Re: [tuning] Minors chords one example (BIS)

My chords have been destroyed by inter(not)net... I try to restore my
poor stuff
:-(
Xavier J.-P. CHARLES wrote:
>
> This example is the n�37 of violin studies of O. SEVCIK, Opus 2 part
> 5.
>
> When the note is "A", it's a whole string, when it's written "a" the
> note is made by a finger.
>
> Made the email in FULL SCREAN for a good reading...
>
> ���������������������������������������������������������������������������������������
> ***First part :
> chord number : 1 2 3 4 5 6 7 8 9 10 11 12 13
> A string - b b c b A A d c b A e #d e
> D string - D e e D #f D D D D e g #f e
> G string - G G G G D c b a G c b b G
>
> Tonality : G major-------------------------------- E minor ------
> degree I (VI) IV I V V I V I IV I V I
>
> ���������������������������������������������������������������������������������������
> ***Second part :
> chord number : 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
> E string - g #f b a g #f #g a #f a g e g #f g
> A string - A A d d A A d #c A c b c b A b
> D string - e D g #f e D e a D #d e a D D D
> (G string)- G
>
> Tonality : D major ---------------- A major ----E minor---- G major ----
> Degree V I IV I V I V I IV V I IV I V I
>
> ���������������������������������������������������������������������������������������
>
> I remember you that I try to play just intonation on my violin with
> the
> help of combination tones. Then I try to do those chords with the
> following intonation :
>
> Major chords ("4-5-6") :
> Chords numbers 1, 3, 4, 5, 7, 9, 15, 16, 17, 19, 21, 22, 26, 27 and
> 28.
>
> Dominant chords ("4-5-6-7")
> n�6 ("7-8-12")
> n�8 ("3-4-7")
> n�14 ("3-4-7")
> n�18 ("3-4-7")
> n�20 ("4-7-10")
>
> Minor chords ("16-19-24")
> n�10 ("19-24-32")
> n�11 ("12-19-32")
> n�24 ("8-12-19")
> n�25 ("16-19-24")
>
> Chords with difficulties :
> n�2 : for me it isn't a real minor chord, just a "passing chord". I
> think it's better that both b and both G are really equal, then this
> chord is rather a "10-12-15" (here : "6-10-15").
>
> n�13 : it's really a minor chord (then "16-19-24") but on the violin
> we
> must use G string, then it's a "pythagorean chord" "27-32-54" (here :
> "32-54-108"... ;-) yes it's possible to play it because of the 3
> fifth
> of a violin! ).
>
> n�23 : this chord is quite difficult. I try to play 9th minor dominant
> ("8-10-12-14-17")
> (here : "10-17-28"), but here combination tones can't help me. If I
> play
> a b (on A string) instead of c it's easier (then it's "5-8-14").
>
> Problem of the modulations :
> Chord n� 9 to n�10, the e (n�10) is one comma (81/80) of the e of 2nd
> chord. On a violin it's because of the whole strings but I think it's
> the good choice : then the D of 15th chord is really in tune with
> whole
> string.
>
> 19 to 20 : no problem... d-e is like 8-9. Both d are differents but...
> it's a modulation...
>
> On a violin, those chords involve the following singularities :
> n�1 : the b is out of tune with E string (4th 27/20).
> n�2 : the e // A // // .
> n�8 : the c made a 9/7 3rd with E string
>
> Sorry, I don't write just on minor chord, but, for me it's difficult
> to
> speak of a chord without a real context. (I know that here it'sn't a
> real score, just an exercise...)
>
> Xavier

Hi Xavier.

I have just been discussing with John deLaubenfels, the adaptive JI master,
how many who like purely tuned chords have only considered systems where the
melodic intervals are derived as ratios as well.
I hope John will take a stab at suggesting a tuning or two for your
exercise, perhaps even one where the minor triads are 16:19:24, as you
desire. John? (Please?) His program, I expect, will eliminate for all
audible purposes all the "problems" you bring up, and some that you don't!

-Paul

Paul H. Erlich wrote:
>
> Hi Xavier.
>
> I have just been discussing with John deLaubenfels, the adaptive JI
> master,
> how many who like purely tuned chords have only considered systems
> where the
> melodic intervals are derived as ratios as well.
> I hope John will take a stab at suggesting a tuning or two for your
> exercise, perhaps even one where the minor triads are 16:19:24, as you
> desire. John? (Please?) His program, I expect, will eliminate for all
> audible purposes all the "problems" you bring up, and some that you
> don't!

Good
:-)
I will try to record this exercice with my violin. But I have actually a
problem with my sound card (I have no sound :-( ).
I need help of a friend, then it's not for today...
Xavier

[Paul E wrote:]
>Hi Xavier.

>I have just been discussing with John deLaubenfels, the adaptive JI
>master, how many who like purely tuned chords have only considered
>systems where the melodic intervals are derived as ratios as well.
>I hope John will take a stab at suggesting a tuning or two for your
>exercise, perhaps even one where the minor triads are 16:19:24, as you
>desire. John? (Please?) His program, I expect, will eliminate for all
>audible purposes all the "problems" you bring up, and some that you
>don't!

Paul, when you say such nice things, how can I say no? My difficulty is
that I'm going crazy keeping all the balls I'm juggling up in the air
(and believe me, the "chord" that these activities represent wouldn't
make the top 36 by a long stretch!). Can anyone else make an actual
midi sequence for tuning? Xavier? Paul, you don't make midi sequences,
do you?

As for a 16:19:24 minor - I don't currently have a tuning file which
targets that. Here's the challenge: the tuning file format I currently
use presents a self-consistent tuning (meaning, each pitch class is
given a tuning offset from 12-tET, with all intervals implied
therefrom); how would one tune all 12 pitch classes in a way that would
prominently feature minor chord(s) tuned 16:19:24 and also handle other
chords in a reasonable way? Am I stating this clearly?

There is a similar problem with targeting the 6:7:9 minor chord, as I
believe we discussed to some degree a year or so ago.

Then there are dynamic challenges: consider A,C,E -> A,C,E,G -> C,E,G,
with notes tied when possible. G is pretty much forced to be a fifth up
from C, so some horror of a "major" chord results, unless there is
painful shifting of continuously sounding notes. The 10:12:15 minor, of
course, sidesteps such challenges by revealing a 4:5:6 major chord on
top.

BTW, keeping melodic intervals at, or close to, JI, would be aided by
a kind of spring I don't currently include in my model: horizontal but
non-unison. I have considered adding springs of this sort especially
for small intervals (minor and major seconds), in inverse importance of
their vertical tuning. That is, I'm suggesting that small melodic steps
need more tuning consideration than large melodic steps. When I raised
this issue a while back, most responses disagreed, as I recall, but I'm
still not convinced. For now, I let grounding and harmonic (vertical)
considerations limit the extent of melodic step deviations, which seems
to work pretty well.

JdL

John deLaubenfels wrote,

>As for a 16:19:24 minor - I don't currently have a tuning file which
>targets that. Here's the challenge: the tuning file format I currently
>use presents a self-consistent tuning (meaning, each pitch class is
>given a tuning offset from 12-tET, with all intervals implied
>therefrom); how would one tune all 12 pitch classes in a way that would
>prominently feature minor chord(s) tuned 16:19:24 and also handle other
>chords in a reasonable way? Am I stating this clearly?

Not really. Could you elaborate a little?

>Then there are dynamic challenges: consider A,C,E -> A,C,E,G -> C,E,G,
>with notes tied when possible. G is pretty much forced to be a fifth up
>from C, so some horror of a "major" chord results, unless there is
>painful shifting of continuously sounding notes. The 10:12:15 minor, of
>course, sidesteps such challenges by revealing a 4:5:6 major chord on
>top.

I think Xavier has some opinion on how this should be negotiated.

>BTW, keeping melodic intervals at, or close to, JI, would be aided by
>a kind of spring I don't currently include in my model: horizontal but
>non-unison.

But why would you want that???

>I have considered adding springs of this sort especially
>for small intervals (minor and major seconds), in inverse importance of
>their vertical tuning. That is, I'm suggesting that small melodic steps
>need more tuning consideration than large melodic steps. When I raised
>this issue a while back, most responses disagreed, as I recall, but I'm
>still not convinced.

I'm failing to see any possible justification. I might be in favor of a
related process that, sensitive to notation (not expressed in the MIDI file)
would try to equalize melodic major seconds with one another but not
equalize them with, say, diminished thirds. But of course that's far removed
from what you're doing.

>For now, I let grounding and harmonic (vertical)
>considerations limit the extent of melodic step deviations, which seems
>to work pretty well.

I guess I was hoping, John, that you'd take a stab at explaining the idea
behind your scheme to Xavier, since we were just talking about the pedagogy
of adaptive JI vs. strict JI.

[I wrote:]
>>As for a 16:19:24 minor - I don't currently have a tuning file which
>>targets that. Here's the challenge: the tuning file format I
>>currently use presents a self-consistent tuning (meaning, each pitch
>>class is given a tuning offset from 12-tET, with all intervals implied
>>therefrom); how would one tune all 12 pitch classes in a way that
>>would prominently feature minor chord(s) tuned 16:19:24 and also
>>handle other chords in a reasonable way? Am I stating this clearly?

[Paul E:]
>Not really. Could you elaborate a little?

Another way of putting it would be: if A,C,E is tuned 16:19:24, how is
A,C,E,G to be tuned?

[JdL:]
>>Then there are dynamic challenges: consider A,C,E -> A,C,E,G -> C,E,G,
>>with notes tied when possible. G is pretty much forced to be a fifth
>>up from C, so some horror of a "major" chord results, unless there is
>>painful shifting of continuously sounding notes. The 10:12:15 minor,
>>of course, sidesteps such challenges by revealing a 4:5:6 major chord
>>on top.

[Paul:]
>I think Xavier has some opinion on how this should be negotiated.

Xavier, what was that again?

[JdL:]
>>BTW, keeping melodic intervals at, or close to, JI, would be aided by
>>a kind of spring I don't currently include in my model: horizontal but
>>non-unison.

[Paul:]
>But why would you want that???

Because: especially now that I'm grounding to COFT values, which are
uneven in tuning space (i.e., not 12-tET!), I notice that scales played
with a single voice have a noticeably uneven sound that I'm not sure I
like. I think the tuning might benefit from weak horizontal non-unison
springs that would partially counteract this.

[JdL:]
>>I have considered adding springs of this sort especially for small
>>intervals (minor and major seconds), in inverse importance of their
>>vertical tuning. That is, I'm suggesting that small melodic steps
>>need more tuning consideration than large melodic steps. When I
>>raised this issue a while back, most responses disagreed, as I recall,
>>but I'm still not convinced.

[Paul:]
>I'm failing to see any possible justification.

But, other than that, you like the idea, right Paul? ;->

>I might be in favor of a related process that, sensitive to notation
>(not expressed in the MIDI file) would try to equalize melodic major
>seconds with one another but not equalize them with, say, diminished
>thirds. But of course that's far removed from what you're doing.

I do not have the notation available to me and am not sure I would agree
with the distinction in any case. When do "diminished thirds" come into
play again? Just looked in the index of Forte; no mention.

[Paul:]
>I guess I was hoping, John, that you'd take a stab at explaining the
>idea behind your scheme to Xavier, since we were just talking about the
>pedagogy of adaptive JI vs. strict JI.

Oh, sorry, I misunderstood you! There's a good summary of my scheme at

http://www.egroups.com/message/tuning/12668

JdL

John deLaubenfels wrote,

>Another way of putting it would be: if A,C,E is tuned 16:19:24, how is
>A,C,E,G to be tuned?

Xavier will probably give you an answer to that -- and it will be either
10:12:15:18 or 32:38:48:57. Either way, your program could handle that,
right?

>Then there are dynamic challenges: consider A,C,E -> A,C,E,G -> C,E,G,
>with notes tied when possible. G is pretty much forced to be a fifth
>up from C, so some horror of a "major" chord results, unless there is
>painful shifting of continuously sounding notes. The 10:12:15 minor,
>of course, sidesteps such challenges by revealing a 4:5:6 major chord
>on top.

John, this "painful shifting of continuously sounding notes" is pretty
common in some of your sequences already, right? Like in 7-limit, D,F,A ->
G,B,D,F would have even more of that, right? So what's the problem?

>>>BTW, keeping melodic intervals at, or close to, JI, would be aided by
>>>a kind of spring I don't currently include in my model: horizontal but
>>>non-unison.

>[Paul:]
>>But why would you want that???

>Because: especially now that I'm grounding to COFT values, which are
>uneven in tuning space (i.e., not 12-tET!), I notice that scales played
>with a single voice have a noticeably uneven sound that I'm not sure I
>like. I think the tuning might benefit from weak horizontal non-unison
>springs that would partially counteract this.

But wouldn't playing, say, a major scale in JI, with alternating 9:8 and
10:9 whole tones, have an even more uneven sound than most of your COFT
tunings?

>I do not have the notation available to me and am not sure I would agree
>with the distinction in any case. When do "diminished thirds" come into
>play again? Just looked in the index of Forte; no mention.

The diminished third is the inversion of the augmented sixth.

>>I guess I was hoping, John, that you'd take a stab at explaining the
>>idea behind your scheme to Xavier, since we were just talking about the
>>pedagogy of adaptive JI vs. strict JI.

>Oh, sorry, I misunderstood you! There's a good summary of my scheme at

> http://www.egroups.com/message/tuning/12668

Well, I was hoping for something that replied directly to Xavier's comments.
I was hoping you'd just post your immediate reaction to them. Because what
he wrote up was an attempt at an adaptive (albeit strict) JI tuning, and
brought up a lot of the painful "problems" that he was seeing . . .

[I wrote:]
>>how would one tune all 12 pitch classes in a way that
>>would prominently feature minor chord(s) tuned 16:19:24
>>and also handle other chords in a reasonable way?

[Pierre Lamothe:]
>Is the following "gammier" has sense for that?

>http://www.aei.ca/~plamothe/pix/hindem.gif

Neat graphic, Pierre! I count 14 locations, of which 2/1 is a
repeat of 1/1, which still seems to leave one extra slot.

[Carl Lumma:]
>Trouble is, as Paul always points out, the diatonic scale doesn't work
>in JI. Somehow, your software uses key-guessing to work around this...
>how, BTW, do you deal with the V vs. ii chord problem?

Uhhh, what is the V vs. ii chord problem again?

[Carl:]
>Does your software distinguish between major and minor keys? I'll need
>to know where in a given key your software expects to find a usable
>minor chord in order to design a scale for it. Probably your key-
>guessing algorithm will need to be changed, since 19:24 is not usually
>considered a desirable major third.

See below.

[JdL:]
>>There is a similar problem with targeting the 6:7:9 minor chord, as I
>>believe we discussed to some degree a year or so ago.

[Carl:]
>I don't remember this, but perhaps what you mean is that you don't like
>9:7 major thirds, and your current approach has been depending on the
>fact that strictly 5-limit major and minor triads interlock.

>My approach is much more flexible in situations like this, since it is
>entirely chord-based, rather than scale-based.

Go Carl!

[Paul E:]
>Pierre, Xavier wanted all the major triads as 4:5:6, and all the minor
>triads as 16:19:24. But neither Xavier nor John were thinking in terms
>of a fixed-pitch 12-tone scale, although I would have thought so to
>from reading John's comment:

[JdL:]
<< how would one tune all 12 pitch classes in a way that
would prominently feature minor chord(s) tuned 16:19:24
and also handle other chords in a reasonable way? >>

[Paul:]
>John, what exactly did you mean by that?

My tuning files specify twelve offsets from 12-tET, one for each pitch
class (C, C#, ... B). Then, each interval's tuning desirability (66
per file) is quantified: good if JI, bad if not. With this approach, it
is possible to steer the tuning into otonal chords, or, if desired,
utonal instead.

Perhaps I've overstated the challenge of 16:19:24 minor chords: the
tuning file could tune other notes any way at all and simply rate the
intervals thus formed as very undesirable, thus steering the tuning in
some other direction except for minor chords.

A given run of my program includes any number of tuning files, so that's
not a problem.

JdL

>>http://www.aei.ca/~plamothe/pix/hindem.gif

John deLaubenfels wrote,

Neat graphic, Pierre! I count 14 locations, of which 2/1 is a
repeat of 1/1, which still seems to leave one extra slot.

Well there is no tritone, and two each of major second and minor seventh.

>Uhhh, what is the V vs. ii chord problem again?

Carl is referring to the fact that if you try to make a strict JI "tuning
file", the major second above the tonic can fit into a V chord (if it's a
9/8) or a ii chord if it's a 10/9), but not both.

>My tuning files specify twelve offsets from 12-tET, one for each pitch
>class (C, C#, ... B). Then, each interval's tuning desirability (66
>per file) is quantified: good if JI, bad if not.

I understand the second sentence but not the first.

>Perhaps I've overstated the challenge of 16:19:24 minor chords: the
>tuning file could tune other notes any way at all and simply rate the
>intervals thus formed as very undesirable, thus steering the tuning in
>some other direction except for minor chords.

>A given run of my program includes any number of tuning files, so that's
>not a problem.

I guess, once again, I'm not quite clear on what purpose the tuning files
serve in your program.

>>Trouble is, as Paul always points out, the diatonic scale doesn't work
>>in JI. Somehow, your software uses key-guessing to work around this...
>>how, BTW, do you deal with the V vs. ii chord problem?
>
>Uhhh, what is the V vs. ii chord problem again?

The fact that the diatonic scale cannot support both ii and V chords in
JI without having more than 7 notes -- the famous syntonic comma problem.

-Carl

[I wrote:]
>>Another way of putting it would be: if A,C,E is tuned 16:19:24, how is
>>A,C,E,G to be tuned?

[Paul E:]
>Xavier will probably give you an answer to that -- and it will be
>either 10:12:15:18 or 32:38:48:57. Either way, your program could
>handle that, right?

Yes. More below.

[JdL:]
>>Then there are dynamic challenges: consider A,C,E -> A,C,E,G -> C,E,G,
>>with notes tied when possible. G is pretty much forced to be a fifth
>>up from C, so some horror of a "major" chord results, unless there is
>>painful shifting of continuously sounding notes. The 10:12:15 minor,
>>of course, sidesteps such challenges by revealing a 4:5:6 major chord
>>on top.

[Paul:]
>John, this "painful shifting of continuously sounding notes" is pretty
>common in some of your sequences already, right? Like in 7-limit,
>D,F,A -> G,B,D,F would have even more of that, right? So what's the
>problem?

You are correct in saying that this is a similar challenge. I guess my
only point is that there inevitably WILL be pain introduced as a price
for modifying the tuning of minor chords from 10:12:15.

[JdL:]
>>Because: especially now that I'm grounding to COFT values, which are
>>uneven in tuning space (i.e., not 12-tET!), I notice that scales
>>played with a single voice have a noticeably uneven sound that I'm not
>>sure I like. I think the tuning might benefit from weak horizontal
>>non-unison springs that would partially counteract this.

[Paul:]
>But wouldn't playing, say, a major scale in JI, with alternating 9:8
>and 10:9 whole tones, have an even more uneven sound than most of your
>COFT tunings?

I haven't tracked this down with numbers yet, but I suspect that COFT-
induced deviations are sometimes more extreme than 81/80.

[Paul:]
>Well, I was hoping for something that replied directly to Xavier's
>comments. I was hoping you'd just post your immediate reaction to
>them. Because what he wrote up was an attempt at an adaptive (albeit
>strict) JI tuning, and brought up a lot of the painful "problems" that
>he was seeing . . .

Sorry, clearly I came into this late; I must've missed the posts leading
up to it. My methods are best illustrated against an actual sequence,
however, which, if it is short, we can tear apart looking at the numbers
and discussing how they got that way, and perhaps how they should be
different.

[JdL:]
>>Uhhh, what is the V vs. ii chord problem again?

[Paul:]
>Carl is referring to the fact that if you try to make a strict JI
>"tuning file", the major second above the tonic can fit into a V chord
>(if it's a /8) or a ii chord if it's a 10/9), but not both.

Ah. Yes, I can deal with that.

[JdL:]
>>My tuning files specify twelve offsets from 12-tET, one for each pitch
>>class (C, C#, ... B). Then, each interval's tuning desirability (66
>>per file) is quantified: good if JI, bad if not.

[Paul:]
>I understand the second sentence but not the first.

Dang! I'll give another try at explaining below.

[JdL:]
>>Perhaps I've overstated the challenge of 16:19:24 minor chords: the
>>tuning file could tune other notes any way at all and simply rate the
>>intervals thus formed as very undesirable, thus steering the tuning in
>>some other direction except for minor chords.

>>A given run of my program includes any number of tuning files, so
>>that's not a problem.

[Paul:]
>I guess, once again, I'm not quite clear on what purpose the tuning
>files serve in your program.

For the most part, the program itself does not understand tuning; it
relies on targeting the intervals specified in one or more tuning files
invoked with a run (this distinction is gradually getting blurred; for
example, the latest trick of re-targeting the tuning taken from 12-tET
is in the program, not the tuning files).

So, for example, a 7-limit otonal tuning file would start by specifying
that C is unchanged from 12-tET, E is about -14 cents from 12-tET, G is
about +2 cents from 12-tET, and Bb is about -31 cents from 12-tET (the
program will separately "center" the deviations given it). In order to
capture minor chords, the file tunes A at about -16 cents from 12-tET.
I think I also tune Eb at +16, allowing a good C,Eb,G as well as A,C,E;
they will give the same tuning results.

The program understands that each tuning file can be applied in 12 keys.

To steer a given set of notes into a particular tuning vs. another, the
tuning file rates each of the 66 intervals it forms; thus the above file
would rate the 386 cent interval from C to E as very desirable, etc.
The backside major third, from E to G#, is approximately 428 cents and
is given very low desirability. The 7:9 third from Bb to D, approx 435
cents, is given fairly high desirability so that a dom 7 will align to
it, but not so high that a bare major third sticks to it instead of to
5:4.

The numbers I use for interval desirability are completely seat of the
pants; when the program makes a bad choice, often the problem can be
fixed by changing interval desirability in one or more tuning files to
steer the tuning some other way than it was going.

The process starts by assigning a best tuning to each small period of
time with a consistent set of notes. Then it goes back and merges
adjacent tunings when doing so eliminates bad retune motion without
giving up too much tuning goodness. Then, using the condensed tuning
set, it wires up springs and relaxes the spring matrix to achieve the
final tuning to be used.

Clearer yet?

JdL

[JdL:]
>>>Because: especially now that I'm grounding to COFT values, which are
>>>uneven in tuning space (i.e., not 12-tET!), I notice that scales
>>>played with a single voice have a noticeably uneven sound that I'm not
>>>sure I like. I think the tuning might benefit from weak horizontal
>>>non-unison springs that would partially counteract this.

[Paul:]
>>But wouldn't playing, say, a major scale in JI, with alternating 9:8
>>and 10:9 whole tones, have an even more uneven sound than most of your
>>COFT tunings?

>I haven't tracked this down with numbers yet, but I suspect that COFT-
>induced deviations are sometimes more extreme than 81/80.

I'll bet the contents of my wallet that _all_ of your COFTs have melodic
whole tone sizes (that actually appear in the piece) within a range
_smaller_ than 81:80. Especially for the Scarlatti, where you essentially
got meantone, all the melodic whole tones would be about equal -- thus a
high degree of melodic smoothness.

>So, for example, a 7-limit otonal tuning file would start by specifying
>that C is unchanged from 12-tET, E is about -14 cents from 12-tET, G is
>about +2 cents from 12-tET, and Bb is about -31 cents from 12-tET (the
>program will separately "center" the deviations given it). In order to
>capture minor chords, the file tunes A at about -16 cents from 12-tET.
>I think I also tune Eb at +16, allowing a good C,Eb,G as well as A,C,E;
>they will give the same tuning results.

>The program understands that each tuning file can be applied in 12 keys.

uhh . . . right . . . .

>To steer a given set of notes into a particular tuning vs. another, the
>tuning file rates each of the 66 intervals it forms; thus the above file
>would rate the 386 cent interval from C to E as very desirable, etc.
>The backside major third, from E to G#, is approximately 428 cents and
>is given very low desirability. The 7:9 third from Bb to D, approx 435
>cents, is given fairly high desirability so that a dom 7 will align to
>it, but not so high that a bare major third sticks to it instead of to
>5:4.

>The numbers I use for interval desirability are completely seat of the
>pants; when the program makes a bad choice, often the problem can be
>fixed by changing interval desirability in one or more tuning files to
>steer the tuning some other way than it was going.

I'm not sure you explained what interval desirability does. Does the program
determine which tuning file maximizes the desirability at each moment of the
piece, and use that tuning file?

And what about your recent development to allow the intervallic springs to
compete with one another in the case of a stack-of-fifths chord, etc.? Does
that do away with tuning files?

>The process starts by assigning a best tuning to each small period of
>time with a consistent set of notes.

That sounds like a yes to my question above. But what exactly is a "small
period of time"?

Now in the tuning file you mention above, I can't see why you would want to
have Eb at +16. The tuning file will evidently be applied only in dominant
situations, using 4:5:6:7 for a C dominant seventh chord; so shouldn't the
Eb be a 7/3 or -33?

Maybe if we think through this we can figure out a way to eliminate tuning
files altogether.

John A. deLaubenfels wrote:

> [JdL:]
> >>Then there are dynamic challenges: consider A,C,E -> A,C,E,G ->
> C,E,G,
> >>with notes tied when possible. G is pretty much forced to be a
> fifth
> >>up from C, so some horror of a "major" chord results, unless there
> is
> >>painful shifting of continuously sounding notes. The 10:12:15
> minor,
> >>of course, sidesteps such challenges by revealing a 4:5:6 major
> chord
> >>on top.
>
> [Paul:]
> >I think Xavier has some opinion on how this should be negotiated.
>
> Xavier, what was that again?

Sorry, my english is too poor here, I need help of a translator...
wait
;-)

Hi Xavier,

I think what John wanted to know was, roughly, how would you tune A,C,E ->
A,C,E,G -> C,E,G?

-Paul

Paul H. Erlich wrote:
>
> John deLaubenfels wrote,
>
> >Another way of putting it would be: if A,C,E is tuned 16:19:24, how
> is
> >A,C,E,G to be tuned?
>
> Xavier will probably give you an answer to that -- and it will be
> either
> 10:12:15:18 or 32:38:48:57. Either way, your program could handle
> that,
> right?

It depends of the musical context, for me 10-12-15-18 is probably a
tetrad in F major or C major and 32-38-48-57 probably in A minor or D
minor.
Xavier

Xavier wrote (concering A-C-E-G),

>It depends of the musical context, for me 10-12-15-18 is probably a
>tetrad in F major or C major and 32-38-48-57 probably in A minor or D
>minor.

Oh -- well that doesn't bode well for John deLaubenfels to be able to
accomodate your wishes in his program. If you're willing to be a little
flexible on this, we might be able to come up with some solutions to your
"problems" that might amaze you.

Paul H. Erlich wrote:
>
> Hi Xavier,
>
> I think what John wanted to know was, roughly, how would you tune
> A,C,E ->
> A,C,E,G -> C,E,G?
>
> -Paul

Does my previous email answers this question?
Thank you for your patience
:-)

Xavier wrote,

>Does my previous email answers this question?

For now, yes. I wonder if someone can produce a MIDI-file of your exercise,
in regular 12-tET, so that we can compare various retuned versions of it . .
.

Paul H. Erlich wrote:
>
> Xavier wrote (concering A-C-E-G),
>
> >It depends of the musical context, for me 10-12-15-18 is probably a
> >tetrad in F major or C major and 32-38-48-57 probably in A minor or D
> >minor.
>
> Oh -- well that doesn't bode well for John deLaubenfels to be able to
> accomodate your wishes in his program. If you're willing to be a
> little
> flexible on this, we might be able to come up with some solutions to
> your
> "problems" that might amaze you.

I try to be flexible...
Thank you very much for your interest for my little problems!
I'll go to bed in few minutes. Late in France... Good evening
Xavier

Paul H. Erlich wrote:
>
> Xavier wrote,
>
> >Does my previous email answers this question?
>
> For now, yes. I wonder if someone can produce a MIDI-file of your
> exercise,
> in regular 12-tET, so that we can compare various retuned versions of
> it . .

Thanks a lot
:-)

[Paul E:]
>>>But wouldn't playing, say, a major scale in JI, with alternating 9:8
>>>and 10:9 whole tones, have an even more uneven sound than most of
>>>your COFT tunings?

[JdL:]
>>I haven't tracked this down with numbers yet, but I suspect that COFT-
>>induced deviations are sometimes more extreme than 81/80.

[Paul:]
>I'll bet the contents of my wallet that _all_ of your COFTs have
>melodic whole tone sizes (that actually appear in the piece) within a
>range _smaller_ than 81:80. Especially for the Scarlatti, where you
>essentially got meantone, all the melodic whole tones would be about
>equal -- thus a high degree of melodic smoothness.

How big is your wallet, Paul? ;-> Actually, at the moment, I'm trying
to recall which piece seemed to whap me in the face with this. I'll get
back to you when possible; you can keep the contents of your wallet.

[JdL:]
>>So, for example, a 7-limit otonal tuning file would start by
>>specifying that C is unchanged from 12-tET, E is about -14 cents from
>>12-tET, G is about +2 cents from 12-tET, and Bb is about -31 cents
>>from 12-tET (the program will separately "center" the deviations given
>>it). In order to capture minor chords, the file tunes A at about -16
>>cents from 12-tET. I think I also tune Eb at +16, allowing a good
>>C,Eb,G as well as A,C,E; they will give the same tuning results.

>>The program understands that each tuning file can be applied in 12
>>keys.

[Paul:]
>uhh . . . right . . . .

What's with the "uhh"? This seems so intuitive to me; how am I failing
to convey the idea(s) here?

[JdL:]
>>To steer a given set of notes into a particular tuning vs. another,
>>the tuning file rates each of the 66 intervals it forms; thus the
>>above file would rate the 386 cent interval from C to E as very
>>desirable, etc. The backside major third, from E to G#, is
>>approximately 428 cents and is given very low desirability. The 7:9
>>third from Bb to D, approx 435 cents, is given fairly high
>>desirability so that a dom 7 will align to it, but not so high that a
>>bare major third sticks to it instead of to 5:4.

(I meant dom 9, not dom 7)

>>The numbers I use for interval desirability are completely seat of the
>>pants; when the program makes a bad choice, often the problem can be
>>fixed by changing interval desirability in one or more tuning files to
>>steer the tuning some other way than it was going.

[Paul:]
>I'm not sure you explained what interval desirability does. Does the
>program determine which tuning file maximizes the desirability at each
>moment of the piece, and use that tuning file?

Yes. By summing the weighted "goodness" of all the dyadic intervals,
much as your dyadic harmonic entropy calculations do.

[Paul:]
>>And what about your recent development to allow the intervallic
>>springs to compete with one another in the case of a stack-of-fifths
>>chord, etc.? Does that do away with tuning files?

Partially; it jumps in ONLY when the previous logic has specified
12-tET.

[JdL:]
>>The process starts by assigning a best tuning to each small period of
>>time with a consistent set of notes.

[Paul:]
>That sounds like a yes to my question above. But what exactly is a
>"small period of time"?

A period when there are no notes on or notes off. However, in what I
consider to be a very important refinement possible only with "leisure"
retuning, I do create "pseudo-simultaneous events" (PSE's) which for
the purposes of modelling compress small transition times together,
times when typically some notes end and others begin.

[Paul:]
>Now in the tuning file you mention above, I can't see why you would
>want to have Eb at +16. The tuning file will evidently be applied only
>in dominant situations, using 4:5:6:7 for a C dominant seventh chord;
>so shouldn't the Eb be a 7/3 or -33?

Perhaps it should. I haven't thought about that permutation. It's true
that redundancy in the provision for minor chords is not necessary.

[Paul:]
>Maybe if we think through this we can figure out a way to eliminate
>tuning files altogether.

Yes, we might! And, as I've said before, the continuous function
represented by your harmonic entropy graphs is appealing to me as a
tool to move toward that goal. The problem is the "traps": the
question of how to get past local minima that hide better minima nearby.
My current methods, messy though they are, have a rough-and-ready
approach for dealing with this challenge, and it may take a fair number
of new techniques to navigate a consistently better path. Better
solutions will undoubtedly come in time. It's wide open.

JdL