[tuning] Retuning sounding notes in JI

I've just been doing some thinking about retuning sounding notes in JI.
Should have done that earlyer.

First of all, I can come to no other conclusion than that retuning sounding
notes is still 100% pure JI.
As long as you're retuning the note to another JI ratio offcourse.

Now there's another story about what the composition sais.
Is the composition for a "fluid" retune able instrument like a choir or
violin etc, then one can retune all one wants.
It is up to the player to interpret the composition / music since 12tet
doesn't notate a synthonic comma for instance and since there's no extra
"percussive" occurence it does not warrant an extra note.

Another story is when the composition is for an instrument that cannot do
"fluid" retuning. For instance a piano.
First of all, assuming the composition was written for 12tet, this assumes
the piano to actually be able to do what a retune able instrument does, only
within one semitone range.
12tet makes commas equal so when playing in 12tet the piano is actually
fluidly retuning sounding notes allready!
12tet or another tempered tuning capable of "psychoacoustic enharmonicity"
actually gives the piano magic new powers :)
When playing in JI the piano (also a piano with unlimited keys per octave)
loses this magic power and there are several ways to look the situation you
have then.
1. See the piano as incapable to play the composition correctly. Piano's
fault, not JI fault and actually not composition fault either since the
composition is for a magic power piano which doesn't exist in JI land.
2. In the case of an electronic piano, retune sounding notes without
striking them again. May do injustice to the pure sound of the instrument,
but leaves the composition intact.
3. Strike again a new note when retuning should happen (this modifies the
composition). Piano's fault to modify the composition, not JI fault.
4. Make a rest where the piano note should retune. Modifies
composition. Piano's fault to modify the composition, not JI fault.
5. Interpret the composition differently so that the piano doesn't need to
retune. Piano's fault to modify the composition, not JI fault.

Another case is where the composition is written without an instrument
defined but played by an instrument that cannot do "fluid" retuning, for
instance a piano.
Then the piano is incompetent in playing the composition as required.
Piano's fault, not JI fault. See also all other points above.

In all these cases JI is never to blame, except perhaps to take away (or
more correctly, not give) special powers to incapable instruments.
The ground structure of music is allways 100% pure JI.

Marcel

> Then the piano is incompetent in playing the composition as required.
> Piano's fault, not JI fault. See also all other points above.
> In all these cases JI is never to blame, except perhaps to take away (or
> more correctly, not give) special powers to incapable instruments.
> The ground structure of music is allways 100% pure JI.
> Marcel

I do agree with you that tempered tunings do have some kind of JI base
that we perceive. If you're interested in this subject, I suggest
doing some research into the concept of harmonic entropy, as that
deals specifically with things like that.

Another example, and one I've posted a few times already. Take this chord:

D F+ A C+ E G+ B D+

Where the D-F+ dyads are 6/5 and the F+-A dyads are 5/4.

The D+ on top will be 81/80 sharp of 4/1. When tuned in JI, I very
very much like the sound of that note on top. To my ears, it sounds
like a chord extension on top of the m13 chord below it. It doesn't
sound like a screwed up 4/1 because it isn't a screwed up 4/1. If you
replace it with a normal 4/1 D, it won't sound as good. That D on top
will sound like a benign doubling of the root two octaves below, and
not sound like a new "color" on the chord. Plus it will beat quite a
bit.

Now if you get rid of all of the notes in between the outer dyad,
you'll just get

D-D+

where the D+ is tuned as 4/1 * 81/80. And it will beat like crazy,
although you might retain some of the "color" of the way it sounded
when you had it on top of the chord.

If I play the same chord in 12-tet, I can sort of flip flop between
the outer note sounding like 2/1 and the whole chord having the
"quality" that it has, which would imply there not being 4/1 on the
outside no matter what interval you perceive the minor thirds at
unless you hear them as being 32/27.

-Mike

Hi Mike :)

I do agree with you that tempered tunings do have some kind of JI base
> that we perceive. If you're interested in this subject, I suggest
> doing some research into the concept of harmonic entropy, as that
> deals specifically with things like that.
>

It seems to me harmonic entropy deals with consonance mostly, and what one
hears when hearing a dyad or chord.
I'm personally thinking that one doesn't hear very well which chord it is by
listening to a chord, but for a more precise part subconsciously understand
the composition of the chord by which chord came before and which chord
comes after.
So I mean the mathematical logic connecting the chords tells something about
the chords. The combination beeing music.

Another example, and one I've posted a few times already. Take this chord:
>
> D F+ A C+ E G+ B D+
>
> Where the D-F+ dyads are 6/5 and the F+-A dyads are 5/4.
>
> The D+ on top will be 81/80 sharp of 4/1. When tuned in JI, I very
> very much like the sound of that note on top. To my ears, it sounds
> like a chord extension on top of the m13 chord below it. It doesn't
> sound like a screwed up 4/1 because it isn't a screwed up 4/1. If you
> replace it with a normal 4/1 D, it won't sound as good. That D on top
> will sound like a benign doubling of the root two octaves below, and
> not sound like a new "color" on the chord. Plus it will beat quite a
> bit.
>
> Now if you get rid of all of the notes in between the outer dyad,
> you'll just get
>
> D-D+
>
> where the D+ is tuned as 4/1 * 81/80. And it will beat like crazy,
> although you might retain some of the "color" of the way it sounded
> when you had it on top of the chord.
>
> If I play the same chord in 12-tet, I can sort of flip flop between
> the outer note sounding like 2/1 and the whole chord having the
> "quality" that it has, which would imply there not being 4/1 on the
> outside no matter what interval you perceive the minor thirds at
> unless you hear them as being 32/27.
>

Ok interesting.
I did not see this example before.
1/1 6/5 3/2 9/5 9/4 27/10 27/8 81/20
Yes maybe the last minor third is a 32/27 making 4/1 (which is a very common
minor third) but both seem fine to me with the 81/80 version simpler.
If you're hearing it differently than 4/1 I beleive you.

Marcel

Btw I'd like to add about retuning sounding notes.
That I think a comma shift, 81/80 is perfectly normal as long as it means
the melody (the real melody, not nessecarily the line played by one of the
instruments) is not shifting by 81/80. (which seems almost impossible to do
anyhow, unless one shifts wrongly where one shouldn't shift)
So the 81/80 "shift" is a new different note.
It can be that the melody (at 81/ ) moves to a different note, and the focus
shifts onto a new note at the shifted location ( /80) and this is presented
as the continuation of the melody (if you can follow what I mean, sorry if
you can't).
This should sound ok in theory when it is all done correctly.
Does anybody know of any examples of the above, either sounding good or bad?

Marcel

2009/2/18 Marcel de Velde <m.develde@...>

> I've just been doing some thinking about retuning sounding notes in JI.
> Should have done that earlyer.
>
> First of all, I can come to no other conclusion than that retuning sounding
> notes is still 100% pure JI.
> As long as you're retuning the note to another JI ratio offcourse.
>
> Now there's another story about what the composition sais.
> Is the composition for a "fluid" retune able instrument like a choir or
> violin etc, then one can retune all one wants.
> It is up to the player to interpret the composition / music since 12tet
> doesn't notate a synthonic comma for instance and since there's no extra
> "percussive" occurence it does not warrant an extra note.
>
> Another story is when the composition is for an instrument that cannot do
> "fluid" retuning. For instance a piano.
> First of all, assuming the composition was written for 12tet, this assumes
> the piano to actually be able to do what a retune able instrument does, only
> within one semitone range.
> 12tet makes commas equal so when playing in 12tet the piano is actually
> fluidly retuning sounding notes allready!
> 12tet or another tempered tuning capable of "psychoacoustic enharmonicity"
> actually gives the piano magic new powers :)
> When playing in JI the piano (also a piano with unlimited keys per octave)
> loses this magic power and there are several ways to look the situation you
> have then.
> 1. See the piano as incapable to play the composition correctly. Piano's
> fault, not JI fault and actually not composition fault either since the
> composition is for a magic power piano which doesn't exist in JI land.
> 2. In the case of an electronic piano, retune sounding notes without
> striking them again. May do injustice to the pure sound of the instrument,
> but leaves the composition intact.
> 3. Strike again a new note when retuning should happen (this modifies the
> composition). Piano's fault to modify the composition, not JI fault.
> 4. Make a rest where the piano note should retune. Modifies
> composition. Piano's fault to modify the composition, not JI fault.
> 5. Interpret the composition differently so that the piano doesn't need to
> retune. Piano's fault to modify the composition, not JI fault.
>
> Another case is where the composition is written without an instrument
> defined but played by an instrument that cannot do "fluid" retuning, for
> instance a piano.
> Then the piano is incompetent in playing the composition as required.
> Piano's fault, not JI fault. See also all other points above.
>
> In all these cases JI is never to blame, except perhaps to take away (or
> more correctly, not give) special powers to incapable instruments.
> The ground structure of music is allways 100% pure JI.
>

Marcel wrote:
>> It can be that the melody (at 81/) moves to a different note,
>> and the focus shifts onto a new note at the shifted location ( /80)
>> and this is presented as the continuation of the melody
>>(if you can follow what I mean, sorry if you can't).

Yes I follow you perfectly.

>> This should sound ok in theory when it is all done correctly.

If I understood you OK it shouldn't Marcel.
(If I understood you wrongly, my apologies).
You seem to refer to the old conundrum of preserving melody pitch in
variable JI. The best known historical remark on why this is not possible is
by Rameau, but Barbieri recently found the issue described-with a musical
example-in a letter dated before 1565.
Of course we all know that playing in JI is possible: in keyboards, minding
some "wolves", in variable intonation instruments, by compensating every
shift with another one carefully planned shift later, to avoid the pitch
rising or falling.

Guess other members of the list-who are obviously very much into the
advanced intricacies of JI-can elaborate further.

Kind regards

Claudio

Hi Claudio,

If I understood you OK it shouldn't Marcel.
> (If I understood you wrongly, my apologies).
> You seem to refer to the old conundrum of preserving melody pitch in
> variable JI. The best known historical remark on why this is not possible
> is by Rameau, but Barbieri recently found the issue described-with a
> musical example-in a letter dated before 1565.
> Of course we all know that playing in JI is possible: in keyboards, minding
> some "wolves", in variable intonation instruments, by compensating every
> shift with another one carefully planned shift later, to avoid the pitch
> rising or falling.
>
> Guess other members of the list-who are obviously very much into the
> advanced intricacies of JI-can elaborate further.
>

Thanks for your reply.

I think you may have understood me wrongly (for which I should give my
apologies not you :)
I'm of the belief that melody follows an underlying harmonic structure which
in it's simplest form is a diatonic mode, including harmonic minor etc, and
a few other modes that are not usually mentioned, so add to normal smallest
diatonic stepsizes 27/25 and 75/64.
In the next simplest form this extends to what I see as extended modes which
are 2 diatonic modes on top of eachother 4/3 apart. This will give a more
complex underlying harmonic structure and chromatic melody.
81/80 is not a normal melodic step in these 2 forms of modes.

When there is a modulation, and it is done in such a way that one note
shifts by 81/80, there is a melody on the original note, which moves to
another note (wether it is played or not) but not the 81/80, or better put
it is no longer at the original note and it has the potential to move to
many other notes according to the underlying harmonic structure, but not the
old note shifted by 81/80.
Yet, melody also has what I see as the ability to be made up of not 1
melodic structure, but for one melody to stop sounding, and a completely new
melody to start sounding and take over thesame melody spotlight as you could
call it from the old melody so to continue as this melody.
An easy to understand example of this is an "echo" to a melody. However
these are still fairly distinguishable, it can be done much more subtle. One
melody taking over from the other. I beleive it's found a lot in common
music.
Now this melody taking over from the other melody CAN be in the new location
of the 81/80 shift.

So one can have a melody shifting by 81/80 (though it is in actuality 2
different melodies, one taking over from the other).
My theory is that this should still make sense (though only in the context
of the modulation) and sound ok.
I was wondering if there were examples of this where it sounds right and or
where it sounds wrong.

Marcel

>
> If I understood you OK it shouldn't Marcel.

Claudio sorry, I misread your reply.
I read it as should instead of shouldn't, which then didn't make sense with
the rest of your reply so I thought you had misunderstood me :)
But you did understand me right.

Marcel

I see, you mean to differentiate two melody levels one S.c. apart.
Interesting it is.
Not even Helmholtz in mid 19th c. was thinking along those lines, in spite
of the fact that his famous 24-note JI harmonium would fit the two-levels
very well.
So it is definitely a modern idea.
How good it is, I leave it to the experts in modern JI music.

Claudio

Marcel wrote:
Claudio sorry, I misread your reply.
I read it as should instead of shouldn't, which then didn't make sense with
the rest of your reply so I thought you had misunderstood me :)
But you did understand me right.

Yet, melody also has what I see as the ability to be made up of not 1
melodic structure, but for one melody to stop sounding, and a completely new
melody to start sounding and take over thesame melody spotlight as you could
call it from the old melody so to continue as this melody

--- In tuning@yahoogroups.com, "Claudio Di Veroli" <dvc@...> wrote:
>
> I see, you mean to differentiate two melody levels one S.c. apart.
> Interesting it is.

Not a modern idea at all. Willaert experimented with
notating 81/80 shifts. Bosanquet did so as well with his
53-tone harmonium.

But what's even more interesting is to differentiate melody
lines 1/4-S.c. apart. That's what the Adaptive JI midi file
does. And neither is this a modern idea -- as I mentioned,
it was proposed by Vicentino (a student of Willaert's).

Willaert was a good dutchman, but he defected to Italy.
Much later, Fokker (another dutchman), decided against the
S.c. and chose 31 for his organ.

-Carl

Carl wrote:
> Claudio Wrote: I see, you mean to differentiate two melody levels one
S.c. apart.
> Interesting it is.
Not a modern idea at all. Willaert experimented with
notating 81/80 shifts.
Bosanquet did so as well with his 53-tone harmonium.
But what's even more interesting is to differentiate melody
lines 1/4-S.c. apart. That's what the Adaptive JI midi file
does. And neither is this a modern idea -- as I mentioned,
it was proposed by Vicentino (a student of Willaert's).

Thanks Carl.

Yes I knew about Bosanquet and I read Vicentino in facsimile in the 1970's.

Did not know about Willaert's S.c. shifts however.
Could you give me a link to the source?

Thanks!

Claudio

> Did not know about Willaert's S.c. shifts however.
> Could you give me a link to the source?
>
> Thanks!
>
> Claudio

I was remembering these two MTO papers:

http://societymusictheory.org/mto/issues/mto.04.10.1/mto.04.10.1.wibberley1.html

http://societymusictheory.org/mto/issues/mto.04.10.1/mto.04.10.1.wibberley2.html

But I misremembered about Willaert having a notation,
sorry. The examples show comma markings, but it seems
they are entirely the work of the author.

-Carl

Hello Claudio.

I see, you mean to differentiate two melody levels one S.c. apart.
> Interesting it is.
> Not even Helmholtz in mid 19th c. was thinking along those lines, in spite
> of the fact that his famous 24-note JI harmonium would fit the two-levels
> very well.
> So it is definitely a modern idea.
> How good it is, I leave it to the experts in modern JI music.
>

Thank you for you kind remarks, made my day :) (which I needed after
yesterdays fiasco)

Marcel

Well I think it has been used in practice since forever.
Since I beleive 12tet to be a tempering of pure JI, in which 12tet gives
enharmonically equal notes.
This makes all 12tet composers comma experts without them having to realise
this themselves.

What I was trying to do is to understand how the underlying structure works.

Not a modern idea at all. Willaert experimented with
> notating 81/80 shifts. Bosanquet did so as well with his
> 53-tone harmonium.
>
> But what's even more interesting is to differentiate melody
> lines 1/4-S.c. apart. That's what the Adaptive JI midi file
> does. And neither is this a modern idea -- as I mentioned,
> it was proposed by Vicentino (a student of Willaert's).
>
> Willaert was a good dutchman, but he defected to Italy.
> Much later, Fokker (another dutchman), decided against the
> S.c. and chose 31 for his organ.
>

I can't see 1/4-S.c. as JI offcourse and see no need for it when the problem
can be solved in pure JI.

I did a few experiments with melody lines shifting by a S.c the way I
discribed a few posts above, and it sounds perfectly natural to me.

Marcel

Hi Carl,

indeed I suspected so, well known "Quid non ebrietas?"!
Lots of ink on this piece. In the 1st link that you quote,
http://societymusictheory.org/mto/issues/mto.04.10.1/mto.04.10.1.wibberley1.
html
Footnote 4 reads
"
<http://societymusictheory.org/mto/issues/mto.04.10.1/mto.04.10.1.wibberley1
.html> Lowinsky, in his edition and discussion of the piece, concurred with
the view of an intended equal-temperament performance"
Barbieri supports this conclusion in his recent Barbieri "Enharmonic
Instruments", 2008. p.283.
It has been interpreted as implying lots of other tunings, including of
course JI with shifting pitches.
I checked among the Examples: this one renders the work into modern
notation:
http://societymusictheory.org/mto/issues/mto.04.10.1/wibberley1_ex4a_gif.htm
l
I can see 6 flats being used: I see no circularity.
The work looks playable in 1/4 S.c. meantone (surely known to Willaert from
before 1516, date at which Aron already knew it) with wolf fifth at E-Cb.
Kind regards,

Claudio

_____

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of
Carl Lumma
Sent: 18 February 2009 23:04
To: tuning@yahoogroups.com
Subject: [tuning] Re: Retuning sounding notes in JI

> Did not know about Willaert's S.c. shifts however.
> Could you give me a link to the source?
>
> Thanks!
>
> Claudio

I was remembering these two MTO papers:

http://societymusic
<http://societymusictheory.org/mto/issues/mto.04.10.1/mto.04.10.1.wibberley1
.html> theory.org/mto/issues/mto.04.10.1/mto.04.10.1.wibberley1.html

http://societymusic
<http://societymusictheory.org/mto/issues/mto.04.10.1/mto.04.10.1.wibberley2
.html> theory.org/mto/issues/mto.04.10.1/mto.04.10.1.wibberley2.html

But I misremembered about Willaert having a notation,
sorry. The examples show comma markings, but it seems
they are entirely the work of the author.

-Carl