Re: Adaptive tuning

Hi John,

Thanks for turning me on to the tuning list! It has been an interesting read. Also, I think I want to take this part of our discussion out to the list, now that I have looked around a bit, so, "Hi, everyone!"

Okay, down to business. I've been going through the posts on the tuning list and have seen yours, as well as the discussion about consonance vs. concordance. To me, it's so much hoo hah. After looking up the two terms in various dictionaries at work, some music, some not, I have come to the conclusion that they are essentially two senses of the same term, therefore I can't say that I agree with Paul Erlich on his distinction (or Blackwood, though I have yet to read his book cover-to-cover). If we're going to make such a distinction, then it seems to me that we also have to come up with a term that will separate mathematical consonance from subjective consonance. A 4:5:6:7 chord is mathematically consonant, since each interval within it exists in symetry with the others, with difference tones that are octave transpositions of tones already present in the chord. A 4:5:6:7 could sound dissonant is if it was voiced too low, in which case the difference tones could be low enough to be perceived as beats instead of logical bass tones, but it would still be mathematically consonant. On the other hand, there seem to be those who say that tunings other than just are consonant (or is it concordant?). Interesting. I see no mathematical basis for this viewpoint. Maybe I've misinterpreted? Of course there are plenty of "dissonant" constructs that sound great, but they're still dissonant. As a player, my ears tell me what is consonant, and they usually agree with the mathematical model. Onward...

At 11:50 AM -0600 8/18/00, John A. deLaubenfels wrote:
>How nice it would be to be able to go back to the past and make
>actual observations! The clues we're left are very unsatisfactory
>in resolving what actually happened. 'Course, the world was
>very fragmented then, too, so local variations may have provided
>hundreds of answers.

I think you'd find that performers have always been more concerned with what sounds good than with theory. We are and always have been doers, not thinkers. It's as old as the hills. Having played historic brasses, I can tell you that most are difficult to play in tune, but not impossible (with practice!).

The simple ratios that are mathematically consonant are perceived thus because our ears can easily decode the relationships between the pitches. Without knowing anything about the math, musicians have always been able to hear these relationships. Just because it isn't in the history books doesn't mean it wasn't done.

I'll grant that tuners of fixed pitch instruments have had to go to great mathematical lengths to find workable tunings for these instruments to play in more than one key, but players of variable pitched instruments and vocalists have always been free of such constraints (unless we have to play with keyboards!). Remember, the keyboard tuners and theoreticians were the ones who wrote down what they did. No one else thought to do that, or needed to, for that matter. Good, simple, garden variety intonation just _is_.

>Like you, my attitude ultimately is that, whatever people did
>in the past, I'm going to tune today to suit my own ear, however
>it got the way it did. My ear embraces 7-limit dom 7ths.

To bring another post I saw into this, I find it interesting that people consider just intervals to be "dead" sounding. As a player, I always find the difference tones created by just intervals to be exhilirating! A treble-only quartet can manufacture its own bass notes! Here the 7-limit dom7 is a must, since if it is NOT a 7-limit (7/4) the dom7 chord is ruined by dissonance. The 5-limit 4/3 and 12tET substitutes cause conflict within the chord by generating bass notes that are quite out of tune with the triad, and other tunings are at least as bad. Students ask me about the bass notes they heard but knew weren't being played, thus beginning their education in tuning...

Time to digress: Having said all this about how just intervals are so cool, I have to admit that there are instances where 12tET or other tunings do sound good. I am a jazz player too, and there are many jazz chords that don't work well in the just scale, 7-limit or not. In fact, 12tET has spawned harmonic extensions that sound really cool in 12tET, but not so good when tuned to just intervals. As if such a thing could even be done with some chords. Try tuning the beats out of a G13#11! But it sounds very nice in 12tET. So when I play jazz, I play just intervals when I can, but don't worry about it much otherwise.

Well, there you have it, my 2 cents.
Well, I guess it was more like a comma... -- groan! --

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
Patrick K. Mullen |
California State University, Long Beach | .___TTT____/
http://www.csulb.edu/~mullen | (_u|||o_) \
(562) 985-7937 |
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

[Patrick K. Mullen wrote:]
>Hi John,
>
>Thanks for turning me on to the tuning list! It has been an
>interesting read. Also, I think I want to take this part of our
>discussion out to the list, now that I have looked around a bit, so,
>"Hi, everyone!"

You should get some interesting posts back pretty quick! Try not
to burn out early, ok?

>Okay, down to business. I've been going through the posts on the
>tuning list and have seen yours, as well as the discussion about
>consonance vs. concordance. To me, it's so much hoo hah. After
>looking up the two terms in various dictionaries at work, some music,
>some not, I have come to the conclusion that they are essentially two
>senses of the same term, therefore I can't say that I agree with Paul
>Erlich on his distinction (or Blackwood, though I have yet to read
>his book cover-to-cover). If we're going to make such a distinction,
>then it seems to me that we also have to come up with a term that
>will separate mathematical consonance from subjective consonance. A
>4:5:6:7 chord is mathematically consonant, since each interval within
>it exists in symetry with the others, with difference tones that are
>octave transpositions of tones already present in the chord. A
>4:5:6:7 could sound dissonant is if it was voiced too low, in which
>case the difference tones could be low enough to be perceived as
>beats instead of logical bass tones, but it would still be
>mathematically consonant. On the other hand, there seem to be those
>who say that tunings other than just are consonant (or is it
>concordant?). Interesting. I see no mathematical basis for this
>viewpoint. Maybe I've misinterpreted? Of course there are plenty of
>"dissonant" constructs that sound great, but they're still dissonant.
>As a player, my ears tell me what is consonant, and they usually
>agree with the mathematical model. Onward...

My main concern is to agree on a meaning for a set of words so that
communication can proceed clearly. It is true that there will always
be some fuzziness of meaning, though.

[JdL:]
>>How nice it would be to be able to go back to the past and make
>>actual observations! The clues we're left are very unsatisfactory
>>in resolving what actually happened. 'Course, the world was
>>very fragmented then, too, so local variations may have provided
>>hundreds of answers.

[Pat:]
>I think you'd find that performers have always been more concerned
>with what sounds good than with theory. We are and always have been
>doers, not thinkers. It's as old as the hills. Having played historic
>brasses, I can tell you that most are difficult to play in tune, but
>not impossible (with practice!).
>
>The simple ratios that are mathematically consonant are perceived
>thus because our ears can easily decode the relationships between the
>pitches. Without knowing anything about the math, musicians have
>always been able to hear these relationships. Just because it isn't
>in the history books doesn't mean it wasn't done.

I won't disagree.

>I'll grant that tuners of fixed pitch instruments have had to go to
>great mathematical lengths to find workable tunings for these
>instruments to play in more than one key, but players of variable
>pitched instruments and vocalists have always been free of such
>constraints (unless we have to play with keyboards!). Remember, the
>keyboard tuners and theoreticians were the ones who wrote down what
>they did. No one else thought to do that, or needed to, for that
>matter. Good, simple, garden variety intonation just _is_.

True.

[JdL:]
>>Like you, my attitude ultimately is that, whatever people did
>>in the past, I'm going to tune today to suit my own ear, however
>>it got the way it did. My ear embraces 7-limit dom 7ths.

[Pat:]
>To bring another post I saw into this, I find it interesting that
>people consider just intervals to be "dead" sounding. As a player, I
>always find the difference tones created by just intervals to be
>exhilirating! A treble-only quartet can manufacture its own bass
>notes! Here the 7-limit dom7 is a must, since if it is NOT a 7-limit
>(7/4) the dom7 chord is ruined by dissonance. The 5-limit 4/3 and
>12tET substitutes cause conflict within the chord by generating bass
>notes that are quite out of tune with the triad, and other tunings
>are at least as bad. Students ask me about the bass notes they heard
>but knew weren't being played, thus beginning their education in
>tuning...

Good! That's a very real phenomenon, as you've experienced.

>Time to digress: Having said all this about how just intervals are so
>cool, I have to admit that there are instances where 12tET or other
>tunings do sound good. I am a jazz player too, and there are many
>jazz chords that don't work well in the just scale, 7-limit or not.
>In fact, 12tET has spawned harmonic extensions that sound really cool
>in 12tET, but not so good when tuned to just intervals. As if such a
>thing could even be done with some chords. Try tuning the beats out
>of a G13#11! But it sounds very nice in 12tET. So when I play jazz, I
>play just intervals when I can, but don't worry about it much
>otherwise.

And there are of course an infinitude of ET's; some on the list use
13-tET precisely because it is so dissonant/discordant. Also in
use are 19, 22, 31, 34, etc., etc.

JdL

In a discussion of adaptive tuning, Patrick Mullen wrote ...

>... I find it interesting that
>people consider just intervals to be "dead" sounding. As a player, I
>always find the difference tones created by just intervals to be
>exhilirating! A treble-only quartet can manufacture its own bass
>notes! Here the 7-limit dom7 is a must, since if it is NOT a 7-limit
>(7/4) the dom7 chord is ruined by dissonance. The 5-limit 4/3 and
>12tET substitutes cause conflict within the chord by generating bass
>notes that are quite out of tune with the triad, and other tunings
>are at least as bad. Students ask me about the bass notes they heard
>but knew weren't being played, thus beginning their education in
>tuning...

... and I'm responding mostly in order that this 'well-tuned' paragraph may reside twice in the archives. What power there is in an interval or chord when difference tones in the bass support it! I believe this is why it is so very natural for amateur a capella singers (I'm thinking particularly of barbershop quartet singers in the club SPEBSQSA) to lock in the 7/4 dom 7th in spite of its rarity in the music to which they may be accustomed.

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:
> I don't think you've understood Partch correctly. A major chord would be
> otonal whether dominant or subdominant, and a minor chord would be utonal
> whether dominant or subdominant.

Oh well. I guess I'll have to stick with my own terminology on this one. I view dominant and subdominant as reciprocal intervals from a key center. For example, the supertonic can either be 9/8 (dominant) or 10/9 (plagal), depending on context.

> I suggest you have a look at what John deLaubenfels's program does to this
> sequence, which to my ears is much more satisfactory than the sudden 81:80
> and 64:63 pitch-shifts you're proposing here, even while attaining
> essentially the same vertical sonorities (in the 7-limit version of his
> method).

That may be, but as I said in my original post, the point of the excercise is to examine the mathematical tyranny imposed by strict adaptive tuning, not its aesthetic quality.

Patrick K. Mullen wrote,

> The simple ratios that are mathematically consonant are perceived
thus because our ears can easily decode the relationships between the
pitches. Without knowing anything about the math, musicians have
always been able to hear these relationships. Just because it isn't in
the history books doesn't mean it wasn't done.

Hello Patrick, and welcome to the list. I Just wanted to pass on a
brief point that I once came across (and that I've already posted to
the list before regarding this; especially in the context of the
tuning of the dominant seventh chord)... I remember reading in Joseph
Yasser's 1930s "A Theory of Evolving Tonality," a bit where he
specifically mentions that the a cappella music of the Russian
church -- free from the influence of equal temperament -- avoids the
4:5:6:7 dominant seventh... that the seven tone diatonic scale itself
(so constructed), 'necessitates' a more 'tense' intonation... and that
the overall context (i.e., the need to establish resolution here),
even in this variable pitch, a cappella context, overrides whatever
the most aurally expedient isolated tuning of this chord itself might
be... While I can't pretend to vouch for the accuracy of the account,
I thought I'd pass it on as I found it interesting in the context of
this discussion.

Dan

I was listening to some examples of this very interesting idea, and
to Verklarte Nacht in particular. It seems to me one is asking for
trouble by using 11 or 13-limit harmonies for something originally
written in 12-et. What I think should be tried are the 7-limit plus
17, and the 7-limit plus 17 and 19. The diminished seventh turns into
harmonies using 17 very easily, for example.

I was also wondering if anyone has thought of a program for lifting
something from 12-et into JI in various ways, eg 7-limit+17. A JI
score with comma slides identified would be interesting in itself.

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

/tuning/topicId_11701.html#27989

> I was listening to some examples of this very interesting idea, and
> to Verklarte Nacht in particular. It seems to me one is asking for
> trouble by using 11 or 13-limit harmonies for something originally
> written in 12-et. What I think should be tried are the 7-limit plus
> 17, and the 7-limit plus 17 and 19. The diminished seventh turns
into
> harmonies using 17 very easily, for example.
>
> I was also wondering if anyone has thought of a program for lifting
> something from 12-et into JI in various ways, eg 7-limit+17. A JI
> score with comma slides identified would be interesting in itself.

Hi genewardsmith...

I believe Joe Monzo could give you a little "rap" on his view of
Schoenberg actually wanting to go to higher limits than those of 12-
tET. Monzo is, as you probably know, in Europe at the moment, but
you might be interested in his argument when he returns...

best,

________ _________ _____
Joseph Pehrson

--- In tuning@y..., genewardsmith@j... wrote:
> I was listening to some examples of this very interesting idea, and
> to Verklarte Nacht in particular. It seems to me one is asking for
> trouble by using 11 or 13-limit harmonies for something originally
> written in 12-et.

We had quite a bit of discussion about this way back . . . Monz
specifically wanted to hear harmonies with 11s and 13s . . . so John
made a version like that . . . with not a little thought behind it.

> What I think should be tried are the 7-limit plus
> 17, and the 7-limit plus 17 and 19. The diminished seventh turns
into
> harmonies using 17 very easily, for example.

John can probably code up the appropriate tuning files fairly
easily . . .
>
> I was also wondering if anyone has thought of a program for lifting
> something from 12-et into JI in various ways, eg 7-limit+17. A JI
> score with comma slides identified would be interesting in itself.

Comma slides identified? I object to the idea that any piece of
Western common-practice music "implies" comma slides at any
particular points in the score.

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

> Comma slides identified? I object to the idea that any piece of
> Western common-practice music "implies" comma slides at any
> particular points in the score.

In C major take the chord sequence I-IV-II-V-I. Each of these chords
has at least one note in common with each neighboring chord, so the
harmonic meaning is rigidly enforced; I would say the sequence
clearly transposes down a comma if lifted to JI. Even if you don't
agree, wouldn't you think such a sequence should be identified?

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> > Comma slides identified? I object to the idea that any piece of
> > Western common-practice music "implies" comma slides at any
> > particular points in the score.
>
> In C major take the chord sequence I-IV-II-V-I. Each of these
chords
> has at least one note in common with each neighboring chord, so the
> harmonic meaning is rigidly enforced; I would say the sequence
> clearly transposes down a comma if lifted to JI.

Yes it does, but is that a desirable thing?

> Even if you don't
> agree, wouldn't you think such a sequence should be identified?

Yes -- by slides I thought you meant in the sense of sliding subtly
along a violin string to subtly disguise a comma shift, rather than
anything having to do with comma drift.

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

> > In C major take the chord sequence I-IV-II-V-I. Each of these
> chords
> > has at least one note in common with each neighboring chord, so
the
> > harmonic meaning is rigidly enforced; I would say the sequence
> > clearly transposes down a comma if lifted to JI.

> Yes it does, but is that a desirable thing?

Not if you don't want it to, which is the point of adaptively
tempering it out.