re-tuning methods

On Wed, 17 Dec 2003 07:55:58 +0100 Werner wrote

> Yes - and this shows that this approach to just intonation is not a very
>practical one.

I agree that Hermode tuning and adaptive tuning are probably better methods
for many cases. However, if the pitch shift does not matter ( as seems to be the
case with ( some of ) Peter Saults' music ) then dynamic re-tuning is the perfect
solution as it requires no compromise. That is the context in which I raised the
matter. Similarly, if the key modulations of a piece are reversed in a there-and-back
journey or some other sequence which reverses all the shifts then again
dynamic re-tuning is a superior solution (in my opinion) as it requires
no compromise.

Like Carl said, its apples and oranges.

>Indeed,
> the problem shown above, caused by the syntonic comma and some others,
>caused
> by other commas, show that it is impossible to create a closen system of
>just intonation
> without any break.
> If you feel interest to know how different ideas of just intonation handle
>this problem
> you will find examples on our websites www.hermode.com at the end of the
>"historical"
> chapter, at "software driven tunings".
> We present four different ideas in a just intonation model by a musical
>example.
> The third one (I called it "pulk idea") is the same than with the model
>described above,

It doesn't look anything like it to me. The essential feature of dynamic
re-tuning is that the performer chooses the time and key of modulation.
This does not seem to be covered by any of the four models you describe.

> the forth one is mine (Hermode Tuning), a more compromise model.

I shall contact you off-list about the possibility of using this in
Midicode Synth or other software.

Best wishes
Peter
www.midicode.com

> Kind regards
> Werner

On Tue, 16 Dec 2003 23:32:29 -0800 Kraig wrote

> Hello Peter and Paul!
> The d-f-a chord is a great and very musical useful chord. Trhe objection to it ereminds me of
>the dreaded tritone 400 years ago. As music ventured out, it began to realized how important the
>tritone is chords was in helping to 'define' where one is in a scale this wolf can and does this
>very thing. In fact by the time of Wagner chords with tritone practally out numbered those
>without. As Carl jung pointed outm there is not life without tension. the absence is death

>>
>> From: Peter Frazer <paf@easynet.co.uk>
> Subject:
>>
>>
>> > At the point D-F-A the fifth D-A shows a "Wolf". If yo accept this, the
>> >idea of "just intonation" has a break.
>> > I f you change the scale at this point to a D Scale, you will climb 22
>> >Cents deeper and if you repeat
>> > this sequence 4 times, you will end in B major.
>> > Changing the key without any modulation...
>>
>> > Werner Mohrlok
>>
>> Yes, that is the basic flaw of dynamic re-tuning which I alluded to
>> in my original post when I said :
>>
>> Paul Erlich and others have pointed out that a problem with this
>> approach is that it leads to a shift of absolute pitch with each
>> modulation which is difficult to reverse.
>>
>

>-- -Kraig Grady

Sorry about the lack of clarity Kraig. I only meant that the shift in
pitch could be a problem.

Peter
www.midicode.com

on 12/17/03 10:12 AM, Peter Frazer <paf@easynet.co.uk> wrote:

> On Wed, 17 Dec 2003 07:55:58 +0100 Werner wrote
>
>> Yes - and this shows that this approach to just intonation is not a very
>> practical one.
>
> I agree that Hermode tuning and adaptive tuning are probably better methods
> for many cases. However, if the pitch shift does not matter ( as seems to
> be the
> case with ( some of ) Peter Saults' music ) then dynamic re-tuning is the
> perfect
> solution as it requires no compromise. That is the context in which I
> raised the
> matter. Similarly, if the key modulations of a piece are reversed in a
> there-and-back
> journey or some other sequence which reverses all the shifts then again
> dynamic re-tuning is a superior solution (in my opinion) as it requires
> no compromise.
>
> Like Carl said, its apples and oranges.
>
>> Indeed,
>> the problem shown above, caused by the syntonic comma and some others,
>> caused
>> by other commas, show that it is impossible to create a closen system of
>> just intonation
>> without any break.
>> If you feel interest to know how different ideas of just intonation handle
>> this problem
>> you will find examples on our websites www.hermode.com at the end of the
>> "historical"
>> chapter, at "software driven tunings".
>> We present four different ideas in a just intonation model by a musical
>> example.
>> The third one (I called it "pulk idea") is the same than with the model
>> described above,
>
> It doesn't look anything like it to me. The essential feature of dynamic
> re-tuning is that the performer chooses the time and key of modulation.

I agree. This is the reason that I am not *at the moment* very interested
in automatic retuning. I am looking for "protocols" that a keyboard
musician can use with an instrument to make the exact choice that is wanted.
The intention may be very specific when it is a composition process that is
in question, to which the keyboard is an aid.

It is conceivable that disappearing commas may in some cases be accepted and
so enter implicitly into the picture of the explicit choices that the
musician/composer is making. This is not something I have investigated as
of yet, however I have it in mind as a piece of the picture of what may be
desired for purposes of controlling "compositional keyboard playing". This
is approaching the whole question from a different end. There may likely be
some overlap with the concepts of automatic retuning. Yet the goals as I
currently see them, are different from the goals that automatic retuning
addresses.

-Kurt

> This does not seem to be covered by any of the four models you describe.
>
>> the forth one is mine (Hermode Tuning), a more compromise model.
>
> I shall contact you off-list about the possibility of using this in
> Midicode Synth or other software.
>
> Best wishes
> Peter
> www.midicode.com

On Wed, 17 Dec 2003 18:10:24 -0800 Kurt wrote

>>> The scale before and after modulation are the same scale with the 16..30
>>> ratios shown above. The 16 corresponds to the "tonic" and the tonic is
>>> shifted to a new position. In this case the tonic is shifted one note down
>>> from C to B. Lets measure frequencies in units contrived to make the
>>> frequency of C equal to 1 in the first chord.
>>
>>> Then the G-C-E 3:4:5 (or equally 12:16:20) chord is initially:
>>
>> 3/4 : 1 : 5/4
>>
>>> and after the modulation the G-C-E chord is, because I specified that it
>>> have the ratios 11:15:19 and that the top note remain at constant pitch:
>>
>>> (5/4)*(11/19) : (5/4)*(15/19) : 5/4
>>
>>> which makes the calculations explicit but can be simplified to
>>
>>> 55/76 : 75/76 : 5/4
>>
>> OK, I think I got it, but it looks to me like you have gone up
>> to C# not down to B.

>>Yes, pretty much, though I might rather say that I brought B up to C
>>(because the 11:15:19 chord appeared at Gb-B-Eb prior to modulation). In
>>any case it was that thinking that was the source of my confusion. In the
>>truest description I brough Eb up to E.

>> So you could achieve the re-tuning you require using the dynamic
>> re-tuning of Midicode Synth and hitting a new key note of C#,
>> in this particular example.

>Really? I doubt that it is the E pitch that would remain constant then,
>based on what you have written elsewhere. I understood your retuining
>method to agree with what Robert Walker was doing, which in "xmw" terms is
>equivalen to "crossfree" mode, in which the current note played on the
>modulation channel determines the new tonic, and specifically that the new
>tonic retains the pitch that that note had prior to modulation. That is,
>the pitch of C# would remain constant rather than the pitch of E remaining
>constant. As a result none of the pitches in the G-C-E chord would remain
>constant. The result would be "close" but not at the same absolute pitch.
>I gave up on trying to calculate the absolute result because of the
>complexities of the fractions involved, but I think you can get the idea.
>Otherwise let me know.

Yes, Kurt, you are right. The E does shift a bit ( and the others as we
would expect ). I overlooked that first time through.

So it looks like two pedal key-presses are required.

My suggestion would be to hit the new tonic first but this has no
immediate effect and just goes into some re-tune pending state.
Then hit the bridge note on the pedal board at the moment of
modulation..

I have re-read your earlier post and this sounds similar to what
you were suggesting. I can't think of anything better.

I also take on board your comments in other messages.
I shall let you know if I have any ideas.

Peter
www.midicode.com

on 12/19/03 4:43 AM, Peter Frazer <paf@easynet.co.uk> wrote:

> On Wed, 17 Dec 2003 18:10:24 -0800 Kurt wrote
>
>>>> The scale before and after modulation are the same scale with the 16..30
>>>> ratios shown above. The 16 corresponds to the "tonic" and the tonic is
>>>> shifted to a new position. In this case the tonic is shifted one note
> down
>>>> from C to B. Lets measure frequencies in units contrived to make the
>>>> frequency of C equal to 1 in the first chord.
>>>
>>>> Then the G-C-E 3:4:5 (or equally 12:16:20) chord is initially:
>>>
>>> 3/4 : 1 : 5/4
>>>
>>>> and after the modulation the G-C-E chord is, because I specified that it
>>>> have the ratios 11:15:19 and that the top note remain at constant pitch:
>>>
>>>> (5/4)*(11/19) : (5/4)*(15/19) : 5/4
>>>
>>>> which makes the calculations explicit but can be simplified to
>>>
>>>> 55/76 : 75/76 : 5/4
>>>
>>> OK, I think I got it, but it looks to me like you have gone up
>>> to C# not down to B.
>
>>> Yes, pretty much, though I might rather say that I brought B up to C
>>> (because the 11:15:19 chord appeared at Gb-B-Eb prior to modulation). In
>>> any case it was that thinking that was the source of my confusion. In the
>>> truest description I brough Eb up to E.
>
>>> So you could achieve the re-tuning you require using the dynamic
>>> re-tuning of Midicode Synth and hitting a new key note of C#,
>>> in this particular example.
>
>> Really? I doubt that it is the E pitch that would remain constant then,
>> based on what you have written elsewhere. I understood your retuining
>> method to agree with what Robert Walker was doing, which in "xmw" terms is
>> equivalen to "crossfree" mode, in which the current note played on the
>> modulation channel determines the new tonic, and specifically that the new
>> tonic retains the pitch that that note had prior to modulation. That is,
>> the pitch of C# would remain constant rather than the pitch of E remaining
>> constant. As a result none of the pitches in the G-C-E chord would remain
>> constant. The result would be "close" but not at the same absolute pitch.
>> I gave up on trying to calculate the absolute result because of the
>> complexities of the fractions involved, but I think you can get the idea.
>> Otherwise let me know.
>
> Yes, Kurt, you are right. The E does shift a bit ( and the others as we
> would expect ). I overlooked that first time through.
>
> So it looks like two pedal key-presses are required.
>
> My suggestion would be to hit the new tonic first but this has no
> immediate effect and just goes into some re-tune pending state.
> Then hit the bridge note on the pedal board at the moment of
> modulation..

That's interesting. It gets even more interesting when you want to play
notes on the pedal too. This all suggests to me that there are likely to be
several different modes reflecting different musical priorities.

But your suggestion of specifying the tonic and the bridge note explicitly
may be closest to what will be intuitive in many circumstances.

So another possibility would be to simply reverse this, and play the bridge
tone first, and then the new tonic at the moment of modulation. This is
potentially more useful if you want to *play* the tonic on the pedal. It
could be that an overlapping keypress is ignored for the purposes of
playing, and is treated as specifying a bridge tone, while a non-overlapping
press specifies the tonic and also plays a note. But this has the problem
of what to do when there is no previous note playing at the moment you want
to specify a bridge. It could also be with a multi-octave pedalboard that
one octaves specifies bridges and the other plays and specifies tonics.

It could also be that you just always require a sequence of 2 presses and
maybe this is what you meant. I was kind of looking for a way to use
"overlap" so that a simple mode (with no overlap) could be used when the new
tonic is the common tone.

All this of course has to be tried! Then it will get much clearer what
works and what does not.

> I have re-read your earlier post and this sounds similar to what
> you were suggesting. I can't think of anything better.
>
> I also take on board your comments in other messages.
> I shall let you know if I have any ideas.

Thanks. I figure there are some interesting possibilities yet to be thought
of, and I'll be glad to have your input.

Trying to think (especially alone) only gets so far, and we never know when
musical necessity will clarify things so that something new can be invented.

-Kurt

>
> Peter
> www.midicode.com

>

On Fri, 19 Dec 2003 18:29:13 -0800 Kurt wrote

>> So it looks like two pedal key-presses are required.
>>
>> My suggestion would be to hit the new tonic first but this has no
>> immediate effect and just goes into some re-tune pending state.
>> Then hit the bridge note on the pedal board at the moment of
>> modulation..
>
>That's interesting. It gets even more interesting when you want to play
>notes on the pedal too. This all suggests to me that there are likely to be
>several different modes reflecting different musical priorities.

I have only tried to deal with the case where there is a dedicated pedal
board or keyboard, or at least a dedicated midi channel for re-tuning.
Please keep me posted of your work in this area.

>But your suggestion of specifying the tonic and the bridge note explicitly
>may be closest to what will be intuitive in many circumstances.

>So another possibility would be to simply reverse this, and play the bridge
>tone first, and then the new tonic at the moment of modulation. This is
>potentially more useful if you want to *play* the tonic on the pedal.

If the new tonic is part of the chord, particularly the bass, at the time
of modulation then I strongly suspect that this amounts to the re-tuning
mode I have already, in most practical cases ?

>It could be that an overlapping keypress is ignored for the purposes of
>playing, and is treated as specifying a bridge tone, while a non-overlapping
>press specifies the tonic and also plays a note. But this has the problem
>of what to do when there is no previous note playing at the moment you want
>to specify a bridge. It could also be with a multi-octave pedalboard that
>one octaves specifies bridges and the other plays and specifies tonics.

This seems a bit complex for the performer ( and the programmer ).

>It could also be that you just always require a sequence of 2 presses and
>maybe this is what you meant. I was kind of looking for a way to use
>"overlap" so that a simple mode (with no overlap) could be used when the new
>tonic is the common tone.

>All this of course has to be tried! Then it will get much clearer what
>works and what does not.

I shall probably implement a dual key press re-tuning mode in a future
release of Midicode Synth. Do you have Midicode Synth, Kurt ?
Have you tried my dynamic re-tuning ?

Peter
www.midicode.com

>> I have re-read your earlier post and this sounds similar to what
>> you were suggesting. I can't think of anything better.
>>
>> I also take on board your comments in other messages.
>> I shall let you know if I have any ideas.
>
>Thanks. I figure there are some interesting possibilities yet to be thought
>of, and I'll be glad to have your input.
>
>Trying to think (especially alone) only gets so far, and we never know when
>musical necessity will clarify things so that something new can be invented.
>
>-Kurt