listening in my file folder
> nt1
> >>>sample or the same canon12 played by my card and
> with
> >>>my instrument in my temperament :))(canon12
> retuned)
>
> [JdL:]
> >>Sorry, where is that?
>
> [Dimitrov:]
> >Where ?! In the forum tunning Yahoo...hmm Do you
> not
> >know really where is it ?
> >Each forum have file areas for share...
>
> Yes, thanks, I'm aware of the file area. Just
> didn't realize your file
> was there! Sorry to say that with my slow dial-up
> connection, Yahoo
> aborts file downloads of more then 100K to 200K, so
> I'm not able to
> listen to your files. I envy you your DSL
> connection!
>

I dont know how to do for that you can listen...
Do you know and use the L3 format ?
It reduce by 10 the mp3 files !
How do you listen the samples ?
Only midi files?
Very very relative "method"...

> [Dimitrov:]
> >>>One question...why we have a vibrato in this midi
> >>>files ? It's strange bescause the frequency
> deviation
> >>>is too much important for listen the samples
> there!
>
> [JdL:]
> >>Which pieces? I don't hear vibrato in the canon.
>
>
> [Dimitrov:]
> >Strange...I can prove you with one little mp3, but
> if
> >it's (for more one time) my sound card...I can
> remove
> >the vibrato, np
>
> I've just looked Herman Miller's canon49.mid, and
> the only control
> messages I find are of the form:
>
> B0 07 78 (channel volume)
> B0 0A 41 (pan position)
>
> This should not cause vibrato. I suggest that you
> reset your sound
> card before playing anything, if in doubt. Again,
> see my web page,
> about 2/3 of the way down, for files to do this.
> Your AWE32 should be
> a reasonably good card.
>
I know ...If I use all of the possibility, my card is
correct reasonably, np

> >Thank you for your attention
>
> My pleasure!
>
> JdL
>
Greatings
Dimitrov

=====

___________________________________________________________
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:

>
> Ok, maybe my card is not perfect...
> I invite you to try listening in my file folder nt1
> sample or the same canon12 played by my card and with
> my instrument in my temperament :))(canon12 retuned)
> One question...why we have a vibrato in this midi
> files ? It's strange bescause the frequency deviation
> is too much important for listen the samples there !
>
> Dimitrov
>

Hi Latchezar!

Herman Miller carefully chose the MIDI settings so that there would
be a minimum of vibrato on most people's sound cards. Unfortunately,
your sound card may not have been one of those considered! For that I
am sorry. Perhaps you can speak to Herman and better versions can be
created.

-Paul

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:
> In 7-limit, dom 7th chords get mapped to 4:5:6:7,
> > and the top note (F if a G7 dom 7th resolves to tonic in C) is a
> full 31
> > cents flat of 12-tET! Most ears find this excessive, while a few
> of us
> > delight in it.
>
> What is the evidence most ears find the 7-limit excessive? The
> dominant seventh in 12-et sounds out of tune to me, I would have
> thought that was generally true.

In my opinion, 4:5:6:7 has rather little to do with the dominant
seventh chord in Western Music, traditionally introduced by
Monteverdi.

One opinion...

The 7th degree of any major scale when one violinist
play it=very sharp et near to the tonic...
Why? !!! Is it not more attractif when that 7th is
"normaly" distant?
It's only one question :)

Dimitrov

--- "John A. deLaubenfels" <jdl@adaptune.com> a
�crit�: > [I wrote:]
> >>In 7-limit, dom 7th chords get mapped to 4:5:6:7,
> and the top note (F
> >>if a G7 dom 7th resolves to tonic in C) is a full
> 31 cents flat of
> >>12-tET! Most ears find this excessive, while a
> few of us delight in
> >>it.
>
> [Gene wrote:]
> >What is the evidence most ears find the 7-limit
> excessive? The
> >dominant seventh in 12-et sounds out of tune to me,
> I would have
> >thought that was generally true.
>
> I'm basing my conclusion on the very unscientific
> small sampling of
> people who've listened to my various treatments over
> the past two years.
> About 40% to 50% like 7-limit, but many more like
> 5-limit. Some, for
> example Paul E, think that 7-limit treatments of
> past works (19th
> century and earlier) sound _terrible_.
>
> I've actually gotten a taste recently for tuning a
> dom 7th chord with
> two 6:5 minor thirds, putting the 7th degree very
> high, higher than
> 12-tET or even meantone, but I love 7-limit
> treatments, with that
> wonderful sweet low 7th degree, even more.
>
> JdL
>
>

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

John, hi again :)

Will try to respond you with...my english :)
Excuse-me...

--- "John A. deLaubenfels" <jdl@adaptune.com> a
�crit�: > [Dimitrov wrote:]
> >I try to think "tunning" like you just now...
> >It's strange, but, ok.
> >Dont have any words for the rest in english...
>
> I'm sorry that I'm unable to converse in any
> language but English! We
> English speakers can easily fall into the habit of
> expecting the rest
> of the world to come to us. Kind of unfair, really,
> and I wish I had
> more knowledge of other languages.
>
> [Dimitrov:]
> >Maybe my sound card dont play the supposed thing...
> >Can you explate me what's 7-limit ?
> >Thanks
>
> Well, I have details on my web site,
> http://www.adaptune.com . Change
> to the "Studio J" directory, then follow the links
> at the top of the
> page.
>
> In brief, 5-limit music tries to tune four 12-tET
> semitones (i.e., a
> major third) as the interval 5:4 (about 14 cents
> flatter than 12-tET)
> and three 12-tET semitones (a minor third) as 6:5,
> about 16 cents
> sharper than 12-tET. In 7-limit, dom 7th chords get
> mapped to 4:5:6:7,
> and the top note (F if a G7 dom 7th resolves to
> tonic in C) is a full 31
> cents flat of 12-tET! Most ears find this
> excessive, while a few of us
> delight in it.
>
Ok, ok...In "my" temperament(NT1) "at less" the octave
is "respected" with no more 2-2.5 cents(wide of
course) and the fifth-0.8 cents !
I dont take care with the rest of intervals, ok...
But my conception of tunning is the folow:
I work ONLY with a K's... My "K" reference of Bach is
naturally 12's "square" of 2 and for Mr Cordier's
theory(fifth juste)
the "K" is the 7's of 1.5, ok ? K= "multiplicator"
only for the semi-tone frequency ...for up of A=440 I
multiplicate... if not-for lower= I divide by "K"...
all of that's logic... The question is about the
value of this "K" between the two "extremities" of
possibles...(hmm no time for reading if the word
existe:) ) More and more sorry !

> [Dimitrov:]
> >>>I invite you to try listening in my file folder
> nt1
> >>>sample or the same canon12 played by my card and
> with
> >>>my instrument in my temperament :))(canon12
> retuned)
>
> [JdL:]
> >>Sorry, where is that?
>
> [Dimitrov:]
> >Where ?! In the forum tunning Yahoo...hmm Do you
> not
> >know really where is it ?
> >Each forum have file areas for share...
>
> Yes, thanks, I'm aware of the file area. Just
> didn't realize your file
> was there! Sorry to say that with my slow dial-up
> connection, Yahoo
> aborts file downloads of more then 100K to 200K, so
> I'm not able to
> listen to your files. I envy you your DSL
> connection!
>
I dont know how how to do for that you ca
> [Dimitrov:]
> >>>One question...why we have a vibrato in this midi
> >>>files ? It's strange bescause the frequency
> deviation
> >>>is too much important for listen the samples
> there!
>
> [JdL:]
> >>Which pieces? I don't hear vibrato in the canon.
>
>
> [Dimitrov:]
> >Strange...I can prove you with one little mp3, but
> if
> >it's (for more one time) my sound card...I can
> remove
> >the vibrato, np
>
> I've just looked Herman Miller's canon49.mid, and
> the only control
> messages I find are of the form:
>
> B0 07 78 (channel volume)
> B0 0A 41 (pan position)
>
> This should not cause vibrato. I suggest that you
> reset your sound
> card before playing anything, if in doubt. Again,
> see my web page,
> about 2/3 of the way down, for files to do this.
> Your AWE32 should be
> a reasonably good card.
>
> >Thank you for your attention
>
> My pleasure!
>
> JdL
>
>

=====

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

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:
> In 7-limit, dom 7th chords get mapped to 4:5:6:7,
> > and the top note (F if a G7 dom 7th resolves to tonic in C) is a
> full 31
> > cents flat of 12-tET! Most ears find this excessive, while a few
> of us
> > delight in it.
>
> What is the evidence most ears find the 7-limit excessive? The
> dominant seventh in 12-et sounds out of tune to me, I would have
> thought that was generally true.

Historically, musicians who attempted to introduce 7-limit into
Western harmony did not think that it had anything to do with the
dominant seventh chord -- even though they were unanimous that the 5-
limit had much to do with the major chord. Tartini and Kirnberger,
for example, introduced new notational symbols for accidentals that
would produce 7-limit ratios with "standard" notes. Huygens and
others realized that the _augmented sixth_, in use since the
Renaissance, did approximate 7:4 very well . . . see Blackwood for
more.

However, with the advent of 12-tone equal temperament, the deviations
of the dominant seventh chord from 7-limit were less than previously,
and it has been argued that some 7-limit thinking is present in the
music of Wagner, Stravinsky, and even Chopin.

--- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:

> I _do_ want to support taking 19-tET pieces as input, using those
pitch
> degrees for grounding, while adjusting the vertical intervals at
least
> part way toward JI.

It would be interesting to have your program output a text file
showing where the primes (or other JI generators) are being
implicitly mapped during an adaptive tuning. That would involve
specifying the notes which the adaptive tuning is pulling towards,
and solving linear equations, so you would need enough data to get
determined solutions; you might also have a problem with slightly
inconsistent overdetermined solutions. However it would be
interesting to see a plot of what is happening to various commas
(81/80 and 64/63 in particular) as the adaptive tuning progresses.
That would allow us to see how similar or how different adaptive
tuning is in practice to my proposal of adaptive tempering.

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

> In my opinion, 4:5:6:7 has rather little to do with the dominant
> seventh chord in Western Music, traditionally introduced by
> Monteverdi.

I think under most circumstances it works as a V7 chord, and under
all circumstances it sounds more consonant. The V7 chord with the
fourth in it sounds harsh and clangy in comparison.

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

> Historically, musicians who attempted to introduce 7-limit into
> Western harmony did not think that it had anything to do with the
> dominant seventh chord -- even though they were unanimous that the
5-
> limit had much to do with the major chord. Tartini and Kirnberger,
> for example, introduced new notational symbols for accidentals that
> would produce 7-limit ratios with "standard" notes. Huygens and
> others realized that the _augmented sixth_, in use since the
> Renaissance, did approximate 7:4 very well . . . see Blackwood for
> more.

This looks like an artifact of the meantone system, not anything deep
in the nature of the harmonic meaning of the V7. I am skeptical that
the 7-limit version of the V7 sounds wrong unless there is a melodic
consideration which overrides the vertical one; my experience is that
normally it works quite well. Your historical information is entirely
predicable given the nature and evolution of the tuning systems in
use when the 5 and then the 7 limits were approached, so it tell us
nothing for our purpose.

If you think otherwise, could you provide an example?

> However, with the advent of 12-tone equal temperament, the
deviations
> of the dominant seventh chord from 7-limit were less than
previously,
> and it has been argued that some 7-limit thinking is present in the
> music of Wagner, Stravinsky, and even Chopin.

7-limit thinking has been absolutely fundamental since Monteverdi,
IMHO.

[Gene wrote:]
>It would be interesting to have your program output a text file
>showing where the primes (or other JI generators) are being
>implicitly mapped during an adaptive tuning. That would involve
>specifying the notes which the adaptive tuning is pulling towards,
>and solving linear equations, so you would need enough data to get
>determined solutions; you might also have a problem with slightly
>inconsistent overdetermined solutions. However it would be
>interesting to see a plot of what is happening to various commas
>(81/80 and 64/63 in particular) as the adaptive tuning progresses.
>That would allow us to see how similar or how different adaptive
>tuning is in practice to my proposal of adaptive tempering.

Gene, are you familiar with how my spring model works? I _do_ set up
target JI intervals, which _could_ be reported in a text file for each
harmonic moment in the piece, but my relaxation of the spring matrix
substitutes for any solving of linear equations, and allows very
naturally for non-self-consistent vertical tunings such as
chain-of-fifth chords.

Actually, I view the entire sequence in text form (files with .hp
extensions, harkening back to my use of HP computers for early tuning
work). I can send you an (PC) executable that'll produce such a file
from any .mid file if you like. Tunings are shown in cents offset from
12-tET, and scale degrees are expressed as octaves plus offset
(0 .. 11 for C thru B). Also the absolute timing of the piece is shown,
down to a thousandth of a second. It's quite easy to track what happens
to commas. As I've described earlier, I can distribute the comma
vertically, horizontally, or some combination of the two. One thing I
_don't_ show explicitly is information about target vertical intervals,
which is a shame, though usually it's not hard to glean from the
information present.

JdL

[Paul E wrote:]
>>In my opinion, 4:5:6:7 has rather little to do with the dominant
>>seventh chord in Western Music, traditionally introduced by
>>Monteverdi.

[Gene wrote:]
>I think under most circumstances it works as a V7 chord, and under
>all circumstances it sounds more consonant. The V7 chord with the
>fourth in it sounds harsh and clangy in comparison.

I agree with you, Gene, but...

[Paul:]
>>Historically, musicians who attempted to introduce 7-limit into
>>Western harmony did not think that it had anything to do with the
>>dominant seventh chord -- even though they were unanimous that the 5-
>>limit had much to do with the major chord. Tartini and Kirnberger,
>>for example, introduced new notational symbols for accidentals that
>>would produce 7-limit ratios with "standard" notes. Huygens and
>>others realized that the _augmented sixth_, in use since the
>>Renaissance, did approximate 7:4 very well . . . see Blackwood for
>>more.

[Gene:]
>This looks like an artifact of the meantone system, not anything deep
>in the nature of the harmonic meaning of the V7. I am skeptical that
>the 7-limit version of the V7 sounds wrong unless there is a melodic
>consideration which overrides the vertical one; my experience is that
>normally it works quite well. Your historical information is entirely
>predicable given the nature and evolution of the tuning systems in
>use when the 5 and then the 7 limits were approached, so it tell us
>nothing for our purpose.

>If you think otherwise, could you provide an example?

I still agree with you, but...

[Paul:]
>>However, with the advent of 12-tone equal temperament, the deviations
>>of the dominant seventh chord from 7-limit were less than previously,
>>and it has been argued that some 7-limit thinking is present in the
>>music of Wagner, Stravinsky, and even Chopin.

(aside to Paul: the 7th degree in 12-tET differs little from meantone,
and hugely from 7-limit; I doubt very much that 12-tET per se made much
difference to anyone's perceptions in this regard)

[Gene:]
>7-limit thinking has been absolutely fundamental since Monteverdi,
>IMHO.

Gene, from all I can tell, the guys 'n' gals with their fingers on the
pulse of history are unanimous in their assertion that 7-limit tunings
were not used for dom 7ths by pretty much _anybody_ in the past.

Isn't this the wrong battle, though? I think it unfortunate that
7-limit tunings of past works are only now coming into the repertoire of
available options, but at least we've got them now! Like you, I
consider 4:5:6:7 to be the perfect dom 7th, wonderfully consonant yet
longing; the 21:20 resolution (F to E when G7 -> C) a lovely vivid small
step.

I believe it's important for us 7-limit fanatics to acknowledge that
we're following our ears, not past history. We don't want to be saddled
with accusations of trying to distort historical fact. I say, better
late than never!

When I first joined the list, I had a kind of 7-limit chip on my
shoulder. Now I just welcome those who feel as I do and don't try to
convert others. Heck, I even try to find 5-limit tunings to satisfy
'em!

JdL

[Dimitrov wrote:]
>The 7th degree of any major scale when one violinist
>play it=very sharp et near to the tonic...
>Why? !!! Is it not more attractif when that 7th is
>"normaly" distant?
>It's only one question :)

You are speaking of the major 7th, when functioning as leading tone
to the tonic above. My belief is that a small melodic step is more
dramatic than a larger step. So, for example, when a 4:5:6:7 dom 7th
resolves to JI tonic, the leading tone to tonic, 15:16 or 112 cents, is
not as dramatic as the 21:20, 84 cents, resolving to the tonic's third
degree.

(if the step gets _too_ small, the ear no longer considers it dramatic,
or even a step, but in the range 70 .. 200 cents, at least, I think this
principle applies).

[Dimitrov:]
>Will try to respond you with...my english :)
>Excuse-me...

I'm sure we will both do our best! :-)

>Ok, ok...In "my" temperament(NT1) "at less" the octave
>is "respected" with no more 2-2.5 cents(wide of
>course) and the fifth-0.8 cents !
>I dont take care with the rest of intervals, ok...
>But my conception of tunning is the folow:
>I work ONLY with a K's... My "K" reference of Bach is
>naturally 12's "square" of 2 and for Mr Cordier's
>theory(fifth juste)
> the "K" is the 7's of 1.5, ok ? K= "multiplicator"
>only for the semi-tone frequency ...for up of A=440 I
>multiplicate... if not-for lower= I divide by "K"...
>all of that's logic... The question is about the
>value of this "K" between the two "extremities" of
>possibles...(hmm no time for reading if the word
>existe:) ) More and more sorry !

As I understand it, you are stretching 12-tET, making major thirds less
just than they are in 12-tET. Is that right? Are you familiar with
converting ratios to cents and back, and applying stretch as a
multiplier to the cents intervals? I think I've missed the details of
some of your past posts, sorry.

[JdL:]
>>Yes, thanks, I'm aware of the file area. Just
>>didn't realize your file
>>was there! Sorry to say that with my slow dial-up
>>connection, Yahoo
>>aborts file downloads of more then 100K to 200K, so
>>I'm not able to
>>listen to your files. I envy you your DSL
>>connection!

[Dimitrov:]
>I dont know how to do for that you can listen...
>Do you know and use the L3 format ?
>It reduce by 10 the mp3 files !
>How do you listen the samples ?
>Only midi files?
>Very very relative "method"...

I mostly listen only to MIDI files or CD's physically mailed to me. I
_can_ download (very slowly!) large files from any server but Yahoo's,
however; Yahoo seems to have a policy of terminating any download
(irritatingly, with the erroneous message "download complete") that goes
beyond a very few minutes.

If you'd like to e-mail me anything smaller than a megabyte off-list,
please do so! Send to jdl"at"adaptune.com (change "at" to the symbol).

[JdL:]
>>This should not cause vibrato. I suggest that you reset your sound
>>card before playing anything, if in doubt. Again, see my web page,
>>about 2/3 of the way down, for files to do this. Your AWE32 should be
>>a reasonably good card.

[Dimitrov:]
>I know ...If I use all of the possibility, my card is
>correct reasonably, np

Well, I encourage you to explore this question using your own MIDI
files, if possible. I see that there have been other list members who
have other specific suggestions. Good luck!

JdL

Yes, Gene! Thank you! Further, historical evidence is often if not
always insufficient to reflect the realities of the times in
question. Then we must take recourse to common sense and the larger
human realities that tie us all together not just in space, but also
in time.

It is difficult for me to imagine that with the freedom to choose
just intervals available in musics dating from at least the early
Renaissance if not further back, many of the evidently brilliant
musical ears of the time did not naturally savor both harmonically
and melodically the 4:5:6:7 ratios that some of us find so naturally
enjoyable today.

We should ask ourselves how much of the objection to this today is a
product of some kind of spurious intellection rather than a natural
result of the "musical economics" and tradeoffs intrinsic to the
psychoacoustic terrains through which we navigate. If we unbias our
ears and simply deal innocently with the fundamental acoustic terrain
that nature provides us in common with what it did centuries ago,
perhaps we'll begin to sift out something closer to the historical
realities.

I think we can learn something about the distortion of historical
reality from our own recent history. Only a short time ago, the
accepted academic view was that ancient music was performed at a much
lower standard of quality than we have today. The "primitive" nature
of the instruments, the frequent musical incompetence of the rare
modern academics who specialized in playing them in those days, etc.,
the relatively low standard of technical virtuosity in SOME of the
music (not vocal, for sure, if we look at Monteverdi, for example)
were factors contributing to this viewpoint. The modern early music
revival has given the lie to all this.

On the contrary, common practice musicians of today have been lulled
to sleep on intonation with the pervasive use of 12-tET and almost
total relegation of fixed tuning to professionals. This has
eliminated the need and even the option for most students of music to
ever confront something so fundamental and historically well-
understood as the syntonic comma. How many musicians of a random
sample today would even know what that is?

So the relatively fine and unavoidable (microtonal) pitch anomolies
that were a common, daily experience in days of yore are off map for
most students of music today. That arrogant cultural chauvinism that
assumed out of hand that we're superior in all things to what came
before, or that a Paganini or Lizst having raised standards of
technical virtuosity to new heights implies musical superiority in
general, etc. was clearly out of kilter with reality.

I think we all know here that superior technical virtuousity together
with a modern scientific and technologically advanced culture does
not imply that singers are also better today or that we are deeper
musically in any other way. Paganini and Liszt are among my least
favorite composers. I personally find their music technical flashy
and commensurately superficial. It is more about circus and less
about music than say Josquin Des Prez.

And so it is with many other off-the-mark interpretations of
historical evidence to which we here are not completely invulnerable.
I think we need to pay more attention to the global considerations in
piecing together historical evidence.

For example, we know that in western music harmony and melody
interact polyphonically in ways that are fairly unique to this
tradition. The melodic scales we use are FUNDAMENTALLY BASED on
HARMONIC considerations. Even the essentially melodic traditions that
use a drone, such as Indian classical music, use scales that are
derived from whole number relationships. They are justly tuned to the
drone. (Trash the 12-tET harmonium, please).

So all this erudite talk of melodic considerations forcing
compromises in harmonic considerations is a source of wonder to me.
Here I have seen the same people who rail against the tendency in
"expressive intonation" to reverse the size relationship of the
smaller just chromatic half-step and larger just diatonic half-step
turn right around and promote analagous things with other and even
the same intervals with the same kind of melodic "justifications".

Without harmonic considerations and no drone, melodic intervals are
completely arbitrary. I love the exotic flavors of melodic variety
that essentially melodic traditions bring to the table. Finding ways
to integrate them into a polyphonically workable framework using
higher prime limits in JI fascinates me. I am fundamentally a singer,
and I love melody! But I don't think we have to sacrifice what I
experience personally as the awesome power of pure harmony in its
service, and to pretend we do disturbs me.

Sincerely,

Bob

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> > Historically, musicians who attempted to introduce 7-limit into
> > Western harmony did not think that it had anything to do with the
> > dominant seventh chord -- even though they were unanimous that
the
> 5-
> > limit had much to do with the major chord. Tartini and
Kirnberger,
> > for example, introduced new notational symbols for accidentals
that
> > would produce 7-limit ratios with "standard" notes. Huygens and
> > others realized that the _augmented sixth_, in use since the
> > Renaissance, did approximate 7:4 very well . . . see Blackwood
for
> > more.
>
> This looks like an artifact of the meantone system, not anything
deep
> in the nature of the harmonic meaning of the V7. I am skeptical
that
> the 7-limit version of the V7 sounds wrong unless there is a
melodic
> consideration which overrides the vertical one; my experience is
that
> normally it works quite well. Your historical information is
entirely
> predicable given the nature and evolution of the tuning systems in
> use when the 5 and then the 7 limits were approached, so it tell us
> nothing for our purpose.
>
> If you think otherwise, could you provide an example?
>
> > However, with the advent of 12-tone equal temperament, the
> deviations
> > of the dominant seventh chord from 7-limit were less than
> previously,
> > and it has been argued that some 7-limit thinking is present in
the
> > music of Wagner, Stravinsky, and even Chopin.
>
> 7-limit thinking has been absolutely fundamental since Monteverdi,
> IMHO.

--- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:

> I believe it's important for us 7-limit fanatics to acknowledge
that
> we're following our ears, not past history. We don't want to be
saddled
> with accusations of trying to distort historical fact.

I'm not saying we are following history, I am saying the historical
argument fails to prove what Paul thinks it proves.

The music of common practice was written by musicians, not
mathematicians. A musician operating in a Pythagorean conceptual
framework begins to employ thirds as harmonies. Do we say Dunstaple
or Dufay are thinking "5"? If we do (and people do), we had better be
prepared to say Monteverdi was thinking "7", because it's the same
phenomenon.

A musician using the Pythagorean thirds may began tempering the
fifths to help the thirds. By splitting the comma between 10/9 and
9/8, the fifth is flattened. Once this has become the practice, one
cannot *also* decide to split the septimal comma between 9/8 and 8/7
and sharpen the fifth. However, as an augmented sixth a good 7 will
magically appear in the meantone circle of fifths. It is this
mathematical fact which drives the musical practice; it strikes me as
manifestly invalid to attempt to draw conclusions from musical
practice which go beyond what is obvious from the mathematics when
the mathematics seems to explain everything. One cannot conclude in a
simple-minded way that the iv element of a dominant seventh has the
meaning of a 4/3 without a further argument.

I say, better
> late than never!
>
> When I first joined the list, I had a kind of 7-limit chip on my
> shoulder.

I'd say I have a mathematical chip on my shoulder, and I won't buy an
argument from common practice which I can explain to my satisfaction
as a mathematical artifact, with no further meaning.

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> > Historically, musicians who attempted to introduce 7-limit into
> > Western harmony did not think that it had anything to do with the
> > dominant seventh chord -- even though they were unanimous that
the
> 5-
> > limit had much to do with the major chord. Tartini and
Kirnberger,
> > for example, introduced new notational symbols for accidentals
that
> > would produce 7-limit ratios with "standard" notes. Huygens and
> > others realized that the _augmented sixth_, in use since the
> > Renaissance, did approximate 7:4 very well . . . see Blackwood
for
> > more.
>
> This looks like an artifact of the meantone system, not anything
deep
> in the nature of the harmonic meaning of the V7.

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.

> I am skeptical that
> the 7-limit version of the V7 sounds wrong unless there is a
melodic
> consideration which overrides the vertical one;

Exactly.

> my experience is that
> normally it works quite well. Your historical information is
entirely
> predicable given the nature and evolution of the tuning systems in
> use when the 5 and then the 7 limits were approached, so it tell us
> nothing for our purpose.

What do you mean? The aesthetic judgments of our great musicians tell
us nothing?

> If you think otherwise, could you provide an example?

I've heard lots of examples . . . Joe Monzo and George Kahrimanis had
some on their webpages . . . don't recall the URL . . .

> 7-limit thinking has been absolutely fundamental since Monteverdi,
> IMHO.

We will have to agree to disagree, then.

--- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:

> Gene, are you familiar with how my spring model works? I _do_ set
up
> target JI intervals, which _could_ be reported in a text file for
each
> harmonic moment in the piece, but my relaxation of the spring
matrix
> substitutes for any solving of linear equations, and allows very
> naturally for non-self-consistent vertical tunings such as
> chain-of-fifth chords.

What I'm interested in at the moment is how the effect you achieve in
this way relates to retunings of the factors.

> Actually, I view the entire sequence in text form (files with .hp
> extensions, harkening back to my use of HP computers for early
tuning
> work). I can send you an (PC) executable that'll produce such a
file
> from any .mid file if you like.

I'd like that. Perhaps I can work on a simple example and see if I
can understand what is happening.

Tunings are shown in cents offset from
> 12-tET, and scale degrees are expressed as octaves plus offset
> (0 .. 11 for C thru B). Also the absolute timing of the piece is
shown,
> down to a thousandth of a second. It's quite easy to track what
happens
> to commas.

Could you take such a file, and turn it back into midi? I've been
looking for something like that.

As I've described earlier, I can distribute the comma
> vertically, horizontally, or some combination of the two. One
thing I
> _don't_ show explicitly is information about target vertical
intervals,
> which is a shame, though usually it's not hard to glean from the
> information present.

It would help to add it to the program.

Bob, I think it's very important to sit down and read the aesthetic
opinions of musicians of the period in question, rather than impose
our own aesthetics upon their music.

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

> For example, we know that in western music harmony and melody
> interact polyphonically in ways that are fairly unique to this
> tradition. The melodic scales we use are FUNDAMENTALLY BASED on
> HARMONIC considerations.

I completely disagree. The melodic scales we use derive from a time
in our culture before harmony or polyphony were ever used. It is
lucky that they turned out to lend themselves to harmony with only
very minor modifications.

And to both you and Gene: the major and minor modes of the diatonic
scale only relatively recently came to the fore. In older times, the
Dorian, Phrygian, Lydian, and Mixolydian modes were more important.
>
> So all this erudite talk of melodic considerations forcing
> compromises in harmonic considerations is a source of wonder to me.
> Here I have seen the same people who rail against the tendency in
> "expressive intonation" to reverse the size relationship of the
> smaller just chromatic half-step and larger just diatonic half-step
> turn right around and promote analagous things with other and even
> the same intervals with the same kind of melodic "justifications".

Hmm?

> Without harmonic considerations and no drone, melodic intervals are
> completely arbitrary.

You don't think one can hear, and sing, with a fair degree of
accuracy, the perfect fourth and fifth, melodically? Because that is
all that is needed to construct the diatonic scale melodically. It
has two identical tetrachords, a fourth or fifth apart, in _every_
octave species.

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:

> A musician using the Pythagorean thirds may began tempering the
> fifths to help the thirds. By splitting the comma between 10/9 and
> 9/8, the fifth is flattened. Once this has become the practice, one
> cannot *also* decide to split the septimal comma between 9/8 and
8/7
> and sharpen the fifth. However, as an augmented sixth a good 7 will
> magically appear in the meantone circle of fifths.

Augmented sixths were used in harmony since the Renaissance, and were
always considered _completely different_ from minor sevenths.

> It is this
> mathematical fact whicn drives the musical pracice;

You're defeating your own argument here . . . if the augmented sixth
represents 7:4, and if musicians took care to distinguish the
augmented sixth from the dominant seventh (for example, they always
resolve in their own, completely different, ways), that seems to show
that the dominant seventh _did not_ represent the same sonority,
i.e., the 7-limit one.

> it strikes me as
> manifestly invalid to attempt to draw conclusions from musical
> practice which go beyond what is obvious from the mathematics when
> the mathematics seems to explain everything.

??? We have not only musical practice, but written testimony from
musicians of the time. And how do the mathematics explain
everything . . . your mathematics specifically? How do you explain
that, around the time of Monteverdi or the succeeding couple of
generations, the time in which dominant seventh chords, and other
chords with diminished fifths, became more and more used, the set of
diatonic modes used began to favor just two of the modes, until
eventually the others fell out of use? Mathematically or otherwise, I
don't believe this is a coincidence, and I don't believe melodic
considerations are irrelevant in explaining the evolution of Western
musical practice.

> One cannot conclude in a
> simple-minded way that the iv element of a dominant seventh has the
> meaning of a 4/3 without a further argument.

I don't think it comes down to anything "having the meaning of a 4/3"
at all. But one cannot conclude in a simple-minded way that the
dominant seventh has the meaning of a 4:5:6:7 without further
argument.
>
> I'd say I have a mathematical chip on my shoulder, and I won't buy
an
> argument from common practice which I can explain to my
satisfaction
> as a mathematical artifact, with no further meaning.

1/1 9/8 5/4 4/3 3/2 5/3 15/8 is a mathematical artifact, with no
musical meaning. The major and minor modes came to the fore because
they are the only modes in which the diminished fifth, which occurs
in dominant seventh chords and other chords, resolves in contrary
motion to notes of the tonic triad. This is very important if you
trace cadential practice from the Medieval period onwards. If you
wish to tune the dominant seventh chord to 4:5:6:7, and assuming that
for some reason you are not sensitive to the melodic and contrapuntal
trouble this causes, you still have to explain why the set of modes
was whittled down as it was . . . or why the major mode was _not_ one
of the important ones _before_ the use of diminished fifths at
cadential points became common practice.

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

> For example, we know that in western music harmony and melody
> interact polyphonically in ways that are fairly unique to this
> tradition. The melodic scales we use are FUNDAMENTALLY BASED on
> HARMONIC considerations.

I disagree. In our culture, before harmony or polyphony, we had
purely melodic music using the same scales that we have today
(luckily, the scales turned out to work very nicely harmonically,
with only very minor modificiations). They can be derived from the
similarity of notes an octave, fifth, or fourth apart, and from the
condition that each octave species will have two identical
tetrachords (that is, fourth species) either a fourth or fifth apart.
In the later period ancient Greece, for instance, these were the
scales primarily in use, though harmony (other than at octaves) was
unused and unwanted in the music.

I love it, Gene! Yes, this is what I was aiming at when I said in
post 28179:

"...historical evidence is often if not always insufficient to
reflect the realities of the times in question. Then we must take
recourse to common sense and the larger human realities that tie us
all together not just in space, but also in time."

I should have also added mathematical realities as well as the more
fundamental and eternal realities basic to human perception.

Bob

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:
>
> > I believe it's important for us 7-limit fanatics to acknowledge
> that
> > we're following our ears, not past history. We don't want to be
> saddled
> > with accusations of trying to distort historical fact.
>
> I'm not saying we are following history, I am saying the historical
> argument fails to prove what Paul thinks it proves.
>
> The music of common practice was written by musicians, not
> mathematicians. A musician operating in a Pythagorean conceptual
> framework begins to employ thirds as harmonies. Do we say Dunstaple
> or Dufay are thinking "5"? If we do (and people do), we had better
be
> prepared to say Monteverdi was thinking "7", because it's the same
> phenomenon.
>
> A musician using the Pythagorean thirds may began tempering the
> fifths to help the thirds. By splitting the comma between 10/9 and
> 9/8, the fifth is flattened. Once this has become the practice, one
> cannot *also* decide to split the septimal comma between 9/8 and
8/7
> and sharpen the fifth. However, as an augmented sixth a good 7 will
> magically appear in the meantone circle of fifths. It is this
> mathematical fact which drives the musical practice; it strikes me
as
> manifestly invalid to attempt to draw conclusions from musical
> practice which go beyond what is obvious from the mathematics when
> the mathematics seems to explain everything. One cannot conclude in
a
> simple-minded way that the iv element of a dominant seventh has the
> meaning of a 4/3 without a further argument.
>
> I say, better
> > late than never!
> >
> > When I first joined the list, I had a kind of 7-limit chip on my
> > shoulder.
>
> I'd say I have a mathematical chip on my shoulder, and I won't buy
an
> argument from common practice which I can explain to my
satisfaction
> as a mathematical artifact, with no further meaning.

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

Your historical information is
> entirely
> > predicable given the nature and evolution of the tuning systems
in
> > use when the 5 and then the 7 limits were approached, so it tell
us
> > nothing for our purpose.

> What do you mean? The aesthetic judgments of our great musicians
tell
> us nothing?

They tell us nothing about aethetics unless they actually are
aesthetic judgments, and that is precisely what needs to be shown. If
they are simple consequences of the tuning system, I don't see how
you can presume they are aesthetic judgments.

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

> And to both you and Gene: the major and minor modes of the diatonic
> scale only relatively recently came to the fore.

I'm well aware of that, though it would not have any effect on my
calculation. I did that not because of any presumed historical
importance for that scale but because I was thinking of problems
arising from PBs, of which more anon on tuning-math. However, it's a
good scale for some things--I think it works for Pachelbel's canon,
for instance.

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> Your historical information is
> > entirely
> > > predicable given the nature and evolution of the tuning systems
> in
> > > use when the 5 and then the 7 limits were approached, so it
tell
> us
> > > nothing for our purpose.
>
> > What do you mean? The aesthetic judgments of our great musicians
> tell
> > us nothing?
>
> They tell us nothing about aethetics unless they actually are
> aesthetic judgments, and that is precisely what needs to be shown.

Hmm . . . the aesthetic jugdments tell us nothing unless they
actually are aesthetic judgments . . . hard to argue with that! :)

> If
> they are simple consequences of the tuning system,

What are you envisioning here?

I don't see how
> you can presume they are aesthetic judgments.

I'm talking about the fact, for instance, that musicians who sought
to introduce 7-limit consonances into music, including Tartini,
Kirnberger, and as I recall, even Rameau, did not speak of them as
something they heard already in the dominant seventh chord, or as a
new way of tuning the dominant seventh chord. Instead they were
considered new sounds, with new notation invented for them. The major
scale was, in most cases (see Mathieu, for instance) supplied with a
7/4 and a 7/6, but not a 21/16, which would be required for a
septimal dominant seventh chord.

--- In tuning@y..., genewardsmith@j... wrote:

> However, it's a
> good scale for some things--I think it works for Pachelbel's canon,
> for instance.

Well, almost . . . there are some spots where the 2nd scale degree
appears over the IV chord . . . and one hears an audible dissonance
there in the JI version of the Canon on Herman Miller's page.

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> > And to both you and Gene: the major and minor modes of the
diatonic
> > scale only relatively recently came to the fore.
>
> I'm well aware of that, though it would not have any effect on my
> calculation. I did that not because of any presumed historical
> importance for that scale but because I was thinking of problems
> arising from PBs, of which more anon on tuning-math. However, it's
a
> good scale for some things--I think it works for Pachelbel's canon,
> for instance.

Yes, you're right . . . but what does one care about optimizing? One
cares about optimizing the simultaneously sounding harmonic
intervals . . . not about optimizing a set of ratios only from the
tonic, including some that are two consonant steps removed from it.
The former makes sense to me as an artistically motivated
calculation . . . the latter does not.

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

> Augmented sixths were used in harmony since the Renaissance, and
were
> always considered _completely different_ from minor sevenths.

I don't see what you think to prove by this--of course they were
considered completely different; they *are* completely different. A
Pythagorean third is likewise completely different from a 5/4, but at
least when using a meantone approximation they are approximated in
the same way. Here, not even that is happening.

> > It is this
> > mathematical fact whicn drives the musical pracice;
>
> You're defeating your own argument here . . . if the augmented
sixth
> represents 7:4, and if musicians took care to distinguish the
> augmented sixth from the dominant seventh (for example, they always
> resolve in their own, completely different, ways), that seems to
show
> that the dominant seventh _did not_ represent the same sonority,
> i.e., the 7-limit one.

If one sounds like a dissonace and the other does not, what would you
expect? If one appears in one relation to the tonic and the other in
a completely different one, what would you expect? Again, this really
does not seem to be telling us anything we could not deduce without
reference to practice.

>How do you explain
> that, around the time of Monteverdi or the succeeding couple of
> generations, the time in which dominant seventh chords, and other
> chords with diminished fifths, became more and more used, the set
of
> diatonic modes used began to favor just two of the modes, until
> eventually the others fell out of use?

Considering that triadic harmony works more easily in the modes which
began to be favored, that does not seem like much of a mystery. The
situation looks very different if you view the scale as a string of
fifths and write monophonic chant sequences than if you view it as I,
IV and V chords, with the harmonic aspect of fundamental importance.

Mathematically or otherwise, I
> don't believe this is a coincidence, and I don't believe melodic
> considerations are irrelevant in explaining the evolution of
Western
> musical practice.

I think what you have just described is hardly melodic considerations
in action! Quite the reverse.

> 1/1 9/8 5/4 4/3 3/2 5/3 15/8 is a mathematical artifact, with no
> musical meaning. The major and minor modes came to the fore because
> they are the only modes in which the diminished fifth, which occurs
> in dominant seventh chords and other chords, resolves in contrary
> motion to notes of the tonic triad.

Oh, please. What about the fact that in major mode, you have major
tonic, dominant and subdoominant *chords*?

--- In tuning@y..., genewardsmith@j... wrote:
>
> The music of common practice was written by musicians, not
> mathematicians. A musician operating in a Pythagorean conceptual
> framework begins to employ thirds as harmonies. Do we say Dunstaple
> or Dufay are thinking "5"? If we do (and people do), we had better be
> prepared to say Monteverdi was thinking "7", because it's the same
> phenomenon.

Hold on. It is true that at the end of the Medieval era, composers began to use thirds in
_stable_, concordant sonorities, implying a departure from the Pythagorean tuning paradigm.
But for centuries, throughout the Medieval era, thirds, and even entire "triads" as we call them
today, has been used as _unstable_ sonorities that had to resolve in certain ways. Such
sonorities express their unstable nature very well in Pythagorean tuning, and Margo has
provided, in my opinion, ample evidence that Pythagorean tuning was the most appropriate
one through most of the Medieval era.

In the common-practice era, dominant and diminished seventh chords, and the diminished fifth in
particular, play the role that thirds played in most of the Medieval era -- they are unstable
sonorities which "point" to the intervals to which they must resolve in specific ways. As such, I
don't feel it is proper to try to tune them as smoothly or consonantly as possible -- instead,
melodic correctness in the resolving motion is of greater importance in giving these progressions
their intended effect. It is true that in isolated examples in Wagner, Stravinsky, and Chopin, and
more commonly in some American music styles, we see seventh chords acting _stably_ as
_tonics_, not bound to resolve in a specific way, but free to progress in any way desired, or to
serve as an ending. As such, one might profitably contemplate how to aid the effect through
tuning considerations, adding stability to these chords through 7-limit tuning, and ultimately
developing a tonal language in which the 7-limit chords act as stable consonances. I see this as
the "next step", as opposed to atonality or serialism .

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

> Yes, you're right . . . but what does one care about optimizing?

I was thinking of the problem of deriving a temperament suited to
tempering a PB, and one approach would be to match the scale elements
of the PB to the remaining generators in an optimal way. For
instance, we could start with the notation [h7, h12, h3] and
corresponding basis (128/125, 25/24, 81/80). If we have a 7-note PB
and decide to temper out 81/80, we want to find a and b such that
7a + 12b = 1 and some PB scale belonging to this notation is
optimized, for instance we might minimize

(a+2b-log_2(9/8))^2+(2a+4b-log_2(5/4))^2+...+(6a+11b-log_2(15/8))^2

in which case we get the 3/14 comma meantone system. Unfortunately it
seems to depend quite a bit on the particular choice of PB, rather
than just the notation.

What the heck, 3/14 seems like a fine value anyway.

One
> cares about optimizing the simultaneously sounding harmonic
> intervals . . . not about optimizing a set of ratios only from the
> tonic, including some that are two consonant steps removed from it.

Doing that is one way of giving greater weight to smaller primes, so
I don't think it is unmotivated.

--- In tuning@y..., genewardsmith@j... wrote:

> >How do you explain
> > that, around the time of Monteverdi or the succeeding couple of
> > generations, the time in which dominant seventh chords, and other
> > chords with diminished fifths, became more and more used, the set
> of
> > diatonic modes used began to favor just two of the modes, until
> > eventually the others fell out of use?
>
> Considering that triadic harmony works more easily in the modes which
> began to be favored, that does not seem like much of a mystery.

Works more easily? Without regard to how the tritone resolves?

> The
> situation looks very different if you view the scale as a string of
> fifths and write monophonic chant sequences than if you view it as I,
> IV and V chords, with the harmonic aspect of fundamental importance.

I, IV, and V chords did not have more importance than the other triads. To this day, even in
common-practice major music, some theorists regard I, ii, and V as the three triads of most
importance. Given the body of Renaissance music and the variety of diatonic folk music in
various modes that uses triadic harmony, with no particular favoritism given to IV and V chords
over others, I can't buy the Schoenbergian argument of "genesis from I, IV, V". In any case, a
free play of I, IV, and V sounds just as good to me in the Mixolydian and Dorian modes as it
does in the Aeolian and Ionian modes -- the "consistency" in the triad qualities has no particular
appeal -- and note that in common-practice minor, V usually becomes major instead of minor.
>
> Mathematically or otherwise, I
> > don't believe this is a coincidence, and I don't believe melodic
> > considerations are irrelevant in explaining the evolution of
> Western
> > musical practice.
>
> I think what you have just described is hardly melodic considerations
> in action! Quite the reverse.

I consider the action of voices resolving by step in contrary motion to involve, at least partially,
melodic considerations.
>
> > 1/1 9/8 5/4 4/3 3/2 5/3 15/8 is a mathematical artifact, with no
> > musical meaning. The major and minor modes came to the fore because
> > they are the only modes in which the diminished fifth, which occurs
> > in dominant seventh chords and other chords, resolves in contrary
> > motion to notes of the tonic triad.
>
> Oh, please. What about the fact that in major mode, you have major
> tonic, dominant and subdoominant *chords*?

It's a nice feature, but if it were very important, the major mode would probably have achieved
prominence long before the use of guided tritone resolutions -- yet it didn't! The diatonic scale is
so much more than this. At the very least, one can object to this set of ratios because there is no
musical justification for "demoting" the ii chord below the vi and iii chords. In fact, some
common-practice theorists view ii and vi as valid chord functions but iii is "demoted" -- clearly this
has no correlation with the ratio-interpretation you propose.

I've been arguing these points on this list for about six years but it's not very easy right now,
with the weight of the recent tragedy weighing on my mind. I did recover from my paralyzed
shock yesterday evening, but I'm still sluggish . . .

--- In tuning@y..., paul@s... wrote:
> Works more easily? Without regard to how the tritone resolves?

"Works more easily" was not the right way to put it. With new
emphasis on triads, however, it becomes important if I, V, IV are all
major chords, making all of the most important chords major. This
gives the sense of "major", and we have a similar point for "minor
though there a tendency to want to make the V a major chord appears.
This sort of consideration arises after people start thinking
vertically in terms of tonal structure, not just as consonance _per
se_. It doesn't arise at all if you are only thinking horizontally.

> I, IV, and V chords did not have more importance than the other
triads.

To whom? Dufay? Monteverdi? Mozart? Schubert?

To this day, even in
> common-practice major music, some theorists regard I, ii, and V as
the three triads of most
> importance.

"Three chord" composers don't use those three chords, however. I
don't think you should underrate the importance of the subdominant in
CP.

Given the body of Renaissance music and the variety of diatonic folk
music in
> various modes that uses triadic harmony, with no particular
favoritism given to IV and V chords
> over others, I can't buy the Schoenbergian argument of "genesis
from I, IV, V".

I don't think the Renaissance defines "common practice", in fact it
used to be excluded from consideration.

In any case, a
> free play of I, IV, and V sounds just as good to me in the
Mixolydian and Dorian modes as it
> does in the Aeolian and Ionian modes -- the "consistency" in the
triad qualities has no particular
> appeal -- and note that in common-practice minor, V usually becomes
major instead of minor.

I think modal harmony sounds fine, but it isn't the core of CP by any
means, and I think that was driven by harmonic considerations.

> > Oh, please. What about the fact that in major mode, you have
major
> > tonic, dominant and subdoominant *chords*?

> It's a nice feature, but if it were very important, the major mode
would probably have achieved
> prominence long before the use of guided tritone resolutions -- yet
it didn't! The diatonic scale is
> so much more than this. At the very least, one can object to this
set of ratios because there is no
> musical justification for "demoting" the ii chord below the vi and
iii chords.

It is certainly true that this does *not* fit CP, which gives ii more
importance (as a fifth above the dominant more than as a third below
the subdominant, but partly because it is the fulcrum of the comma
pump bridging these two interpretations, I think) than iii or vi,
which have fewer dynamic possibilities.

In fact, some
> common-practice theorists view ii and vi as valid chord functions
but iii is "demoted" -- clearly this
> has no correlation with the ratio-interpretation you propose.

I don't know what you mean by demoted--regarded as not a consonance?
Given that it shares notes with both I and V, and bridges them, I
don't see why that would be. It isn't regarded as very dynamic, or
with much individual flavor. The vi goes to the relative minor, and
ii has a dual role, but iii is pretty quiet.

> I've been arguing these points on this list for about six years but
it's not very easy right now,
> with the weight of the recent tragedy weighing on my mind. I did
recover from my paralyzed
> shock yesterday evening, but I'm still sluggish . . .

I've been in a strange mood also, no surprise.

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

> In the common-practice era, dominant and diminished seventh chords,
and the diminished fifth in
> particular, play the role that thirds played in most of the
Medieval era -- they are unstable
> sonorities which "point" to the intervals to which they must
resolve in specific ways.

Correct.

As such, I
> don't feel it is proper to try to tune them as smoothly or
consonantly as possible -- instead,
> melodic correctness in the resolving motion is of greater
importance in giving these progressions
> their intended effect.

I think the musical effect can only be determined by listening to
examples; though a purist would insist on always tuning according to
the tuning the composer himself had in mind, as best that can be
determined, we haven't actually applied that principle with any
consistency so it hardly need be our guiding star. Certainly a
1-5/4-3/2-7/4 does not carry the same sense that it must resolve as
does a 1-5/4-3/2-16/9. That is not necessarily a bad thing!

Why is 7-limit tuning any less legitimate than playing a meantone
piece in 12-et, as a matter of principle?

[Paul E wrote:]
>If you wish to tune the dominant seventh chord to 4:5:6:7, and assuming
>that for some reason you are not sensitive to the melodic and
>contrapuntal trouble this causes, you still have to explain why the set
>of modes was whittled down as it was . . .

Paul, I have to object to this wording. I don't believe that any of us
who prefer 4:5:6:7 dom 7ths do so because we lack "sensitivity" ("for
some reason"). The price is very clear, and to us, so is the payoff.

As you will have seen, I am not arguing with your knowledge of history.
But settling the historical question is completely different from
settling the question of which tuning option sounds better. For the
latter, we are all bound to use our own judgement, and it is not
helpful, I believe, to call each other "insensitive".

JdL

[Dimitrov wrote:]
>>>The 7th degree of any major scale when one violinist
>>>play it=very sharp et near to the tonic...
>>>Why? !!! Is it not more attractif when that 7th is
>>>"normaly" distant?
>>>It's only one question :)

[I wrote:]
>>You are speaking of the major 7th, when functioning as leading tone
>>to the tonic above. My belief is that a small melodic step is more
>>dramatic than a larger step. So, for example, when a 4:5:6:7 dom 7th
>>resolves to JI tonic, the leading tone to tonic, 15:16 or 112 cents,
>>is not as dramatic as the 21:20, 84 cents, resolving to the tonic's
>>third degree.

>>(if the step gets _too_ small, the ear no longer considers it
>>dramatic, or even a step, but in the range 70 .. 200 cents, at least,
>>I think this principle applies).

[Wim wrote:]
>John, I don't think Mr. Dimitrov is speaking in terms of JI.

You are right, and rereading my response I see that I should have made
acknowledgement of this more clear. I introduced a JI calculation to
illustrate that JI and nice small steps don't have to be incompatible.

>I noticed that musicians with a classical education, especially in the
>orchestra, respect the principle of high sharps and low flats.

So I have heard. And often (usually) at an explicit harmonic price.

>(A conductor who wants a low C#, because it sounds out of tune against
>a low A, simply asks to play it as if it was a Db.) It's 'logic'
>therefore for them to raise for example the F# in the key of G. In the
>same time, musicians who play an instrument with flexible pitch, as the
>violin, always say that the F# is attracted toward the G and 'therefore
>should be sharpened'.

>As Mr. Dimitrov says, as a violinist (!), why not 'normally' distant? I
>wonder why as well. OK, undeniable, the leading-tone (la note sensible)
>wants to go up to the tonic, but should we help it to make the move? On
>my quartertone guitar a leadingtone going up precisely a quartertone
>towards the tonic doesn't produce a dramatic result at all. It sounds
>as if the note already half arrived and just needed to be tuned up a
>little. If there is something as an attraction force, something you
>lift up and than let it fall, perhaps a certain distance should be
>respected to produce an effect.

I agree! From your experience, 50 cents is too narrow. Maybe the edge
of a plausible and vivid ("incisive" is Paul E's term) minor second is
around 70 cents (approximately 25:24). As with so many musical issues,
taste will vary. I believe that Margo has said that she sometimes uses
commas as melodic steps. That's _narrow_!

>Besides, a F# higher than in 12-tet will sound pretty much out of tune
>if played within a D or a D7. chord. So, I think I understand Mr.
>Dimitrov's question, but still can't give a definite reply.

Oh, absolutely. As if major thirds weren't bad enough already! I'd
rather let the step grow, and (as I stated) take a smaller step from the
other half of the tritone. Such an option is not, of course, possible
in the more popular and historically accurate 5-limit tunings.

JdL

--- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:
> [Paul E wrote:]

> Paul, I have to object to this wording. I don't believe that any
of us
> who prefer 4:5:6:7 dom 7ths do so because we lack "sensitivity"
("for
> some reason"). The price is very clear, and to us, so is the
payoff.

I don't think Paul meant insensitivity in any pejorative sense, but I
also think he is being inconsistent. He in one place argues that
CEGAD "wants" to be read as having pure fifths and thirds and sixths,
but won't accept a similar teleological mandate for GBDF, despite the
fact that it seems much more straightforward. So far as history goes,
it seems to me he wants to treat thirds one way, and sevenths in
another. He argues that the tendency tones in the resolution of V7
show it is "melodic", without so far as I have heard accepting a
similar argument for the tendency of the B in GBD to head for a C.
One could argue that triads are melodic and not harmonic and use as
evidence this business of tuning sharps sharp for meoldic reasons,
and you would have basically the same argument that Paul gives.

> As you will have seen, I am not arguing with your knowledge of
history.

There's knowledge, and then there's the interpretation of that
knowledge. Confusing tuning decisions with practical ones isn't a
matter of knowledge. If one wants to argue that composers *wanted* a
sharp seventh degree, instead of simply accepting it because that was
the only alternative, then you need more than Paul has supplied.

I'm tryng to guess if at any point of time anyone
here has tried to think differently...
Are you sure ( all of you :) ) that we must believe in
the mathematic formulae and not in our own ears ?
:))))
Because it could be the opposite! When we are sure in
one temperament, we can "teach" our ears too...
Can't we?
JI is one chimera that has no justification! (at least
I think so...) And all of our efforts lead nowhere!!!
I wonder who plays actively an instrument among you.

Dimitrov

--- genewardsmith@juno.com a �crit�: > --- In
tuning@y..., "John A. deLaubenfels"
> <jdl@a...> wrote:
> > [Paul E wrote:]
>
> > Paul, I have to object to this wording. I don't
> believe that any
> of us
> > who prefer 4:5:6:7 dom 7ths do so because we lack
> "sensitivity"
> ("for
> > some reason"). The price is very clear, and to
> us, so is the
> payoff.
>
> I don't think Paul meant insensitivity in any
> pejorative sense, but I
> also think he is being inconsistent. He in one place
> argues that
> CEGAD "wants" to be read as having pure fifths and
> thirds and sixths,
> but won't accept a similar teleological mandate for
> GBDF, despite the
> fact that it seems much more straightforward. So far
> as history goes,
> it seems to me he wants to treat thirds one way, and
> sevenths in
> another. He argues that the tendency tones in the
> resolution of V7
> show it is "melodic", without so far as I have heard
> accepting a
> similar argument for the tendency of the B in GBD to
> head for a C.
> One could argue that triads are melodic and not
> harmonic and use as
> evidence this business of tuning sharps sharp for
> meoldic reasons,
> and you would have basically the same argument that
> Paul gives.
>
> > As you will have seen, I am not arguing with your
> knowledge of
> history.
>
> There's knowledge, and then there's the
> interpretation of that
> knowledge. Confusing tuning decisions with practical
> ones isn't a
> matter of knowledge. If one wants to argue that
> composers *wanted* a
> sharp seventh degree, instead of simply accepting it
> because that was
> the only alternative, then you need more than Paul
> has supplied.
>
>
>

___________________________________________________________
Do You Yahoo!? -- Un e-mail gratuit @yahoo.fr !
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Hello -

Message 18 from tuning 1587 - "genewardsmith"'s post
sparked quick thoughts which may already have been posted,
but forgive me if I repeat. On a piano tuned to quarter
comma mean tone temperament, there are different inversions
of diminished seventh chords which a knowledgeable mean
tone listener with a musical ear would distinguish naturally,
although a modern listener might not immediately hear as
intuitively obviously different and belonging in different places.
These chords, and also various just renditions of diminished
seventh and other kinds of 7th chords, as well as the French
Sixth chord, which has an intriguing 11- ratio interpretation,
have a pleasing fascinating "bite" which, if they weren't
fully exploited in earlier times, deserve to be explored
as musical materials now.
I suspect that composers of the 17th and even 18th and
perhaps early 19th centuries - even Chopin? - had first hand
knowledge of the effects of the mean tone diminished 7th
chords and may have intended these effects in some of their
compositions. The performance of their works in equal temperament
would cause some of these effects - at least in their original
form with the characteristic "bite" they had - to be lost. It's
frustrating that composers of those times said so little - at least
as far as I know - about their thoughts on tuning and its effects
on the sound of music. However, I have some hopes that buried in
libraries around Europe, there are old tomes and old newspapers going
back well into the 18th century and perhaps earlier where some
very telling insights might be gained by someone with the patience
to go through mountains of old newspapers, journals, books, etc.

Dave Hill, Borrego Springs, CA

latchezar_d@yahoo.com (=?iso-8859-1?q?Latchezar=20Dimitrov?=) wrote:

> I'm tryng to guess if at any point of time anyone
> here has tried to think differently...
> Are you sure ( all of you :) ) that we must believe in
> the mathematic formulae and not in our own ears ?
> :))))
> Because it could be the opposite! When we are sure in
> one temperament, we can "teach" our ears too...
> Can't we?
> JI is one chimera that has no justification! (at least
> I think so...) And all of our efforts lead nowhere!!!
> I wonder who plays actively an instrument among you.

You'll find that on the Tuning List, nobody else thinks differently,
everybody else believes the mathematic formulae and not their own ears,
and nobody else actively plays any instruments. The only exception to
these rules is the author of any given message.

Graham

Hi Dimitrov

A good starting point for understanding our interest in j.i. is the harmonic series.

On the violin, play the harmonics on the C open string in the series C C G C E G A# C.

You will find that the E is a bit flat. That's the 5/4 major third above the previous C.
The F# is very flat, and is the 7/4 of the 1/1 5/4 3/2 7/4 dom7th chord your ears find
so hard to accept.

However, think about this. In the violin timbre, those partials are very loud. You can
listen to them - play a partial, then go back to the open string C, and you'll be able
to hear that the partial continues into the open string sound.

In a violin concerto, these partials will actually be as loud as some of the instruments
of the orchestra at times.

So violinists have been playing them all along without realising it.

New thing in j.i. is to use these musical intervals melodically, or as notes
in chords that are heard as separate notes (even if not listening out for the partials).

New that is to a classically trained violinist. Actually, historically the harmonic series
most likely came first.

Five limit j.i. ratios are used, for example, in Indian classical music, and to the classically
trained Indian musician, the 12-tet major third sounds sharp.

The 7/4 is also widely used, though not in Indian music (correct me if I'm wrong in this Haresh).

Some of those on this list are primariily mathematicians. Many play a musical intrument.
A fair number are professional musicians; some of whom may have come to the subject
as a result of listening with discerning ears to the harmonic series!

Try this experiment on the voilin. Tune the open strings to non beating perfect fifths.
Now find the fifth harmonic E on the G string. You will find it is flat compared with the
open E. The ratio between the two is the 81/80 syntonic comma.

You'll find a demo midi clip of a cello note, alternating with the partials, at the start
of the latest version of my tunes page:

http://members.tripod.com/~robertinventor/tunes/tunes.htm

This page has a couple of demo clips of all the harmonic series notes played in unison.

http://www.tunesmithy.connectfree.co.uk/harmonic_series_notes_sound_well_together.htm

Robert

[Dimitrov wrote:]
>I'm tryng to guess if at any point of time anyone
>here has tried to think differently...
>Are you sure ( all of you :) ) that we must believe in
>the mathematic formulae and not in our own ears ?
>:))))
>Because it could be the opposite! When we are sure in
>one temperament, we can "teach" our ears too...
>Can't we?
>JI is one chimera that has no justification! (at least
>I think so...) And all of our efforts lead nowhere!!!
>I wonder who plays actively an instrument among you.

I think we all believe our ears. May I ask what you have heard in the
way of JI music? Perhaps for you it will never sound better than other
alternatives, but I assure you it does for me!

Most of us play instruments of some sort or other, I think.

[Gene wrote:]
>There's knowledge, and then there's the interpretation of that
>knowledge. Confusing tuning decisions with practical ones isn't a
>matter of knowledge. If one wants to argue that composers *wanted* a
>sharp seventh degree, instead of simply accepting it because that was
>the only alternative, then you need more than Paul has supplied.

Ok. I don't want to discourage you, or anyone, from trying to unearth
clues about past practice, or from engaging in pure speculation, for
that matter. But would you agree that we are free to make tuning
decisions today without apology irrespective of the past? There may or
may not have been hoards of people tuning up 4:5:6:7 dom 7ths in private
throughout the years (it seems that none of them documented this
practice in a way that has survived). Does it really matter? What we
do now is much more important, IMHO.

JdL

--- In tuning@y..., "Robert Walker" <robertwalker@n...> wrote:

> Some of those on this list are primariily mathematicians.

That would be me, and I could contribute even if I was stone deaf
(which I'm not) and fumble-fingered (which I am.) Who else here is
primarily a mathematician--Pierre? We should have introductions all
around.

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...>

> > You're defeating your own argument here . . . if the augmented
> sixth
> > represents 7:4, and if musicians took care to distinguish the
> > augmented sixth from the dominant seventh (for example, they always
> > resolve in their own, completely different, ways), that seems to
> show
> > that the dominant seventh _did not_ represent the same sonority,
> > i.e., the 7-limit one.
>
> If one sounds like a dissonace and the other does not, what would you
> expect?

So it sounds like you're agreeing with me here,
no? The dominant seventh is meant to be a
dissonance, and had a Baroque composer wished
to use a dominant seventh chord that sounded
like 4:5:6:7, say in the key of Eb major, they
could have written Bb-D-F-G# resolving to Eb
major. This resolution is never found in the
Baroque period.

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., paul@s... wrote:
> > Works more easily? Without regard to how the tritone resolves?
>
> "Works more easily" was not the right way to put it. With new
> emphasis on triads, however, it becomes important if I, V, IV are all
> major chords, making all of the most important chords major.

They weren't the most important chords in
general, and probably only in the Classical
(Haydn, Mozart) period can you find any sense
in which they are most important. But again, ii
often stands in place of IV here.

> This
> gives the sense of "major", and we have a similar point for "minor
> though there a tendency to want to make the V a major chord appears.

I totally disagree with your definitions of "major"
and "minor" or the "sense" thereof.

>
> To this day, even in
> > common-practice major music, some theorists regard I, ii, and V as
> the three triads of most
> > importance.
>
> "Three chord" composers don't use those three chords, however. I
> don't think you should underrate the importance of the subdominant in
> CP.

ii is subdominant as well as IV.
>
> Given the body of Renaissance music and the variety of diatonic folk
> music in
> > various modes that uses triadic harmony, with no particular
> favoritism given to IV and V chords
> > over others, I can't buy the Schoenbergian argument of "genesis
> from I, IV, V".
>
> I don't think the Renaissance defines "common practice", in fact it
> used to be excluded from consideration.

You're right, but what I'm saying is that diatonic
scale plus triadic harmony does not imply
common practice, until the tritone takes on an
important cadential role. Only then do we see
major and minor modes as more common or
more important than the others. Otherwise, we
see i IV v i in dorian, I IV v I in mixolydian, and
plenty of other non-common-practice chord
progressions.
>
> In any case, a
> > free play of I, IV, and V sounds just as good to me in the
> Mixolydian and Dorian modes as it
> > does in the Aeolian and Ionian modes -- the "consistency" in the
> triad qualities has no particular
> > appeal -- and note that in common-practice minor, V usually becomes
> major instead of minor.
>
> I think modal harmony sounds fine, but it isn't the core of CP by any
> means,

Exactly -- it's non-CP.

>and I think that was driven by harmonic >considerations.

Namely, the tritone. The tritone is disjoint from
the tonic triad, and resolves to it by contrary
motion, only in the major and minor modes. The
harmonic minor scale, through the diminished
seventh chord, allows two tritones to
simultaneously resolve _in contrary motion_ to
the tonic triad. These _linear_ (i.e., non-vertical)
considerations here are at the heart of common
practice harmony and how it works. See, for
example, Allen Forte, _Tonal Harmony In
Concept and Practice_.
>
> > > Oh, please. What about the fact that in major mode, you have
> major
> > > tonic, dominant and subdoominant *chords*?
>
> > It's a nice feature, but if it were very important, the major mode
> would probably have achieved
> > prominence long before the use of guided tritone resolutions -- yet
> it didn't! The diatonic scale is
> > so much more than this. At the very least, one can object to this
> set of ratios because there is no
> > musical justification for "demoting" the ii chord below the vi and
> iii chords.
>
> It is certainly true that this does *not* fit CP, which gives ii more
> importance (as a fifth above the dominant more than as a third below
> the subdominant, but partly because it is the fulcrum of the comma
> pump bridging these two interpretations, I think) than iii or vi,
> which have fewer dynamic possibilities.

I don't understand this statement. What does not
fit CP? And ii is _always_ a subdominant
function -- a dominant of the dominant would be
II or II7. Often, in Mozart for example, one can't
distinguish ii from IV, because all the tones from
both chords may be present, and one gets into
questions of whether a certain note is a chord
tone or a passing tone, etc . . . but one can say
for sure that a subdominant harmony is at work.
>
> In fact, some
> > common-practice theorists view ii and vi as valid chord functions
> but iii is "demoted" -- clearly this
> > has no correlation with the ratio-interpretation you propose.
>
> I don't know what you mean by demoted--regarded as not a consonance?

Well there are many such theorists you could
read . . . iii is often regarded as a non-existent
harmonic function, and apparant occurences of
the iii chord are explained in other ways, such as
a V chord with a suspended 6th, just to give one
possible example.

> Given that it shares notes with both I and V, and bridges them, I
> don't see why that would be. It isn't regarded as very dynamic, or
> with much individual flavor. The vi goes to the relative minor, and
> ii has a dual role, but iii is pretty quiet.

Well that may be related about iii . . . but I don't
think ii has a dual role, for any but overly
mathematical JI theorists! Perceptually,
musically, the ii chord is no more or less "dual"
than any other chord, and its function is quite
clear in a tonal context -- it's a subdominant.

[I wrote:]
>>Gene, are you familiar with how my spring model works? I _do_ set up
>>target JI intervals, which _could_ be reported in a text file for each
>>harmonic moment in the piece, but my relaxation of the spring matrix
>>substitutes for any solving of linear equations, and allows very
>>naturally for non-self-consistent vertical tunings such as
>>chain-of-fifth chords.

[Gene wrote:]
>What I'm interested in at the moment is how the effect you achieve in
>this way relates to retunings of the factors.

The factors? Does this mean the JI intervals? They all give a bit,
meantone-like, so that neither fifths or thirds are terribly out of
tune. I can provide specific examples for specific chords if you like.

>>Actually, I view the entire sequence in text form (files with .hp
>>extensions, harkening back to my use of HP computers for early tuning
>>work). I can send you an (PC) executable that'll produce such a file
>>from any .mid file if you like.

[Gene:]
>I'd like that. Perhaps I can work on a simple example and see if I
>can understand what is happening.

OK! It took me a couple of days, but I've uploaded a zip file to the
tuning area, JdL directory, that has the .exe to do this. I've
included a few .bat files, and explained it the process in a .txt file
inside the zip. If this doesn't provide enough info, please ask q's.

[JdL:]
>>Tunings are shown in cents offset from 12-tET, and scale degrees are
>>expressed as octaves plus offset (0 .. 11 for C thru B). Also the
>>absolute timing of the piece is shown, down to a thousandth of a
>>second. It's quite easy to track what happens to commas.

[Gene:]
>Could you take such a file, and turn it back into midi? I've been
>looking for something like that.

Yes, it does that as well. You can edit the text file, change it back
to MIDI, and play the changes the same way you play any MIDI file. Fun!

[JdL:]
>>As I've described earlier, I can distribute the comma vertically,
>>horizontally, or some combination of the two. One thing I _don't_
>>show explicitly is information about target vertical intervals,
>>which is a shame, though usually it's not hard to glean from the
>>information present.

[Gene:]
>It would help to add it to the program.

Understood. All I need is time!

JdL

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> > Yes, you're right . . . but what does one care about optimizing?
>
> I was thinking of the problem of deriving a temperament suited to
> tempering a PB, and one approach would be to match the scale elements
> of the PB to the remaining generators in an optimal way. For
> instance, we could start with the notation [h7, h12, h3] and
> corresponding basis (128/125, 25/24, 81/80). If we have a 7-note PB
> and decide to temper out 81/80, we want to find a and b such that
> 7a + 12b = 1 and some PB scale belonging to this notation is
> optimized, for instance we might minimize
>
> (a+2b-log_2(9/8))^2+(2a+4b-log_2(5/4))^2+...+(6a+11b-log_2(15/8))^2
>
> in which case we get the 3/14 comma meantone system. Unfortunately it
> seems to depend quite a bit on the particular choice of PB, rather
> than just the notation.
>
> What the heck, 3/14 seems like a fine value anyway.

Yes . . . but my approach to optimization
considers _only_ the consonant intervals and the
relationships implied by the commatic unison
vectors. The chromatic unison vectors, and any
specific choice of periodicity block, shouldn't, I
believe, come into it.

>
> One
> > cares about optimizing the simultaneously sounding harmonic
> > intervals . . . not about optimizing a set of ratios only from the
> > tonic, including some that are two consonant steps removed from it.
>
> Doing that is one way of giving greater weight to smaller primes, so
> I don't think it is unmotivated.

In this case it does so, and you're lucky :) In
general I think you should just give whatever
weight you think is appropriate to the consonant
intervals; pinning dissonant intervals to just
values is unjustified, in my opinion.

--- In tuning@y..., Latchezar Dimitrov <
latchezar_d@y...> wrote:
> I'm tryng to guess if at any point of time anyone
> here has tried to think differently...
> Are you sure ( all of you :) ) that we must believe in
> the mathematic formulae and not in our own ears ?

The ears must always come first.

> :))))
> Because it could be the opposite! When we are sure in
> one temperament, we can "teach" our ears too...
> Can't we?
> JI is one chimera that has no justification! (at least
> I think so...) And all of our efforts lead nowhere!!!
> I wonder who plays actively an instrument among you.

I do -- guitar and synthesizer and piano (and
clarinet . . .) . Playing and listening are primary . .
. mathematics can only be a tool, and our models
are never perfect . . . so one must always listen
with a true and open heart, and with lots of
patience (old habits die hard), and with
knowledge of the testimonials of musicians of
past generations.

--- In tuning@y..., ASCEND11@A... wrote:
> Hello -
>
> Message 18 from tuning 1587 - "genewardsmith"'s post
> sparked quick thoughts which may already have been posted,
> but forgive me if I repeat. On a piano tuned to quarter
> comma mean tone temperament, there are different inversions
> of diminished seventh chords which a knowledgeable mean
> tone listener with a musical ear would distinguish naturally,
> although a modern listener might not immediately hear as
> intuitively obviously different and belonging in different places.
> These chords, and also various just renditions of diminished
> seventh and other kinds of 7th chords, as well as the French
> Sixth chord, which has an intriguing 11- ratio interpretation,

I'd probably dispute that, but go on . . .

> have a pleasing fascinating "bite" which, if they weren't
> fully exploited in earlier times, deserve to be explored
> as musical materials now.
> I suspect that composers of the 17th and even 18th and
> perhaps early 19th centuries - even Chopin? - had first hand
> knowledge of the effects of the mean tone diminished 7th
> chords and may have intended these effects in some of their
> compositions.

I don't think Chopin was familar with mean-tone
temperament. In the Romantic period, the
ambiguous quality of 4-tET diminished seventh
chord (it could resolve equally easily in four
different directions) was valued and used very
frequently, for suprise modulations, etc. The
meantone diminished seventh chord, which was
probably very important in the Baroque and
Classical eras, resolves in a very particular way
(through three diatonic semitones and one
diatonic whole tone) and is not amenable to the
Romantic, 4-directional treatment, without
considerable melodic awkwardness.

--- In tuning@y..., genewardsmith@j... wrote:
>
> I think the musical effect can only be determined by listening to
> examples;

There are plenty of examples, tuned with both
dominant seventh chords tuned to 4:5:6:7 and
with a 5-limit paradigm, on John deLaubenfels'
website. For Baroque and Classical works, I find
myself preferring the latter.

> though a purist would insist on always tuning according to
> the tuning the composer himself had in mind, as best that can be
> determined, we haven't actually applied that principle with any
> consistency so it hardly need be our guiding star.

Who's we?

> Certainly a
> 1-5/4-3/2-7/4 does not carry the same sense that it must resolve as
> does a 1-5/4-3/2-16/9.

Or better yet, 1-5/4-3/2-9/5 (though
distinguishing the latter two is kind of
meaningless because 81:80 was always assumed
to be an identity).

> That is not necessarily a bad thing!

Well, sure, all kinds of distortions can be fun.
And for new music, use whatever paradigm you
see fit!

> Why is 7-limit tuning any less legitimate than playing a meantone
> piece in 12-et, as a matter of principle?

At least in the latter case, there are no pitch shifts
or drifts (I'm assuming you mean, take a piece
notated in meantone, and tune it such that the
dominant seventh chords are 4:5:6:7).

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:
> > [Paul E wrote:]
>
> > Paul, I have to object to this wording. I don't believe that any
> of us
> > who prefer 4:5:6:7 dom 7ths do so because we lack "sensitivity"
> ("for
> > some reason"). The price is very clear, and to us, so is the
> payoff.
>
> I don't think Paul meant insensitivity in any pejorative sense, but I
> also think he is being inconsistent. He in one place argues that
> CEGAD "wants" to be read as having pure fifths and thirds and sixths,
> but won't accept a similar teleological mandate for GBDF,

Sure I do. The D-F interval "wants" to be a 6:5.

> despite the
> fact that it seems much more straightforward. So far as history goes,
> it seems to me he wants to treat thirds one way, and sevenths in
> another.

It's completely consistent. Thirds were treated as
consonances, and thus needed to be tuned close
to their 5-limit specifications. Sevenths were
considered dissonant, and were not _directly_
tuned to any given target ratio.

> He argues that the tendency tones in the resolution of V7
> show it is "melodic", without so far as I have heard accepting a
> similar argument for the tendency of the B in GBD to head for a C.

Why wouldn't there also be a tendency for the C
to head for a B in GBD? I'm not sure what
you're implying here . . . can you spell it out
more explicitly?

> One could argue that triads are melodic and not harmonic and use as
> evidence this business of tuning sharps sharp for meoldic reasons,
> and you would have basically the same argument that Paul gives.

Huh? You must be misunderstanding my
argument.

> If one wants to argue that composers *wanted* a
> sharp seventh degree, instead of simply accepting it because that was
> the only alternative, then you need more than Paul has supplied.

What about the fact that musicians of that era
who _wanted_ septimal harmony (Tartini and
Kirnberger . . . any others?), none of them
suggested that it be used for the dominant
seventh chord . . . rather they wanted to use it to
enrich tonic and subdominant harmonies.

Do we look for only formulaes ?
This questions dont entry in the categorie simple
and convenient...I know...
Microtonal is it one domain with future ?
What's the music who touch all of auditors ?
Never mind microtonal...It's only artificial and
intellectual thing, nothing more !
The true music is not into !
We dont need to have that for composing !
In our heads no one think "microtonal mode" !
Why tryng and tryng to prove the contrary ?
Spending everytime all of ours ressources...
Compose is possible out of any temperament :)
If we are capables to...sure :)
Any temperament is good to compose !
Dont mistake composition here with reshearsh to divide
for persuading =that's the truth :)
Thanks to all who had employed all... for wound me
when I have defend the music :P
And propose me to try anything with my violin :)
Nobody have listen my samples in my folder...Why ?
I have listen many samples but not entirely...false
!!!
That's my reason= it's too false to listen !
And the way is false !
Nobody and never will like microtonal compositions :)
The true music dont have one future in this
direction...
The rest is "bla bla " in french...
Persisting or no...no way :)
When I have asked if anyone believe in one universal
base of temperament ...hmm my letter is been
...filtered !
Why ? And who do that ?
Political question ? Yes !
I suppose to find other forums to discute tunning
problem soon...
Is there one free forum ? Or one "free" ...

Dimitrov

--- genewardsmith@juno.com a �crit�: > --- In
tuning@y..., "Robert Walker"
> <robertwalker@n...> wrote:
>
> > Some of those on this list are primariily
> mathematicians.
>
> That would be me, and I could contribute even if I
> was stone deaf
> (which I'm not) and fumble-fingered (which I am.)
> Who else here is
> primarily a mathematician--Pierre? We should have
> introductions all
> around.
>
>
>

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--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "Robert Walker" <robertwalker@n...> wrote:
>
> > Some of those on this list are primariily mathematicians.
>
> That would be me, and I could contribute even if I was stone deaf
> (which I'm not) and fumble-fingered (which I am.) Who else here is
> primarily a mathematician--Pierre? We should have introductions all
> around.

Hi Gene. I am a recovering musician and instrument maker about 2
semesters away from my Ph.D. in mathematics.

John Starrett

Hi , John !

--- "John A. deLaubenfels" <jdl@adaptune.com> a
�crit�: > [Dimitrov wrote:]
> >I'm tryng to guess if at any point of time anyone
> >here has tried to think differently...
> >Are you sure ( all of you :) ) that we must believe
> in
> >the mathematic formulae and not in our own ears ?
> >:))))
> >Because it could be the opposite! When we are sure
> in
> >one temperament, we can "teach" our ears too...
> >Can't we?
> >JI is one chimera that has no justification! (at
> least
> >I think so...) And all of our efforts lead
> nowhere!!!
> >I wonder who plays actively an instrument among
> you.
>
> I think we all believe our ears. May I ask what you
> have heard in the
> way of JI music?

BTW JI=chimera, ok ? Because if the temperament is
equal you can't respect more one interval at time...
it's a math. law :) And that we use when we play
just, is not this JI !
When I hear good intonation I know and I guess that's
one adaptive tuning, but I still try to prove that one
universal tunning existe(like one base who respect all
of intervals , ok ? :)We have also expressive
intonation when we play...

>Perhaps for you it will never
> sound better than other
> alternatives, but I assure you it does for me!

It = ?
I look for before years :))

>
> Most of us play instruments of some sort or other, I
> think.
>

When we play, we dont write :))
We hear and try direct !
And never divide the octave more that 12 steps...
Why we do not inventing more letters in the alphabet ?
Why ?! Think about,pls :)

> [Gene wrote:]
> >There's knowledge, and then there's the
> interpretation of that
> >knowledge. Confusing tuning decisions with
> practical ones isn't a
> >matter of knowledge. If one wants to argue that
> composers *wanted* a
> >sharp seventh degree, instead of simply accepting
> it because that was
> >the only alternative, then you need more than Paul
> has supplied.
>

If the intonation in the music has simple thing this
forum =dont exist...
The practic of playng any instrument is not easy about
just intonation because if we play no only melodic
mode we are disturbed by ! No one singer sing more one
note at time :))
I believe in one temperament "referance mode" ET 12,
ok- but no octave based, no one interval based !
Do you understand me ? I try to write english, ok...
:))

> Ok. I don't want to discourage you, or anyone, from
> trying to unearth
> clues about past practice, or from engaging in pure
> speculation, for
> that matter. But would you agree that we are free
> to make tuning
> decisions today without apology irrespective of the
> past? There may or
> may not have been hoards of people tuning up 4:5:6:7
> dom 7ths in private
> throughout the years (it seems that none of them
> documented this
> practice in a way that has survived). Does it
> really matter? What we
> do now is much more important, IMHO.
>
> JdL

All is important :))
Sometime also that we dont do now...

Dimitrov

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Hi , Robert

--- Robert Walker <robertwalker@ntlworld.com> a
�crit�: > Hi Dimitrov
>
> A good starting point for understanding our interest
> in j.i. is the harmonic series.
>

Ok , I have learn about before ...15 years :)

> On the violin, play the harmonics on the C open
> string in the series C C G C E G A# C.
>

I see what you mean, but (sorry for the joke) dont
find one string "c" :))) I know -viola have that...
My instrument is the violin...

> You will find that the E is a bit flat. That's the
> 5/4 major third above the previous C.
> The F# is very flat, and is the 7/4 of the 1/1 5/4
> 3/2 7/4 dom7th chord your ears find
> so hard to accept.
>

The harmonics or partials is very strange phenomen...
In the same time we have there all intervals JI :)
Paradox ! Octave juste, fifth juste but...hmm third is
not one perfect interval to be just !
And you want to me to compare one natural third
parcial with one string who is tuned using just
fifth's ?!
No way because the half ton when the fifth is
reference is too big ! In the 12Et is smaller...
BTW I dont accord my violin like...My fifth's are
"limit" tempereds :))

> However, think about this. In the violin timbre,
> those partials are very loud. You can
> listen to them - play a partial, then go back to the
> open string C, and you'll be able
> to hear that the partial continues into the open
> string sound.
>
I still like to have string C :)) Like double
guitars=solo+bass or for me =alto + violin :))

> In a violin concerto, these partials will actually
> be as loud as some of the instruments
> of the orchestra at times.
>
> So violinists have been playing them all along
> without realising it.
>
> New thing in j.i. is to use these musical intervals
> melodically, or as notes
> in chords that are heard as separate notes (even if
> not listening out for the partials).
>

I never will accept to have two places for C# and
Db...
It's false supposition...

> New that is to a classically trained violinist.
> Actually, historically the harmonic series
> most likely came first.
>
> Five limit j.i. ratios are used, for example, in
> Indian classical music, and to the classically
> trained Indian musician, the 12-tet major third
> sounds sharp.
>
> The 7/4 is also widely used, though not in Indian
> music (correct me if I'm wrong in this Haresh).
>
> Some of those on this list are primariily
> mathematicians. Many play a musical intrument.
> A fair number are professional musicians; some of
> whom may have come to the subject
> as a result of listening with discerning ears to the
> harmonic series!
>
> Try this experiment on the voilin. Tune the open
> strings to non beating perfect fifths.

Ok , but I would to say...non beating=dead for me...
All must beating :)) In the right direction, ok...

> Now find the fifth harmonic E on the G string. You
> will find it is flat compared with the
> open E. The ratio between the two is the 81/80
> syntonic comma.
>

I know that and it's so logic !
I never had agree this partial(for reference source)
and the perfect fifth also !

> You'll find a demo midi clip of a cello note,
> alternating with the partials, at the start
> of the latest version of my tunes page:
>
>
http://members.tripod.com/~robertinventor/tunes/tunes.htm
>
> This page has a couple of demo clips of all the
> harmonic series notes played in unison.
>
>
A propos ... You say unisson...Between C# and Db we
have what ?
:))

http://www.tunesmithy.connectfree.co.uk/harmonic_series_notes_sound_well_together.htm
>
> Robert

Finally I would repeat my position :
Like only 12 step division and equal (only for
reference)
Use the parcials but also the differencials !
With my violin = no problem for hear them...
Diff1 = F2-F1 ; Diff2 = P1/F1-F2 ect...
The Differencials are in JI...

Dimitrov

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However the resultats here had
opposing your bright type of responding :))

Dimitrov

--- graham@microtonal.co.uk a �crit�: >
latchezar_d@yahoo.com
> (=?iso-8859-1?q?Latchezar=20Dimitrov?=) wrote:
>
> > I'm tryng to guess if at any point of time anyone
> > here has tried to think differently...
> > Are you sure ( all of you :) ) that we must
> believe in
> > the mathematic formulae and not in our own ears ?
> > :))))
> > Because it could be the opposite! When we are sure
> in
> > one temperament, we can "teach" our ears too...
> > Can't we?
> > JI is one chimera that has no justification! (at
> least
> > I think so...) And all of our efforts lead
> nowhere!!!
> > I wonder who plays actively an instrument among
> you.
>
>
> You'll find that on the Tuning List, nobody else
> thinks differently,
> everybody else believes the mathematic formulae and
> not their own ears,
> and nobody else actively plays any instruments. The
> only exception to
> these rules is the author of any given message.
>
>
> Graham
>
>

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:))
--- "John A. deLaubenfels" <jdl@adaptune.com> a
�crit�: > [Dimitrov wrote:]
> >>>The 7th degree of any major scale when one
> violinist
> >>>play it=very sharp et near to the tonic...
> >>>Why? !!! Is it not more attractif when that 7th
> is
> >>>"normaly" distant?
> >>>It's only one question :)
>
> [I wrote:]
> >>You are speaking of the major 7th, when
> functioning as leading tone
> >>to the tonic above. My belief is that a small
> melodic step is more
> >>dramatic than a larger step. So, for example,
> when a 4:5:6:7 dom 7th
> >>resolves to JI tonic, the leading tone to tonic,
> 15:16 or 112 cents,
> >>is not as dramatic as the 21:20, 84 cents,
> resolving to the tonic's
> >>third degree.
>
Ok, np

> >>(if the step gets _too_ small, the ear no longer
> considers it
> >>dramatic, or even a step, but in the range 70 ..
> 200 cents, at least,
> >>I think this principle applies).
>

That's right i think...

> [Wim wrote:]
> >John, I don't think Mr. Dimitrov is speaking in
> terms of JI.
>

Sure...JI dont existe :)

> You are right, and rereading my response I see that
> I should have made
> acknowledgement of this more clear. I introduced a
> JI calculation to
> illustrate that JI and nice small steps don't have
> to be incompatible.
>
> >I noticed that musicians with a classical
> education, especially in the
> >orchestra, respect the principle of high sharps and
> low flats.
>

No more :)) It's one past conseption and no usual
today !
sharp=flat ! Ok ?

> So I have heard. And often (usually) at an explicit
> harmonic price.
>
> >(A conductor who wants a low C#, because it sounds
> out of tune against
> >a low A, simply asks to play it as if it was a Db.)
> It's 'logic'
> >therefore for them to raise for example the F# in
> the key of G. In the
> >same time, musicians who play an instrument with
> flexible pitch, as the
> >violin, always say that the F# is attracted toward
> the G and 'therefore
> >should be sharpened'.
>

No, dont agree :))
Today a conductor dont ask nothing :) We can play
just without any help :))
The phenomen is logic because nobody play the same
frequence and in the result we have many choice ...

> >As Mr. Dimitrov says, as a violinist (!), why not
> 'normally' distant? I
> >wonder why as well. OK, undeniable, the
> leading-tone (la note sensible)
> >wants to go up to the tonic, but should we help it
> to make the move? On
> >my quartertone guitar a leadingtone going up
> precisely a quartertone
> >towards the tonic doesn't produce a dramatic result
> at all. It sounds
> >as if the note already half arrived and just needed
> to be tuned up a
> >little. If there is something as an attraction
> force, something you
> >lift up and than let it fall, perhaps a certain
> distance should be
> >respected to produce an effect.
>

What guitar do you had say ? :))

> I agree! From your experience, 50 cents is too
> narrow. Maybe the edge
> of a plausible and vivid ("incisive" is Paul E's
> term) minor second is
> around 70 cents (approximately 25:24). As with so
> many musical issues,
> taste will vary. I believe that Margo has said that
> she sometimes uses
> commas as melodic steps. That's _narrow_!
>

Dont forget = we use vibrato also :))

> >Besides, a F# higher than in 12-tet will sound
> pretty much out of tune
> >if played within a D or a D7. chord. So, I think I
> understand Mr.
> >Dimitrov's question, but still can't give a
> definite reply.
>
> Oh, absolutely. As if major thirds weren't bad
> enough already! I'd
> rather let the step grow, and (as I stated) take a
> smaller step from the
> other half of the tritone. Such an option is not,
> of course, possible
> in the more popular and historically accurate
> 5-limit tunings.
>
> JdL
>
Would one time for alls understanding what's all of
yours X-limit's :))
Pls !

Dimitrov

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--- In tuning@y..., paul@s... wrote:

> In this case it does so, and you're lucky :)

It's not luck--the smaller primes, because they *are* smaller, turn
up more and show up with powers.

In
> general I think you should just give whatever
> weight you think is appropriate to the consonant
> intervals; pinning dissonant intervals to just
> values is unjustified, in my opinion.

I wanted to see how well it worked, and when I got a known value I
came over here to talk about it instead of putting it up on the math
group; I thought someone might find it interesting.

Hi Dimitrov,

> I see what you mean, but (sorry for the joke) dont
> find one string "c" :))) I know -viola have that...
> My instrument is the violin...

Sorry about that. I used to play the cello a little,
some time back, and I don't have a cello or violin to hand.
Of course, violin lowest string is G so you don't have a
C string :-)

G G D G B D G B D F.
So it's the B on the G string. For the B on the E string
you need the third harmonic, and compare the two.

I think I've got it right now?

Of course, also a classically trained violinist would
prob. tune by tempered fifths rather than pure ones,
but for this experiment one would retune to pure fifths.

Robert

[Paul E wrote:]
>Playing and listening are primary . .
>. mathematics can only be a tool, and our models
>are never perfect . . . so one must always listen
>with a true and open heart, and with lots of
>patience (old habits die hard), and with
>knowledge of the testimonials of musicians of
>past generations.

Agreed on all counts. But, when knowledge and testimonials of the past
conflict with one's "true and open heart", what do you recommend?

[Paul:]
>Well, sure, all kinds of distortions can be fun.
>And for new music, use whatever paradigm you
>see fit!

The word "distortions" is a loaded one, but I do not want to dwell on
it. In some sense, all music is a "distortion" of actual life, an
artistic distillation of sounds which vaguely resemble sounds of nature.

Perhaps I'm flogging a dead horse; I know we've pretty much agreed to
disagree about what kind of treatments for old music sound best, but
I can't help but feel that you continuously interject the hint that it's
bad to touch past works. Thus the reference "for new music".

How do you feel about the following example? The Beatles cut from Sgt.
Pepper, "With a Little Help from My Friends." Here's a song that's in
2/4 time (or 4/4, depending on the construction of the measure), with
a one male singer and the instrumentation of a rock'n'roll group. Some
time later, a version of this song came out, in 3/4 time (or 6/8, I have
not seen the score), with several female voices doing harmony, different
chords, different pretty much everything. A total "distortion" of the
original, if you will, far more "egregious" than altering the tuning of
a dom 7th.

Is that cover "inappropriate"? Something that one should not "see fit"
to do, or even consider doing? I happen to think it's not bad, though I
prefer the original. But even if I thought it sucked, isn't its musical
value, or lack thereof, the important point, not its faithfulness to the
composers' vision?

I do not dispute the assertion that one should label one's alterations
clearly.

Isn't this an important point, and shouldn't we apply the same standards
to all music? 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.

JdL

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

> Nobody and never will like microtonal compositions :)

The scale of 12 equal semitones per octave is only a phenomenon of
the last 200 years and of European culture. If you think this is the
end-all and be-all of music, you are awfully ethnocentric and
temporocentric(?).

> The true music dont have one future in this
> direction...

Harry Partch, Ben Johnston, Wendy Carlos, Easley Blackwood, Jon
Catler, Erv Wilson, music of India, Arabia, Turkey, Indonesia,
Thailand . . . these musics inspire us and help us look farther into
the future than a narrow focus on Western conservatory tradition
since 1800 would allow.

> The rest is "bla bla " in french...
> Persisting or no...no way :)
> When I have asked if anyone believe in one universal
> base of temperament ...hmm my letter is been
> ...filtered !

What???

> Why ? And who do that ?

This is an open forum. No one can tamper with any posts. There must
have been a technical/internet problem. Please try to post that again.

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

> Nobody and never will like microtonal compositions :)

Lots of people like my microtonal compositions . . . there should be
a few more appearing in Tuning Punks shortly . . .

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

> When we play, we dont write :))
> We hear and try direct !
> And never divide the octave more that 12 steps...

Mozart himself specifically taught string players that C# is lower
than Db, etc . . . so if you're not dividing the octave into more
than 12 steps, you're disrespecting Mozart!

> If the intonation in the music has simple thing this
> forum =dont exist...
> The practic of playng any instrument is not easy about
> just intonation because if we play no only melodic
> mode we are disturbed by ! No one singer sing more one
> note at time :))
> I believe in one temperament "referance mode" ET 12,
> ok- but no octave based, no one interval based !
> Do you understand me ? I try to write english, ok...
> :))

Are you familiar with the theory and practice of meantone
temperament, which was the standard tuning system in the West c. 1480-
1780?

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

>
> I never will accept to have two places for C# and
> Db...
> It's false supposition...

Mozart taught that C# is lower than Db . . . this was the tuning
tradition for centuries already in Mozart's time.

> A propos ... You say unisson...Between C# and Db we
> have what ?

A diminished second.

--- In tuning@y..., "Robert Walker" <robertwalker@n...> wrote:

> Of course, also a classically trained violinist would
> prob. tune by tempered fifths rather than pure ones,

This is very rare. Most classical violinists tune by pure fifths.

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., paul@s... wrote:
>
> > In this case it does so, and you're lucky :)
>
> It's not luck--the smaller primes, because they *are* smaller, turn
> up more and show up with powers.

For this scale, they happen to . . . so you're lucky. For some other
scale, this might not be the case . . . for example, a just
interpretation of one of the MIRACLE scales is going to show higher
powers of 7 than of 5 or 3 . . . right?

Bob had said:
For example, we know that in western music harmony and melody
> interact polyphonically in ways that are fairly unique to this
> tradition. The melodic scales we use are FUNDAMENTALLY BASED on
> HARMONIC considerations.

Paul had replied:
I completely disagree. The melodic scales we use derive from a time
in our culture before harmony or polyphony were ever used. It is
lucky that they turned out to lend themselves to harmony with only
very minor modifications.

Bob answers:
Well, if the way harmony and melody interact in our tradition is not
fairly unique (thought "fairly" was a conservative term), then I'd
sure like to know about those traditions that are "fairly close" to
us in that regard. And as in many melodic traditions, especially
those that frequently use drones, even they had just relationships in
their structure.

As you well know (but seem to be ignoring for the moment?), the times
to which you refer used 3-limit JI, which is by definition
harmonically derived even if they didn't conceive of it that way. The
psychoacoustic basis for their prediliction for just fifths and
fourths had no dependence on their being explicitly aware it.

This is an important point, and it bears on universals implicit in a
common human perceptual metastructure INDEPENDENT of the age. This
has nothing to do with imposing current aesthetics on another
age!!!!!

Bob had also said:
So all this erudite talk of melodic considerations forcing
> compromises in harmonic considerations is a source of wonder to me.
> Here I have seen the same people who rail against the tendency in
> "expressive intonation" to reverse the size relationship of the
> smaller just chromatic half-step and larger just diatonic half-step
> turn right around and promote analagous things with other and even
> the same intervals with the same kind of melodic "justifications".

Paul had replied:
Hmm?

Bob answers:
What does "Hmm" mean? All of us familiar with JI know that the
diatonic half-step is over half again as wide as the chromatic. Some
of us have discussed at length and very critically the "expressive
intonation" advocates who feel that leading tones want to be skinny
and chromatic ones fat out of melodic considerations, and sometimes
actually reverse the JI size relationship, going beyond their
equalization by 12-tET. Yet I have seen threads here in which lesser
inclinations in the same direction are vigorously promoted as
melodically superior.

Paul had also replied:
And to both you and Gene: the major and minor modes of the diatonic
scale only relatively recently came to the fore. In older times, the
Dorian, Phrygian, Lydian, and Mixolydian modes were more important.>

Bob Answers:
I think most, if not everyone even a little versed in the "classical"
western tradition and the evolution of style from Gregorian chant
into Renaissance polyphony and beyond is at least vaguely cognizant
of this, to put it mildly! I savor the old modal flavors,
polyphonically as well as melodically, and have played with them
liberally, and even to some degree with historical allusions to
compositional elements of the pre V-I cadential formulae such as the
Landini cadence in what little dabbling I've done in modern
composition.

Bob had also said:
> Without harmonic considerations and no drone, melodic intervals are
> completely arbitrary.

Paul had replied:
You don't think one can hear, and sing, with a fair degree of
accuracy, the perfect fourth and fifth, melodically? Because that is
all that is needed to construct the diatonic scale melodically. It
has two identical tetrachords, a fourth or fifth apart, in _every_
octave species.

Bob answers:
Of course we can! I'm frankly at a loss to find any relevance to my
statements in this response, other than a "perfect" confirmation of
them. The perfect fourth and fifth are wonderful cases in point in
the argument for a harmonic basis underlying our melodic scales. What
intervals are more consonant harmonically than these?!

My statement here only says that WITHOUT any harmonic basis or even a
drone, there is no reason to choose such harmonic consonances over
any other arbitrary sequence of pitches. Some ethnic melodic
structures do not, and as long as they are melodic in this strictest
of senses, why should they? They would simply be sacrificing an
infinite potential for variation in melodic color with no harmonic
advantages to show for it.

On the other hand, arguments that I've run across here that there is
some melodic disadvantage in the difference between 8:9 and 9:10
whole steps in JI are totally puzzling to me. These intervals are
both stepwise and sequential in the harmonic series and differ by
only a microtonal comma! Their SLIGHTLY unequal division of the major
3rd is no different in principle from the division of the fifth into
major and minor thirds. Are we getting into some kind of melodic
"princess and the pea" syndrome here?

By contrast some absolutely beautiful middle eastern scales use
augmented seconds in alternation with diatonic half and whole steps
to create gorgeous melodic color in the absence of any significant
harmonic structure. Nevertheless, even these have their harmonic
derivations usually, if not always, even if they sometimes invoke the
use of higher primes.

Paul had also replied:
Bob, I think it's very important to sit down and read the aesthetic
opinions of musicians of the period in question, rather than impose
our own aesthetics upon their music.

Bob answers:
I don't think either Gene or I are promoting the imposition of our
easthetics upon another time. I believe we are both saying something
quite different. There are certain universals that apply to both
physical and psychoacoustics that are behind the demonstrable
preoccupation of cultures with the mathematics of music involving
whole number relationships between frequencies (in our terms, or
inversely, string lengths in theirs) over thousands of years.

Historical evidence must always be placed in the context of other
elements of reality, such as our observation that water runs
downhill. There are things about history we could not conclude from
the evidence if we didn't know that certain things remain common to
the physical universe in which we all have have lived, independent of
when we lived.

Often the historical evidence is ambiguous or inconclusive without
these considerations as a foundation for their interpretation. They
then become the fundamental context without which the historical
evidence would have no meaning.

There are even times when our conclusions rest less on physical and
more on emotional or psychological commonalities that remain
relatively stable over millenia. This is less reliable, but sometimes
still necessary. And then there is the elusive element of good old
common sense and deeper human insight. Of course, who has and doesn't
have these becomes a very difficult issue to resolve.

--- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:
> [Paul E wrote:]
> >Playing and listening are primary . .
> >. mathematics can only be a tool, and our models
> >are never perfect . . . so one must always listen
> >with a true and open heart, and with lots of
> >patience (old habits die hard), and with
> >knowledge of the testimonials of musicians of
> >past generations.
>
> Agreed on all counts. But, when knowledge and testimonials of the
past
> conflict with one's "true and open heart", what do you recommend?

Hmm . . . what was the context again? I don't want to generalize
beyond the immediate topic I was responding to. What's with
the " . . . ."'s?
>
> Perhaps I'm flogging a dead horse; I know we've pretty much agreed
to
> disagree about what kind of treatments for old music sound best, but
> I can't help but feel that you continuously interject the hint that
it's
> bad to touch past works. Thus the reference "for new music".

Well, if you're a concert director and you're going to present a
performance of an old piece of music, don't you think it's worth _a
bit_ of consideration into the historically appropriate instruments,
tempo, dynamics, and tuning? I'm already meeting you more than half
way by accepting your spring model and all its premises.

> How do you feel about the following example? The Beatles cut from
Sgt.
> Pepper, "With a Little Help from My Friends." Here's a song that's
in
> 2/4 time (or 4/4, depending on the construction of the measure),
with
> a one male singer and the instrumentation of a rock'n'roll group.
Some
> time later, a version of this song came out, in 3/4 time (or 6/8, I
have
> not seen the score), with several female voices doing harmony,
different
> chords, different pretty much everything. A total "distortion" of
the
> original, if you will, far more "egregious" than altering the
tuning of
> a dom 7th.
>
> Is that cover "inappropriate"?

No.

> Something that one should not "see fit"
> to do, or even consider doing?

Who suggested anything like that? Not me!

OK, the rest of this message had nothing to do with me. Who are you
talking to?
>
> I do hope that faithful renditions of old works remain in our ears,
as
> a point of comparison if nothing else.
>
Me too. Never claimed anything beyond that. More Switched-on, Swingle-
sung, Disco Bach, please! :)

--- In tuning@y..., paul@s... wrote:

> > It's not luck--the smaller primes, because they *are* smaller,
turn
> > up more and show up with powers.

> For this scale, they happen to . . . so you're lucky. For some
other
> scale, this might not be the case . . . for example, a just
> interpretation of one of the MIRACLE scales is going to show higher
> powers of 7 than of 5 or 3 . . . right?

You still seem to be missing the point--if a scale shows more powers
of 7, then that tells us we had better have good approximations of
the 7's. The weighting introduced automatically by optimizing to
scale steps should therefore correspond, more or less, to what we
want.

--- In tuning@y..., BobWendell@t... wrote:
> Bob had said:
> For example, we know that in western music harmony and melody
> > interact polyphonically in ways that are fairly unique to this
> > tradition. The melodic scales we use are FUNDAMENTALLY BASED on
> > HARMONIC considerations.
>
> Paul had replied:
> I completely disagree. The melodic scales we use derive from a time
> in our culture before harmony or polyphony were ever used. It is
> lucky that they turned out to lend themselves to harmony with only
> very minor modifications.
>
> Bob answers:
> Well, if the way harmony and melody interact in our tradition is
not
> fairly unique (thought "fairly" was a conservative term), then I'd
> sure like to know about those traditions that are "fairly close" to
> us in that regard.

I only disgreed with your last sentence: "The melodic scales we use
are FUNDAMENTALLY BASED on HARMONIC considerations".

> And as in many melodic traditions, especially
> those that frequently use drones, even they had just relationships
in
> their structure.

They did, but melodic considerations come into play too -- why does
the Indian diatonic scale (like a "major" scale) use 27/16 instead of
5/3?
>
> As you well know (but seem to be ignoring for the moment?), the
times
> to which you refer used 3-limit JI, which is by definition
> harmonically derived even if they didn't conceive of it that way.

If it was derived from music with no harmony, how can you say it was
harmonically derived?

> The
> psychoacoustic basis for their prediliction for just fifths and
> fourths had no dependence on their being explicitly aware it.

Agreed . . . but harmonically derived? And beyond fifths and fourths,
no just intervals can be "melodically derived", IMO.

> This is an important point, and it bears on universals implicit in
a
> common human perceptual metastructure INDEPENDENT of the age. This
> has nothing to do with imposing current aesthetics on another
> age!!!!!

Why is it that the music of so many cultures seems to violate the
supposed "universals implicit in a common human perceptual
metastructure" as understood by listeners of another culture?
>
> Bob had also said:
> So all this erudite talk of melodic considerations forcing
> > compromises in harmonic considerations is a source of wonder to
me.
> > Here I have seen the same people who rail against the tendency in
> > "expressive intonation" to reverse the size relationship of the
> > smaller just chromatic half-step and larger just diatonic half-
step
> > turn right around and promote analagous things with other and
even
> > the same intervals with the same kind of melodic "justifications".
>
> Paul had replied:
> Hmm?
>
> Bob answers:
> What does "Hmm" mean?

It means "what exactly are you talking about"?

All of us familiar with JI know that the
> diatonic half-step is over half again as wide as the chromatic.
Some
> of us have discussed at length and very critically the "expressive
> intonation" advocates who feel that leading tones want to be skinny
> and chromatic ones fat out of melodic considerations, and sometimes
> actually reverse the JI size relationship, going beyond their
> equalization by 12-tET. Yet I have seen threads here in which
lesser
> inclinations in the same direction are vigorously promoted as
> melodically superior.

That wouldn't be me . . . would it?
>
>
> Bob had also said:
> > Without harmonic considerations and no drone, melodic intervals
are
> > completely arbitrary.
>
> Paul had replied:
> You don't think one can hear, and sing, with a fair degree of
> accuracy, the perfect fourth and fifth, melodically? Because that
is
> all that is needed to construct the diatonic scale melodically. It
> has two identical tetrachords, a fourth or fifth apart, in _every_
> octave species.
>
> Bob answers:
> Of course we can! I'm frankly at a loss to find any relevance to my
> statements in this response, other than a "perfect" confirmation of
> them. The perfect fourth and fifth are wonderful cases in point in
> the argument for a harmonic basis underlying our melodic scales.
What
> intervals are more consonant harmonically than these?!

It's quite different to say, "some melodically important intervals
coincide with harmonically important ones", than to say, "the melodic
scales are harmonically based".
>
> My statement here only says that WITHOUT any harmonic basis or even
a
> drone, there is no reason to choose such harmonic consonances over
> any other arbitrary sequence of pitches. Some ethnic melodic
> structures do not,

True, but fifths and fourths are much more common than they should
be "randomly".

> and as long as they are melodic in this strictest
> of senses, why should they? They would simply be sacrificing an
> infinite potential for variation in melodic color with no harmonic
> advantages to show for it.

There's a melodic advantage to being able to take compositional use
of audible similarity relations within the musical materials.

> On the other hand, arguments that I've run across here that there
is
> some melodic disadvantage in the difference between 8:9 and 9:10
> whole steps in JI are totally puzzling to me. These intervals are
> both stepwise and sequential in the harmonic series and differ by
> only a microtonal comma! Their SLIGHTLY unequal division of the
major
> 3rd is no different in principle from the division of the fifth
into
> major and minor thirds.

I think I've answered this latter contention sufficiently already. As
to the former, I'm disturbed by the melodic difference between 8:9
and 9:10 in 27-tET (where they're 44 cents different) but not often
in JI. There have been a few examples, though, in the strict-JI
renditions of Western music I've heard . . . have you heard any?

> By contrast some absolutely beautiful middle eastern scales use
> augmented seconds in alternation with diatonic half and whole steps
> to create gorgeous melodic color in the absence of any significant
> harmonic structure.

Yup!

Nevertheless, even these have their harmonic
> derivations usually, if not always, even if they sometimes invoke
the
> use of higher primes.

I dispute these derivations. You can describe any conceivable scale
in terms of higher primes, but that doesn't constitute
a "derivation". You have to show that the scale was somehow
influenced by these particular higher primes, as opposed to some
simpler hypothesis (such as a random "frozen accident" hypothesis).

> are certain universals that apply to both
> physical and psychoacoustics that are behind the demonstrable
> preoccupation of cultures with the mathematics of music involving
> whole number relationships between frequencies (in our terms, or
> inversely, string lengths in theirs) over thousands of years.

Most cultures have not been so preoccupied. But I'm mostly on your
side about psychoacoustics being relevant to music . . . compared
with the nutty professor (great movie, just watched it).

> Historical evidence must always be placed in the context of other
> elements of reality, such as our observation that water runs
> downhill. There are things about history we could not conclude from
> the evidence if we didn't know that certain things remain common to
> the physical universe in which we all have have lived, independent
of
> when we lived.

There's a long, long, long, long jump between our understanding of
the physical universe and our understanding of past musical practice.

> Often the historical evidence is ambiguous or inconclusive without
> these considerations as a foundation for their interpretation. They
> then become the fundamental context without which the historical
> evidence would have no meaning.

True.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> Agreed . . . but harmonically derived? And beyond fifths and
fourths,
> no just intervals can be "melodically derived", IMO.

I think other intervals have their own melodic effect. One can just
put FTS into gear and see how that works; I've been noticing how
pleasant those evil 5s sound simply as melody.

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

> Well, if you're a concert director and you're going to present a
> performance of an old piece of music, don't you think it's worth _a
> bit_ of consideration into the historically appropriate
instruments,
> tempo, dynamics, and tuning?

The authentic performence music has lead to a lot of fine things, but
I don't think it proves that a Hogwood interpretation of a Beethoven
symphony *must* be preferred over Furtwaengler.

Dont agree, Paul :)

Robert say one very important think about how the
violinist modern tune the fifth's !!!
Me too...
But not more that one bit per sec :)))

Dimitrov

--- Paul Erlich <paul@stretch-music.com> a �crit�: >
--- In tuning@y..., "Robert Walker"
> <robertwalker@n...> wrote:
>
> > Of course, also a classically trained violinist
> would
> > prob. tune by tempered fifths rather than pure
> ones,
>
> This is very rare. Most classical violinists tune by
> pure fifths.
>
>

___________________________________________________________
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[Paul E wrote:]
>>>Playing and listening are primary . .
>>>. mathematics can only be a tool, and our models
>>>are never perfect . . . so one must always listen
>>>with a true and open heart, and with lots of
>>>patience (old habits die hard), and with
>>>knowledge of the testimonials of musicians of
>>>past generations.

[I wrote:]
>>Agreed on all counts. But, when knowledge and testimonials of the
>>past conflict with one's "true and open heart", what do you recommend?

[Paul:]
>Hmm . . . what was the context again? I don't want to generalize
>beyond the immediate topic I was responding to. What's with
>the " . . . ."'s?

The quotes? I'm quoting your words immediately above, nothing more.

[JdL:]
>>Perhaps I'm flogging a dead horse; I know we've pretty much agreed to
>>disagree about what kind of treatments for old music sound best, but
>>I can't help but feel that you continuously interject the hint that
>>it's bad to touch past works. Thus the reference "for new music".

[Paul:]
>Well, if you're a concert director and you're going to present a
>performance of an old piece of music, don't you think it's worth _a
>bit_ of consideration into the historically appropriate instruments,
>tempo, dynamics, and tuning?

Yes, the more knowledge one has, the better.

>I'm already meeting you more than half way by accepting your spring
>model and all its premises.

Huh? What's the connection? That model is just one way to tune. I'm
asking a more general question.

[JdL:]
>>How do you feel about the following example? The Beatles cut from
>>Sgt. Pepper, "With a Little Help from My Friends." Here's a song
>>that's in 2/4 time (or 4/4, depending on the construction of the
>>measure), with a one male singer and the instrumentation of a
>>rock'n'roll group. Some time later, a version of this song came out,
>>in 3/4 time (or 6/8, I have not seen the score), with several female
>>voices doing harmony, different chords, different pretty much
>>everything. A total "distortion" of the original, if you will, far
>>more "egregious" than altering the tuning of a dom 7th.

>>Is that cover "inappropriate"?

[Paul:]
>No.

>>Something that one should not "see fit" to do, or even consider doing?

[Paul:]
>Who suggested anything like that? Not me!

Good...

>OK, the rest of this message had nothing to do with me. Who are you
>talking to?

I'm talking to _you_, and I'm asking if the same principles that apply
to the Beatles should or should not apply to past composers. I am very
sorry if you found my post offensive (?). I'm at a bit of a loss to
know what to make of your reply, but I _think_ you're agreeing with me.

[JdL:]
>>I do hope that faithful renditions of old works remain in our ears, as
>>a point of comparison if nothing else.

>Me too. Never claimed anything beyond that. More Switched-on, Swingle-
>sung, Disco Bach, please! :)

There will always be crap. The good news is that it never lasts very
long, while the good stuff does.

JdL

Well, Paul, you seem to insist that the human ear's gravitation
toward the melodic use of perfect fifths and fourths has nothing to
do with the fundamental psychoacoustic preferences for just intervals
that forms the basis of harmonic structure.

I have witnessed and used in choral training for many years now the
power of just intervals and the inherent attraction in them for the
most innocent and musically untrained and unprejudiced of human ears.
The perfect fourth and fifth are the most powerful of all, since they
form the simplest harmonic relationships and their acoustic
components are most intimately and obviously related to the
fundamental.

It seems implicit in your comments from where I sit that you have
therefore concluded that this exceptionally great power somehow takes
these relationships out of the realm of harmonic consideration and
qualifies them as purely melodic in nature. I would posit that this
great power is harmonic in nature in the most FUNDAMENTAL sense.

If you assume that the third harmonic is so prominent in some timbres
that this qualifies the fourths and fifths as fundamentally melodic,
I would humbly submit that this is a kind of useless, even
counterproductive semantic play. These HARMONICS and any other of the
lower ones, as I cannot imagine you would fail to agree, form a
basis at a very FUNDAMENTAL level for harmonic structure in music.

I would further posit that the often, even usually UNCONSCIOUS
preference of the human ear for these relationships melodically or
otherwise has its basis in their HARMONIC power, independent of when
harmony began to evolve as a consciously recognized component of
musical structure.

Why don't we ask ourselves on what basis harmony began to evolve in
the first place? Surely no one thinks it was purely random
happenstance with no physical or psychoacoustic basis whatsoever.
Whether a particular culture was consciously aware of harmony or
harmonic considerations of any kind is utterly beside the point from
the fundmental perspective of the time- and culture-independent
physical acoustic and psychoacoustic phenomena to which I refer.

As I have stated before in other threads, there is another side to
harmonic relationships that I have personally and empirically found
to be more powerful and reliable by far than the intuitive perception
of harmonic overtones in musical timbres. The harmonically (make that
also coherently) related DIFFERENCE PRODUCTS of justly related tones
are incredibly powerful tools for developing the intuitive
recognition of just intervals.

In the case of the perfect fifth, the primary difference product is
an octave below the lower note of the interval. This is by far the
simplest, most intimate, and most powerful relationship that can
exist bewtween any two harmonically related tones.

In my humble opinion and quite a lot of significant evidence, this is
a timeless universal that has both a physical and neurological basis.
The physical basis is well-understood in electronics and analog
signal processing. It has nothing to with imposing the aesthetics of
one culture on another. And it does NOT represent, as you seem to
declare, either a physical OR a neurological reality that is "a long,
long way from past musical practice".

Let's try to get past academic nit-picking and be practical. A lot of
music history is a record of practice and practical musical
considerations. We cannot interpret it intelligently divorced from
the context of an essential and deep perspective based on first
principles that derive directly from, yes, timeless universals, both
human and physical.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., BobWendell@t... wrote:
> > Bob had said:
> > For example, we know that in western music harmony and melody
> > > interact polyphonically in ways that are fairly unique to this
> > > tradition. The melodic scales we use are FUNDAMENTALLY BASED on
> > > HARMONIC considerations.
> >
> > Paul had replied:
> > I completely disagree. The melodic scales we use derive from a
time
> > in our culture before harmony or polyphony were ever used. It is
> > lucky that they turned out to lend themselves to harmony with
only
> > very minor modifications.
> >
> > Bob answers:
> > Well, if the way harmony and melody interact in our tradition is
> not
> > fairly unique (thought "fairly" was a conservative term), then
I'd
> > sure like to know about those traditions that are "fairly close"
to
> > us in that regard.
>
> I only disgreed with your last sentence: "The melodic scales we use
> are FUNDAMENTALLY BASED on HARMONIC considerations".
>
> > And as in many melodic traditions, especially
> > those that frequently use drones, even they had just
relationships
> in
> > their structure.
>
> They did, but melodic considerations come into play too -- why does
> the Indian diatonic scale (like a "major" scale) use 27/16 instead
of
> 5/3?
> >
> > As you well know (but seem to be ignoring for the moment?), the
> times
> > to which you refer used 3-limit JI, which is by definition
> > harmonically derived even if they didn't conceive of it that way.
>
> If it was derived from music with no harmony, how can you say it
was
> harmonically derived?
>
> > The
> > psychoacoustic basis for their prediliction for just fifths and
> > fourths had no dependence on their being explicitly aware it.
>
> Agreed . . . but harmonically derived? And beyond fifths and
fourths,
> no just intervals can be "melodically derived", IMO.
>
> > This is an important point, and it bears on universals implicit
in
> a
> > common human perceptual metastructure INDEPENDENT of the age.
This
> > has nothing to do with imposing current aesthetics on another
> > age!!!!!
>
> Why is it that the music of so many cultures seems to violate the
> supposed "universals implicit in a common human perceptual
> metastructure" as understood by listeners of another culture?
> >
> > Bob had also said:
> > So all this erudite talk of melodic considerations forcing
> > > compromises in harmonic considerations is a source of wonder to
> me.
> > > Here I have seen the same people who rail against the tendency
in
> > > "expressive intonation" to reverse the size relationship of the
> > > smaller just chromatic half-step and larger just diatonic half-
> step
> > > turn right around and promote analagous things with other and
> even
> > > the same intervals with the same kind of melodic
"justifications".
> >
> > Paul had replied:
> > Hmm?
> >
> > Bob answers:
> > What does "Hmm" mean?
>
> It means "what exactly are you talking about"?
>
> All of us familiar with JI know that the
> > diatonic half-step is over half again as wide as the chromatic.
> Some
> > of us have discussed at length and very critically the
"expressive
> > intonation" advocates who feel that leading tones want to be
skinny
> > and chromatic ones fat out of melodic considerations, and
sometimes
> > actually reverse the JI size relationship, going beyond their
> > equalization by 12-tET. Yet I have seen threads here in which
> lesser
> > inclinations in the same direction are vigorously promoted as
> > melodically superior.
>
> That wouldn't be me . . . would it?
> >
> >
> > Bob had also said:
> > > Without harmonic considerations and no drone, melodic intervals
> are
> > > completely arbitrary.
> >
> > Paul had replied:
> > You don't think one can hear, and sing, with a fair degree of
> > accuracy, the perfect fourth and fifth, melodically? Because that
> is
> > all that is needed to construct the diatonic scale melodically.
It
> > has two identical tetrachords, a fourth or fifth apart, in
_every_
> > octave species.
> >
> > Bob answers:
> > Of course we can! I'm frankly at a loss to find any relevance to
my
> > statements in this response, other than a "perfect" confirmation
of
> > them. The perfect fourth and fifth are wonderful cases in point
in
> > the argument for a harmonic basis underlying our melodic scales.
> What
> > intervals are more consonant harmonically than these?!
>
> It's quite different to say, "some melodically important intervals
> coincide with harmonically important ones", than to say, "the
melodic
> scales are harmonically based".
> >
> > My statement here only says that WITHOUT any harmonic basis or
even
> a
> > drone, there is no reason to choose such harmonic consonances
over
> > any other arbitrary sequence of pitches. Some ethnic melodic
> > structures do not,
>
> True, but fifths and fourths are much more common than they should
> be "randomly".
>
> > and as long as they are melodic in this strictest
> > of senses, why should they? They would simply be sacrificing an
> > infinite potential for variation in melodic color with no
harmonic
> > advantages to show for it.
>
> There's a melodic advantage to being able to take compositional use
> of audible similarity relations within the musical materials.
>
> > On the other hand, arguments that I've run across here that there
> is
> > some melodic disadvantage in the difference between 8:9 and 9:10
> > whole steps in JI are totally puzzling to me. These intervals are
> > both stepwise and sequential in the harmonic series and differ by
> > only a microtonal comma! Their SLIGHTLY unequal division of the
> major
> > 3rd is no different in principle from the division of the fifth
> into
> > major and minor thirds.
>
> I think I've answered this latter contention sufficiently already.
As
> to the former, I'm disturbed by the melodic difference between 8:9
> and 9:10 in 27-tET (where they're 44 cents different) but not often
> in JI. There have been a few examples, though, in the strict-JI
> renditions of Western music I've heard . . . have you heard any?
>
> > By contrast some absolutely beautiful middle eastern scales use
> > augmented seconds in alternation with diatonic half and whole
steps
> > to create gorgeous melodic color in the absence of any
significant
> > harmonic structure.
>
> Yup!
>
> Nevertheless, even these have their harmonic
> > derivations usually, if not always, even if they sometimes invoke
> the
> > use of higher primes.
>
> I dispute these derivations. You can describe any conceivable scale
> in terms of higher primes, but that doesn't constitute
> a "derivation". You have to show that the scale was somehow
> influenced by these particular higher primes, as opposed to some
> simpler hypothesis (such as a random "frozen accident" hypothesis).
>
> > are certain universals that apply to both
> > physical and psychoacoustics that are behind the demonstrable
> > preoccupation of cultures with the mathematics of music involving
> > whole number relationships between frequencies (in our terms, or
> > inversely, string lengths in theirs) over thousands of years.
>
> Most cultures have not been so preoccupied. But I'm mostly on your
> side about psychoacoustics being relevant to music . . . compared
> with the nutty professor (great movie, just watched it).
>
> > Historical evidence must always be placed in the context of other
> > elements of reality, such as our observation that water runs
> > downhill. There are things about history we could not conclude
from
> > the evidence if we didn't know that certain things remain common
to
> > the physical universe in which we all have have lived,
independent
> of
> > when we lived.
>
> There's a long, long, long, long jump between our understanding of
> the physical universe and our understanding of past musical
practice.
>
> > Often the historical evidence is ambiguous or inconclusive
without
> > these considerations as a foundation for their interpretation.
They
> > then become the fundamental context without which the historical
> > evidence would have no meaning.
>
> True.

Bob had said:
> My statement here only says that WITHOUT any harmonic basis or even
a
> drone, there is no reason to choose such harmonic consonances over
> any other arbitrary sequence of pitches. Some ethnic melodic
> structures do not,

Paul had replied:
True, but fifths and fourths are much more common than they should
be "randomly".

Bob answers:
Precisely my point! To me it seems crystal clear that there is a
psychoacoustic basis at the root of the tendency for harmonic systems
to ever develop that explains why fourths and fifths are so
universally preferred above random choices.

The psychoacoustic phenomena that predispose humans from a large
variety of cultures across thousands of years to these very specific
and precise intervals are what I meant by "the universals implicit in
a common human perceptual metastructure INDEPENDENT of the age." This
has nothing to do with imposing current aesthetics on another
age!!!!!

But Pual had already answered:
> Why is it that the music of so many cultures seems to violate the
> supposed "universals implicit in a common human perceptual
> metastructure" as understood by listeners of another culture?

Bob Answers:
Why is this reply so off the point as are so many others?! And there
often seems to be a tremendous lack context, of taking the points
separately with no regard for how other intimately related points
tie it all together and eliminate the ambiguities of interpretation
that otherwise generate such wide misses.

I feel like I'm continually having to plug up a whole in this part of
the dyke, then am forced to run over to another one, unplugging the
first. Maybe it's my fault, but I'm trying to be as clear as
possible. Please allow for a coherent, unifying foundation for my
points that should be accumulating in your awareness, but for
whatever reason, are not.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., BobWendell@t... wrote:
> > Bob had said:
> > For example, we know that in western music harmony and melody
> > > interact polyphonically in ways that are fairly unique to this
> > > tradition. The melodic scales we use are FUNDAMENTALLY BASED on
> > > HARMONIC considerations.
> >
> > Paul had replied:
> > I completely disagree. The melodic scales we use derive from a
time
> > in our culture before harmony or polyphony were ever used. It is
> > lucky that they turned out to lend themselves to harmony with
only
> > very minor modifications.
> >
> > Bob answers:
> > Well, if the way harmony and melody interact in our tradition is
> not
> > fairly unique (thought "fairly" was a conservative term), then
I'd
> > sure like to know about those traditions that are "fairly close"
to
> > us in that regard.
>
> I only disgreed with your last sentence: "The melodic scales we use
> are FUNDAMENTALLY BASED on HARMONIC considerations".
>
> > And as in many melodic traditions, especially
> > those that frequently use drones, even they had just
relationships
> in
> > their structure.
>
> They did, but melodic considerations come into play too -- why does
> the Indian diatonic scale (like a "major" scale) use 27/16 instead
of
> 5/3?
> >
> > As you well know (but seem to be ignoring for the moment?), the
> times
> > to which you refer used 3-limit JI, which is by definition
> > harmonically derived even if they didn't conceive of it that way.
>
> If it was derived from music with no harmony, how can you say it
was
> harmonically derived?
>
> > The
> > psychoacoustic basis for their prediliction for just fifths and
> > fourths had no dependence on their being explicitly aware it.
>
> Agreed . . . but harmonically derived? And beyond fifths and
fourths,
> no just intervals can be "melodically derived", IMO.
>
> > This is an important point, and it bears on universals implicit
in
> a
> > common human perceptual metastructure INDEPENDENT of the age.
This
> > has nothing to do with imposing current aesthetics on another
> > age!!!!!
>
> Why is it that the music of so many cultures seems to violate the
> supposed "universals implicit in a common human perceptual
> metastructure" as understood by listeners of another culture?
> >
> > Bob had also said:
> > So all this erudite talk of melodic considerations forcing
> > > compromises in harmonic considerations is a source of wonder to
> me.
> > > Here I have seen the same people who rail against the tendency
in
> > > "expressive intonation" to reverse the size relationship of the
> > > smaller just chromatic half-step and larger just diatonic half-
> step
> > > turn right around and promote analagous things with other and
> even
> > > the same intervals with the same kind of melodic
"justifications".
> >
> > Paul had replied:
> > Hmm?
> >
> > Bob answers:
> > What does "Hmm" mean?
>
> It means "what exactly are you talking about"?
>
> All of us familiar with JI know that the
> > diatonic half-step is over half again as wide as the chromatic.
> Some
> > of us have discussed at length and very critically the
"expressive
> > intonation" advocates who feel that leading tones want to be
skinny
> > and chromatic ones fat out of melodic considerations, and
sometimes
> > actually reverse the JI size relationship, going beyond their
> > equalization by 12-tET. Yet I have seen threads here in which
> lesser
> > inclinations in the same direction are vigorously promoted as
> > melodically superior.
>
> That wouldn't be me . . . would it?
> >
> >
> > Bob had also said:
> > > Without harmonic considerations and no drone, melodic intervals
> are
> > > completely arbitrary.
> >
> > Paul had replied:
> > You don't think one can hear, and sing, with a fair degree of
> > accuracy, the perfect fourth and fifth, melodically? Because that
> is
> > all that is needed to construct the diatonic scale melodically.
It
> > has two identical tetrachords, a fourth or fifth apart, in
_every_
> > octave species.
> >
> > Bob answers:
> > Of course we can! I'm frankly at a loss to find any relevance to
my
> > statements in this response, other than a "perfect" confirmation
of
> > them. The perfect fourth and fifth are wonderful cases in point
in
> > the argument for a harmonic basis underlying our melodic scales.
> What
> > intervals are more consonant harmonically than these?!
>
> It's quite different to say, "some melodically important intervals
> coincide with harmonically important ones", than to say, "the
melodic
> scales are harmonically based".
> >
> > My statement here only says that WITHOUT any harmonic basis or
even
> a
> > drone, there is no reason to choose such harmonic consonances
over
> > any other arbitrary sequence of pitches. Some ethnic melodic
> > structures do not,
>
> True, but fifths and fourths are much more common than they should
> be "randomly".
>
> > and as long as they are melodic in this strictest
> > of senses, why should they? They would simply be sacrificing an
> > infinite potential for variation in melodic color with no
harmonic
> > advantages to show for it.
>
> There's a melodic advantage to being able to take compositional use
> of audible similarity relations within the musical materials.
>
> > On the other hand, arguments that I've run across here that there
> is
> > some melodic disadvantage in the difference between 8:9 and 9:10
> > whole steps in JI are totally puzzling to me. These intervals are
> > both stepwise and sequential in the harmonic series and differ by
> > only a microtonal comma! Their SLIGHTLY unequal division of the
> major
> > 3rd is no different in principle from the division of the fifth
> into
> > major and minor thirds.
>
> I think I've answered this latter contention sufficiently already.
As
> to the former, I'm disturbed by the melodic difference between 8:9
> and 9:10 in 27-tET (where they're 44 cents different) but not often
> in JI. There have been a few examples, though, in the strict-JI
> renditions of Western music I've heard . . . have you heard any?
>
> > By contrast some absolutely beautiful middle eastern scales use
> > augmented seconds in alternation with diatonic half and whole
steps
> > to create gorgeous melodic color in the absence of any
significant
> > harmonic structure.
>
> Yup!
>
> Nevertheless, even these have their harmonic
> > derivations usually, if not always, even if they sometimes invoke
> the
> > use of higher primes.
>
> I dispute these derivations. You can describe any conceivable scale
> in terms of higher primes, but that doesn't constitute
> a "derivation". You have to show that the scale was somehow
> influenced by these particular higher primes, as opposed to some
> simpler hypothesis (such as a random "frozen accident" hypothesis).
>
> > are certain universals that apply to both
> > physical and psychoacoustics that are behind the demonstrable
> > preoccupation of cultures with the mathematics of music involving
> > whole number relationships between frequencies (in our terms, or
> > inversely, string lengths in theirs) over thousands of years.
>
> Most cultures have not been so preoccupied. But I'm mostly on your
> side about psychoacoustics being relevant to music . . . compared
> with the nutty professor (great movie, just watched it).
>
> > Historical evidence must always be placed in the context of other
> > elements of reality, such as our observation that water runs
> > downhill. There are things about history we could not conclude
from
> > the evidence if we didn't know that certain things remain common
to
> > the physical universe in which we all have have lived,
independent
> of
> > when we lived.
>
> There's a long, long, long, long jump between our understanding of
> the physical universe and our understanding of past musical
practice.
>
> > Often the historical evidence is ambiguous or inconclusive
without
> > these considerations as a foundation for their interpretation.
They
> > then become the fundamental context without which the historical
> > evidence would have no meaning.
>
> True.

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., paul@s... wrote:
>
> > > It's not luck--the smaller primes, because they *are* smaller,
> turn
> > > up more and show up with powers.
>
> > For this scale, they happen to . . . so you're lucky. For some
> other
> > scale, this might not be the case . . . for example, a just
> > interpretation of one of the MIRACLE scales is going to show
higher
> > powers of 7 than of 5 or 3 . . . right?
>
> You still seem to be missing the point--if a scale shows more
powers
> of 7, then that tells us we had better have good approximations of
> the 7's.

I disagree! I only care that each consonant ratio of 7 is
approximated well . . . if large errors accumulate in a long chain of
ratios of 7 relative to JI, I DON'T CARE, in fact I might like that
if it makes new features possible.

> The weighting introduced automatically by optimizing to
> scale steps should therefore correspond, more or less, to what we
> want.

Nosireebob!

--- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:

> I'm talking to _you_, and I'm asking if the same principles that
apply
> to the Beatles should or should not apply to past composers.

I'm all in favor of creative re-interpretations. But there's a
difference. The classical composers did not _record_ their own music.
They wrote it out to be played by others. Thus if you turn on the
radio and are told "that was Bach" or "that was Mozart" without
further qualification, I would expect that the performers tried to be
faithful to the score and to the performance practices of the time.
If you are told "that was the Beatles" without further qualification,
I would expect that to be an actual Beatles recording, and not a
cover.

> >Me too. Never claimed anything beyond that. More Switched-on,
Swingle-
> >sung, Disco Bach, please! :)
>
> There will always be crap.

I _like_ Switched-on and Swingle-sung Bach!

--- In tuning@y..., BobWendell@t... wrote:
> Well, Paul, you seem to insist that the human ear's gravitation
> toward the melodic use of perfect fifths and fourths has nothing to
> do with the fundamental psychoacoustic preferences for just
intervals
> that forms the basis of harmonic structure.

Not "nothing to do".
>
> It seems implicit in your comments from where I sit that you have
> therefore concluded that this exceptionally great power somehow
takes
> these relationships out of the realm of harmonic consideration and
> qualifies them as purely melodic in nature. I would posit that this
> great power is harmonic in nature in the most FUNDAMENTAL sense.

I guess it all depends on how you define "harmonic".
>
> If you assume that the third harmonic is so prominent in some
timbres
> that this qualifies the fourths and fifths as fundamentally melodic,

Where did I assume that? No, I don't think prominence of partials has
much to do with it -- in fact, the attraction to some sort of
approximate fourths and fifths persists with timbres that have no
such partials.
>
> As I have stated before in other threads, there is another side to
> harmonic relationships that I have personally and empirically found
> to be more powerful and reliable by far than the intuitive
perception
> of harmonic overtones in musical timbres. The harmonically (make
that
> also coherently) related DIFFERENCE PRODUCTS of justly related
tones
> are incredibly powerful tools for developing the intuitive
> recognition of just intervals.

These combinational tones are only possible when harmony (that is,
simultaneous sounding of tones) is being used (and at a loud volume).
I don't see the relevance of combinational tones to melody, or to the
construction of scales to be used only for melody.

--- In tuning@y..., BobWendell@t... wrote:
> Bob had said:
> > My statement here only says that WITHOUT any harmonic basis or
even
> a
> > drone, there is no reason to choose such harmonic consonances
over
> > any other arbitrary sequence of pitches. Some ethnic melodic
> > structures do not,
>
> Paul had replied:
> True, but fifths and fourths are much more common than they should
> be "randomly".
>
> Bob answers:
> Precisely my point! To me it seems crystal clear that there is a
> psychoacoustic basis at the root of the tendency for harmonic
systems
> to ever develop that explains why fourths and fifths are so
> universally preferred above random choices.

OK. But "harmonically based" to me means "based on the qualities of
the simultaneous sounding of tones". If you didn't mean that then
fine.
>
> The psychoacoustic phenomena that predispose humans from a large
> variety of cultures across thousands of years to these very
specific
> and precise intervals are what I meant by "the universals implicit
in
> a common human perceptual metastructure INDEPENDENT of the age."
This
> has nothing to do with imposing current aesthetics on another
> age!!!!!
>
> But Pual had already answered:
> > Why is it that the music of so many cultures seems to violate the
> > supposed "universals implicit in a common human perceptual
> > metastructure" as understood by listeners of another culture?
>
> Bob Answers:
> Why is this reply so off the point as are so many others?!

Maybe I'm not communicating well. It's not off the point at all. I'm
just trying to point out that understanding music of another age
must, like understanding the music of another culture, be fraught
with all sorts of perils and traps when one tries to frame the issues
in terms of "universals implicit in a common human perceptual
metastructure".

> And there
> often seems to be a tremendous lack context, of taking the points
> separately with no regard for how other intimately related points
> tie it all together and eliminate the ambiguities of interpretation
> that otherwise generate such wide misses.
>
> I feel like I'm continually having to plug up a whole in this part
of
> the dyke, then am forced to run over to another one, unplugging the
> first. Maybe it's my fault, but I'm trying to be as clear as
> possible. Please allow for a coherent, unifying foundation for my
> points that should be accumulating in your awareness, but for
> whatever reason, are not.

That goes both ways. Vice-versa. Communications are poor right now.

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

> Thus if you turn on the
> radio and are told "that was Bach" or "that was Mozart" without
> further qualification, I would expect that the performers tried to
be
> faithful to the score and to the performance practices of the time.

You can expect this if you must but even today you really should not,
and formerly you could expect just the opposite for anything from
very far back in the past. Even now, if you listen to older
recordings you might well wonder how authentically we are performing
Verdi these days, much less Monteverdi; and authentic Monteverdi is,
one presumes, harder to recreate.

[Paul wrote:]
>I'm all in favor of creative re-interpretations. But there's a
>difference. The classical composers did not _record_ their own music.
>They wrote it out to be played by others. Thus if you turn on the
>radio and are told "that was Bach" or "that was Mozart" without
>further qualification, I would expect that the performers tried to be
>faithful to the score and to the performance practices of the time.
>If you are told "that was the Beatles" without further qualification,
>I would expect that to be an actual Beatles recording, and not a
>cover.

Fair enough. I'm all for complete and accurate labeling. Heck, if I'm
making a change I think adds to the musical impact, I'd _want_ to trumpet
it. As you say, in the case of the Beatles song, the cover artist knows
that everyone knows how many changes he/she has made.

[Paul:]
>I _like_ Switched-on and Swingle-sung Bach!

Oops! I incorrectly assumed you were being ironic. It delights me
that there's something with names that silly that you find musically
interesting! :-)

JdL

Bob had said:
> > Well, Paul, you seem to insist that the human ear's gravitation
> > toward the melodic use of perfect fifths and fourths has nothing
to
> > do with the fundamental psychoacoustic preferences for just
> intervals
> > that forms the basis of harmonic structure.

Paul replied:
> Not "nothing to do".

Bob:
Then just what DO you think they have to do with it?

Paul:
> I don't see the relevance of combinational tones to melody, or to
the
> construction of scales to be used only for melody.

So, Paul, why do you think the perfect fifth and fourth are so
prominently favored in our world's music since ancient times beyond
any reasonable assumption of a statistical fluke? If it is not based
on harmonic partials and it's not based on difference products, what
is it based on, magic?

Even melodies do not usually live in a total harmonic vacuum. There
is the overlapping melodic imitation common to many traditions. At
least an occasional use of drones is also quite common and sometimes
perpetual, as in Indian classical music and some middle-eastern, as
well as some early Greek Orthodox and other eastern Christian music.

You seem to restrict your definition of harmony to its explicit
presence in music?...its conscious use and cultivation...?...? I find
this an arbitrary and powerful dilution of explanatory power in
understanding musical evolution and the how and why of harmonic music
ever having evolved in the first place.

The acquisition of spoken language in children used to be modeled in
terms of behavioristic conditioning theory. Now research has
irrefutably demonstrated that this is a totally inadequate model. It
is now well recognized that the MAJOR portion of language acquisition
is based on the unconscious use of the human intuition implicit in
the brain's own internal structure. Music is also a language!

Paul:
> These combinational tones are only possible when harmony (that is,
> simultaneous sounding of tones) is being used (and at a loud
volume).

Bob:
Wrong! They are subtle at first, but later clearly audible to ears
trained to listen for them. They are hidden from us at first by a
psychogical phenomenon known as masking, as are any phenomena that
are perpetually there, especially if they're not primary to the
initial sonic objects that generate our aural experience. Ever notice
how loud harmonic partials are once you learn to pick them out with
your ear? Yet you won't have much trouble finding people, musicians
included, who fail to hear them no matter how they try.

Granted, even then once you're actually performing music instead of
sitting on sustained harmonies, explicit recognition of the
difference products is not easy, and per se they are not at the
forefront of the hearing experience. Nevertheless, having made them
explicit under ideal conditions develops an intuitive sensitivity to
their underlying presence that is unmistakably clear and reliable.

Having heard them explicitly leaves their indelible "footprint" in
the mind's ear so that even when they are not explicit, their mark is
clearly recognizable in the same way as timbre is appreciated without
necessarily noticing its constituent partials and other relevant
subcomponents, such as subtleties of attack and delay, timbre shifts,
etc.

When I first founded Cantus Angelicus, we were a few weeks away from
our first concert and the intonation was way under par for anything I
wanted to be associated with. I went home and brainstormed on how I
extend the use of the difference products so prominent in double-
stopping just intervals on the violin to exercises that would be time-
efficient and work for voices.

I played with sustained tones on my synth and my own voice and cooked
up something that would involve all four voice parts together. I took
the synth to the next rehearsal and tried the exercises. The results
were nothing short of miraculous! I would have never predicted the
power they would have!

Within three rehearsals using the exercises only for a few minutes at
the beginning, we had a totally different choir. One member who was
aloso involved in another singing group got me an invitation to help
them. They were truly awful when I walked in. Much worse than our
choir had ever been. In three sessions they were singing
unrecognizably beautiful harmony. Even after the first session, they
were floored with the results. I was, too!

I had doubts, though, about how that would last, since I didn't have
any further contact after the three sessions. A year later I happened
to hear them perform at a friend's birthday party. They weren't
perfect, but they were quite decent and vastly superior to what they
had been before the training.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., BobWendell@t... wrote:
> > Well, Paul, you seem to insist that the human ear's gravitation
> > toward the melodic use of perfect fifths and fourths has nothing
to
> > do with the fundamental psychoacoustic preferences for just
> intervals
> > that forms the basis of harmonic structure.
>
> Not "nothing to do".
> >
> > It seems implicit in your comments from where I sit that you have
> > therefore concluded that this exceptionally great power somehow
> takes
> > these relationships out of the realm of harmonic consideration
and
> > qualifies them as purely melodic in nature. I would posit that
this
> > great power is harmonic in nature in the most FUNDAMENTAL sense.
>
> I guess it all depends on how you define "harmonic".
> >
> > If you assume that the third harmonic is so prominent in some
> timbres
> > that this qualifies the fourths and fifths as fundamentally
melodic,
>
> Where did I assume that? No, I don't think prominence of partials
has
> much to do with it -- in fact, the attraction to some sort of
> approximate fourths and fifths persists with timbres that have no
> such partials.
> >
> > As I have stated before in other threads, there is another side
to
> > harmonic relationships that I have personally and empirically
found
> > to be more powerful and reliable by far than the intuitive
> perception
> > of harmonic overtones in musical timbres. The harmonically (make
> that
> > also coherently) related DIFFERENCE PRODUCTS of justly related
> tones
> > are incredibly powerful tools for developing the intuitive
> > recognition of just intervals.
>
> These combinational tones are only possible when harmony (that is,
> simultaneous sounding of tones) is being used (and at a loud
volume).
> I don't see the relevance of combinational tones to melody, or to
the
> construction of scales to be used only for melody.

> But Paul had already answered:
> > Why is it that the music of so many cultures seems to violate the
> > supposed "universals implicit in a common human perceptual
> > metastructure" as understood by listeners of another culture?>
>
Bob Answers:> Why is this reply so off the point as are so many
others?!

Paul:
Maybe I'm not communicating well. It's not off the point at all. I'm
just trying to point out that understanding music of another age
must, like understanding the music of another culture, be fraught
with all sorts of perils and traps when one tries to frame the issues
in terms of "universals implicit in a common human perceptual
metastructure".

Bob:
If one takes into account the overall context of this last phrase
from previous communications, it should be clear that this does not
refer to aesthetic impositions. I am not invoking magic here either.
Music is a language. Quoting from myself in the previous posting:

"The acquisition of spoken language in children used to be modeled in
terms of behavioristic conditioning theory. Now research has
irrefutably demonstrated that this is a totally inadequate model. It
is now well recognized that the MAJOR portion of language acquisition
is based on the unconscious use of the human intuition implicit in
the brain's own internal structure. Music is also a language!"

I think that it should be clear from this that to speak of such a
metastucture does NOT have to imply spurious means to justify an
"anything goes" approach to drawing conclusions from historical
evidence. A greater peril lies in ignoring that such a metastructure
does indeed exist and a mindset that believes everything
derives strictly from the explicit expressions available to us in
historical writings and physical objects such as ancient instruments,
including our own conclusions from them.

A more complete development and personal, practical, objectively
verifiable example of applying the kind of metastructure to which I
refer is already available in the previous posting 28350 in this
thread - Re: MIDI files and tuning.

> And there > often seems to be a tremendous lack context, of taking
the points
> separately with no regard for how other intimately related points
> tie it all together and eliminate the ambiguities of interpretation
> that otherwise generate such wide misses.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., BobWendell@t... wrote:
> > Bob had said:
> > > My statement here only says that WITHOUT any harmonic basis or
> even
> > a
> > > drone, there is no reason to choose such harmonic consonances
> over
> > > any other arbitrary sequence of pitches. Some ethnic melodic
> > > structures do not,
> >
> > Paul had replied:
> > True, but fifths and fourths are much more common than they
should
> > be "randomly".
> >
> > Bob answers:
> > Precisely my point! To me it seems crystal clear that there is a
> > psychoacoustic basis at the root of the tendency for harmonic
> systems
> > to ever develop that explains why fourths and fifths are so
> > universally preferred above random choices.
>
> OK. But "harmonically based" to me means "based on the qualities of
> the simultaneous sounding of tones". If you didn't mean that then
> fine.
> >
> > The psychoacoustic phenomena that predispose humans from a large
> > variety of cultures across thousands of years to these very
> specific
> > and precise intervals are what I meant by "the universals
implicit
> in
> > a common human perceptual metastructure INDEPENDENT of the age."
> This
> > has nothing to do with imposing current aesthetics on another
> > age!!!!!
> >
> > But Pual had already answered:
> > > Why is it that the music of so many cultures seems to violate
the
> > > supposed "universals implicit in a common human perceptual
> > > metastructure" as understood by listeners of another culture?
> >
> > Bob Answers:
> > Why is this reply so off the point as are so many others?!
>
> Maybe I'm not communicating well. It's not off the point at all.
I'm
> just trying to point out that understanding music of another age
> must, like understanding the music of another culture, be fraught
> with all sorts of perils and traps when one tries to frame the
issues
> in terms of "universals implicit in a common human perceptual
> metastructure".
>
> > And there
> > often seems to be a tremendous lack context, of taking the points
> > separately with no regard for how other intimately related
points
> > tie it all together and eliminate the ambiguities of
interpretation
> > that otherwise generate such wide misses.
> >
> > I feel like I'm continually having to plug up a whole in this
part
> of
> > the dyke, then am forced to run over to another one, unplugging
the
> > first. Maybe it's my fault, but I'm trying to be as clear as
> > possible. Please allow for a coherent, unifying foundation for my
> > points that should be accumulating in your awareness, but for
> > whatever reason, are not.
>
> That goes both ways. Vice-versa. Communications are poor right now.

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

> So, Paul, why do you think the perfect fifth and fourth are so
> prominently favored in our world's music since ancient times beyond
> any reasonable assumption of a statistical fluke? If it is not
based
> on harmonic partials and it's not based on difference products,
what
> is it based on, magic?

I would say it is based on how we hear, and that is a very
sophisticated analysis of sound.

Humans are not alone in the emphasis they give to some intervals and
tone relationships. The hermit thrush reportedly sings in a pentaonic
scale, while the wood thrush of eastern North America uses a diatonic
scale. Bird songs are musical enough that we call them "songs" and
even incorporate them into our own music at times. It's even been
suggested the white-breasted wood wren came up with the idea for the
motive of Beethoven's Fifth. Nor are birds the only animal musicians--
in a recent issue of Science, it was reported that humpback whales
use recognizable interval relationships in their songs (which note,
again, we also call "songs".)

These songs, of course, are melody, so this would seem to be relevant
to melody.

> I played with sustained tones on my synth and my own voice and
cooked
> up something that would involve all four voice parts together. I
took
> the synth to the next rehearsal and tried the exercises. The
results
> were nothing short of miraculous! I would have never predicted the
> power they would have!

Facinating--you might consider writing your experiences up.

Thanks for your interest, Gene. I'm seeking a grant to develop a full-
blown choral workshop incorporating these techniques as a major
component. Even seeking a grant is time-comsuming, however, and I am
swamped with a full-time non-musical job and running Cantus
Angelicus, a non-profit that is all-volunteer, including me (no pay).

I have had at least three on this list already request that I send
them material for implementing these exercises. All I have now is
hand-written scores that are useless without explanation. I need to
use my music software to put them into more legible format and write
up instructions for their implementation.

I'm feeling hopelessly behind on higher priority tasks directly
related to Cantus Angelicus and work. I have no time to even get
agressive about seeking a grant. I need administratvie help, but
oddly not enough has not been fothcoming for the six years of our
existence in spite of our success in other respects.

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., BobWendell@t... wrote:
>
> > So, Paul, why do you think the perfect fifth and fourth are so
> > prominently favored in our world's music since ancient times
beyond
> > any reasonable assumption of a statistical fluke? If it is not
> based
> > on harmonic partials and it's not based on difference products,
> what
> > is it based on, magic?
>
> I would say it is based on how we hear, and that is a very
> sophisticated analysis of sound.
>
> Humans are not alone in the emphasis they give to some intervals
and
> tone relationships. The hermit thrush reportedly sings in a
pentaonic
> scale, while the wood thrush of eastern North America uses a
diatonic
> scale. Bird songs are musical enough that we call them "songs" and
> even incorporate them into our own music at times. It's even been
> suggested the white-breasted wood wren came up with the idea for
the
> motive of Beethoven's Fifth. Nor are birds the only animal
musicians--
> in a recent issue of Science, it was reported that humpback whales
> use recognizable interval relationships in their songs (which note,
> again, we also call "songs".)
>
> These songs, of course, are melody, so this would seem to be
relevant
> to melody.
>
> > I played with sustained tones on my synth and my own voice and
> cooked
> > up something that would involve all four voice parts together. I
> took
> > the synth to the next rehearsal and tried the exercises. The
> results
> > were nothing short of miraculous! I would have never predicted
the
> > power they would have!
>
> Facinating--you might consider writing your experiences up.

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., BobWendell@t... wrote:
>
> > So, Paul, why do you think the perfect fifth and fourth are so
> > prominently favored in our world's music since ancient times
beyond
> > any reasonable assumption of a statistical fluke? If it is not
> based
> > on harmonic partials and it's not based on difference products,
> what
> > is it based on, magic?
>
Gene:
I would say it is based on how we hear, and that is a very
> sophisticated analysis of sound.
>
> Humans are not alone in the emphasis they give to some intervals
and
> tone relationships. The hermit thrush reportedly sings in a
pentaonic
> scale, while the wood thrush of eastern North America uses a
diatonic
> scale...
> These songs, of course, are melody, so this would seem to be
relevant
> to melody.
>

Bob replies:
Fine. My main and simple position is that the tendency of human or
other creatures to do this melodically does not have a coincidental
relationship to either the physical acoustics that allow harmony to
work at all, or the psychoacoustics with which evolution has endowed
us to perceive, process, and yes, even adapt to it. Adaptation is
necessary, of course. I have talked to people, Iranians, who were
quite musical, and who told me that the harmony of western music
initially sounded to them like a massive, indecipherable jumble of
melodies.

Physical and psychoacoustics are related intimately, just as are
optics and the evolution of human and animal sight, including its
neurological processing in our brains. I'm simply saying that if we
put such intellectual blinders on that we factor this out of
consideration, we are missing a major piece of the REAL PIE, just as
the behaviorists were with language learning. And in order not to
factor it out, we have to have at least some inkling of how it
functions in order to adequately inform the conclusions we can
validly draw from external historical sources.

I feel I've been seeing a lot of this kind of fundamentally important
stuff getting left out in some of the objections to my statements on
this list. In my view, many of these objections have been very
historically informed, but lacking in this kind of fundamental
substance in a great many instances.

If you agree...

Harmony respecting is only for bads ears !!!!!!!
Any good singer dont need to respect noting verticaly
!
When will you understand that,Paul ? !

Dimitrov

--- BobWendell@technet-inc.com a �crit�: > Bob had
said:
> > > Well, Paul, you seem to insist that the human
> ear's gravitation
> > > toward the melodic use of perfect fifths and
> fourths has nothing
> to
> > > do with the fundamental psychoacoustic
> preferences for just
> > intervals
> > > that forms the basis of harmonic structure.
>
> Paul replied:
> > Not "nothing to do".
>
> Bob:
> Then just what DO you think they have to do with it?
>
> Paul:
> > I don't see the relevance of combinational tones
> to melody, or to
> the
> > construction of scales to be used only for melody.
>
> So, Paul, why do you think the perfect fifth and
> fourth are so
> prominently favored in our world's music since
> ancient times beyond
> any reasonable assumption of a statistical fluke? If
> it is not based
> on harmonic partials and it's not based on
> difference products, what
> is it based on, magic?
>
> Even melodies do not usually live in a total
> harmonic vacuum. There
> is the overlapping melodic imitation common to many
> traditions. At
> least an occasional use of drones is also quite
> common and sometimes
> perpetual, as in Indian classical music and some
> middle-eastern, as
> well as some early Greek Orthodox and other eastern
> Christian music.
>
> You seem to restrict your definition of harmony to
> its explicit
> presence in music?...its conscious use and
> cultivation...?...? I find
> this an arbitrary and powerful dilution of
> explanatory power in
> understanding musical evolution and the how and why
> of harmonic music
> ever having evolved in the first place.
>
> The acquisition of spoken language in children used
> to be modeled in
> terms of behavioristic conditioning theory. Now
> research has
> irrefutably demonstrated that this is a totally
> inadequate model. It
> is now well recognized that the MAJOR portion of
> language acquisition
> is based on the unconscious use of the human
> intuition implicit in
> the brain's own internal structure. Music is also a
> language!
>
> Paul:
> > These combinational tones are only possible when
> harmony (that is,
> > simultaneous sounding of tones) is being used (and
> at a loud
> volume).
>
> Bob:
> Wrong! They are subtle at first, but later clearly
> audible to ears
> trained to listen for them. They are hidden from us
> at first by a
> psychogical phenomenon known as masking, as are any
> phenomena that
> are perpetually there, especially if they're not
> primary to the
> initial sonic objects that generate our aural
> experience. Ever notice
> how loud harmonic partials are once you learn to
> pick them out with
> your ear? Yet you won't have much trouble finding
> people, musicians
> included, who fail to hear them no matter how they
> try.
>
> Granted, even then once you're actually performing
> music instead of
> sitting on sustained harmonies, explicit recognition
> of the
> difference products is not easy, and per se they are
> not at the
> forefront of the hearing experience. Nevertheless,
> having made them
> explicit under ideal conditions develops an
> intuitive sensitivity to
> their underlying presence that is unmistakably clear
> and reliable.
>
> Having heard them explicitly leaves their indelible
> "footprint" in
> the mind's ear so that even when they are not
> explicit, their mark is
> clearly recognizable in the same way as timbre is
> appreciated without
> necessarily noticing its constituent partials and
> other relevant
> subcomponents, such as subtleties of attack and
> delay, timbre shifts,
> etc.
>
> When I first founded Cantus Angelicus, we were a few
> weeks away from
> our first concert and the intonation was way under
> par for anything I
> wanted to be associated with. I went home and
> brainstormed on how I
> extend the use of the difference products so
> prominent in double-
> stopping just intervals on the violin to exercises
> that would be time-
> efficient and work for voices.
>
> I played with sustained tones on my synth and my own
> voice and cooked
> up something that would involve all four voice parts
> together. I took
> the synth to the next rehearsal and tried the
> exercises. The results
> were nothing short of miraculous! I would have never
> predicted the
> power they would have!
>
> Within three rehearsals using the exercises only for
> a few minutes at
> the beginning, we had a totally different choir. One
> member who was
> aloso involved in another singing group got me an
> invitation to help
> them. They were truly awful when I walked in. Much
> worse than our
> choir had ever been. In three sessions they were
> singing
> unrecognizably beautiful harmony. Even after the
> first session, they
> were floored with the results. I was, too!
>
> I had doubts, though, about how that would last,
> since I didn't have
> any further contact after the three sessions. A year
> later I happened
> to hear them perform at a friend's birthday party.
> They weren't
> perfect, but they were quite decent and vastly
> superior to what they
> had been before the training.
>
>
>
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> > --- In tuning@y..., BobWendell@t... wrote:
> > > Well, Paul, you seem to insist that the human
> ear's gravitation
> > > toward the melodic use of perfect fifths and
> fourths has nothing
> to
> > > do with the fundamental psychoacoustic
> preferences for just
> > intervals
> > > that forms the basis of harmonic structure.
> >
> > Not "nothing to do".
> > >
> > > It seems implicit in your comments from where I
> sit that you have
> > > therefore concluded that this exceptionally
> great power somehow
> > takes
> > > these relationships out of the realm of harmonic
> consideration
> and
> > > qualifies them as purely melodic in nature. I
> would posit that
> this
> > > great power is harmonic in nature in the most
> FUNDAMENTAL sense.
> >
> > I guess it all depends on how you define
> "harmonic".
> > >
> > > If you assume that the third harmonic is so
> prominent in some
> > timbres
> > > that this qualifies the fourths and fifths as
> fundamentally
> melodic,
> >
> > Where did I assume that? No, I don't think
> prominence of partials
> has
> > much to do with it -- in fact, the attraction to
> some sort of
> > approximate fourths and fifths persists with
> timbres that have no
> > such partials.
> > >
> > > As I have stated before in other threads, there
> is another side
> to
> > > harmonic relationships that I have personally
> and empirically
> found
> > > to be more powerful and reliable by far than the
> intuitive
> > perception
> > > of harmonic overtones in musical timbres. The
> harmonically (make
> > that
> > > also coherently) related DIFFERENCE PRODUCTS of
> justly related
> > tones
> > > are incredibly powerful tools for developing the
> intuitive
> > > recognition of just intervals.
> >
> > These combinational tones are only possible when
> harmony (that is,
> > simultaneous sounding of tones) is being used (and
> at a loud
> volume).
> > I don't see the relevance of combinational tones
> to melody, or to
> the
> > construction of scales to be used only for melody.
>
>

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

on 9/20/01 4:34 AM, tuning@yahoogroups.com at tuning@yahoogroups.com wrote:

List!

I would like to respectfully request that people please trim their posts! If
one is on digest mode, as I am, then one has to scroll through miles of
these multiple quoted posts to read the new comments. I include the below
message only to illustrate the sort of thing that is cluttering my e-box. It
makes it hard for me to want to know what you're saying.

Many thanks,

Seth

> Message: 20
> Date: Thu, 20 Sep 2001 01:53:43 +0200 (CEST)
> From: Latchezar Dimitrov <latchezar_d@yahoo.com>
> Subject: Re: Re: MIDI files and tuning+ADD...
>
> If you agree...
>
> Harmony respecting is only for bads ears !!!!!!!
> Any good singer dont need to respect noting verticaly
> !
> When will you understand that,Paul ? !
>
> Dimitrov
>
>
>
> --- BobWendell@technet-inc.com a écrit : > Bob had
> said:
>>>> Well, Paul, you seem to insist that the human
>> ear's gravitation
>>>> toward the melodic use of perfect fifths and
>> fourths has nothing
>> to
>>>> do with the fundamental psychoacoustic
>> preferences for just
>>> intervals
>>>> that forms the basis of harmonic structure.
>>
>> Paul replied:
>>> Not "nothing to do".
>>
>> Bob:
>> Then just what DO you think they have to do with it?
>>
>> Paul:
>>> I don't see the relevance of combinational tones
>> to melody, or to
>> the
>>> construction of scales to be used only for melody.
>>
>> So, Paul, why do you think the perfect fifth and
>> fourth are so
>> prominently favored in our world's music since
>> ancient times beyond
>> any reasonable assumption of a statistical fluke? If
>> it is not based
>> on harmonic partials and it's not based on
>> difference products, what
>> is it based on, magic?
>>
>> Even melodies do not usually live in a total
>> harmonic vacuum. There
>> is the overlapping melodic imitation common to many
>> traditions. At
>> least an occasional use of drones is also quite
>> common and sometimes
>> perpetual, as in Indian classical music and some
>> middle-eastern, as
>> well as some early Greek Orthodox and other eastern
>> Christian music.
>>
>> You seem to restrict your definition of harmony to
>> its explicit
>> presence in music?...its conscious use and
>> cultivation...?...? I find
>> this an arbitrary and powerful dilution of
>> explanatory power in
>> understanding musical evolution and the how and why
>> of harmonic music
>> ever having evolved in the first place.
>>
>> The acquisition of spoken language in children used
>> to be modeled in
>> terms of behavioristic conditioning theory. Now
>> research has
>> irrefutably demonstrated that this is a totally
>> inadequate model. It
>> is now well recognized that the MAJOR portion of
>> language acquisition
>> is based on the unconscious use of the human
>> intuition implicit in
>> the brain's own internal structure. Music is also a
>> language!
>>
>> Paul:
>>> These combinational tones are only possible when
>> harmony (that is,
>>> simultaneous sounding of tones) is being used (and
>> at a loud
>> volume).
>>
>> Bob:
>> Wrong! They are subtle at first, but later clearly
>> audible to ears
>> trained to listen for them. They are hidden from us
>> at first by a
>> psychogical phenomenon known as masking, as are any
>> phenomena that
>> are perpetually there, especially if they're not
>> primary to the
>> initial sonic objects that generate our aural
>> experience. Ever notice
>> how loud harmonic partials are once you learn to
>> pick them out with
>> your ear? Yet you won't have much trouble finding
>> people, musicians
>> included, who fail to hear them no matter how they
>> try.
>>
>> Granted, even then once you're actually performing
>> music instead of
>> sitting on sustained harmonies, explicit recognition
>> of the
>> difference products is not easy, and per se they are
>> not at the
>> forefront of the hearing experience. Nevertheless,
>> having made them
>> explicit under ideal conditions develops an
>> intuitive sensitivity to
>> their underlying presence that is unmistakably clear
>> and reliable.
>>
>> Having heard them explicitly leaves their indelible
>> "footprint" in
>> the mind's ear so that even when they are not
>> explicit, their mark is
>> clearly recognizable in the same way as timbre is
>> appreciated without
>> necessarily noticing its constituent partials and
>> other relevant
>> subcomponents, such as subtleties of attack and
>> delay, timbre shifts,
>> etc.
>>
>> When I first founded Cantus Angelicus, we were a few
>> weeks away from
>> our first concert and the intonation was way under
>> par for anything I
>> wanted to be associated with. I went home and
>> brainstormed on how I
>> extend the use of the difference products so
>> prominent in double-
>> stopping just intervals on the violin to exercises
>> that would be time-
>> efficient and work for voices.
>>
>> I played with sustained tones on my synth and my own
>> voice and cooked
>> up something that would involve all four voice parts
>> together. I took
>> the synth to the next rehearsal and tried the
>> exercises. The results
>> were nothing short of miraculous! I would have never
>> predicted the
>> power they would have!
>>
>> Within three rehearsals using the exercises only for
>> a few minutes at
>> the beginning, we had a totally different choir. One
>> member who was
>> aloso involved in another singing group got me an
>> invitation to help
>> them. They were truly awful when I walked in. Much
>> worse than our
>> choir had ever been. In three sessions they were
>> singing
>> unrecognizably beautiful harmony. Even after the
>> first session, they
>> were floored with the results. I was, too!
>>
>> I had doubts, though, about how that would last,
>> since I didn't have
>> any further contact after the three sessions. A year
>> later I happened
>> to hear them perform at a friend's birthday party.
>> They weren't
>> perfect, but they were quite decent and vastly
>> superior to what they
>> had been before the training.
>>
>>
>>
>> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>>> --- In tuning@y..., BobWendell@t... wrote:
>>>> Well, Paul, you seem to insist that the human
>> ear's gravitation
>>>> toward the melodic use of perfect fifths and
>> fourths has nothing
>> to
>>>> do with the fundamental psychoacoustic
>> preferences for just
>>> intervals
>>>> that forms the basis of harmonic structure.
>>>
>>> Not "nothing to do".
>>>>
>>>> It seems implicit in your comments from where I
>> sit that you have
>>>> therefore concluded that this exceptionally
>> great power somehow
>>> takes
>>>> these relationships out of the realm of harmonic
>> consideration
>> and
>>>> qualifies them as purely melodic in nature. I
>> would posit that
>> this
>>>> great power is harmonic in nature in the most
>> FUNDAMENTAL sense.
>>>
>>> I guess it all depends on how you define
>> "harmonic".
>>>>
>>>> If you assume that the third harmonic is so
>> prominent in some
>>> timbres
>>>> that this qualifies the fourths and fifths as
>> fundamentally
>> melodic,
>>>
>>> Where did I assume that? No, I don't think
>> prominence of partials
>> has
>>> much to do with it -- in fact, the attraction to
>> some sort of
>>> approximate fourths and fifths persists with
>> timbres that have no
>>> such partials.
>>>>
>>>> As I have stated before in other threads, there
>> is another side
>> to
>>>> harmonic relationships that I have personally
>> and empirically
>> found
>>>> to be more powerful and reliable by far than the
>> intuitive
>>> perception
>>>> of harmonic overtones in musical timbres. The
>> harmonically (make
>>> that
>>>> also coherently) related DIFFERENCE PRODUCTS of
>> justly related
>>> tones
>>>> are incredibly powerful tools for developing the
>> intuitive
>>>> recognition of just intervals.
>>>
>>> These combinational tones are only possible when
>> harmony (that is,
>>> simultaneous sounding of tones) is being used (and
>> at a loud
>> volume).
>>> I don't see the relevance of combinational tones
>> to melody, or to
>> the
>>> construction of scales to be used only for melody.
>>
>>
>
> ___________________________________________________________
> Do You Yahoo!? -- Un e-mail gratuit @yahoo.fr !
> Yahoo! Courrier : http://fr.mail.yahoo.com
>
>
> ________________________________________________________________________
> ________________________________________________________________________
>
>
>
> Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
>
>

--
Seth Austen

http://www.sethausten.com
emails: seth@sethausten.com
klezmusic@earthlink.net

--- In tuning@y..., BobWendell@t... wrote:
> Bob had said:
> > > Well, Paul, you seem to insist that the human ear's gravitation
> > > toward the melodic use of perfect fifths and fourths has
nothing
> to
> > > do with the fundamental psychoacoustic preferences for just
> > intervals
> > > that forms the basis of harmonic structure.
>
> Paul replied:
> > Not "nothing to do".
>
> Bob:
> Then just what DO you think they have to do with it?

It's far from scientifically clear what the forces behind these
tendencies are. Some of it may be inborn, some may have to do with
learning the harmonic series intervals in the mother's voice through
prenatal exposure . . . perhaps a thousand years of psychological and
neurological research will have to take place before we can begin to
scratch the surface of these questions.

> Paul:
> > I don't see the relevance of combinational tones to melody, or to
> the
> > construction of scales to be used only for melody.
>
> So, Paul, why do you think the perfect fifth and fourth are so
> prominently favored in our world's music since ancient times beyond
> any reasonable assumption of a statistical fluke? If it is not
based
> on harmonic partials and it's not based on difference products,
what
> is it based on, magic?

See above. My best guess at the moment is that the fifth and fourth
are familiar from prenatal exposure to the harmonic partials in the
mother's voice. But I wouldn't bet on it.
>
> You seem to restrict your definition of harmony to its explicit
> presence in music?...its conscious use and cultivation...?...? I
find
> this an arbitrary and powerful dilution of explanatory power in
> understanding musical evolution and the how and why of harmonic
music
> ever having evolved in the first place.

Perhaps the point of view is a reaction to yours . . . I think that
melodic forces of all sorts, of which we have little "scientific"
understanding at the moment, have been more important for the most
part . . . explicit presence of harmony changed musical style
completely . . . consider again the modes of the diatonic scale that
were preferred in the days of chant vs. those preferred in the days
of harmony.

> The acquisition of spoken language in children used to be modeled
in
> terms of behavioristic conditioning theory. Now research has
> irrefutably demonstrated that this is a totally inadequate model.
It
> is now well recognized that the MAJOR portion of language
acquisition
> is based on the unconscious use of the human intuition implicit in
> the brain's own internal structure. Music is also a language!

I believe strongly that the linguistic features of the internal
structure of the brain bear strongly on how music works. Our brains
evolved for language, and no music can be listened to without the
linguistic parts of the brain jumping into action. These are the
sorts of issues that will have to come to be understood during the
next millenium of psychological research (one can hope). But did the
brain evolve for music? Is there a universal "music-wiring" in the
brain, analogous to the "language-wiring"? That's where I'm doubtful.

> Paul:
> > These combinational tones are only possible when harmony (that
is,
> > simultaneous sounding of tones) is being used (and at a loud
> volume).
>
> Bob:
> Wrong! They are subtle at first, but later clearly audible to ears
> trained to listen for them.

You're saying you can hear difference tones produced by _successive_,
rather than simultaneous, pitches? I've never heard of such a
phenomenon anywhere in the psychoacoustical literature. It's quite a
radical claim. I'm not saying I don't believe you . . .

I'm very happy for your successes in training choirs in intonation,
and believe that difference tones produced by _simultaneous_ pitches
may have a lot to do with that. Congratulations, and may your methods
and reputation spread far and wide!

--- In tuning@y..., BobWendell@t... wrote:
> > But Paul had already answered:
> > > Why is it that the music of so many cultures seems to violate
the
> > > supposed "universals implicit in a common human perceptual
> > > metastructure" as understood by listeners of another culture?>
> >
> Bob Answers:> Why is this reply so off the point as are so many
> others?!
>
> Paul:
> Maybe I'm not communicating well. It's not off the point at all.
I'm
> just trying to point out that understanding music of another age
> must, like understanding the music of another culture, be fraught
> with all sorts of perils and traps when one tries to frame the
issues
> in terms of "universals implicit in a common human perceptual
> metastructure".
>
> Bob:
> If one takes into account the overall context of this last phrase
> from previous communications, it should be clear that this does not
> refer to aesthetic impositions.

I wasn't referring to aesthetic impositions either. I'm thinking, for
example, of how most Western listeners today will hear a diatonic
melody and automatically "hear it" in terms of the relative major
mode, "hearing" the music in a major key, until a strong cadence
refutes that tendency. I don't think there was any such tendency for
diatonic melodies to be "heard" as major before the advent of common-
practice harmony. Yet one hears again and again the derivation of the
diatonic scale in terms of harmonic partials over roots on I, IV, and
V . . . totally anachronistic, IMO.
>
> I think that it should be clear from this that to speak of such a
> metastucture does NOT have to imply spurious means to justify an
> "anything goes" approach to drawing conclusions from historical
> evidence.

I don't understand this sentence.

> A greater peril lies in ignoring that such a metastructure
> does indeed exist

That's exactly what I fear many JI thinkers, and perhaps you, are
doing! The metastructure, evolved to allow linguistic capacity,
imposes constraints and tendencies on musical style that we've barely
begun to understand, but operate (I believe) primarily on the level
of ideas unfolding through time -- theme & variation, repetition,
etc. . . . i.e., _melody_.

> and a mindset that believes everything
> derives strictly from the explicit expressions available to us in
> historical writings and physical objects such as ancient
instruments,
> including our own conclusions from them.

Everything? No, I think even less was known about the psychology of
music historically than today! But aesthetic choices and judgments
made by musicians about their own music -- that should be worth
something.
>
> A more complete development and personal, practical, objectively
> verifiable example of applying the kind of metastructure to which I
> refer is already available in the previous posting 28350 in this
> thread - Re: MIDI files and tuning.

I'll look at that again . . .

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., BobWendell@t... wrote:
>
> > So, Paul, why do you think the perfect fifth and fourth are so
> > prominently favored in our world's music since ancient times
beyond
> > any reasonable assumption of a statistical fluke? If it is not
> based
> > on harmonic partials and it's not based on difference products,
> what
> > is it based on, magic?
>
> I would say it is based on how we hear, and that is a very
> sophisticated analysis of sound.
>
> Humans are not alone in the emphasis they give to some intervals
and
> tone relationships. The hermit thrush reportedly sings in a
pentaonic
> scale, while the wood thrush of eastern North America uses a
diatonic
> scale.

Do you have any references? I've heard certain bird songs that, when
slowed down, are clearly sweeping through a harmonic series (perhaps
because of the underlying mechanism with which the sound is
produced). But my prior guess is that you'd find that pentatonic and
diatonic scales are about as common among bird species (7000 or so?)
as you'd expect due to chance.

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

/tuning/topicId_27964.html#28148

> In my opinion, 4:5:6:7 has rather little to do with the dominant
> seventh chord in Western Music, traditionally introduced by
> Monteverdi.

Hi Paul...

Could you please quickly review for me why this is?? I'm not getting
it...

________ _______ _______
Joseph Pehrson

--- In tuning@y..., Latchezar Dimitrov <latchezar_d@y...> wrote:
> If you agree...
>
> Harmony respecting is only for bads ears !!!!!!!
> Any good singer dont need to respect noting verticaly
> !
> When will you understand that,Paul ? !
>
> Dimitrov

Latchezar . . . You seem to be agreeing with me and not Bob . . . so
what are you asking me?
>
>
>
>
> --- BobWendell@t... a écrit : > Bob had
> said:
> > > > Well, Paul, you seem to insist that the human
> > ear's gravitation
> > > > toward the melodic use of perfect fifths and
> > fourths has nothing
> > to
> > > > do with the fundamental psychoacoustic
> > preferences for just
> > > intervals
> > > > that forms the basis of harmonic structure.
> >
> > Paul replied:
> > > Not "nothing to do".
> >
> > Bob:
> > Then just what DO you think they have to do with it?
> >
> > Paul:
> > > I don't see the relevance of combinational tones
> > to melody, or to
> > the
> > > construction of scales to be used only for melody.
> >
> > So, Paul, why do you think the perfect fifth and
> > fourth are so
> > prominently favored in our world's music since
> > ancient times beyond
> > any reasonable assumption of a statistical fluke? If
> > it is not based
> > on harmonic partials and it's not based on
> > difference products, what
> > is it based on, magic?
> >
> > Even melodies do not usually live in a total
> > harmonic vacuum. There
> > is the overlapping melodic imitation common to many
> > traditions. At
> > least an occasional use of drones is also quite
> > common and sometimes
> > perpetual, as in Indian classical music and some
> > middle-eastern, as
> > well as some early Greek Orthodox and other eastern
> > Christian music.
> >
> > You seem to restrict your definition of harmony to
> > its explicit
> > presence in music?...its conscious use and
> > cultivation...?...? I find
> > this an arbitrary and powerful dilution of
> > explanatory power in
> > understanding musical evolution and the how and why
> > of harmonic music
> > ever having evolved in the first place.
> >
> > The acquisition of spoken language in children used
> > to be modeled in
> > terms of behavioristic conditioning theory. Now
> > research has
> > irrefutably demonstrated that this is a totally
> > inadequate model. It
> > is now well recognized that the MAJOR portion of
> > language acquisition
> > is based on the unconscious use of the human
> > intuition implicit in
> > the brain's own internal structure. Music is also a
> > language!
> >
> > Paul:
> > > These combinational tones are only possible when
> > harmony (that is,
> > > simultaneous sounding of tones) is being used (and
> > at a loud
> > volume).
> >
> > Bob:
> > Wrong! They are subtle at first, but later clearly
> > audible to ears
> > trained to listen for them. They are hidden from us
> > at first by a
> > psychogical phenomenon known as masking, as are any
> > phenomena that
> > are perpetually there, especially if they're not
> > primary to the
> > initial sonic objects that generate our aural
> > experience. Ever notice
> > how loud harmonic partials are once you learn to
> > pick them out with
> > your ear? Yet you won't have much trouble finding
> > people, musicians
> > included, who fail to hear them no matter how they
> > try.
> >
> > Granted, even then once you're actually performing
> > music instead of
> > sitting on sustained harmonies, explicit recognition
> > of the
> > difference products is not easy, and per se they are
> > not at the
> > forefront of the hearing experience. Nevertheless,
> > having made them
> > explicit under ideal conditions develops an
> > intuitive sensitivity to
> > their underlying presence that is unmistakably clear
> > and reliable.
> >
> > Having heard them explicitly leaves their indelible
> > "footprint" in
> > the mind's ear so that even when they are not
> > explicit, their mark is
> > clearly recognizable in the same way as timbre is
> > appreciated without
> > necessarily noticing its constituent partials and
> > other relevant
> > subcomponents, such as subtleties of attack and
> > delay, timbre shifts,
> > etc.
> >
> > When I first founded Cantus Angelicus, we were a few
> > weeks away from
> > our first concert and the intonation was way under
> > par for anything I
> > wanted to be associated with. I went home and
> > brainstormed on how I
> > extend the use of the difference products so
> > prominent in double-
> > stopping just intervals on the violin to exercises
> > that would be time-
> > efficient and work for voices.
> >
> > I played with sustained tones on my synth and my own
> > voice and cooked
> > up something that would involve all four voice parts
> > together. I took
> > the synth to the next rehearsal and tried the
> > exercises. The results
> > were nothing short of miraculous! I would have never
> > predicted the
> > power they would have!
> >
> > Within three rehearsals using the exercises only for
> > a few minutes at
> > the beginning, we had a totally different choir. One
> > member who was
> > aloso involved in another singing group got me an
> > invitation to help
> > them. They were truly awful when I walked in. Much
> > worse than our
> > choir had ever been. In three sessions they were
> > singing
> > unrecognizably beautiful harmony. Even after the
> > first session, they
> > were floored with the results. I was, too!
> >
> > I had doubts, though, about how that would last,
> > since I didn't have
> > any further contact after the three sessions. A year
> > later I happened
> > to hear them perform at a friend's birthday party.
> > They weren't
> > perfect, but they were quite decent and vastly
> > superior to what they
> > had been before the training.
> >
> >
> >
> > --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> > > --- In tuning@y..., BobWendell@t... wrote:
> > > > Well, Paul, you seem to insist that the human
> > ear's gravitation
> > > > toward the melodic use of perfect fifths and
> > fourths has nothing
> > to
> > > > do with the fundamental psychoacoustic
> > preferences for just
> > > intervals
> > > > that forms the basis of harmonic structure.
> > >
> > > Not "nothing to do".
> > > >
> > > > It seems implicit in your comments from where I
> > sit that you have
> > > > therefore concluded that this exceptionally
> > great power somehow
> > > takes
> > > > these relationships out of the realm of harmonic
> > consideration
> > and
> > > > qualifies them as purely melodic in nature. I
> > would posit that
> > this
> > > > great power is harmonic in nature in the most
> > FUNDAMENTAL sense.
> > >
> > > I guess it all depends on how you define
> > "harmonic".
> > > >
> > > > If you assume that the third harmonic is so
> > prominent in some
> > > timbres
> > > > that this qualifies the fourths and fifths as
> > fundamentally
> > melodic,
> > >
> > > Where did I assume that? No, I don't think
> > prominence of partials
> > has
> > > much to do with it -- in fact, the attraction to
> > some sort of
> > > approximate fourths and fifths persists with
> > timbres that have no
> > > such partials.
> > > >
> > > > As I have stated before in other threads, there
> > is another side
> > to
> > > > harmonic relationships that I have personally
> > and empirically
> > found
> > > > to be more powerful and reliable by far than the
> > intuitive
> > > perception
> > > > of harmonic overtones in musical timbres. The
> > harmonically (make
> > > that
> > > > also coherently) related DIFFERENCE PRODUCTS of
> > justly related
> > > tones
> > > > are incredibly powerful tools for developing the
> > intuitive
> > > > recognition of just intervals.
> > >
> > > These combinational tones are only possible when
> > harmony (that is,
> > > simultaneous sounding of tones) is being used (and
> > at a loud
> > volume).
> > > I don't see the relevance of combinational tones
> > to melody, or to
> > the
> > > construction of scales to be used only for melody.
> >
> >
>
> ___________________________________________________________
> Do You Yahoo!? -- Un e-mail gratuit @yahoo.fr !
> Yahoo! Courrier : http://fr.mail.yahoo.com

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> /tuning/topicId_27964.html#28148
>
> > In my opinion, 4:5:6:7 has rather little to do with the dominant
> > seventh chord in Western Music, traditionally introduced by
> > Monteverdi.
>
> Hi Paul...
>
> Could you please quickly review for me why this is?? I'm not
getting
> it...

For one thing, I believe that in Monteverdi's time, vertical minor
thirds were always sung or played very close to 5:6. So in the key of
C major, whenever D and F appeared simultaneously, they would be
close to 316 cents apart. Now for a dominant seventh chord to be
4:5:6:7, D and F would have to form a 6:7 ratio, a kind of minor
third about 50 cents narrower than the "usual" one. Though we find
all kinds of microtonal pitch problems/adjustments discussed in the
literature of this era, this is not one of them. Considering that D
and F were often held over from a previous sonority, you'd expect at
least _some_ mention of some kind of effect, and perhaps an attempt
to capture it on a microtonal keyboard, etc., if 4:5:6:7 was in fact
used for the dominant seventh chord. As far as I know, those
_musicians_ who did in fact experiment with ratios of 7 (such as
Tartini and Kirnberger) suggested that they be added to our musical
resources in various ways, but none suggested that they had anything
to do with the existing practice of the dominant seventh chord, or
that they be adopted as for providing improved or alternative
versions of the dominant seventh chord.

I'd suggest Easley Blackwood's book _The Structure of Recognizable
Diatonic Tunings_ for more.

Paul said:
I'm very happy for your successes in training choirs in intonation,
> and believe that difference tones produced by _simultaneous_
pitches
> may have a lot to do with that. Congratulations, and may your
methods
> and reputation spread far and wide!

Bob said:
My sincerest thanks for your kind wishes, Paul. There is no doubt
about the difference tones having everything to do with it. The
exercises are competely based on that phenomenon and none other. And
the results were so rapid and profound that it shocked me, pleasantly
of course!

Pual said:
> You're saying you can hear difference tones produced by
_successive_,
> rather than simultaneous, pitches? I've never heard of such a
> phenomenon anywhere in the psychoacoustical literature. It's quite
a
> radical claim. I'm not saying I don't believe you . . .

Bob:
No. You said the simultaneous tones had to be loud. They don't. I'm
also saying you can't eliminate simultaneously sounded pitches ever
occurring or even not frequently occurring simply because the culture
is melodic and not harmonic.

Paul:
These are the
> sorts of issues that will have to come to be understood during the
> next millenium of psychological research (one can hope). But did
the
> brain evolve for music?

Bob:
OK, Paul, but I dont' share your pessimism about discovering the
sources of these things. I don't see them as buried so deeply at all.

For instance, why take recourse to partials in one's mother's voice
as heard from the womb? This seems especially odd since you have
reacted so strongly against my default supposition that you were
referring to that same thing real-time outside the womb when opining
so strongly against my suggestion for the role of difference products
in simultaneously sounded tones. (Although I don't discount the whole
idea of the ear/voice linkage that goes with Dr. Tomatis' thinking.
I'm fascinated by it and feel his discoveries and similar new ones to
come have tremendous power for good and wonderful implications for
the practical and spiritual power of music.)

Additionally, why do we keep ignoring the drones and the imitative
following, overlapping melodic interactions often prevalent in
melodic traditions that would give rise to difference products? Is it
reasonable to assume that no one in melodic cultures ever sounds
intervals simultaneously and that this would have no effect on
melodic tendencies?

There is a "scientific" culture today that would have never
discovered Volta's frog leg contraction upon applying an electrical
potential across the muscle tissue. The members of this culture are
not responsible for many scientific advances or for much more than
academic polemics. Typically, they work outside of the so-called hard
sciences (e.g., psychology, sociology) and have an axe to grind in
terms of qualifying themselves as even practicing a science in the
first place.

Their investigative habits and mindset tend generally to imitate very
poorly those of the great discoverers and successful theorists in the
more traditional sciences. They would have had to repeat Volta's frog
leg experiment a few thousand times and then wait a few centuries for
the mathematics to evolve that would be adequate to establish
statistical significance. Please forgive me if I refuse to deny what
I find to be empirically obvious in my own practice while awaiting
their approval.

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

> Bob said:
> My sincerest thanks for your kind wishes, Paul. There is no doubt
> about the difference tones having everything to do with it. The
> exercises are competely based on that phenomenon and none other.

Are you sure that eliminating beating between upper partials plays no
role whatsover? And that the virtual pitch phenomenon plays no role
whatsoever?

> You said the simultaneous tones had to be loud. They don't.

Well, my point in saying that was that, for the most part,
combinational tones vary in amplitude as the square, or cube, or
fourth power, etc., of the amplitudes of the objective tones. You can
understand why this is so with a little math (see, for example, the
Feynman Lectures in Physics). So if you decrease the amplitudes of
the singers by, say, a factor of 10 (10dB), the majority of the
combinational tones will decrease in amplitude by at least a factor
of 100 (20 dB). That means that they will fall below the limen of
audibility much faster than the sung tones will.

But there is an exception. One of the second-order combinational
tones (2x-y) appears to maintain audibility even when the input tones
are rather quiet, and the relationship with amplitude is much flatter
than a square law (let alone the cubic law you would expect for a
second-order difference tone). So the supposition is that this tone
comes from higher-order processing, perhaps within the brain.

> I'm
> also saying you can't eliminate simultaneously sounded pitches ever
> occurring or even not frequently occurring simply because the
culture
> is melodic and not harmonic.

True, but in such melodic cultures, one tends to see dissonances
(such as seconds and sevenths) appearing as often as, and with no
stylistic distinction from, "consonances", in those cases where
simultaneously sounding pitches occur.
>
> For instance, why take recourse to partials in one's mother's voice
> as heard from the womb?

That's just one theory, defended by Parncutt in his book, _Harmony: A
Psychoacoustical Approach_.

> This seems especially odd since you have
> reacted so strongly against my default supposition that you were
> referring to that same thing real-time outside the womb

It wasn't anything like that same thing, or at least that's how I
interpreted it at the time.

when opining
> so strongly against my suggestion for the role of difference
products
> in simultaneously sounded tones. (Although I don't discount the
whole
> idea of the ear/voice linkage that goes with Dr. Tomatis' thinking.

Who?
>
> Additionally, why do we keep ignoring the drones

I think JI intervals are very important wherever there are drones.
But not directly JI intervals between melodic pitches . . . rather,
just JI intervals against the drone.

> and the imitative
> following, overlapping melodic interactions often prevalent in
> melodic traditions that would give rise to difference products?

One often finds extremely "dissonant" intervals in such musics . . .
listen to the non-Western-inclined songs sung by the Georgians (can't
recall the exact group I'm thinking of at the moment).
>
> There is a "scientific" culture today that would have never
> discovered Volta's frog leg contraction upon applying an electrical
> potential across the muscle tissue. The members of this culture are
> not responsible for many scientific advances or for much more than
> academic polemics. Typically, they work outside of the so-called
hard
> sciences (e.g., psychology, sociology) and have an axe to grind in
> terms of qualifying themselves as even practicing a science in the
> first place.
>
> Their investigative habits and mindset tend generally to imitate
very
> poorly those of the great discoverers and successful theorists in
the
> more traditional sciences. They would have had to repeat Volta's
frog
> leg experiment a few thousand times and then wait a few centuries
for
> the mathematics to evolve that would be adequate to establish
> statistical significance. Please forgive me if I refuse to deny
what
> I find to be empirically obvious in my own practice while awaiting
> their approval.

I'm not seeing the analogy here. You're well aware, I am sure, that
we agree on almost all the issues discussed on this list. I'm simply
trying to point out that there may be _some_ aesthetic considerations
that have _some_ importance to my ears and to others' ears, which you
may be giving short shrift because you've come up with a neat
theoretical framework that seems to nicely account for many powerful
experiences you've had with your singers. What I'm trying to suggest
to you (and Margo, Robert, and Latchezar as well) is that it may not
be quite so cut-and-dried; there may be more "to it".

I wrote,

> What I'm trying to suggest
> to you (and Margo, Robert, and Latchezar as well) is that it may
not
> be quite so cut-and-dried; there may be more "to it".

I meant that Margo, Robert, and Latchezar seem to be agreeing with me
and suggesting reasons why there may be more "to it".

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>>>> I think JI intervals are very important wherever there are
drones.
> But not directly JI intervals between melodic pitches . . . rather,
> just JI intervals against the drone. >>>>

Hi Paul, I think I am missing something here, because, in Indian
music we always perceive and discuss JI intervals that show how the
notes in a raga are interrelated. We do not even think of the drone
at that time. We always want to study the 4th and the 5th
relationships. We also critically apply our mind to how we aim at a
high degree of dissonance, to be resolved into a high degree of
consonance.

Could you elaborate, please?

Regards,
Haresh.

--- In tuning@y..., "Haresh BAKSHI" <hareshbakshi@h...> wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> >>>> I think JI intervals are very important wherever there are
> drones.
> > But not directly JI intervals between melodic pitches . . .
rather,
> > just JI intervals against the drone. >>>>
>
> Hi Paul, I think I am missing something here, because, in Indian
> music we always perceive and discuss JI intervals that show how the
> notes in a raga are interrelated. We do not even think of the
drone
> at that time. We always want to study the 4th and the 5th
> relationships. We also critically apply our mind to how we aim at
a
> high degree of dissonance, to be resolved into a high degree of
> consonance.
>
> Could you elaborate, please?
>
> Regards,
> Haresh.

Haresh, you and I have seen that, in some cases, preserving a JI
conception of Indian scales requires us to assume that the
relationships between notes must often be compromised, or off by a
comma. Do you remember all the discussion we had (for example, of one
raga being another raga transposed to A), which led us finally to
conclude that a "flexible", "adaptive" conception of shrutis would be
necessary?

I agree that 4th (4:3) and 5th (3:2) relationships are important
melodically . . . but I'm claiming that ratios involving 5 spring up
specifically because one or more notes are tuned to a consonant ratio
of 5 against the drone . . . do you disagree?

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., "Haresh BAKSHI" <hareshbakshi@h...> wrote:
> > --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

...................

>>>> Haresh, you and I have seen that, in some cases, preserving a JI
> conception of Indian scales requires us to assume that the
> relationships between notes must often be compromised, or off by a
> comma. Do you remember all the discussion we had (for example, of
one raga being another raga transposed to A), which led us finally to
conclude that a "flexible", "adaptive" conception of shrutis would
be necessary? >>>>

Yes, I distinctly recall how you patiently answered my queries on
transposing the Sa of a raga, so that it became a different raga as a
result. Yes, we did find flexibility imperative in such cases.

[Paul added:]
>>>> I agree that 4th (4:3) and 5th (3:2) relationships are important
> melodically . . . but I'm claiming that ratios involving 5 spring
up specifically because one or more notes are tuned to a consonant
ratio of 5 against the drone . . . do you disagree? >>>>

I entirely agree. But I think there is more to it: We would find 3:2
aesthetically very tension-resolving and soothing even when singing
without the drone accompaniement. Of course, we would hold a certain
note to be the Sa mentally, even if there is no drone accompaniement.
Is this, therefore, a question related to psychoacoustics of music?

Have I got your point right?

Regards,
Haresh.

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

> Do you have any references?

There was an article in Science a while back by the late Luis
Baptista and others, and here is a url of a Science News article on
his talk to the AAAS, with some references and sound files below:

<url: http://www.blarg.net/~critter/AvianFamily/song_4.htm>

<url: http://www.sciencenews.org/20000415/bob2ref.asp>

<url: http://www.sciencenews.org/20000415/sounds/sounds.asp>

--- In tuning@y..., "Haresh BAKSHI" <hareshbakshi@h...> wrote:
> [Paul added:]
> >>>> I agree that 4th (4:3) and 5th (3:2) relationships are
important
> > melodically . . . but I'm claiming that ratios involving 5 spring
> up specifically because one or more notes are tuned to a consonant
> ratio of 5 against the drone . . . do you disagree? >>>>
>
> I entirely agree. But I think there is more to it: We would find
3:2
> aesthetically very tension-resolving and soothing even when singing
> without the drone accompaniement.

That's what I meant by "important melodically".

> Of course, we would hold a certain
> note to be the Sa mentally, even if there is no drone >
accompaniement.

Modern Western listeners will often misinterpret older melodies in
terms of a supposed Sa (say, the tonic of the relative major scale)
that turns not to play the role of a _finalis_ at all in the music in
question.

> Is this, therefore, a question related to psychoacoustics of music?

Primarily psychology, yes. But the hearing of pitches as ratios with
respect to a tonic that is not heard but merely "held" in the memory
is a supposition, while made by some (Boomsliter & Creel, for
example), seems to have little support (so far) in terms of known
psychoacoustic phenomena. Something like it may be at work for
melodic fifths and fourths, but I am inclined to believe it is not so
simple: for example, looking at the modal melodies of many cultures,
one often sees modes with no perfect fifth over the tonic . . . how,
then, are we to see the tonic as a "fundamental" in a harmonic sense?
I think there may be melodic "senses" at work in these musics which
are foreign to our harmonically (dronal or chordal) shaped
sensibilities.

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> > Do you have any references?
>
> There was an article in Science a while back by the late Luis
> Baptista and others, and here is a url of a Science News article on
> his talk to the AAAS, with some references and sound files below:
>
> <url: http://www.blarg.net/~critter/AvianFamily/song_4.htm>
>
> <url: http://www.sciencenews.org/20000415/bob2ref.asp>
>
> <url: http://www.sciencenews.org/20000415/sounds/sounds.asp>

Can you find sound clips of the reputed diatonic and pentatonic songs
(I couldn't), and/or estimate their likelihood of occuring in a large
enough sample of bird species, just by chance?

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

> Can you find sound clips of the reputed diatonic and pentatonic
songs
> (I couldn't), and/or estimate their likelihood of occuring in a
large
> enough sample of bird species, just by chance?

Some of the links seem to be broken, but

<url: http://www.naturesongs.com/trogpeuc.html#heth>

works.

On Thu, 20 Sep 2001 23:23:53 -0000, genewardsmith@juno.com wrote:

>--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
>> Do you have any references?
>
>There was an article in Science a while back by the late Luis
>Baptista and others, and here is a url of a Science News article on
>his talk to the AAAS, with some references and sound files below:

Here's a few more white-breasted wood-wren songs for comparison:

(from http://www.naturesongs.com/CRsounds.html#trogl)
http://www.naturesongs.com/wbww1.wav
http://www.naturesongs.com/wbww2.wav
http://www.naturesongs.com/wbww7.wav
http://www.naturesongs.com/wbww6.wav
http://www.naturesongs.com/wbww5.wav
http://www.naturesongs.com/wbww4.wav

It seems that this species (like many kinds of birds) sings a variety of
songs; it's almost certainly a coincidence that one of them sounds a bit
like Beethoven's Fifth. (Besides, it's unlikely Beethoven would have been
familiar with a Central or South American bird.)

--
see my music page ---> ---<http://www.io.com/~hmiller/music/index.html>--
hmiller (Herman Miller) "If all Printers were determin'd not to print any
@io.com email password: thing till they were sure it would offend no body,
\ "Subject: teamouse" / there would be very little printed." -Ben Franklin

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

/tuning/topicId_27964.html#28179

> On the contrary, common practice musicians of today have been
lulled to sleep on intonation with the pervasive use of 12-tET and
almost total relegation of fixed tuning to professionals. This has
> eliminated the need and even the option for most students of music
to ever confront something so fundamental and historically well-
> understood as the syntonic comma. How many musicians of a random
> sample today would even know what that is?

Bob makes a really interesting point here. I managed to go through
grad school and only encountered this term in *one* class... a class
in acoustics taught by John Clough!

_________ _______ __________
Joseph Pehrson

Paul:
Modern Western listeners will often misinterpret older melodies in
terms of a supposed Sa (say, the tonic of the relative major scale)
that turns not to play the role of a _finalis_ at all in the music in
question.

Haresh:
> Is this, therefore, a question related to psychoacoustics of music?

Paul:
Primarily psychology, yes.

Bob comments:
Psychological, yes, but I think we would all agree that such an
inappropriate imposition of modal perception is a CONDITIONED
phenomenon. This is in contradistinction to phenomena that are
psychoacoustically intrinsic to human auditory perception, including
both its acoustically physical and its neurological components.

I feel a good part of the communications problem we've been
experiencing is coming from a failure to make this distinction
clearly and consistently, as well as a reluctance to accept or at
least give sufficient weight to certain components of psychoacoustics
as intrinsic to human auditory perception.

--- In tuning@y..., BobWendell@t... wrote:
> Paul:
> Modern Western listeners will often misinterpret older melodies in
> terms of a supposed Sa (say, the tonic of the relative major scale)
> that turns not to play the role of a _finalis_ at all in the music
in
> question.
>
> Haresh:
> > Is this, therefore, a question related to psychoacoustics of
music?
>
> Paul:
> Primarily psychology, yes.
>
> Bob comments:
> Psychological, yes, but I think we would all agree that such an
> inappropriate imposition of modal perception is a CONDITIONED
> phenomenon.

Absolutely! That's the point.

> This is in contradistinction to phenomena that are
> psychoacoustically intrinsic to human auditory perception,
including
> both its acoustically physical and its neurological components.

Precisely.
>
> I feel a good part of the communications problem we've been
> experiencing is coming from a failure to make this distinction
> clearly and consistently, as well as a reluctance to accept or at
> least give sufficient weight to certain components of
psychoacoustics
> as intrinsic to human auditory perception.

Hmm . . . what do you have in mind?

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> > Can you find sound clips of the reputed diatonic and pentatonic
> songs
> > (I couldn't), and/or estimate their likelihood of occuring in a
> large
> > enough sample of bird species, just by chance?
>
> Some of the links seem to be broken, but
>
> <url: http://www.naturesongs.com/trogpeuc.html#heth>
>
> works.

Not convinced.

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

/tuning/topicId_27964.html#28198

> I'm talking about the fact, for instance, that musicians who sought
> to introduce 7-limit consonances into music, including Tartini,
> Kirnberger, and as I recall, even Rameau, did not speak of them as
> something they heard already in the dominant seventh chord, or as a
> new way of tuning the dominant seventh chord. Instead they were
> considered new sounds, with new notation invented for them. The
major scale was, in most cases (see Mathieu, for instance) supplied
with a 7/4 and a 7/6, but not a 21/16, which would be required for a
> septimal dominant seventh chord.

Thanks, Paul... This answered my earlier question...

_______ _______ _______
Joseph Pehrson

--- In tuning@y..., paul@s... wrote:

/tuning/topicId_27964.html#28237

> You're right, but what I'm saying is that diatonic
> scale plus triadic harmony does not imply
> common practice, until the tritone takes on an
> important cadential role. Only then do we see
> major and minor modes as more common or
> more important than the others. Otherwise, we
> see i IV v i in dorian, I IV v I in mixolydian, and
> plenty of other non-common-practice chord
> progressions.
> >

This is a really interesting point, and it seems that a *lot* of the
diatonic collection, certainly in a *triadic* sense, is seen in the
works of such composers as Lassus. It would be interesting to hear
what Margo Schulter thinks about the use of the diatonic scale and
triadic harmony in non "functional harmony" Renaissance composers...

__________ _______ _______
Joseph Pehrson

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

/tuning/topicId_27964.html#28248

> Never mind microtonal...It's only artificial and
> intellectual thing, nothing more !
> The true music is not into !
> We dont need to have that for composing !

> That's my reason= it's too false to listen !
> And the way is false !
> Nobody and never will like microtonal compositions :)
> The true music dont have one future in this
> direction...
> The rest is "bla bla " in french...

Hi Latch.... I think you might get an argument from Johnny Reinhard
on this one...

______ ______ _______
Joseph Pehrson

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

/tuning/topicId_27964.html#28283

> Bob had said:
> For example, we know that in western music harmony and melody
> > interact polyphonically in ways that are fairly unique to this
> > tradition. The melodic scales we use are FUNDAMENTALLY BASED on
> > HARMONIC considerations.
>
> Paul had replied:
> I completely disagree. The melodic scales we use derive from a time
> in our culture before harmony or polyphony were ever used. It is
> lucky that they turned out to lend themselves to harmony with only
> very minor modifications.
>
> Bob answers:
> Well, if the way harmony and melody interact in our tradition is
not
> fairly unique (thought "fairly" was a conservative term), then I'd
> sure like to know about those traditions that are "fairly close" to
> us in that regard. And as in many melodic traditions, especially
> those that frequently use drones, even they had just relationships
in their structure.
>
> As you well know (but seem to be ignoring for the moment?), the
times to which you refer used 3-limit JI, which is by definition
> harmonically derived even if they didn't conceive of it that way.
The psychoacoustic basis for their prediliction for just fifths and
> fourths had no dependence on their being explicitly aware it.
>
> This is an important point, and it bears on universals implicit in
a common human perceptual metastructure INDEPENDENT of the age. This
> has nothing to do with imposing current aesthetics on another
> age!!!!!
>

This is really quite interesting, and seems to imply that Medieval
music, for instance, would have a "harmonic" basis even if the
composers weren't thinking of harmony!

In other words, just because the system was created of 3-limit
perfect fifths it would imply an harmonic basis.

I'm not sure I can really buy that, if the *usage* isn't really
harmonic... ??

It seems to me the music of that time is more *linear* than
anything...

In fact, I'm not sure one would really want to classify perfect
fifths and fourths as "harmony.." ??

I guess one could, and it is a value judegment, of course, but
landing on these intervals seems like a "different" breed, kind of
inbetween melody and harmony.

It's kind of like a "medical" virus, perhaps?? Neither life or non-
life...

Is it possible that Medieval "harmony" is something essentially
*between* melody and harmony???

Just a thought...??

Certainly, though, just because a *structure* is made out of
a chain of simultaneous diads, making "harmony" doesn't mean that the
fundamental basis of the music is "harmonic" if it's not used that
way...

???

_________ _______ _______
Joseph Pehrson

Hello, there, Joseph Pehrson.

While the topic of Renaissance diatonicism is one inviting many lines
of discussion, for example the question of modality in its horizontal
and vertical aspects, one starting point for my viewpoints on some of
the issues you raise might be my recent post in response to the
"7-limit" and related threads:

/tuning/topicId_28404.html#28404

Again, I consider these very important questions, and would much
welcome further dialogue.

Most appreciatively,

Margo Schulter
mschulter@value.net

--- In tuning@y..., mschulter <MSCHULTER@V...> wrote:

/tuning/topicId_27964.html#28463

> Hello, there, Joseph Pehrson.
>
> While the topic of Renaissance diatonicism is one inviting many
lines of discussion, for example the question of modality in its
horizontal and vertical aspects, one starting point for my viewpoints
on some of the issues you raise might be my recent post in response
to the "7-limit" and related threads:
>
> /tuning/topicId_28404.html#28404
>
> Again, I consider these very important questions, and would much
> welcome further dialogue.
>
> Most appreciatively,
>
> Margo Schulter
> mschulter@v...

Thank you very much, Margo! I am still behind in my reading, for
understandable reasons... Looking forward to getting to this post!

best wishes,

_________ ________ _______
Joseph Pehrson

Hello, there, Joe Pehrson, and please let me briefly reply to your
remarks on medieval "harmony," which in the 13th-14th century era in
Western Europe represents a fascinating approach to what I might call
in a 20th-century manner diverse "collections" of three or four
voices.

While regular writing for three or four voices becomes standard in the
epoch of Perotin around 1200, theory by around 1300 follows practice
in discussing some of the stable and unstable multi-voice sonorities
or "collections" in use.

I would say that the music is based on stable three-voice trines
(_trina harmoniae perfectio_) at 2:3:4, defining the unit of "perfect"
or "complete" sonority or harmony, if we wish to use that term.

Around 1300, Johannes Grocheio tells us that a consonance is
"perfected" by _three_ voices forming an outer octave (2:1), lower
fifth (3:2), and an upper fourth (4:3) proceeding from both other
intervals.

Another treatise of the same epoch, ascribed by one modern editor at
least to Jacobus of Liege (the Jacobus de Montibus mentioned by a late
14th-century author in the Berkeley Manuscript?), says that the series
of number 2-3-4 describes the "natural" arrangement of a sonority with
an outer octave and a 2:3 fifth below a 3:4 fourth.

Somewhat as in certain 20th-century styles, interestingly, the diverse
unstable sonorities of this era can be derived as various
"collections" of dyads, with the combination sometimes having
qualities different from those of its isolated intervallic elements.

For example, Coussemaker's Anonymous I and Jacobus (very possibly the
same author) both note that the major ninth at 9:4 "seems to concord
better" in a three-voice sonority where it is combined with two 3:2
fifths -- for example, G3-A4 in G3-D4-A4. Since some composers from
Perotin to Machaut use this sonority prominently, Jacobus may be
giving us a clue to their outlook.

The "collection" idea can also apply to multi-voice progressions,
which often can nicely be derived by superimposing or "stacking"
elementary two-voice progressions.

I discuss this kind of approach at some length -- using symbols like
8/5, by the way, to show a "figured bass" kind of notation for
sonorities (e.g. octave and fifth in relation to the lowest note)
rather than tuning ratios -- at

http://www.medieval.org/emfaq/harmony/13c.html
http://www.medieval.org/emfaq/harmony/pyth.html

The idea of stable trines, unstable "collections" with various degrees
of concord or discord, and also collections of two-voice progressions
united to form satisfying directed cadences for three and four voices,
stands in contrast either to the idea of "harmony" in an 18th-century
sense, or to a texture based on isolated melodic lines or dyads.

In 20th-century terms, we have what Ludmilla Ulehla has called a
texture based on "intervallic structures" -- structures built from
diverse types of dyads, with both sometimes subtle degrees of vertical
tension and melodic shapes playing a vital role.

This is a brief statement, but I hope a not unhelpful one of my basic
outlook.

As always, more questions and dialogue are very warmly invited and
encouraged; these are very important topics.

Most appreciatively,

Margo Schulter
mschulter@value.net

mschulter schrieb:
>
> Hello, there, Joseph Pehrson.
>
> While the topic of Renaissance diatonicism is one inviting many lines
> of discussion, for example the question of modality in its horizontal
> and vertical aspects, one starting point for my viewpoints on some of
> the issues you raise might be my recent post in response to the
> "7-limit" and related threads:
>
> /tuning/topicId_28404.html#28404
>
> Again, I consider these very important questions, and would much
> welcome further dialogue.

wrong guy responding :)

I wasn't conscious of the division-of-the-fifth principle being
applied to fifthless inversions, even though I must have read
this post previously.

Could it be that it is necessary to distiguish much more
strictly (than I did so far) between vocal and instrumental
music?

In vocal polyphony the tenor-cantus frame prevails and
determines the cadences, using the old clausulae in the
appropriate voices. In instrumental music, voice leading rules
were loosened for keyboard music and certainly for the lute,
emphasizing the momentary, vertical aspect ("Where do I put my
fingers now?").

klaus

--- In tuning@y..., "John A. deLaubenfels" <jdl@a...> wrote:

/tuning/topicId_27964.html#28345

> [Paul:]
> >I _like_ Switched-on and Swingle-sung Bach!
>
> Oops! I incorrectly assumed you were being ironic. It delights me
> that there's something with names that silly that you find musically
> interesting! :-)
>
> JdL

Well, of course, these citations are significant cultural influences
and not so silly. The influence of Wendy Carlos' _Switched on Bach_
among the synthesizer set of the early 60's is legendary. Ditto
the "Swingle Singers" with their work, not only with jazzed-up Bach,
but with Luciano Berio in his _Sinfonia_ and other efforts...

________ _______ ________
Joseph Pehrson

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

/tuning/topicId_27964.html#28352

> I think that it should be clear from this that to speak of such a
> metastucture does NOT have to imply spurious means to justify an
> "anything goes" approach to drawing conclusions from historical
> evidence. A greater peril lies in ignoring that such a
metastructure does indeed exist and a mindset that believes
everything derives strictly from the explicit expressions available
to us in historical writings and physical objects such as ancient
instruments, including our own conclusions from them.
>

Well, this is interesting, but getting back to the original details
that started this discussion: is it possible to set up a *harmonic*
system, say by creating a chain of fifths and then say that it is
*fundamentally* a *harmonic* construct, if it is never used that way,
if it only used in the construction of scales that create *melody??*

Actually, I'm a great believer in the primacy of harmony in music,
but I have certainly heard other arguments favoring *melody,*
especially given in the light of non-Western cultures, and they seem
persuasive...

_________ ________ _________
Joseph Pehrson

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

/tuning/topicId_27964.html#28356

>
> I'm feeling hopelessly behind on higher priority tasks directly
> related to Cantus Angelicus and work. I have no time to even get
> agressive about seeking a grant. I need administratvie help, but
> oddly not enough has not been fothcoming for the six years of our
> existence in spite of our success in other respects.
>

Umm... sorry about this short off-topic post... but I had to respond
to this. I think you will find there is *no* higher-priority task
than grant writing! And, nobody wants to do it, which is why help is
so hard to find. Ironically, though, it's what makes everything else
possible! Good luck!

_______ _________ _______
Joseph Pehrson

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

/tuning/topicId_27964.html#28385

> I'd suggest Easley Blackwood's book _The Structure of Recognizable
> Diatonic Tunings_ for more.

Hi Paul...

Wouldn't that be nice... I've had this book on "used search order"
on Amazon.com for over a year now.... Similarly on some other used
book Web services.

If anybody knows where I can get one, I will pay $ for it... (if I'm
still employed in our current economy...)

________ _______ ________
Joseph Pehrson

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

/tuning/topicId_27964.html#28387

> I'm not seeing the analogy here. You're well aware, I am sure, that
> we agree on almost all the issues discussed on this list. I'm
simply trying to point out that there may be _some_ aesthetic
considerations that have _some_ importance to my ears and to others'
ears, which you may be giving short shrift because you've come up
with a neat theoretical framework that seems to nicely account for
many powerful experiences you've had with your singers.

Just out of curiousity, has anyone else here besides Bob Wendell,
ever heard "combination tones" in choral singing...??

Not doubting, just curious...

________ ______ _________
Joseph Pehrson

Hello, there, Klaus Schmirler and everyone.

Please let me respond to two important points you raise: Zarlino's
discussion of divisions of the sixth as well as divisions of the
fifth, and the role of traditional two-voice cadential progressions or
_clausulae_ and other elements in 16th-century vocal and instrumental
music.

The second point draws on the contributions of scholars such as
Richard Crocker and Carl Dahlhaus, and I would here like to suggest
that 16th-century practice and theory can be viewed as combining
Gothic and newer elements in such a way to define a unique kind of
style. Here I will look both to Zarlino, and to such contemporaries as
Vicentino and Santa Maria.

------------------------------------
1. Zarlino on divisions of the sixth
------------------------------------

First, I should clarify that Zarlino discusses what I have termed
divisions of the sixth -- e.g. G3-C4-E4 (major sixth, fourth, major
third) or E3-G3-C4 (minor sixth, minor third, fourth) -- in the
context of some rules and suggestions for the treatment of the fourth
in writing for three or more voices.

His famous comparison of the divisions of the fifth -- the harmonic
(e.g. F3-A3-C4) or arithmetic (e.g. A3-C4-E4) -- take a similar
approach, but with an important difference.

With the fifth, Zarlino finds the harmonic division with a
string-ratio of 15:12:10, the 5:4 major third below and the 6:5 minor
third above, as the "natural" division; and the arithmetic division of
6:5:4, with the converse arrangement of the thirds, as "artificial"
and somewhat less ideally concordant.

Here is a diagram showing that the differences between terms in the
first division with the major third below have the same ratio (3:2) as
the outer terms, while in the second division we have an arithmetic
proportion with equal differences between adjacent terms:

F3 A3 C4 A3 C4 E4
15 12 10 6 5 4
3 2 1 1

In his discussion of the three-voice divisions featuring the fourth,
however -- those with an outer major or minor sixth -- he could not
consistently use this test for all the combinations he discusses. In
his approach, he instead takes a more general view in determining
which sonorities are "natural" (more euphonious) or "artificial"
(somewhat less euphonious than their "natural" counterparts).

Interestingly, with the major sixth, we could use the kind of
harmonic/arithmetic contrast Zarlino applies to the divisions of the
fifth in order to reach his result that the string ratio of 20:15:12
(fourth below major third) is more harmonious than 20:16:12 (converse
arrangement):

G3 C4 E4 G3 B3 E4
20 15 12 20 16 12
5 3 4 4

However, with the division of the 8:5 minor sixth into 6:5 minor third
and 4:3 fourth, this approach would not apply, since neither
arrangement is a harmonic or arithmetic division:

A3 C4 F4 A3 D4 F4
24 20 15 24 18 15
4 5 6 3

In neither division do we find either that the differences between
adjacent terms have the same proportion as the extreme terms (8:5), or
that these differences are equal.

For the divisions of the sixth involving the fourth, Zarlino instead
uses the order of the "sonorous numbers" or senario as a criterion to
judge the more pleasing arrangements of these sonorities:

C5-----
|
G4 | 8:5
6:5 |
E4------
5:4
C4
4:3
G3
3:2
C3
2:1
C2

Thus he finds that in this series of ratios the 4:3 fourth occurs _below_
the 5:4 major third -- as in G3-C4-E4; while the 6:5 minor third
occurs _below_ the 4:3 fourth in E4-G4-C5. The latter sonority with
its 8:5 minor sixth is actually outside the senario proper, but is
included by Zarlino so that both major and minor sixths may be
represented.

Here I wish to clarify that Zarlino does not apply the concept of the
harmonic and arithmetic divisions of the fifth to sonorities with no
fifth -- the saturated consonances dividing a sixth into a fourth and
third -- but draws an analogous kind of "natural/artificial"
contrast based on the intervals present in these sonorities.

Along with Dahlhaus, I would emphasize that we must look to the
expansive or contractive character of intervals as well as what
Zarlino terms the "natural" or "artificial" qualities of a sonority.

Thus F3-A3-D4 is at once "artificial" in its arrangement of the major
third below and fourth below -- an arrangement opposite to that found
in the senario -- and "expansive" in the quality of the major third
and major sixth, which seek the fifth and octave respectively.

Both for the divisions of the fifth, and for the divisions of the
sixth into fourth and third, Zarlino is seeking to distinguish between
the more and less harmonious arrangements. I hope that this discussion
may clarify the distinction between his harmonic/arithmetic contrast
and his more general natural/artificial contrast.

For the divisions of the fifth and major sixth, one could take either
approach; for the minor sixth, only the latter approach applies in
this 16th-century setting.

(In a 21st-century setting, one might consider for example an
arithmetic division of 8:5 into a string ratio of 16:13:10.)

----------------------------------------------------------
2. Two-voice clausulae in 16th-century theory and practice
----------------------------------------------------------

Certainly I would agree with Dahlhaus and others that traditional
two-voice cadential formulae, or _clausulae_ in this 16th-century
sense, often guide multi-voice textures, and also that the
tenor-superius pair often holds this guiding progression.

At the same time, I would emphasize both the mixture of old and new
two-voice cadences, both types presented by Zarlino, and the emphasis
on theorists such as Vicentino as well as Santa Maria on the role of
the bass or bass-superius pair.

In addition to some distinctions between vocal and more informal
instrumental styles (e.g. dances), we might find distinctions between
vocal writing in a more elaborate or formal contrapuntal style, and
writing in the kind of "familiar" or note-against-note style featured
in sources such as the Cancionero de Palacio around 1500, as well as
later in the 16th century.

Since it has been commented that Spanish songs of the kind I am
describing often use dancelike patterns, and sometimes dance melodies,
we might look for various connections between such related styles.

From the tenor-superius viewpoint, a cadence like the following might
be viewed as a four-voice harmonization of the M6-8 _clausula_ found
in the two principal voices, moving from the major sixth E4-C#5 to the
octave D4-D5:

C#5 D5
A4 A4
E4 D4
A3 D3

By the time of Vicentino and Zarlino, however, another element has
been recognized in this type of four-voice cadence: the progression of
the bass and another voice, here the superius, from a major third or
tenth (A3-C#5) to a unison, octave, or fifteenth, etc. (here D3-D5).

A characteristic of this "new" two-voice formula is that the upper
voice ascends by a semitone, while the bass falls a fifth or rises a
fourth.

Zarlino's own reaction is somewhat mixed: he regards this kind of
formula as characteristic of pieces for three or more voices, but
would prefer a more traditional cadence such as m3-1 or M6-8 in
two-voice writing, although he grants that it would not be a mistake
to use the this M3-8 or similar cadence there also.

By around 1550, the desire for what both Vicentino and Zarlino
describe as "rich" or "perfect" harmony by the new standards -- a
sonority with a third plus a fifth or a sixth above the bass --
sometimes calls for modifying the traditional formula, as here:

C#5 D5
A4 A4
E4 F#4
A3 D3

In order to arrive at a _harmonia perfetta_ sonority including the
third as well as the fifth, the tenor moves E4-F#4 rather than E4-D4,
so that we actually have parallel sixths between tenor and superius,
rather than the traditional major sixth to octave progression.

Note that this cadence still has the major tenth between the bass and
superius, moving to a fifteenth.

Vicentino takes the bass as the voice defining the mode, and considers
motions of this voice by a fifth or fourth to have a mode-defining
quality. He describes four-voice cadences in terms a customary
"action" or progression for each voice, as in this example:

C#5 -D5
"soprano cadence"
A4 - A4
"alto cadence"
E4 - D4
"tenor cadence"
A3 - D3
"bass cadence"

Thus one might say that typically the bass moves down a fifth or up a
fourth; the tenor descends by a step; the alto remains stationary; and
the soprano ascends by a semitone.

Vicentino shows that these types of cadential roles can be
interchanged, with the bass making a "soprano cadence," for example,
somewhat in the manner of double or multiple counterpoint.

For Tomas de Santa Maria, a charaacteristic of this kind of final
cadence is the role of the dissonance of the eleventh -- the 11-10 or
4-3 suspension typically featured. He presents the bass-superius pair
as the most important.

While Santa Maria is focusing mainly on instrumental music, Vicentino
is at least equally concerned with voices.

By around 1600, we have the kind of viewpoint expressed by Coperario
in his _Rules How to Compose_, where the resolution of an 11-10
suspension followed by a progression with the bass falling a fifth or
rising a fourth while the upper voice ascends by a semitone is taken
as defining a typical two-voice close:

A4 G#4 A4
E3 A3

Here I would add that the balance of bass motions by step, by third,
and by fifth or fourth gives 16th-century music a special character
which the meantone system with its pure or near-pure thirds very
nicely fits.

In surveying the variety of such motions, and four-voice progressions
to fit them, Coperario expresses this pluralistic approach, one
distinct from that of the 18th-century tonal system.

Again, it is a great pleasure to exchange views on these subjects, and
I welcome more dialogue, as well as comments or questions from others.

Most appreciatively,

Margo Schulter
mschulter@value.net

jpehrson@rcn.com wrote:

> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> /tuning/topicId_27964.html#28385
>
>
> > I'd suggest Easley Blackwood's book _The Structure of Recognizable
> > Diatonic Tunings_ for more.
>
> Hi Paul...
>
> Wouldn't that be nice... I've had this book on "used search order"
> on Amazon.com for over a year now.... Similarly on some other used
> book Web services.
>
> If anybody knows where I can get one, I will pay $ for it... (if I'm
> still employed in our current economy...)
>
> ________ _______ ________
> Joseph Pehrson

Someone told me that a fine arts enthusiast from the Scottish island of Arran wanted to start a
gallery so he wrote to some of the top (meaning very big name) artists asking if they'd like to
contribute a painting or two. And many of them did, in fact I think one or two did something just
for him.

So why not try the direct approach? I'd 'borrow' the Blackwood copy from Edinburgh Library and
send it over but I'm friendly with all the staff.

Good Luck

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:

/tuning/topicId_27964.html#28528

>
> So why not try the direct approach? I'd 'borrow' the Blackwood
copy from Edinburgh Library and
> send it over but I'm friendly with all the staff.
>
> Good Luck

You have given me a good idea, Allison.... I'll try to contact Easley
Blackwood directly.

The only problem is that he no longer teaches at the University of
Chicago, and he's not on the roster...

Anybody have an e-mail address for him??

(It's not done as Easley as I hoped --- sorry, that lifted my spirits
for a millisecond...)

________ _______ ________
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> /tuning/topicId_27964.html#28385
>
>
> > I'd suggest Easley Blackwood's book _The Structure of
Recognizable
> > Diatonic Tunings_ for more.
>
> Hi Paul...
>
> Wouldn't that be nice... I've had this book on "used search order"
> on Amazon.com for over a year now.... Similarly on some other used
> book Web services.
>
> If anybody knows where I can get one, I will pay $ for it... (if
I'm
> still employed in our current economy...)
>
Hi Joseph . . .

Many university libraries have this book . . . have you ever used
Inter-Library Loan? You may want to contact Paul Hahn . . .

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> /tuning/topicId_27964.html#28387
>
> > I'm not seeing the analogy here. You're well aware, I am sure,
that
> > we agree on almost all the issues discussed on this list. I'm
> simply trying to point out that there may be _some_ aesthetic
> considerations that have _some_ importance to my ears and to
others'
> ears, which you may be giving short shrift because you've come up
> with a neat theoretical framework that seems to nicely account for
> many powerful experiences you've had with your singers.
>
>
> Just out of curiousity, has anyone else here besides Bob Wendell,
> ever heard "combination tones" in choral singing...??
>
> Not doubting, just curious...
>
When singing loudly in a high register next to another singer singing
loudly in a high register, I can most definitely hear them . . .
everyone's heard them when two piccolos or recorders play together
loudly . . . I think Bob may, at least partially, be using "virtual
pitch" effects where he thinks he's using "combinational tone"
effects . . . the two can be similar but are quite clearly
distinguished in experimental psychoacoustics . . .

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

/tuning/topicId_27964.html#28541

> Hi Joseph . . .
>
> Many university libraries have this book . . . have you ever used
> Inter-Library Loan? You may want to contact Paul Hahn . . .

Hi Paul...

That's a good suggestion... but probably my friend Pat Hardish who
works at the Midtown Manhattan Library could arrange this... Then,
probably, I could just copy it.

good idea

________ __________ ______
Joseph Pehrson

See bottom for answer -

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., jpehrson@r... wrote:
> > --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> >
> > /tuning/topicId_27964.html#28387
> >
> > > I'm not seeing the analogy here. You're well aware, I am sure,
> that
> > > we agree on almost all the issues discussed on this list. I'm
> > simply trying to point out that there may be _some_ aesthetic
> > considerations that have _some_ importance to my ears and to
> others'
> > ears, which you may be giving short shrift because you've come up
> > with a neat theoretical framework that seems to nicely account
for
> > many powerful experiences you've had with your singers.
> >
> >
> > Just out of curiousity, has anyone else here besides Bob Wendell,
> > ever heard "combination tones" in choral singing...??
> >
> > Not doubting, just curious...
> >
> When singing loudly in a high register next to another singer
singing
> loudly in a high register, I can most definitely hear them . . .
> everyone's heard them when two piccolos or recorders play together
> loudly . . . I think Bob may, at least partially, be using "virtual
> pitch" effects where he thinks he's using "combinational tone"
> effects . . . the two can be similar but are quite clearly
> distinguished in experimental psychoacoustics . . .

Bob:
What I am using has traditionally (for a long time) been called
differential or difference tones. They are the primary combinatorial
product of two simultaneously sounded tones with good harmonicity. It
matters little to me what researches have decided to call them. (This
is NOT to say that the research does not interest me, just in case
anyone is tempted to take it that way.) They are the most audible
subtone generated when two tones of harmonic timbres are sounded
together.

My theoretical understanding is that these tones are produced in the
human ear due to a slight non-linearity in our hearing. (Difference
products are produced only when frequencies are mixed in a non-linear
device.) There is also a neurological basis contributing to reinforce
this effect. High, shrill tones of rich harmonic timbre produce very
noticable differential tones. They are very annoying when the
intonation is not just. When it is just, the effect can be absolutely
celestial.

None of this means they don't exist in other, less obvious contexts.
Any sensorially (internally) generated phenomenon that is not an
original component of the source objects perceived (in this case,
musical tones) tends to get nulled out by our brains' sensory data
processing, since it is always present yet not part of the objective
"picture". This is called "masking" in psychology. However, this
psychological masking effect can be overcome.

We all know the ear can be trained to pick out individual harmonics
in a musical timbre, thereby going beyond the usual default
perception of the complete tonal gestalt we call timbre. In the same
way, the ear can learn to pick out these difference tones as
subtones. Once one has learned to do this, it is surprising how LOUD
they are. They are not nearly so subtle as one might suppose.

On the violin, they are so loud it is hard to understand how anyone
could miss them, but most violinists do in my experience. I have
inquired, since I'm curious and play the violin myself. I heard them
from the first day. I think the violin probably exaggerates them for
the player, since a large component of the sound is transmitted to
the player's ear by bone conduction, and the coupling through the
chin from the violin body is bound to be quite non-linear.

To be fair, in a complex musical context they are not always obvious
even to highly trained ears. However, just as we can recognize timbre
intuitively without analyzing or picking out continuously the
individual harmonic components that contribute to it, we can
similarly learn to distinguish clearly when the difference tones are
harmoniously aligned with the source tone fundamentals and their
harmonics.

Assuming timbres of reasonably high harmonicity, there is only one
condition necessary to ensure alignment of both the differential
tones and the fundamentals and harmonics of the source tones. This
condition is whole number ratios between frequencies. 2:3 therefore
produces a difference tone at 1 an octave below the bottom tone of
the fifth.

THIS IS NOT SO SUBTLE once you learn to hear it. 4:5 produces 1, two
octaves below the bottom note. A compact major triad in first
inversion produces both the octave and two octaves below the root
with the lower octave also reinforced by the difference tone from the
third and fifth. This is why the major triad is such a highly stable
and consonant harmonic entity.

Anyone trained to recognize the difference tones' presence is
IMMEDIATELY sensitive to even a slight skewing of these
relationships. This is because, interestingly, pitch is
logarithmically related to frequency and the difference frequency is
a
LINEAR function. So any slight change of the 4:5 third will cause a
pitch change FOUR TIMES AS GREAT in the difference tone two octaves
below.

This should shed a good deal of light on the basis for many of the
positions I have taken in our discussions.

Hi,

Lot of good stuff snipped to trim volume.

> Anyone trained to recognize the difference tones' presence is
> IMMEDIATELY sensitive to even a slight skewing of these
> relationships. This is because, interestingly, pitch is
> logarithmically related to frequency and the difference frequency is
> a
> LINEAR function. So any slight change of the 4:5 third will cause a
> pitch change FOUR TIMES AS GREAT in the difference tone two octaves
> below.
>
> This should shed a good deal of light on the basis for many of the
> positions I have taken in our discussions.

So now comes a related question. How do you tune a tonic minor chord?
Do you notice it as being close to the 12tet version, or is the minor
third raised somewhat, (or lowered somewhat) corresponding to a JI sort
of tonic minor?

The difference tone theory would seem to be most supported by a 16:19:24
ratio tunin for the minor triad, which would be close enough for jazz to
12tet.

Any of the other likely candiates 10:12:15, or 6:7:9 don't seem to have
the right properties.

Bob Valentine