back to list

Re: Read this! Breakthrough, SUCCESS! : )

🔗Marcel <m.develde@...>

3/6/2011 9:49:57 AM

Btw, not sure yet what's the right way to expand.
I can see different ways of logic of going about it.
But for fun I threw some 7th harmonics in there:
1/1 19/18 9/8 7/6 19/16 5/4 21/16 4/3 45/32 189/128 3/2 14/9 19/12 27/16 7/4 16/9 15/8 63/32 2/1
But this is almost certainly not correct JI.
We'll see how fast we'll find the correct expansion way..
Is it further division of the fifth, or division of the fourth (my bet right now) or division of the thirds?
Anyhow here some interesting neutral seconds and neutral thirds coming from the 7th harmonic:

*: 2 608/567 120.867 cents
2: 1 243/224 140.949 cents
2: 3 21/19 173.268 cents
3: 1 448/405 174.692 cents
2: 2 567/512 176.646 cents

6: 1 2048/1701 321.399 cents
5: 2 135/112 323.353 cents
*: 3 76/63 324.777 cents
5: 3 189/152 377.178 cents
*: 3 56/45 378.602 cents

-Marcel

--- In MakeMicroMusic@yahoogroups.com, "Marcel" <m.develde@...> wrote:
>
> 1/1 19/18 9/8 19/16 5/4 4/3 45/32 3/2 19/12 27/16 16/9 15/8 2/1
>
> Yes it is done!
> Just Intonation has been found!! :)
>
> Common practice music works with 2 division of the pure fifth.
> One 5/4, the other 19/16.
> The above scale is how they come together.
> This scale is how common practice music works, it is how our ears interpret 12tet.
> The scale is not a fixed scale but moves along with the music along the chain of fifths.
> No wolfs, no comma shifting in held notes, no drifting.
>
> Here is a demonstration:
>
> Drei Equale no2.
> Midi file:
> /makemicromusic/files/Marcel/Drei_Equale_no2_JI_%2820110306_MdV%29.mid
> MP3 audio file:
> /makemicromusic/files/Marcel/Drei_Equale_no2_12TET_SmplTromb.mp3
>
> Drei Equale no3.
> Midi file:
> /makemicromusic/files/Marcel/Drei_Equale_no3_JI_%2820110306_MdV%29.mid
> MP3 audio file:
> /makemicromusic/files/Marcel/Drei_Equale_no3_12TET_SmplTromb.mp3
>
> Here a PDF of the score with JI ratios written above the notes:
> /makemicromusic/files/Marcel/Drei_Equale_2%263_JI_%2820110306_MdV%29.pdf
>
> Here comparison files in 12TET:
> /makemicromusic/files/Marcel/Drei_Equale_no2_12TET.mid
> /makemicromusic/files/Marcel/Drei_Equale_no2_12TET_SmplTromb.mp3
> /makemicromusic/files/Marcel/Drei_Equale_no3_JI_%2820110306_MdV%29.mid
> /makemicromusic/files/Marcel/Drei_Equale_no3_12TET_SmplTromb.mp3
>
> Here the Scala file of the base scale:
> /makemicromusic/files/Marcel/JI_MdV_12N-19L.scl
>
> Drei Equale no1 will follow soon.
>
>
> It hit me today. I saw that several objections I had against the 19th harmonic were not sound and saw the solution to where I saw problems before.
> I've actually used this exact base scale before and much of its logic, but was missing some other insights.
> Then came to the wrong conclusion (several times actually) that the 19th harmonic wouldn't work.
> My previous system without the 19th harmonic was equal to this one except that I had extended the chain of the 5th harmonic too far in the "collapsed harmony" scale, with the result that many things were hard to see and all minor intervals were off by a few cents (major was correct JI though).
>
> With this scale and the insight how it works, composing music becomes incredibly easy.
> I'm convinced it will change the world! :)
> Enjoy!! :)
>
> Btw, I'm not looking for more negative personal attack with this post.
> If you have critique then please keep it on topic.
>
> -Marcel
>

🔗Marcel <m.develde@...>

3/6/2011 10:06:17 AM

Oooh.. how I managed to mess up some of the links, please check them before you make judgment.
I accidentally linked 12tet audio files under the JI links, and one JI midi file under a 12tet link.
(the files themselves are named correctly)

You can also download the files from my folder:
/makemicromusic/files/Marcel/

Here the correct links:

Just Intonation Audio files:
No2: /makemicromusic/files/Marcel/Drei_Equale_no2_JI_%2820110306_MdV%29_SmplTromb.mp3
No3: /makemicromusic/files/Marcel/Drei_Equale_no3_JI_%2820110306_MdV%29_SmplTromb.mp3

Just Intonation MIDI files:
No2: /makemicromusic/files/Marcel/Drei_Equale_no2_JI_%2820110306_MdV%29.mid
No3: /makemicromusic/files/Drei_Equale_no3_JI_%2820110306_MdV%29.mid

(btw the midi files give a clearer sound, the sampled trombone in the audio files is slightly wobbly on some notes)

12TET Audio files:
No2: /makemicromusic/files/Marcel/Drei_Equale_no2_12TET_SmplTromb.mp3
No3: /makemicromusic/files/Marcel/Drei_Equale_no3_12TET_SmplTromb.mp3

12TET MIDI files:
No2: /makemicromusic/files/Marcel/Drei_Equale_no2_12TET.mid
No3: /makemicromusic/files/Marcel/Drei_Equale_no3_12TET.mid

-Marcel

🔗Mike Battaglia <battaglia01@...>

3/6/2011 10:24:30 AM

On Sun, Mar 6, 2011 at 12:00 PM, Marcel <m.develde@...> wrote:
>
> 1/1 19/18 9/8 19/16 5/4 4/3 45/32 3/2 19/12 27/16 16/9 15/8 2/1
>
> Yes it is done!
> Just Intonation has been found!! :)
>
> Common practice music works with 2 division of the pure fifth.
> One 5/4, the other 19/16.
> The above scale is how they come together.
> This scale is how common practice music works, it is how our ears interpret 12tet.
> The scale is not a fixed scale but moves along with the music along the chain of fifths.
> No wolfs, no comma shifting in held notes, no drifting.

1) Thank you, God, that you have finally clued Marcel into 19-limit
minor chords.
2) I do like this new direction you're going in, but you were
convinced last week that "Just Intonation had been found" with
entirely 5-limit harmony, and now you're throwing the 19-limit into
it.
3) Why don't you just make posts that say "I'm experimenting with
19-limit harmony" instead of "I HAVE SOLVED IT FOR REAL THIS TIME"
every time? Next you'll be using 17-limit harmony for semitones.
4) If you'd just get over your fear of tempering, and equate 32/27 and
19/16, you might be able to do even more interesting stuff.

-Mike

🔗Marcel <m.develde@...>

3/6/2011 10:34:08 AM

Hi Mike,

> 1) Thank you, God, that you have finally clued Marcel into 19-limit
> minor chords.

Haha :)
Well actually I have been into 19-limit minor chords on and off for years.
I've put a lot of effort in it in the past, I just never could make it work before.
There are so many things that have to fall into place.
The end result is incredibly simple, but getting there wasn't.

> 2) I do like this new direction you're going in, but you were
> convinced last week that "Just Intonation had been found" with
> entirely 5-limit harmony, and now you're throwing the 19-limit into
> it.

Thanks! :)
And yeah I know.. (ashamed)
But the thing is, I got most of it right (and all major completely right), and the results spoke to me that too much was right.
Except for the minors that was, 1215/1024 it kept nagging ang nagging me lol.

> 3) Why don't you just make posts that say "I'm experimenting with
> 19-limit harmony" instead of "I HAVE SOLVED IT FOR REAL THIS TIME"
> every time? Next you'll be using 17-limit harmony for semitones.

Oh I've been there with the 17-limit semitones.
I was doing connected harmonic segments a while back (and small ratio harmonic step sizes).

> 4) If you'd just get over your fear of tempering, and equate 32/27 and
> 19/16, you might be able to do even more interesting stuff.
>
> -Mike
>

Why would I. This stuff works like nothing else.
No temperament can do anything like it or provide the information JI gives :)

-Marcel

🔗Mike Battaglia <battaglia01@...>

3/6/2011 10:37:36 AM

On Sun, Mar 6, 2011 at 1:34 PM, Marcel <m.develde@...> wrote:
>
> > 2) I do like this new direction you're going in, but you were
> > convinced last week that "Just Intonation had been found" with
> > entirely 5-limit harmony, and now you're throwing the 19-limit into
> > it.
>
> Thanks! :)
> And yeah I know.. (ashamed)
> But the thing is, I got most of it right (and all major completely right), and the results spoke to me that too much was right.
> Except for the minors that was, 1215/1024 it kept nagging ang nagging me lol.

I'm just saying - you will get much better feedback and results on
this list if you just stop acting like you have finished work on it.
You will continue to improve and work on your methods - why say that
they're done?

You're trying to find an optimal way to retune meantone music to JI.
You want it to sound maximally intelligible and use Pythagorean chords
and wolf fifths intelligibly. That's a worthy cause. Why not just stop
pretending you have it all figured out and just post progress as you
make it?

> Why would I. This stuff works like nothing else.
> No temperament can do anything like it or provide the information JI gives :)

If we were using sine waves, then I doubt you'd be able to tell 32/27
and 19/16 apart.

-Mike

🔗Marcel <m.develde@...>

3/6/2011 10:51:46 AM

I just did a comparison in the Scala scale archive.
And to my surprise, the scale is new :)

So I get the chance to name something after me so atleast I'll be remembered for my JI work haha :)

mdevelde.scl

Download it here:
/makemicromusic/files/Marcel/mdevelde.scl

!
!
12 tone Just Intonation scale. By Marcel de Velde, March 6, 2011, Zwolle, NL
12
!
19/18
9/8
19/16
5/4
4/3
45/32
3/2
19/12
27/16
16/9
15/8
2/1

--- In MakeMicroMusic@yahoogroups.com, "Marcel" <m.develde@...> wrote:
>
> 1/1 19/18 9/8 19/16 5/4 4/3 45/32 3/2 19/12 27/16 16/9 15/8 2/1
>
>
> Here the Scala file of the base scale:
> /makemicromusic/files/Marcel/JI_MdV_12N-19L.scl
>
>
> -Marcel
>

🔗Marcel <m.develde@...>

3/6/2011 10:59:02 AM

Hi Mike,

>
> I'm just saying - you will get much better feedback and results on
> this list if you just stop acting like you have finished work on it.
> You will continue to improve and work on your methods - why say that
> they're done?
>

Ah ok, no I'm not trying to imply the work is done.
In fact one of the main reasons I'm setting up justintonation.com is for people to work on it together.

But I do think (I know I thought it before, but it's here now for real) that I've hit a milestone. This scale I belief to be truly correct Just Intonation if applied in the proper way.
I've got a lot of the theory of how to apply it ready.
But many details can still be worked out. And music is such that I could work on it for the rest of my life.

> You're trying to find an optimal way to retune meantone music to JI.
> You want it to sound maximally intelligible and use Pythagorean chords
> and wolf fifths intelligibly. That's a worthy cause. Why not just stop
> pretending you have it all figured out and just post progress as you
> make it?
>

Ah yes but I see it differently.
I think there are strict "laws of music" and that these are stemming from tuning, and this tuning is JI.
I'll write a long story on my website later on why I believe it is only logical that it is so.

> > Why would I. This stuff works like nothing else.
> > No temperament can do anything like it or provide the information JI gives :)
>
> If we were using sine waves, then I doubt you'd be able to tell 32/27
> and 19/16 apart.
>
> -Mike
>

Yes true.
However, it's not about if it is audible or not.
With this scale and knowledge on how to use it I've spent half an hour improvising on my keyboard.
I've never in my life done such good improvisions. Tears in my eyes.
The possibilities, the emotions, I can see them all clearly now in the numbers. It's truly amazing and humbling.
This is much bigger than me and what I "invented". I did not invent anything, I found things, I found how a very important part of music works :)

-Marcel

🔗Mike Battaglia <battaglia01@...>

3/6/2011 11:17:29 AM

On Sun, Mar 6, 2011 at 1:59 PM, Marcel <m.develde@...> wrote:
>
> > I'm just saying - you will get much better feedback and results on
> > this list if you just stop acting like you have finished work on it.
> > You will continue to improve and work on your methods - why say that
> > they're done?
> >
>
> Ah ok, no I'm not trying to imply the work is done.
> In fact one of the main reasons I'm setting up justintonation.com is for people to work on it together.
>
> But I do think (I know I thought it before, but it's here now for real) that I've hit a milestone. This scale I belief to be truly correct Just Intonation if applied in the proper way.

OK, but you're obviously going to change the scale in the future. And
you've changed it before, and you thought that those scales were also
truly correct just intonation. So there is no scale from you that has
ever actually been "truly correct JI," because the scales always
changing. So what you're really saying is, some future scale I'm
working on will be truly correct JI. Well, I sure hope so. Why not
just phrase it like that?

> I've got a lot of the theory of how to apply it ready.
> But many details can still be worked out. And music is such that I could work on it for the rest of my life.

So you're just convinced that every scale you make is the only correct
way to tune stuff to JI. And we've been saying, this whole time, that
they sound in some sense like they're "out of tune," and you tell us
to get our ears checked and that everything else sounds out of tune.
Then, afterwards, you relent and say it was out of tune, you have a
new scale, repeat forever. And every time you work one of those out,
you say that's the true approach to JI. You have no actual scale that
IS the true approach to JI, you're just saying that you, yourself, are
the true approach to JI, and that whatever you do, that's the true
approach to JI. Why not take a more fair-minded approach and just say
that this is what you're workING on, not that you have already finally
figured it out and everything else sucks!

> > If we were using sine waves, then I doubt you'd be able to tell 32/27
> > and 19/16 apart.
> Yes true.
> However, it's not about if it is audible or not.
> With this scale and knowledge on how to use it I've spent half an hour improvising on my keyboard.
> I've never in my life done such good improvisions. Tears in my eyes.
> The possibilities, the emotions, I can see them all clearly now in the numbers. It's truly amazing and humbling.
> This is much bigger than me and what I "invented". I did not invent anything, I found things, I found how a very important part of music works :)

But you've never given any explanation about why numbers should mean
anything at all.

-Mike

🔗Marcel <m.develde@...>

3/6/2011 12:35:31 PM

Hi Mike,

> > But I do think (I know I thought it before, but it's here now for real) that I've hit a milestone. This scale I belief to be truly correct Just Intonation if applied in the proper way.
>
> OK, but you're obviously going to change the scale in the future. And
> you've changed it before, and you thought that those scales were also
> truly correct just intonation. So there is no scale from you that has
> ever actually been "truly correct JI," because the scales always
> changing. So what you're really saying is, some future scale I'm
> working on will be truly correct JI. Well, I sure hope so. Why not
> just phrase it like that?
>

Well this is not what I believe.
I do not believe I'll ever change this scale for common practice music.
The system behind the scale needs a lot of work yes.
And some things may even change that are already there, but it mostly needs adding rules and insights.
The system behind it goes seamlessly from abstract mathematical and logical things to broader music theoretical insights.

I know I've thought before that I've found the scale into which harmony "collapses" / tells the allowed movements of melodies and sets the limits for musical coherence / continuity.
And I wasn't far off for a long time already.
And I planned not to make a big announcement anymore when I had to change my system but more silently convey it.
However, what makes me more sure now than ever before.
Is that not only do I have more insights and experience.
It is that what it now has come down to is all of a sudden so incredibly simple and easy to oversee. Before it was complex in several ways. I could miss seeing things because of this complexity.
Now it is so simple I'm convinced that I'm not missing anything.
It has to be this way because I can clearly see that it cannot be changed without breaking it.
But I don't expect you to see this already. So let time tell :)

> > I've got a lot of the theory of how to apply it ready.
> > But many details can still be worked out. And music is such that I could work on it for the rest of my life.
>
> So you're just convinced that every scale you make is the only correct
> way to tune stuff to JI. And we've been saying, this whole time, that
> they sound in some sense like they're "out of tune," and you tell us
> to get our ears checked and that everything else sounds out of tune.
> Then, afterwards, you relent and say it was out of tune, you have a
> new scale, repeat forever. And every time you work one of those out,
> you say that's the true approach to JI. You have no actual scale that
> IS the true approach to JI, you're just saying that you, yourself, are
> the true approach to JI, and that whatever you do, that's the true
> approach to JI. Why not take a more fair-minded approach and just say
> that this is what you're workING on, not that you have already finally
> figured it out and everything else sucks!
>

Noo haha I'm not myself JI :)
I merely do research.
And yes there's a lot more research to be done!
A new music theory is being born I think :)

> > > If we were using sine waves, then I doubt you'd be able to tell 32/27
> > > and 19/16 apart.
> > Yes true.
> > However, it's not about if it is audible or not.
> > With this scale and knowledge on how to use it I've spent half an hour improvising on my keyboard.
> > I've never in my life done such good improvisions. Tears in my eyes.
> > The possibilities, the emotions, I can see them all clearly now in the numbers. It's truly amazing and humbling.
> > This is much bigger than me and what I "invented". I did not invent anything, I found things, I found how a very important part of music works :)
>
> But you've never given any explanation about why numbers should mean
> anything at all.
>
> -Mike
>

There are many explanations.
Physical / mathematical ones.
Of course the octave is 2/1 and the fifth 3/2.
But most importantly of all, the ear/brain perceives these as pure.
This is no strange thinking as just about anybody thinks this way and players of an instrument capable of it will play this way.
What is more bizarre is that people think that it can't work in real life.
I've started out as skeptical at first (though with a preference for it being able to work), then I did my research and in time saw that it was absolutely possible.
The question was not "is it possible", but the question was "how", or "which one of these almost infinite amount of possiblities".
The more I knew, the more possibilities I saw in which ways it could work. The question then was "how does music work" how does it work for our brain, which physics / mathematical structures are important. etc.
This took me a looong time to wade through. Making hundreds of wrong turns.
I've now come to the point where enough is clear to make it practical.
And therefore I claim breakthrough and success :)

-Marcel

🔗genewardsmith <genewardsmith@...>

3/6/2011 12:37:31 PM

--- In MakeMicroMusic@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

I would suggest Marcel take a look at 10-12-14-17-20 for the Dim7 chord.

🔗Mike Battaglia <battaglia01@...>

3/6/2011 12:52:20 PM

On Sun, Mar 6, 2011 at 3:35 PM, Marcel <m.develde@...> wrote:
>
> Hi Mike,
>
> > > But I do think (I know I thought it before, but it's here now for real) that I've hit a milestone. This scale I belief to be truly correct Just Intonation if applied in the proper way.
> >
> > OK, but you're obviously going to change the scale in the future. And
> > you've changed it before, and you thought that those scales were also
> > truly correct just intonation. So there is no scale from you that has
> > ever actually been "truly correct JI," because the scales always
> > changing. So what you're really saying is, some future scale I'm
> > working on will be truly correct JI. Well, I sure hope so. Why not
> > just phrase it like that?
> >
>
> Well this is not what I believe.
> I do not believe I'll ever change this scale for common practice music.

If you do ever change this scale then, will you relent and start
phrasing your work in the way that I am saying?

> I know I've thought before that I've found the scale into which harmony "collapses" / tells the allowed movements of melodies and sets the limits for musical coherence / continuity.
> And I wasn't far off for a long time already.
> And I planned not to make a big announcement anymore when I had to change my system but more silently convey it.
> However, what makes me more sure now than ever before.
> Is that not only do I have more insights and experience.
> It is that what it now has come down to is all of a sudden so incredibly simple and easy to oversee. Before it was complex in several ways. I could miss seeing things because of this complexity.
> Now it is so simple I'm convinced that I'm not missing anything.
> It has to be this way because I can clearly see that it cannot be changed without breaking it.
> But I don't expect you to see this already. So let time tell :)

So you're saying that you will never change this scale, and that this
is the finished version, and this is true JI, and you have "done it,"
etc? Because if you change it again and refuse to discuss your work in
more fair-minded terms, I think that you're just trolling us and that
that should be grounds for a ban.

> There are many explanations.
> Physical / mathematical ones.
> Of course the octave is 2/1 and the fifth 3/2.
> But most importantly of all, the ear/brain perceives these as pure.

People generally prefer octaves that are a little bit sharp, if you're
using sine waves.

> This is no strange thinking as just about anybody thinks this way and players of an instrument capable of it will play this way.
> What is more bizarre is that people think that it can't work in real life.
> I've started out as skeptical at first (though with a preference for it being able to work), then I did my research and in time saw that it was absolutely possible.
> The question was not "is it possible", but the question was "how", or "which one of these almost infinite amount of possiblities".
> The more I knew, the more possibilities I saw in which ways it could work. The question then was "how does music work" how does it work for our brain, which physics / mathematical structures are important. etc.
> This took me a looong time to wade through. Making hundreds of wrong turns.
> I've now come to the point where enough is clear to make it practical.
> And therefore I claim breakthrough and success :)

Then let it be your claim. You've made it before, and you've changed
it every single time. Now, you're saying that this time is different,
and you won't change it - no further changes to the scale will be
made. So if you ever change this scale again, then your word is
effectively useless, and furthermore I vote that you be banned if so.

-Mike

🔗genewardsmith <genewardsmith@...>

3/6/2011 12:54:36 PM

--- In MakeMicroMusic@yahoogroups.com, "Marcel" <m.develde@...> wrote:

> 12 tone Just Intonation scale. By Marcel de Velde, March 6, 2011, Zwolle, NL
> 12

This is in the 2.3.5.19 subgroup, and so I've added it to other 12-note subgroup scales on the xenwiki.

🔗Marcel <m.develde@...>

3/6/2011 1:04:50 PM

Hi Gene,

> I would suggest Marcel take a look at 10-12-14-17-20 for the Dim7 chord.
>

There are many reasons why that won't work.
Btw I also don't think it sounds right. It's one thing to play something on a keyboard in isolation, it's another thing to use it in actual musical context.

One reason the above tuning won't work is because the Dim7 must have many functions in it.
One is for instance that it must have a minor triad in it that can function as such if the fifth is made.
Another is for instance that it must function as a dominant 7th when one tone is lowered to make a fifth.
Furthermore it must always be able to reach the Dim7 from ANY chord simply by raising or lowering some tones of that chord.
And then it must be possible to exit that Dim7 in a new key.

Here is the Dim7 in JI:
1/1 19/16 45/32 27/16

If you look at my base scale you'll see that it occurs 3 times:
1/1 19/18 9/8 19/16 5/4 4/3 45/32 3/2 19/12 27/16 16/9 15/8 2/1

1) 1/1 19/16 45/32 27/16
2) 4/3 19/12 15/8 9/4
3) 16/9 19/9 5/4 3/2

Exactly the same chord therefore occurs 3 times at different locations in my JI scale.

One can for instance play a Cmin tonic triad.
1/1 19/16 3/2 -> 1/1 19/16 45/32 27/16
Then lower the 19/16 to 9/8 to make 1/1 9/8 45/32 27/16 chord.
Which one can also reinterpret to be a dominant major 7th resolving to 3/2 57/32 9/4, which can then be made into another Dim7, etc.

There are countless other examples.
Take the whole of common practice music. This scale and system does it! Really!
The scale and system I present isn't just another scale or system.
It's special ;)

-Marcel

🔗genewardsmith <genewardsmith@...>

3/6/2011 1:15:49 PM

--- In MakeMicroMusic@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
> --- In MakeMicroMusic@yahoogroups.com, "Marcel" <m.develde@> wrote:
>
> > 12 tone Just Intonation scale. By Marcel de Velde, March 6, 2011, Zwolle, NL
> > 12
>
> This is in the 2.3.5.19 subgroup, and so I've added it to other 12-note subgroup scales on the xenwiki.

By the way, one reason to like the 2.3.5.19 subgroup is that it could be used as a chromatic pair subgroup for a version of schismatic temperament restricted to this subgroup. I think I'll add it, but I'm trying to think of a good name as "the correct temperament for true music" doesn't appeal to me. Of course, there's also the 2.3.5.17.19 subgroup to consider...

🔗Marcel <m.develde@...>

3/6/2011 2:05:16 PM

Hi Gene,

Let say I'm right with all my claims just for fun..
Then some people will still need to use a temperament.
However.. A temperament can be optimized for a certain key.
Let's say C major and parallel minor.
Let's say most pieces in C major and parallel minor stay within +- 2 shifts up and down the chain of fifths of my base JI scale.

Then one gets the following scale:
1/1 135/128 19/18 10/9 9/8 32/27 19/16 5/4 81/64 4/3 171/128 45/32 38/27 3/2 128/81 405/256 19/12 5/3 27/16 16/9 57/32 15/8 152/81 243/128 2/1

What would be the optimal temperament for this?

-Marcel

--- In MakeMicroMusic@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
> --- In MakeMicroMusic@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> >
> >
> > --- In MakeMicroMusic@yahoogroups.com, "Marcel" <m.develde@> wrote:
> >
> > > 12 tone Just Intonation scale. By Marcel de Velde, March 6, 2011, Zwolle, NL
> > > 12
> >
> > This is in the 2.3.5.19 subgroup, and so I've added it to other 12-note subgroup scales on the xenwiki.
>
> By the way, one reason to like the 2.3.5.19 subgroup is that it could be used as a chromatic pair subgroup for a version of schismatic temperament restricted to this subgroup. I think I'll add it, but I'm trying to think of a good name as "the correct temperament for true music" doesn't appeal to me. Of course, there's also the 2.3.5.17.19 subgroup to consider...
>

🔗purest_intonation@...

3/6/2011 2:08:02 PM

--- In MakeMicroMusic@yahoogroups.com, "Marcel" <m.develde@...> wrote:
>
> 1/1 19/18 9/8 19/16 5/4 4/3 45/32 3/2 19/12 27/16 16/9 15/8 2/1
>
> Yes it is done!
> Just Intonation has been found!! :)

Mr. DeVelde,

Are you now saying that JI must involve three infinite chains of 3/2, one of which is 19/16 off and the other of which is 5/4 off?

I don't know that I can accept this. In fact, one area that I have done my own research and found it to be in conflict with your own is in the case of minor keys.

It is my conclusion that the search for a rooted minor triad that can be a tonic in a minor key is actually a wild goose-chase. The minor chord can NEVER truly be a place of rest, and the only reason that minor keys "work" in common-practice music is because the authentic V-i cadence utilizes the harmonic minor, and the resolution melodically by the leading tone temporarily creates the illusion of being in a major key, "hoodwinking" the brain into accepting a minor tonic as a point of resolution. No matter how you tune the third in a minor chord, it is entirely the 3/2 in the chord that "roots" it. The only third that can actually enhance the rootedness of a triad is the 5/4 major third. All other thirds weaken the rootedness on account of creating difference tones other than octaves of the fundamental. 19/16 leads to a 1/1-19/16-3/2 triad, which would be harmonics 16, 19, and 24, creating difference tones of 3 and 5, suggesting a 3, 5, 16, 19, 24 series, where only the 3 and the 24 are in octave relations with each other. In other words, this emphasizes the fifth of the chord more strongly than the root, leaving the root frequency weak. I do not see how, after all your years of research, you have not realized this.

Instead, I think you should remain with the two chains of 3/2s a 5/4 apart (well, actually, there is also the infinite chains of 2/1's going up and down from every note in each chain of 3/2s; we can't neglect the octave in musical geometry). The proper minor tonic has to be related to a 1/1-5/4-3/2 triad; if we are in A minor, the relative major is C. For C to have a 5/4 major third, the A must be tuned 1/1-6/5-3/2. The major dominant implied by the harmonic minor should of course be tuned as a Pythagorean triad, so the proper JI minor scale (with the raised VII in parentheses) would be:

1/1-9/8-6/5-4/3-3/2-8/5-9/5(243/128)-2/1

Which of course only defines notes in relation to the tonic and can move and shift with the music functionally. But in this tuning of the minor tonic it acts as harmonics 10, 12, and 15 of the relative major tonic, which (despite what some fools would have you believe) is the true tonic of any piece of minor-key music. I repeat, THE TRUE TONIC of any scale is always going to be a 1/1-5/4-3/2 triad, and tonicizing any other triad will be done artificially through melodic devices like the harmonic minor that "trick" the brain into hearing a 1/1-6/5-3/2 chord AS a 1/1-5/4-3/2 major triad.

How can you disagree?

-Dr. G. S. Sullivan

🔗genewardsmith <genewardsmith@...>

3/6/2011 2:30:28 PM

--- In MakeMicroMusic@yahoogroups.com, "Marcel" <m.develde@...> wrote:

> What would be the optimal temperament for this?

Schismatic 2.3.5.19 subgroup temperament would be good. You can tune it in 171 equal. Not that it's going to sound all that much different.

🔗Mike Battaglia <battaglia01@...>

3/6/2011 2:47:46 PM

On Sun, Mar 6, 2011 at 5:08 PM, purest_intonation@...
<purest_intonation@...> wrote:
>
> It is my conclusion that the search for a rooted minor triad that can be a tonic in a minor key is actually a wild goose-chase. The minor chord can NEVER truly be a place of rest, and the only reason that minor keys "work" in common-practice music is because the authentic V-i cadence utilizes the harmonic minor, and the resolution melodically by the leading tone temporarily creates the illusion of being in a major key, "hoodwinking" the brain into accepting a minor tonic as a point of resolution. No matter how you tune the third in a minor chord, it is entirely the 3/2 in the chord that "roots" it. The only third that can actually enhance the rootedness of a triad is the 5/4 major third. All other thirds weaken the rootedness on account of creating difference tones other than octaves of the fundamental. 19/16 leads to a 1/1-19/16-3/2 triad, which would be harmonics 16, 19, and 24, creating difference tones of 3 and 5, suggesting a 3, 5, 16, 19, 24 series, where only the 3 and the 24 are in octave relations with each other. In other words, this emphasizes the fifth of the chord more strongly than the root, leaving the root frequency weak. I do not see how, after all your years of research, you have not realized this.

Difference tones. We're talking about difference tones now. God damn.

> Which of course only defines notes in relation to the tonic and can move and shift with the music functionally. But in this tuning of the minor tonic it acts as harmonics 10, 12, and 15 of the relative major tonic, which (despite what some fools would have you believe) is the true tonic of any piece of minor-key music. I repeat, THE TRUE TONIC of any scale is always going to be a 1/1-5/4-3/2 triad, and tonicizing any other triad will be done artificially through melodic devices like the harmonic minor that "trick" the brain into hearing a 1/1-6/5-3/2 chord AS a 1/1-5/4-3/2 major triad.

Oh right, because you can just ignore octave doubling.
5:10:20:40:48:60 and 2:4:8:16:19:24 - I wonder which one the brain
likes more.

-Mike

🔗Marcel <m.develde@...>

3/6/2011 2:59:03 PM

--- In MakeMicroMusic@yahoogroups.com, "purest_intonation@..." <purest_intonation@...> wrote:
>
> --- In MakeMicroMusic@yahoogroups.com, "Marcel" <m.develde@> wrote:
> >
> > 1/1 19/18 9/8 19/16 5/4 4/3 45/32 3/2 19/12 27/16 16/9 15/8 2/1
> >
> > Yes it is done!
> > Just Intonation has been found!! :)
>
> Mr. DeVelde,
>
> Are you now saying that JI must involve three infinite chains of 3/2, one of which is 19/16 off and the other of which is 5/4 off?
>

Yes, this is the potential total pitch space for common practice music.

> I don't know that I can accept this. In fact, one area that I have done my own research and found it to be in conflict with your own is in the case of minor keys.
>
> It is my conclusion that the search for a rooted minor triad that can be a tonic in a minor key is actually a wild goose-chase. The minor chord can NEVER truly be a place of rest, and the only reason that minor keys "work" in common-practice music is because the authentic V-i cadence utilizes the harmonic minor, and the resolution melodically by the leading tone temporarily creates the illusion of being in a major key, "hoodwinking" the brain into accepting a minor tonic as a point of resolution. No matter how you tune the third in a minor chord, it is entirely the 3/2 in the chord that "roots" it. The only third that can actually enhance the rootedness of a triad is the 5/4 major third. All other thirds weaken the rootedness on account of creating difference tones other than octaves of the fundamental. 19/16 leads to a 1/1-19/16-3/2 triad, which would be harmonics 16, 19, and 24, creating difference tones of 3 and 5, suggesting a 3, 5, 16, 19, 24 series, where only the 3 and the 24 are in octave relations with each other. In other words, this emphasizes the fifth of the chord more strongly than the root, leaving the root frequency weak. I do not see how, after all your years of research, you have not realized this.
>

Very good to hear you have done real just intonation research too!! :)
I was beginning to think I was alone.

As for the minor.
One doesn't need to use harmonic minor V to create a good minor i ending.
It is a very strong cadence because of several reasons (which are present in the dynamics of the JI tuning btw!), but minor will feel like a rooted final in countless other cadences.

The point you make about being in a major key to end the minor is a very very valid one.
It is because there are several "minors".
The relative minor is NOT rooted and indeed not suitable for ending (though when normal music theory talks about relative minor it is still often the parallel minor).
The relative minor is 5/4 3/2 15/8 (or 5/3 2/1 5/2 when you tip the scale a fifth). It is not rooted because it is 1/1 6/5 3/2 seen from the root. Indicating a 1/5 as it's true root. (making a major 7th chord)

The 1/1 19/16 3/2 is a rooted minor.
You provided your own math already for this. The difference tones reinforce the root. It doesn't matter that the 5th harmonic is one of the difference tones, only good.
Btw, I see the difference tones as less important than the "beating" / "periodicity of the combined waveforms". We're not dealing with sines in actual music and the overtones of the actual tones create a wealthy combination of difference tones, which all interfere. And the most audible end result is the "beating" / "synchronicity of the waves".
The 19th harmonic gives a pretty strong 1 as it's "beating root".
Is the 19th harmonic as strong and clear a reinforcement of the root as the 5th or 3rd harmonic, no, but it's much better than 1215/1024 :)

2 reasons I had to reject the 19th harmonic in the past were that through error I had thought the 405/256 was also reinforcing the root and was combinational with 1215/1024. I see now this was wrong.
The other reason was that I thought I could connect the 1215/1024 in several circle progressions with 5/4, I found I was wrong about this too. (the number of errors I've made are countless haha).
In fact, I found I can't connect the 45/32 with the 135/128 without moving the base scale in the chain of fifths.

Btw, one other thing, if you play along Drei Equale no3 with my JI score, you'll see how incredibly fast a minor chord roots! No need to include a 3/2 even.
It does this just as well as a 5/4, only slightly more subtle.
If you listen closely to Drei Equale no3, you'll still hear the emotional "minorness" when 19/18 4/3 19/12 chords play. (yes, minor "major" chords).

> Instead, I think you should remain with the two chains of 3/2s a 5/4 apart (well, actually, there is also the infinite chains of 2/1's going up and down from every note in each chain of 3/2s; we can't neglect the octave in musical geometry). The proper minor tonic has to be related to a 1/1-5/4-3/2 triad; if we are in A minor, the relative major is C. For C to have a 5/4 major third, the A must be tuned 1/1-6/5-3/2. The major dominant implied by the harmonic minor should of course be tuned as a Pythagorean triad, so the proper JI minor scale (with the raised VII in parentheses) would be:
>
> 1/1-9/8-6/5-4/3-3/2-8/5-9/5(243/128)-2/1
>

Thank you for your care to keep me on the straight path :)

Yes this minor scale is part of the JI scale.
The relative minor indeed, it's on 15/8 as 1/1. (reason why so many pieces are not really in relative minor but in parallel minor while normal theory says they're in relative)

As you can see, I agree with you on the relative minor :)
It's not a problem at all.

> -Dr. G. S. Sullivan
>

Cheers!
Marcel

🔗Mike Battaglia <battaglia01@...>

3/6/2011 3:06:51 PM

On Sun, Mar 6, 2011 at 4:15 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In MakeMicroMusic@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> >
> >
> > --- In MakeMicroMusic@yahoogroups.com, "Marcel" <m.develde@> wrote:
> >
> > > 12 tone Just Intonation scale. By Marcel de Velde, March 6, 2011, Zwolle, NL
> > > 12
> >
> > This is in the 2.3.5.19 subgroup, and so I've added it to other 12-note subgroup scales on the xenwiki.
>
> By the way, one reason to like the 2.3.5.19 subgroup is that it could be used as a chromatic pair subgroup for a version of schismatic temperament restricted to this subgroup. I think I'll add it, but I'm trying to think of a good name as "the correct temperament for true music" doesn't appeal to me. Of course, there's also the 2.3.5.17.19 subgroup to consider...

I was calling the 2.3.5.19 96/95 temperament "minor" temperament, for
the same reason that we call 648/625 "diminished" and 128/125
"augmented."

-Mike

🔗Marcel <m.develde@...>

3/6/2011 3:07:25 PM

> > Which of course only defines notes in relation to the tonic and can move and shift with the music functionally. But in this tuning of the minor tonic it acts as harmonics 10, 12, and 15 of the relative major tonic, which (despite what some fools would have you believe) is the true tonic of any piece of minor-key music. I repeat, THE TRUE TONIC of any scale is always going to be a 1/1-5/4-3/2 triad, and tonicizing any other triad will be done artificially through melodic devices like the harmonic minor that "trick" the brain into hearing a 1/1-6/5-3/2 chord AS a 1/1-5/4-3/2 major triad.
> >
> > How can you disagree?
> >
>
>
> As you can see, I agree with you on the relative minor :)
> It's not a problem at all.

Btw I forgot to say that the harmonic minor is usually:
1/1 9/8 19/16 4/3 3/2 19/12 15/8 2/1
The true relative minor is actually quite rare and not so easy to master if one wants to avoid relative major chords to indicate it.
On thing that comes to mind is for instance Chopin - marche funebre, it uses relative major chords constantly, not much confusion there about the real roots.
Something that sounds to me like it is truly in relative minor are three olden pieces by Gorecki (haven't checked though, doing this out of memory impression the pieces left on me) but it's a very different sound than normal minor (which is actually parallel minor, 19th harmonic, not relative as normal music theory says)

-Marcel

🔗genewardsmith <genewardsmith@...>

3/6/2011 3:50:56 PM

--- In MakeMicroMusic@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> I was calling the 2.3.5.19 96/95 temperament "minor" temperament, for
> the same reason that we call 648/625 "diminished" and 128/125
> "augmented."

You mean the rank three temperament?

🔗Mike Battaglia <battaglia01@...>

3/6/2011 4:11:45 PM

On Sun, Mar 6, 2011 at 6:50 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In MakeMicroMusic@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > I was calling the 2.3.5.19 96/95 temperament "minor" temperament, for
> > the same reason that we call 648/625 "diminished" and 128/125
> > "augmented."
>
> You mean the rank three temperament?

I guess. I didn't think it made sense to call the 81/80 and 96/95 rank
2 temperament "minor temperament" when it should probably be called
something that has to do with meantone.

-Mike

🔗purest_intonation@...

3/6/2011 4:14:35 PM

--- In MakeMicroMusic@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> Oh right, because you can just ignore octave doubling.
> 5:10:20:40:48:60 and 2:4:8:16:19:24 - I wonder which one the brain
> likes more.

Mr. Battaglia--

It will not make a difference with that much octave-doubling how the third is tuned. With enough octave-doubling, ANYTHING will sound rooted. It is the case that any triad composed of harmonics above 16 will either sound like an approximation of a simpler identity or else "noise".

The fact of the matter is that minor chords are all heard as major seventh chords with a missing fundamental. Tuning them as anything other than harmonics 10, 12, and 15 will do nothing to alter this.

-Dr. Gilbert S. Sullivan

🔗Mike Battaglia <battaglia01@...>

3/6/2011 4:16:52 PM

On Sun, Mar 6, 2011 at 7:14 PM, purest_intonation@...
<purest_intonation@...> wrote:
>
> --- In MakeMicroMusic@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > Oh right, because you can just ignore octave doubling.
> > 5:10:20:40:48:60 and 2:4:8:16:19:24 - I wonder which one the brain
> > likes more.
>
> Mr. Battaglia--
>
> It will not make a difference with that much octave-doubling how the third is tuned. With enough octave-doubling, ANYTHING will sound rooted. It is the case that any triad composed of harmonics above 16 will either sound like an approximation of a simpler identity or else "noise".
>
> The fact of the matter is that minor chords are all heard as major seventh chords with a missing fundamental. Tuning them as anything other than harmonics 10, 12, and 15 will do nothing to alter this.
>
> -Dr. Gilbert S. Sullivan

I see. Thanks for cluing me in. I think I'm going to go impale myself
on a giant spike now.

-Mike

🔗Marcel <m.develde@...>

3/6/2011 4:40:58 PM

--- In MakeMicroMusic@yahoogroups.com, "purest_intonation@..." <purest_intonation@...> wrote:
>
> --- In MakeMicroMusic@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
>
> > Oh right, because you can just ignore octave doubling.
> > 5:10:20:40:48:60 and 2:4:8:16:19:24 - I wonder which one the brain
> > likes more.
>
> Mr. Battaglia--
>
> It will not make a difference with that much octave-doubling how the third is tuned. With enough octave-doubling, ANYTHING will sound rooted. It is the case that any triad composed of harmonics above 16 will either sound like an approximation of a simpler identity or else "noise".
>
> The fact of the matter is that minor chords are all heard as major seventh chords with a missing fundamental. Tuning them as anything other than harmonics 10, 12, and 15 will do nothing to alter this.
>
> -Dr. Gilbert S. Sullivan
>

Sorry to have to say this, but your reasoning here is wrong.
Hope you take it personal, I've been wrong about these issues countless times.

The thing is, 10:12:15 (1/1 6/5 3/2) and 16:19:32 (1/1 19/16 3/2) and 54:64:81 (1/1 32/27 3/2) are all correct minor chords in common practice music.
And all of them have a relative major chord.
4:5:6 (1/1 5/4 3/2) for 10:12:15 (5/4 3/2 15/8)
38:48:57 (19/12 2/1 19/8) for 16:19:32 (2/1 19/8 3/1)
64:81:96 (16/9 9/4 8/3) for 54:64:81 (9/4 8/3 27/8)
All these chords are much used in actual music.
And the music indicates which chord is played.

-Marcel

🔗Chris Vaisvil <chrisvaisvil@...>

3/6/2011 4:43:27 PM

I disagree. If this were so you could substitute the 7th chords - this
doesn't work and still have it sound minor. It sounds like you've
taken off into a different key.

Chris

On Sun, Mar 6, 2011 at 7:14 PM, purest_intonation@...
<purest_intonation@...> wrote:

>
> The fact of the matter is that minor chords are all heard as major seventh chords with a missing fundamental. Tuning them as anything other than harmonics 10, 12, and 15 will do nothing to alter this.
>
> -Dr. Gilbert S. Sullivan
>

🔗purest_intonation@...

3/6/2011 5:32:56 PM

--- In MakeMicroMusic@yahoogroups.com, "Marcel" <m.develde@...> wrote:

> As for the minor.
> One doesn't need to use harmonic minor V to create a good minor i ending.
> It is a very strong cadence because of several reasons (which are present in the
> dynamics of the JI tuning btw!), but minor will feel like a rooted final in countless other > cadences.

It is true that there are cadences that can effect resolution in minor keys, and a minor tonic may feel somewhat "resolved"--but this is due more to root movement than to the harmonic rootedness of the chord.

> The relative minor is NOT rooted and indeed not suitable for ending (though when
> normal music theory talks about relative minor it is still often the parallel minor).

On the contrary: the relative minor is about as rooted as any non-septimal minor triad can be. For 10, 12, and 15, we have difference tones of 2, 3, and 5. For 16, 19, and 24, we have 3, 5, and 8. However, for a septimal minor of 6, 7, and 9, we have 1, 2, and 3--it is the most rooted of all of them, and also has the simplest periodicity of wave interactions. I once considered deriving this chord from a harmonic series dominant 7th chord with a major 9th, of 1/1-5/4-3/2-7/4-9/8, but the scale that resulted seemed unworkable. It required treating (in the key of C) F as 21/16, which meant that the subdominant would have a 64/63-sharpened wolf fifth. Unacceptable.

> The relative minor is 5/4 3/2 15/8 (or 5/3 2/1 5/2 when you tip the scale a fifth). It is
> not rooted because it is 1/1 6/5 3/2 seen from the root. Indicating a 1/5 as it's true
> root. (making a major 7th chord)

Yes, this is correct! The 1/5 IS the true root, because minor chords are nothing but major 7th chords stripped of their root.

> The 1/1 19/16 3/2 is a rooted minor.
> You provided your own math already for this. The difference tones reinforce the root. It > doesn't matter that the 5th harmonic is one of the difference tones, only good.

The reinforcement is too weak to be audible. Compare 1/1-19/16-3/2 with harmonics 4, 5, and 6: the latter produces difference tones of 1, 1, and 2, giving an incredibly strong reinforcement of 4 as an octave of the fundamental. Yet even this phenomenon is subtle to the most attentive of ears unless blared in perfect tune by a brass trio. 1/1-19/16-3/2 simply does not produce even remotely the same effect.

However, I understand the reasons why you so much want this to work: even the most unschooled musician has an intuitive feeling that minor chords exist on the same musical footing as major chords, that they are equally strong and can fulfill the same "functions" so far as setting the key of a piece is concerned. Sadly this is utterly misguided, and studying Just Intonation reveals this. The only rootedness in a minor chord (other than the septimal minor) comes from the fifth, and varying the tuning of the 3rd has a negligible effect on the end result. In fact, you yourself have proven this by virtue of your long history of indecision of how to tune the minor tonic! If a man can study tuning so deeply as you have, with the best reproducing equipment and the keenest ears, and over many years of study still be flip-flopping over which tuning is correct, the only logical explanation is that your ears cannot decisively select a victor. I came to this conclusion after much less time of studying, because I trust my ears to tell me where there is significance and where there isn't.

> Btw, I see the difference tones as less important than the "beating" / "periodicity of the
> combined waveforms". We're not dealing with sines in actual music and the overtones of > the actual tones create a wealthy combination of difference tones, which all interfere.
> And the most audible end result is the "beating" / "synchronicity of the waves".

I agree that this is true, and this favors either 6, 7, and 9th harmonics or 10, 12, and 15th harmonics as the tuning of a minor triad. Consider that in most musical timbres, the 19th harmonic is inaudible, and in fact it is only up to the 16th harmonic that we can have any hope of hearing clearly. On the cello, for instance, one can apply minute pressure to the string at different fractions of its length to isolate the harmonics of the vibrating string. The clearest harmonic is 1/2 the length of the string, and this is the 2nd harmonic; next is 1/3, 1/4, and 1/5. 1/6 and 1/7 are barely audible and devilishly tricky to sound with volume. When bowing the open string, the lowest harmonics overpower the higher ones by such a great deal that the higher ones provide only color to the sound. How can it be that the 19th harmonic, used as an interval, can compete with the periodicity of the intervals between the 6th and 7th or 10th and 12th harmonics? This I have studied with great intensity, initially to investigate the claims of radical "JI-ists" who speak of "17-limit" or "23-limit" (ad infinitum) "JI". If harmonics 7, 11, 13, and 17 do not fit into the common practice, I simply do not see how you can suggest the 19th harmonic. It is no comparison to the tonic major triad at all, compares unfavorably with 1/1-7/6-3/2 in terms of rootedness, and unfavorably with 1/1-6/5-3/2 in terms of beating.

> The 19th harmonic gives a pretty strong 1 as it's "beating root".

"Beating root"? I do not know how to interpret this except as "difference tone". Beating and difference tones are the same thing--beating refers only to a difference tone that is too low to be heard as a tone and instead is heard as a rhythmic pulsation.

> In fact, I found I can't connect the 45/32 with the 135/128 without moving the base
> scale in the chain of fifths.

If you are using 45/32 and 135/128, that implies that you are either modulating to another key or else trying to tonicize the Locrian mode (which is impossible to do).

> Btw, one other thing, if you play along Drei Equale no3 with my JI score, you'll see how
> incredibly fast a minor chord roots! No need to include a 3/2 even.

I respectfully must disagree. The "rooting" is again more to do with the melodic devices employed--i.e. the movement of chord roots.

> It does this just as well as a 5/4, only slightly more subtle.

Again, I disagree: the difference between them is hardly subtle at all.

> If you listen closely to Drei Equale no3, you'll still hear the emotional "minorness" when > 19/18 4/3 19/12 chords play. (yes, minor "major" chords).

In this case, I do agree that the chords do not sound properly "major"; they sound quite like Pythagorean triads--bordering tension and relaxation, having a slightly unpleasant (though not necessarily musically-inappropriate) roughness that is very distinct from a 1/1-5/4-3/2. Whether this gives them "minorness" I am reluctant to say; they don't sound sad or dark like a minor chord, but they don't sound happy, calm, and bright like a major chord either.

> Thank you for your care to keep me on the straight path :)
>
> Yes this minor scale is part of the JI scale.
> The relative minor indeed, it's on 15/8 as 1/1. (reason why so many pieces are not really > in relative minor but in parallel minor while normal theory says they're in relative)

I believe you may be misusing the term "relative minor" if you say it uses 15/8 as the tonic. The relative minor to a tonic of 1/1 would begin on 27/16, but because the true tonic of the minor scale is the 8 in an 8, 10, 12, and 15th harmonic chord, that would mean that the tonic is the 4/3 of the major scale. However for that chord to be tuned properly, we have shift the 27/16 down to a 5/3. This shift indicates to us how chord progressions must be restructured to allow root- and melodic movements to create the proper illusion of tonicizing the minor tonic.

Of course, this may also indicate that music theorists have had it wrong to consider the Aeolian mode the "relative minor" of the major/Ionian mode. If we treat the Phrygian as the relative minor instead, there is no need to shift anything by a comma, and in point of fact if the I of the Phrygian is tune 10, 12, and 15, the 8 will be the I of the Ionian--as it should be, for the Ionian is the only true tonal mode.

Regardless, I should say that the distinction between relative minor and parallel minor is illusory. All parallel minors are the relative minors of some other key. Using the 19th harmonic will necessitate some very intricate three-dimensional movements to modulate between one of your "parallel minors" and its relative major tonic. To modulate implies tonicizing a different chord, and it is not possible to tonicize a major chord other than a 1/1-5/4-3/2. For the tonicization to work, we will have to swap the 19/16 chain of 3/2s for the 5/4 chain of 3/2s--in composition I could probably accomplish this gracefully, but in retuning another's work where such a modulation occurs would be difficult indeed.

In conclusion, I think the evidence is overwhelming that the existence of "minor keys" is illusory, or at best cannot be explained by the harmonic properties of any tuning of a minor triad.

--Dr. Gilbert. S. Sullivan

🔗Marcel <m.develde@...>

3/6/2011 7:21:14 PM

--- In MakeMicroMusic@yahoogroups.com, "purest_intonation@..." <purest_intonation@...> wrote:
>
> --- In MakeMicroMusic@yahoogroups.com, "Marcel" <m.develde@> wrote:
>
> > As for the minor.
> > One doesn't need to use harmonic minor V to create a good minor i ending.
> > It is a very strong cadence because of several reasons (which are present in the
> > dynamics of the JI tuning btw!), but minor will feel like a rooted final in countless other > cadences.
>
> It is true that there are cadences that can effect resolution in minor keys, and a minor tonic may feel somewhat "resolved"--but this is due more to root movement than to the harmonic rootedness of the chord.
>
> > The relative minor is NOT rooted and indeed not suitable for ending (though when
> > normal music theory talks about relative minor it is still often the parallel minor).
>
> On the contrary: the relative minor is about as rooted as any non-septimal minor triad can be. For 10, 12, and 15, we have difference tones of 2, 3, and 5. For 16, 19, and 24, we have 3, 5, and 8. However, for a septimal minor of 6, 7, and 9, we have 1, 2, and 3--it is the most rooted of all of them, and also has the simplest periodicity of wave interactions. I once considered deriving this chord from a harmonic series dominant 7th chord with a major 9th, of 1/1-5/4-3/2-7/4-9/8, but the scale that resulted seemed unworkable. It required treating (in the key of C) F as 21/16, which meant that the subdominant would have a 64/63-sharpened wolf fifth. Unacceptable.
>

You math in this area is not sufficient.
Let take difference tones of two sines, in 3:5 ratio.
The difference tones arise from nonlinear distortion on the combined wave.
It gives a difference tone of 2 in the case of 3:5 sines.
This difference tone is an actual tone. It is a real sine wave in itself, measurable and recordable.
Therefore the difference tone itself also forms difference tones with the 2 other sines.
In this case producing 2:3 difference tone 1, and 2:5 difference tone 3.
Difference tones making new difference tones etc, it all points to 1 in the end.
Difference tones fill out the lower harmonics of any harmony till 1.
But.. difference tones in most circumstances are extremely weak, and inaudible.

There something else much much more important and audible.
It's called "beating" I don't know if you're familiar with it.
It's the "buzz" of a JI 1/1 5/4 3/2 chord for instance.
It's very audible.
Even if there's not a strong buzz, beating is still audible, and has been tested to be audible in a wide range, from far subsonic till fairly high into the audio range.
Beating is caused by the phase cancellation of waves.
It is very strong when sounds have rich overtones (most sounds)
It is the reason why with sines it's much harder to tell how in tune something is than with a sawtooth wave for instance.
As I said, beating is due to phase cancellation, also of the harmonics of the waves, and results in an "amplitude wave" in the total waveform.
The lowest beating frequency is the periodicity of the waveform (the beating itself is a amplitude waveform with "harmonics" as well btw)
The periodicity of the waveform is all ways the 1 of the harmonic series.
(In the case of tempered intervals or very large ratios it will be hard to hear the fundamental beating though, and you'll tune into the strongest closest beat frequency harmonic and experience "phase drifting" on it)
So in the case of a just 1/1 19/16 3/2 with a sawtooth the beating clearly points to 16/1 8/1 6/1 4/1 etc. Clearly rooted on 1.
It sounds to you like it is "in phase" which it literally is.
Very close you'll find the "in phase" of 32/27, which points to a different root, and close you'll also find 6/5 "in phase" which points to yet another root.

> > The relative minor is 5/4 3/2 15/8 (or 5/3 2/1 5/2 when you tip the scale a fifth). It is
> > not rooted because it is 1/1 6/5 3/2 seen from the root. Indicating a 1/5 as it's true
> > root. (making a major 7th chord)
>
> Yes, this is correct! The 1/5 IS the true root, because minor chords are nothing but major 7th chords stripped of their root.
>
> > The 1/1 19/16 3/2 is a rooted minor.
> > You provided your own math already for this. The difference tones reinforce the root. It > doesn't matter that the 5th harmonic is one of the difference tones, only good.
>
> The reinforcement is too weak to be audible. Compare 1/1-19/16-3/2 with harmonics 4, 5, and 6: the latter produces difference tones of 1, 1, and 2, giving an incredibly strong reinforcement of 4 as an octave of the fundamental. Yet even this phenomenon is subtle to the most attentive of ears unless blared in perfect tune by a brass trio. 1/1-19/16-3/2 simply does not produce even remotely the same effect.
>

No it is audible.
It is "in phase". Beating is important, difference tones not but as as showed above even difference tones tell the same story.
But even with sounds where it is not clearly audible.
Our mind knows :)

> However, I understand the reasons why you so much want this to work: even the most unschooled musician has an intuitive feeling that minor chords exist on the same musical footing as major chords, that they are equally strong and can fulfill the same "functions" so far as setting the key of a piece is concerned. Sadly this is utterly misguided, and studying Just Intonation reveals this. The only rootedness in a minor chord (other than the septimal minor) comes from the fifth, and varying the tuning of the 3rd has a negligible effect on the end result. In fact, you yourself have proven this by virtue of your long history of indecision of how to tune the minor tonic! If a man can study tuning so deeply as you have, with the best reproducing equipment and the keenest ears, and over many years of study still be flip-flopping over which tuning is correct, the only logical explanation is that your ears cannot decisively select a victor. I came to this conclusion after much less time of studying, because I trust my ears to tell me where there is significance and where there isn't.
>

Well actually, I had done test with 2 chord progressions where it was most clear to me the 6/5 minor was way too high.
And then testing the 19/16 and other in it's place.
I found 19/16 to be slightly too high, but very consonant.
Only just now, when I got real close to the correct way of doing things, was I able to tell that the 2 progressions I used for testing should have a 32/27 minor there in correct JI! (no wonder the 6/5 stuck out most there)
So I had been testing the 19/16 in the wrong place!
Errors like this happen all the time in this field of research.
The 19/16 in the correct place sounds absolutely 100% perfect.
Perhaps you conducted listening tests in the wrong way as well (for instance be careful what you play before)

> > Btw, I see the difference tones as less important than the "beating" / "periodicity of the
> > combined waveforms". We're not dealing with sines in actual music and the overtones of > the actual tones create a wealthy combination of difference tones, which all interfere.
> > And the most audible end result is the "beating" / "synchronicity of the waves".
>
> I agree that this is true, and this favors either 6, 7, and 9th harmonics or 10, 12, and 15th harmonics as the tuning of a minor triad. Consider that in most musical timbres, the 19th harmonic is inaudible, and in fact it is only up to the 16th harmonic that we can have any hope of hearing clearly. On the cello, for instance, one can apply minute pressure to the string at different fractions of its length to isolate the harmonics of the vibrating string. The clearest harmonic is 1/2 the length of the string, and this is the 2nd harmonic; next is 1/3, 1/4, and 1/5. 1/6 and 1/7 are barely audible and devilishly tricky to sound with volume. When bowing the open string, the lowest harmonics overpower the higher ones by such a great deal that the higher ones provide only color to the sound. How can it be that the 19th harmonic, used as an interval, can compete with the periodicity of the intervals between the 6th and 7th or 10th and 12th harmonics? This I have studied with great intensity, initially to investigate the claims of radical "JI-ists" who speak of "17-limit" or "23-limit" (ad infinitum) "JI". If harmonics 7, 11, 13, and 17 do not fit into the common practice, I simply do not see how you can suggest the 19th harmonic. It is no comparison to the tonic major triad at all, compares unfavorably with 1/1-7/6-3/2 in terms of rootedness, and unfavorably with 1/1-6/5-3/2 in terms of beating.
>

Yes I've investigates extended JI as well. It's how I started when I got interested in alternative tunings 5 years or so ago.
It's not just about the periodicity.
Not all intervals are created equal :)
The fifth divides into 5/4 and 19/16 consonantly.

> > The 19th harmonic gives a pretty strong 1 as it's "beating root".
>
> "Beating root"? I do not know how to interpret this except as "difference tone". Beating and difference tones are the same thing--beating refers only to a difference tone that is too low to be heard as a tone and instead is heard as a rhythmic pulsation.
>

Ohhh no, they're not the same thing at all!
They are 2 very distinct things, I already explained some above, but I can strongly suggest you read up on it then.
Btw, for an old reference work that's still the best I've found on all these kinds of things is Helmholtz - "On the sensations of tone as a physiological basis for the theory of music".
Big book, haven't read all of it even was always too busy with my own theories haha, but what I did read of it is absolute quality research and well explained.
My favorite book. And it's going very cheap these days. Very recommended.

> > In fact, I found I can't connect the 45/32 with the 135/128 without moving the base
> > scale in the chain of fifths.
>
> If you are using 45/32 and 135/128, that implies that you are either modulating to another key or else trying to tonicize the Locrian mode (which is impossible to do).
>

Ah thanks for telling.
I really know too little of normal music theory.
I found this out the hard way lol.

> > Btw, one other thing, if you play along Drei Equale no3 with my JI score, you'll see how
> > incredibly fast a minor chord roots! No need to include a 3/2 even.
>
> I respectfully must disagree. The "rooting" is again more to do with the melodic devices employed--i.e. the movement of chord roots.
>

Well, the minor is played above the root.
The minor is 19/16.
It works like a charm :)

> > It does this just as well as a 5/4, only slightly more subtle.
>
> Again, I disagree: the difference between them is hardly subtle at all.
>
> > If you listen closely to Drei Equale no3, you'll still hear the emotional "minorness" when > 19/18 4/3 19/12 chords play. (yes, minor "major" chords).
>
> In this case, I do agree that the chords do not sound properly "major"; they sound quite like Pythagorean triads--bordering tension and relaxation, having a slightly unpleasant (though not necessarily musically-inappropriate) roughness that is very distinct from a 1/1-5/4-3/2. Whether this gives them "minorness" I am reluctant to say; they don't sound sad or dark like a minor chord, but they don't sound happy, calm, and bright like a major chord either.
>

The first chords are Pythagorean, they sound very different to me.
Also if you look in that part where those chords are at the melody and resolution of the phrase you'll see that he's really harmonizing minor in relative major chords (19/18 4/3 19/12 etc).

> > Thank you for your care to keep me on the straight path :)
> >
> > Yes this minor scale is part of the JI scale.
> > The relative minor indeed, it's on 15/8 as 1/1. (reason why so many pieces are not really > in relative minor but in parallel minor while normal theory says they're in relative)
>
> I believe you may be misusing the term "relative minor" if you say it uses 15/8 as the tonic. The relative minor to a tonic of 1/1 would begin on 27/16, but because the true tonic of the minor scale is the 8 in an 8, 10, 12, and 15th harmonic chord, that would mean that the tonic is the 4/3 of the major scale. However for that chord to be tuned properly, we have shift the 27/16 down to a 5/3. This shift indicates to us how chord progressions must be restructured to allow root- and melodic movements to create the proper illusion of tonicizing the minor tonic.
>

No I don't see this as a fixed thing.
Relative minor can be from 5/3, 27/16 with 1/1, or 27/16 with a 513/512.
The base JI scale does not corresponds 1 on 1 with what normal music theory considers to be a "key".
Normal music theory is based not only on practice but also for a large part on the Pythagorean system and it's chain of fifths.
There are so many errors in it that it can't translate well to JI without serious re-interpretation.

> Of course, this may also indicate that music theorists have had it wrong to consider the Aeolian mode the "relative minor" of the major/Ionian mode. If we treat the Phrygian as the relative minor instead, there is no need to shift anything by a comma, and in point of fact if the I of the Phrygian is tune 10, 12, and 15, the 8 will be the I of the Ionian--as it should be, for the Ionian is the only true tonal mode.
>
> Regardless, I should say that the distinction between relative minor and parallel minor is illusory. All parallel minors are the relative minors of some other key. Using the 19th harmonic will necessitate some very intricate three-dimensional movements to modulate between one of your "parallel minors" and its relative major tonic. To modulate implies tonicizing a different chord, and it is not possible to tonicize a major chord other than a 1/1-5/4-3/2. For the tonicization to work, we will have to swap the 19/16 chain of 3/2s for the 5/4 chain of 3/2s--in composition I could probably accomplish this gracefully, but in retuning another's work where such a modulation occurs would be difficult indeed.
>

Aaah noo, but here we hit a very important point.
You say "all parallel minors are the relative minors of some other key."
Yes this may be true in 12tet.
But in actual music it is not the same.
The feeling is different and the tuning is different.
It depends veyr much on how you get there in how it will feel.
There is musical coherence / continuity to take into account. This means no comma shifts. It is part of what my base JI scale sets rules / limit for.
And if you manage to break these rules, you break musical continuity.
play for instance a piece in B major, and then all of a sudden in the middle of the piece pitch that piece to F major. Musical continuity / coherence is surely broken there.
Or play 2 random different pieces in different keys at the same. They do not form a coherent whole, a single piece.

> In conclusion, I think the evidence is overwhelming that the existence of "minor keys" is illusory, or at best cannot be explained by the harmonic properties of any tuning of a minor triad.
>
> --Dr. Gilbert. S. Sullivan
>

But the answer and evidence to the contrary is right in front of you :)
I'm confident you'll change your opinion on this in time.

Also, really load up:
1/1 19/18 9/8 19/16 5/4 4/3 45/32 3/2 19/12 27/16 16/9 15/8 2/1
And start improvising some, using the 19 for minors.
Trust me, really do it! :)

-Marcel

🔗purest_intonation@...

3/6/2011 8:01:05 PM

--- In MakeMicroMusic@yahoogroups.com, "Marcel" <m.develde@...> wrote:

> Sorry to have to say this, but your reasoning here is wrong.
> Hope you take it personal, I've been wrong about these issues countless times.
>
> The thing is, 10:12:15 (1/1 6/5 3/2) and 16:19:32 (1/1 19/16 3/2) and 54:64:81 (1/1 32/27 3/2) are all correct minor chords in common practice music.
> And all of them have a relative major chord.
> 4:5:6 (1/1 5/4 3/2) for 10:12:15 (5/4 3/2 15/8)
> 38:48:57 (19/12 2/1 19/8) for 16:19:32 (2/1 19/8 3/1)
> 64:81:96 (16/9 9/4 8/3) for 54:64:81 (9/4 8/3 27/8)
> All these chords are much used in actual music.
> And the music indicates which chord is played.

Mr. DeVelde,
I am sorry I did not take the time to elucidate my pronouncement in greater detail.

I was referring only to minor triads treated as the tonic to a piece. Yes, of course of COURSE in other roles there are different minor chords. The main tenet of your theory that so initially intrigued me (and to this day keeps me thinking) is that there are multiple varieties of both major and minor triads, and the particular tuning of these triads is dictated by their functionality IN MUSIC.

My point is merely that there is no minor triad whose tuning is compatible with common practice that can serve as a tonic with equal or comparable psychoacoustic properties to the major triad. All possible tunings of the minor tonic chord are thus to be determined as secondary concern to the tunings of the majors and their functions within the JI framework. If you look at the three major chords in a major scale, they define the entire scale: I-III-V, IV-VI-I, V-VII-II. There is no need to take the minor chords into account at all.

Now, to me it seems like your suggestion of the 19th harmonic as the third in the tonic minor triad is really a tacit assertion that ALL major chords in a minor key must be stripped of their restfulness in order to allow the minor tonic to seem restful by comparison. This is workable, yes, but also artificial. It is more sensible to admit simply that the minor key is an illusion, one which works because of the power of melody and certain root-movements.

This, I think, is reason for you to study academic common-practice music theory. It is full of fallacies, yes, but before we can understand how to functionally tune triads, we have to understand how single-note progressions create tension and relaxation. Playing only single notes, there is a major difference (no pun intended!) between moving by 16/15, by 4/3, by 3/2, by 5/4, by 27/16, etc. We must build our understanding of JI from the ground up, not the top down! Then and only then will we be able to understand how first to tune dyads and then to tune triads to follow and enhance the functions of the root movements.

And after all, I do recall you posting an example progression using neutral third triads using the 39th harmonic awhile back, perhaps on another list--do you recall it? It sounded exceptionally strong despite the fact that triads involving the 39th harmonic cannot be considered "Just" in any meaningful sense of the word: with harmonics 32, 39, and 48, we have difference tones of 7, 9, and 16--very cloudy, root-wise, if one ignores the effects of the perfect fifth--and the periodicity is off the charts bad. Yet with these unJust chords you created a perfectly functional progression that worked on the strength of the 3/2's and the root movements you selected. Is that not compelling evidence in favor of my theory?

--Dr. Gilbert S. Sullivan

🔗Mike Battaglia <battaglia01@...>

3/6/2011 8:04:22 PM

HEY GUYS

/metatuning/
/tuning-research/

etc

Have you not figured out that you're driving everybody nuts yet?

-Mike

On Sun, Mar 6, 2011 at 11:01 PM, purest_intonation@... <
purest_intonation@...> wrote:
>
>
>
> --- In MakeMicroMusic@yahoogroups.com, "Marcel" <m.develde@...> wrote:
>
> > Sorry to have to say this, but your reasoning here is wrong.
> > Hope you take it personal, I've been wrong about these issues countless
times.
> >
> > The thing is, 10:12:15 (1/1 6/5 3/2) and 16:19:32 (1/1 19/16 3/2) and
54:64:81 (1/1 32/27 3/2) are all correct minor chords in common practice
music.
> > And all of them have a relative major chord.
> > 4:5:6 (1/1 5/4 3/2) for 10:12:15 (5/4 3/2 15/8)
> > 38:48:57 (19/12 2/1 19/8) for 16:19:32 (2/1 19/8 3/1)
> > 64:81:96 (16/9 9/4 8/3) for 54:64:81 (9/4 8/3 27/8)
> > All these chords are much used in actual music.
> > And the music indicates which chord is played.
>
> Mr. DeVelde,
> I am sorry I did not take the time to elucidate my pronouncement in
greater detail.
>
> I was referring only to minor triads treated as the tonic to a piece. Yes,
of course of COURSE in other roles there are different minor chords. The
main tenet of your theory that so initially intrigued me (and to this day
keeps me thinking) is that there are multiple varieties of both major and
minor triads, and the particular tuning of these triads is dictated by their
functionality IN MUSIC.
>
> My point is merely that there is no minor triad whose tuning is compatible
with common practice that can serve as a tonic with equal or comparable
psychoacoustic properties to the major triad. All possible tunings of the
minor tonic chord are thus to be determined as secondary concern to the
tunings of the majors and their functions within the JI framework. If you
look at the three major chords in a major scale, they define the entire
scale: I-III-V, IV-VI-I, V-VII-II. There is no need to take the minor chords
into account at all.
>
> Now, to me it seems like your suggestion of the 19th harmonic as the third
in the tonic minor triad is really a tacit assertion that ALL major chords
in a minor key must be stripped of their restfulness in order to allow the
minor tonic to seem restful by comparison. This is workable, yes, but also
artificial. It is more sensible to admit simply that the minor key is an
illusion, one which works because of the power of melody and certain
root-movements.
>
> This, I think, is reason for you to study academic common-practice music
theory. It is full of fallacies, yes, but before we can understand how to
functionally tune triads, we have to understand how single-note progressions
create tension and relaxation. Playing only single notes, there is a major
difference (no pun intended!) between moving by 16/15, by 4/3, by 3/2, by
5/4, by 27/16, etc. We must build our understanding of JI from the ground
up, not the top down! Then and only then will we be able to understand how
first to tune dyads and then to tune triads to follow and enhance the
functions of the root movements.
>
> And after all, I do recall you posting an example progression using
neutral third triads using the 39th harmonic awhile back, perhaps on another
list--do you recall it? It sounded exceptionally strong despite the fact
that triads involving the 39th harmonic cannot be considered "Just" in any
meaningful sense of the word: with harmonics 32, 39, and 48, we have
difference tones of 7, 9, and 16--very cloudy, root-wise, if one ignores the
effects of the perfect fifth--and the periodicity is off the charts bad. Yet
with these unJust chords you created a perfectly functional progression that
worked on the strength of the 3/2's and the root movements you selected. Is
that not compelling evidence in favor of my theory?
>
> --Dr. Gilbert S. Sullivan
>
>

[Non-text portions of this message have been removed]

🔗purest_intonation@...

3/6/2011 9:18:18 PM

--- In MakeMicroMusic@yahoogroups.com, "Marcel" <m.develde@...> wrote:

> You math in this area is not sufficient.
> Let take difference tones of two sines, in 3:5 ratio.
> The difference tones arise from nonlinear distortion on the combined wave.
> It gives a difference tone of 2 in the case of 3:5 sines.
> This difference tone is an actual tone. It is a real sine wave in itself, measurable and
> recordable.
> Therefore the difference tone itself also forms difference tones with the 2 other sines.
> In this case producing 2:3 difference tone 1, and 2:5 difference tone 3.
> Difference tones making new difference tones etc, it all points to 1 in the end.
> Difference tones fill out the lower harmonics of any harmony till 1.
> But.. difference tones in most circumstances are extremely weak, and inaudible.

Yes, I am aware of all of this. I fail to see what bearing it has on my argument. Difference tones are not all weak in the case of bowed strings. Playing a perfect 4th vs a perfect 5th on the cello for instance sounds very different: C-F as 1/1-4/3 creates a difference tone that reinforces the F, whereas C-G as 1/1-3/2 creates a difference tone that reinforces the C. In the case of the former, you can actually hear the lower F (which is lower in pitch than the C in the latter case) and as a result the dyad sounds actually deeper! It is not subtle at all. Even on an acoustic guitar the effect is audible, to say nothing of a church organ.

> There something else much much more important and audible.
> It's called "beating" I don't know if you're familiar with it.

http://en.wikipedia.org/wiki/Beat_(acoustics)

"In acoustics, a beat is an interference between two sounds of slightly different frequencies, perceived as periodic variations in volume whose rate is the difference between the two frequencies."

Beating thus occurs only between two sounds that are close in pitch, e.g. those that are out-of-tune. You are thinking of "periodicity buzz". They are different phenomena and I am surprised the distinction is not familiar to you!

> It is very strong when sounds have rich overtones (most sounds)
> It is the reason why with sines it's much harder to tell how in tune something is than with > a sawtooth wave for instance.

Yes, that is because the partials also beat with each other, and the loudest partials have the most audible beating. This is why 12-ET sounds out of tune: when playing a major third of 400 cents, it causes the 5th partial of the fundamental to beat strongly with the 4th partial of the major 3rd. Similarly with a minor 3rd of 300 cents, it causes the 6th partial of the fundamental to beat with the 5th partial of the minor 3rd. This is the reason Pythagorean triads are tense and 5-limit triads are relaxed: low-pitched beat-frequencies that sound like a tremolo are unpleasant to the ear. 19/16 too causes beating in the same way the 12-ET minor 3rd does, especially obvious in the baritone range.

> The periodicity of the waveform is all ways the 1 of the harmonic series.

Is that what you meant by "beating root"?

> So in the case of a just 1/1 19/16 3/2 with a sawtooth the beating clearly points to 16/1 > 8/1 6/1 4/1 etc. Clearly rooted on 1.
> It sounds to you like it is "in phase" which it literally is.
> Very close you'll find the "in phase" of 32/27, which points to a different root, and close > you'll also find 6/5 "in phase" which points to yet another root.

Of these I decidedly DO NOT hear the first two as "in phase". They all sound like they are phase-drifting to my ears. Only the 6/5 sounds in phase. But that is not the point, of course. Phase-drifting chords have musical significance because of the logical structure they arise from. Pythagorean chords do not sound in-phase the way 5-limit chords do, and the difference in that quality is the reason Pythagorean chords are appropriate in places 5-limit chords are not. But I still am not convinced that 19-limit chords are ever appropriate. The difference between 19/16 and 32/27 is scarcely 3 cents, and simply the act of moving one's head during listening would be enough to disturb the impinging waveforms enough so as to blur one interval into the other. Are you really so sure that you are hearing the difference and not imagining it? The case for 32/27 as a tonic minor triad seems to me to be stronger--it does not require adding an extra dimension to music, it preserves Pythagorean logic, it explains more about how the roots are moving. And it makes a negligible difference in sound.

> No it is audible.
> It is "in phase". Beating is important, difference tones not but as as showed above even
> difference tones tell the same story.
> But even with sounds where it is not clearly audible.
> Our mind knows :)

How can the mind "know" if the ears do not? If I cannot hear a difference, how can I "know" what is happening? And again, I refer you to the Wikipedia article on beating to remind you that beating and difference tones are the same phenomenon, the only difference is in the frequency of the waves that result from the combination of the two sounds.

> Well actually, I had done test with 2 chord progressions where it was most clear to me
> the 6/5 minor was way too high.

Too high for what? I thought the issue here was beating and/or difference tones. Now you are saying that is simply a matter of being too high in pitch?

Are you quite sure that the reason it sounds too high is not simply because of the tuning of the other chords in the progression? Or that you were tonicizing the right chord? I ask you again to consider my hypothesis that the true "relative minor" is the Phrygian mode, not the Aeolian mode (that would be the mode of E in the key of C major, as opposed to the mode of A, if you are not familiar with the names of the modes).

> So I had been testing the 19/16 in the wrong place!

And thus, the 6/5 as well. Perhaps you should test 6/5 again, in the right place?

> The 19/16 in the correct place sounds absolutely 100% perfect.

I disagree. It sounds familiar, it sounds Pythagorean...it sounds like 12-ET. I am not convinced you are not another hapless victim of a lifetime of 12-ET acculturation. I have been fortunate enough to have been educated as first and foremost a cellist, and have long known to avoid the wrongly-intoned pitches of 12-ET. I can assure you my ears know
true JI; it is only my mind that is still struggling to formalize and articulate what I have long experienced in my own playing.

> Yes I've investigates extended JI as well. It's how I started when I got interested in
> alternative tunings 5 years or so ago.
> It's not just about the periodicity.
> Not all intervals are created equal :)
> The fifth divides into 5/4 and 19/16 consonantly.

It is difficult to say what the fifth divides into consonantly, because the fifth itself is such a powerful consonance. It is on the strength of its fifth that 12-ET has triumphed and endured for so long.

> Ah thanks for telling.
> I really know too little of normal music theory.
> I found this out the hard way lol.

You are in the Netherlands, no? A friend of mine once studied at the Royal Conservatory of the Hague. According to her, there are people there very interested in Just intonation. Perhaps a few e-mails might find you a sympathetic ear with someone who could fill in the gaps in your "normal music theory".

> The first chords are Pythagorean, they sound very different to me.
> Also if you look in that part where those chords are at the melody and resolution of the > phrase you'll see that he's really harmonizing minor in relative major chords (19/18 4/3 > 19/12 etc).

Yes, I see what he is doing, but you still have not sold me on the 19th harmonic. Do you have a rendering where Pythagorean minors are used in place of the 19th harmonic? I would like to compare it if so.

> No I don't see this as a fixed thing.
> Relative minor can be from 5/3, 27/16 with 1/1, or 27/16 with a 513/512.
> The base JI scale does not corresponds 1 on 1 with what normal music theory considers > to be a "key".

Ah, I see. This then is probably why my own composition fell short. I do not yet fully understand how the JI scale diverges from what is considered to be a key. Perhaps you can explain: supposing a piece of music which in 12-ET uses only 7 notes, what is the maximum number of JI notes you would need in a scale to render that same piece in True JI?

> Aaah noo, but here we hit a very important point.
> You say "all parallel minors are the relative minors of some other key."
> Yes this may be true in 12tet.
> But in actual music it is not the same.

Is it not? In actual music, one can modulate, changing keys in the middle of a piece, in the middle of a phrase even. There are progressions--root movements--which can tonicize different chords in a scale. Look at tritone substitutions, for example. It is not uncommon at all to modulate between a relative minor and major. Playing in C major, one can modulate to A minor for instance with a simple I-V-IV-III-vi progression at any point in a composition, and then once in A minor, one can get back to C major with a simple i-V-VI-VII-III (where i is A minor and III is C major). It is absolutely the simplest thing in the world to do, but it loses all sense if we are going back and forth between 19th harmonics and 5th harmonics. Because--consider this: we might start a piece in A minor, using (by your rules) the 19th harmonic, but then modulate to C major at some point. Unless the C major is rendered as a 5-limit triad, we have not truly "modulated" and the effect will not be as intended.

> Also, really load up:
> 1/1 19/18 9/8 19/16 5/4 4/3 45/32 3/2 19/12 27/16 16/9 15/8 2/1
> And start improvising some, using the 19 for minors.
> Trust me, really do it! :)

I will post the unmastered results of my foray, though I am not much of a pianist so I cannot vouch for the performance quality.

--Dr. Sullivan

🔗purest_intonation@...

3/6/2011 9:33:36 PM

--- In MakeMicroMusic@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> HEY GUYS
>
> /metatuning/
> /tuning-research/
>
> etc
>
> Have you not figured out that you're driving everybody nuts yet?

I apologize if you interpret these posts as being irrelevant to making music. I shall post more compositions to demonstrate these principles in short order.

However, I fail to see how it is irrelevant to discuss and constructively criticize the tuning principles on which my ACTUAL MUSIC is based. I apologize if the only discussion appropriate to this forum is a token "thumbs up" or "thumbs down" in response to musical submissions, rather than a detailed criticism of the tuning used and its effect on the piece. The "any tuning goes" mentality of this place, in my opinion, severely undermines the ability of list members to make constructive (or even meaningful) feedback on the scant submissions that make it through the flame-wars and petty off-topic blather that are the NORM here. Mr. DeVelde is the best thing to happen to this forum, as he is the only person here I have ever seen give any relevant criticism in a post. I suppose that is the reason he is so despised: he's the only one NOT indulging in the communal back-patting.

Honestly. You people think you are advancing the study of tuning, but all you do is whine about how this person or that person "posts too much" or "is offensive" or "doesn't post enough music". This place has nothing to do with music, microtonal or otherwise, the way you people carry on. What's the point, really? What are you all getting out of this list? If you're not going to discuss the tunings used, why even have a discussion forum?

And you have the nerve to accuse ME of having irrelevant discussions.

--Dr. Gilbert S. Sullivan

🔗jonszanto <jszanto@...>

3/6/2011 10:16:48 PM

Hey pal,

--- In MakeMicroMusic@yahoogroups.com, "purest_intonation@..." <purest_intonation@...> wrote:
> Honestly. You people think you are advancing the study of tuning...

Give me your Paypal acct, I'll send you five bucks, and you can go buy a clue: this forum wasn't invented to "advance the study of tuning". There are other forums for that. Go there. Now.

> This place has nothing to do with music, microtonal or otherwise, the way you people carry on.

Give it a rest, gasbag. You just joined, right? Guess you made a critical error. I'll give you this, Sullivan: you've elevated trolling to a profound level, because you know *exactly* what you are doing.

🔗lobawad <lobawad@...>

3/6/2011 10:38:34 PM

--- In MakeMicroMusic@yahoogroups.com, "purest_intonation@..." <purest_intonation@...> wrote:
>

How were minor chords heard before major seventh chords were used in music? Or do you claim that M7 chords are inescabable "natural" phenomena?

🔗purest_intonation@...

3/6/2011 10:52:59 PM

--- In MakeMicroMusic@yahoogroups.com, "jonszanto" <jszanto@...> wrote:

> Give me your Paypal acct, I'll send you five bucks, and you can go buy a clue: this forum
> wasn't invented to "advance the study of tuning". There are other forums for that. Go there. > Now.

This is the forum that Marcel DeVelde uses to advance his theories, so this is the forum I decided to join. If he will consent to join me elsewhere, then I will leave you people to stew in your bad attitudes. If no one here is interested in exploring the laws of music through actual composition, then I have nothing to gain from being here.

But perhaps I have sown a few seeds of introspection and some of you may come to learn something from my time here. If nothing else, some humility perhaps.

--Dr. Sullivan

🔗Mike Battaglia <battaglia01@...>

3/6/2011 11:02:13 PM

On Mon, Mar 7, 2011 at 1:52 AM, purest_intonation@...
<purest_intonation@...> wrote:
>
> --- In MakeMicroMusic@yahoogroups.com, "jonszanto" <jszanto@...> wrote:
>
> > Give me your Paypal acct, I'll send you five bucks, and you can go buy a clue: this forum
> > wasn't invented to "advance the study of tuning". There are other forums for that. Go there. > Now.
>
> This is the forum that Marcel DeVelde uses to advance his theories, so this is the forum I decided to join. If he will consent to join me elsewhere, then I will leave you people to stew in your bad attitudes. If no one here is interested in exploring the laws of music through actual composition, then I have nothing to gain from being here.
>
> But perhaps I have sown a few seeds of introspection and some of you may come to learn something from my time here. If nothing else, some humility perhaps.
>
> --Dr. Sullivan

I humbly request that you go to tuning-research.

-Mike

🔗Mike Battaglia <battaglia01@...>

3/6/2011 11:06:28 PM

On Mon, Mar 7, 2011 at 2:02 AM, Mike Battaglia <battaglia01@...> wrote:
>> But perhaps I have sown a few seeds of introspection and some of you may come to learn something from my time here. If nothing else, some humility perhaps.
>>
>> --Dr. Sullivan
>
> I humbly request that you go to tuning-research.

In fact, I'd be happy to join in the discussion if you do. Or if you
go to metatuning. Or anywhere where I don't feel like there are a
million people converging on my house to chop off my fingers so that I
can never type again.

-Mike

🔗jsmith9624@...

3/7/2011 2:58:33 AM

--- In MakeMicroMusic@yahoogroups.com, "purest_intonation@..."
<purest_intonation@...> wrote:

> I apologize if you interpret these posts as being irrelevant to making
music. I shall post more compositions to demonstrate these principles
in short order.<

Please do, I'm interested.

> However, I fail to see how it is irrelevant to discuss and
constructively criticize the tuning principles on which my ACTUAL MUSIC
is based. I apologize if the only discussion appropriate to this forum
is a token "thumbs up" or "thumbs down" in response to musical
submissions, rather than a detailed criticism of the tuning used and its
effect on the piece. The "any tuning goes" mentality of this place, in
my opinion, severely undermines the ability of list members to make
constructive (or even meaningful) feedback on the scant submissions that
make it through the flame-wars and petty off-topic blather that are the
NORM here. Mr. DeVelde is the best thing to happen to this forum, as he
is the only person here I have ever seen give any relevant criticism in
a post. I suppose that is the reason he is so despised: he's the only
one NOT indulging in the communal back-patting.<

I -- and many others, I think -- have no problem with discussions of the
tuning principles behind your music, or Marcel's, or anyone else's. But
a LOT of these most recent discussions are between 2 or 3 particular
people, and perhaps some of it would be better undertaken offlist in
private correspondence, or on another forum. I might add, that "any
tuning goes" is a primary reason for this forum; many of us here do not
share a very narrow view of what constitutes "proper" tuning, excluding
all others. There is a delight & exhilaration to be found exploring
non-traditional modalities. If musical (as opposed to acoustic) laws
were "universal", there would be no difference WHATSOEVER between the
music of one culture & another, in either intonation or structure.
What you call "communal back-patting" & which you seem to hold in some
disdain, is only friendly encouragement among members of this community.
I'm not terribly interested in a "detailed criticism" of someone's use
of a particular tuning, I'm more apt to dwell on the aesthetic
effects...simply *listening* will suffice.

> Honestly. You people think you are advancing the study of tuning, but
all you do is whine about how this person or that person "posts too
much" or "is offensive" or "doesn't post enough music". This place has
nothing to do with music, microtonal or otherwise, the way you people
carry on. What's the point, really? What are you all getting out of
this list? If you're not going to discuss the tunings used, why even
have a discussion forum?<

I am not advancing any such thing, not being a scholar. Hell, I'm barely
a composer (I think the most recent & accurate definition would be
"common peoples" & "music hobbyists"). I'm merely having a good deal of
fun.

Regards,
jls

🔗Ozan Yarman <ozanyarman@...>

3/7/2011 3:04:53 AM

You, whoever the hell you are as the impersonator of a Mr. Dr. Gilbert &
Sullivan, are just one step shy of me activating my filters on you, lest
the moderators spare me the indignation and hurl you out themselves with
your dime-worth theories off of these forums.

Oz.

✩ ✩ ✩
www.ozanyarman.com

purest_intonation@... wrote:
> --- In MakeMicroMusic@yahoogroups.com, "jonszanto"<jszanto@...> wrote:
>
>> Give me your Paypal acct, I'll send you five bucks, and you can go buy a clue: this forum
>> wasn't invented to "advance the study of tuning". There are other forums for that. Go there.> Now.
>
> This is the forum that Marcel DeVelde uses to advance his theories, so this is the forum I decided to join. If he will consent to join me elsewhere, then I will leave you people to stew in your bad attitudes. If no one here is interested in exploring the laws of music through actual composition, then I have nothing to gain from being here.
>
> But perhaps I have sown a few seeds of introspection and some of you may come to learn something from my time here. If nothing else, some humility perhaps.
>
> --Dr. Sullivan
>
>
>

[Non-text portions of this message have been removed]

🔗Mike Battaglia <battaglia01@...>

3/7/2011 3:11:21 AM

On Mon, Mar 7, 2011 at 6:04 AM, Ozan Yarman <ozanyarman@...> wrote:
>
> You, whoever the hell you are as the impersonator of a Mr. Dr. Gilbert &
> Sullivan, are just one step shy of me activating my filters on you, lest
> the moderators spare me the indignation and hurl you out themselves with
> your dime-worth theories off of these forums.

Better watch out, Gilbert, things are getting serious around here.

-Mike