[tuning] 5-limit JI vs 7-limit JI

I'm havind a very hard time finding confirmation 7-limit JI is valid.
I've been looking and looking every which way to confirm for instance 1/1
5/4 7/4 is a valid chord in music but I can't find it.
Every instance I'm looking at a 7-limit chord or interval and work things
out in a musical context it allways turns out it should actually be a
5-limit chord or interval.

I'm not prejudiced against 7-limit.
Infact I really want the harmonic 7th to be valid!
I started out a few years ago expecting music to be based on the harmonic
overtones.
First tried to make things work and make sense of all harmonics, making
scales which used up to the 31th overtone.
Gradually as I worked things out more I received at a theory which makes me
expect the 11th harmonic and higher are not relevant to music. (this is not
what I wish to discuss here now)
But the 7th harmonic is still a little bit open, though I'm allmost ready to
see the 7th as an overtone only and not part of the musical structure.
So without getting into higher harmonics, can anybody give me a musical JI
example of the 7th harmonic?
Preferably 2 chords played one after another of which 1 contains the 7th,
preferably linked to a key/mode.

Up till now I had a little bit of hope for 8/5 2/1 12/5 14/5 -> 3/2 15/8 9/8
3/1
But everywhich way I look it looks like it should be 8/5 2/1 12/5 45/16 ->
3/2 15/8 9/8 3/1
Transposed down by 3/2 it is: 16/15 4/3 8/5 15/8 -> 1/1 5/4 3/2 2/1
Making the 7th chord 1/1 5/4 3/2 225/128
Mode is what I call an extended mode. 1/1 16/15 5/4 4/3 3/2 8/5 15/8 2/1
(subset)
Which is made up of 2 of either the following base modes one transposed by
4/3:
harmonic minor: 1/1 9/8 6/5 4/3 3/2 8/5 15/8 2/1
and/or: 1/1 9/8 5/4 4/3 3/2 8/5 15/8 2/1

Other examples I've confirmed of not beeing the 7th harmonic are:
3/2 15/8 9/8 8/3 -> 1/1 3/2 2/1 5/2
dominant 7th here is 1/1 5/4 3/2 16/9
mode is major: 1/1 9/8 5/4 4/3 3/2 5/3 15/8
or: 1/1 9/8 5/4 4/3 3/2 8/5 15/8

Another example I've confirmed that is not constructed with the harmonic 7th
is the diminished 7th chord which is:
1/1 6/5 45/32 27/16

There's another reason I distrust the 7th harmonic now.
The most basic keys / modes are 5-limit for sure.
Harmony can be seen as arising by playing 2 or more melodies against
eachother in what is called counterpoint.
This way it seems impossible to me that a 7 limit harmony can arise from
playing several 5-limit melodies at once.
I don't think one can distort the melodies for the benefit of more
harmonious 7-limit harmony.
So either the melodies or atleast one of the melodies of the counterpoint
has to be a 7-limit melody.
The only other possibility i see is that all are 5-limi melodies but 1 of
the melodies is constantly in a 7th harmonic relation to the other 5-limit
melodies.
So no 7th in normal classical music it seems from the above?

I also thought I'd need the 7th intervals in arabic music, but I find I can
explain it perfectly within 5-limit. (I'll dedicate a new thread to this
soon)
Also expected it to explain chromatic note sequences but now see the way
this can be contructed from 5-limit much better.
So why should the 7th harmonic have a place in the structure of music and in
musical tuning?

Yes 1/1 5/4 3/2 7/4 does seem more consonant to me than for instance 1/1 5/4
3/2 16/9 or 1/1 5/4 3/2 225/128 or 1/1 5/4 3/2 9/5.
It seems logical to me that 1/1 5/4 3/2 225/128 gets it consonance from
beeing so close to 1/1 5/4 3/2 7/4.
But perhaps consonance in this way isn't relevant to actual music.
And this consonance of just one chord is countered by the dissonant
modulations and interval steps the 7th gives.
Perhaps music is a 3 dimensional form. Primes 2, 3 and 5 making the
structure and the 7th has no musical function and is only a harmonic
overtone?

I'm not trying to get anybody off their faith or use of the 7th with this
message.
I'm really only trying to find it out for myself, openminded and would
really like a contructive discussion on this.
Thanks!

Marcel

I know what you're talking about. It takes a certain musical context
for 7-limit JI to work. Sometimes 4:5:6:7 just doesn't work as a
dominant 7 chord.

It's a question I've been asking myself for a while. I've gotten it to
work in the string quartet I'm writing. I'm not sure what causes it
yet.

I think it has something to do with the fact that we've gotten used to
upper structure triads in chords, like a C major 9 chord - C E G B D.
That GBD rings out in its own way, and it's very colorful. I'm not
sure how it relates to phantom fundamentals or harmonic entropy, but I
do know that the approach where you just keep adding overtones of C
creates one possible sound for C.

Then again, go screw around with some neutral 11 triads and you'll
realize that if they have use, 7-limit harmony must too. And I
personally think neutral triads are beautiful - it's like we've added
gray and brown to a musical palette that previously consisted only of
bright, bold colors.

-Mike

On Thu, Feb 12, 2009 at 10:36 PM, Marcel de Velde <m.develde@...> wrote:
> I'm havind a very hard time finding confirmation 7-limit JI is valid.
>
> I've been looking and looking every which way to confirm for instance 1/1
> 5/4 7/4 is a valid chord in music but I can't find it.
> Every instance I'm looking at a 7-limit chord or interval and work things
> out in a musical context it allways turns out it should actually be a
> 5-limit chord or interval.
> I'm not prejudiced against 7-limit.
> Infact I really want the harmonic 7th to be valid!
> I started out a few years ago expecting music to be based on the harmonic
> overtones.
> First tried to make things work and make sense of all harmonics, making
> scales which used up to the 31th overtone.
> Gradually as I worked things out more I received at a theory which makes me
> expect the 11th harmonic and higher are not relevant to music. (this is not
> what I wish to discuss here now)
> But the 7th harmonic is still a little bit open, though I'm allmost ready to
> see the 7th as an overtone only and not part of the musical structure.
> So without getting into higher harmonics, can anybody give me a musical JI
> example of the 7th harmonic?
> Preferably 2 chords played one after another of which 1 contains the 7th,
> preferably linked to a key/mode.
> Up till now I had a little bit of hope for 8/5 2/1 12/5 14/5 -> 3/2 15/8 9/8
> 3/1
> But everywhich way I look it looks like it should be 8/5 2/1 12/5 45/16 ->
> 3/2 15/8 9/8 3/1
> Transposed down by 3/2 it is: 16/15 4/3 8/5 15/8 -> 1/1 5/4 3/2 2/1
> Making the 7th chord 1/1 5/4 3/2 225/128
> Mode is what I call an extended mode. 1/1 16/15 5/4 4/3 3/2 8/5 15/8 2/1
> (subset)
> Which is made up of 2 of either the following base modes one transposed by
> 4/3:
> harmonic minor: 1/1 9/8 6/5 4/3 3/2 8/5 15/8 2/1
> and/or: 1/1 9/8 5/4 4/3 3/2 8/5 15/8 2/1
> Other examples I've confirmed of not beeing the 7th harmonic are:
> 3/2 15/8 9/8 8/3 -> 1/1 3/2 2/1 5/2
> dominant 7th here is 1/1 5/4 3/2 16/9
> mode is major: 1/1 9/8 5/4 4/3 3/2 5/3 15/8
> or: 1/1 9/8 5/4 4/3 3/2 8/5 15/8
> Another example I've confirmed that is not constructed with the harmonic 7th
> is the diminished 7th chord which is:
> 1/1 6/5 45/32 27/16
> There's another reason I distrust the 7th harmonic now.
> The most basic keys / modes are 5-limit for sure.
> Harmony can be seen as arising by playing 2 or more melodies against
> eachother in what is called counterpoint.
> This way it seems impossible to me that a 7 limit harmony can arise from
> playing several 5-limit melodies at once.
> I don't think one can distort the melodies for the benefit of more
> harmonious 7-limit harmony.
> So either the melodies or atleast one of the melodies of the counterpoint
> has to be a 7-limit melody.
> The only other possibility i see is that all are 5-limi melodies but 1 of
> the melodies is constantly in a 7th harmonic relation to the other 5-limit
> melodies.
> So no 7th in normal classical music it seems from the above?
> I also thought I'd need the 7th intervals in arabic music, but I find I can
> explain it perfectly within 5-limit. (I'll dedicate a new thread to this
> soon)
> Also expected it to explain chromatic note sequences but now see the way
> this can be contructed from 5-limit much better.
> So why should the 7th harmonic have a place in the structure of music and in
> musical tuning?
> Yes 1/1 5/4 3/2 7/4 does seem more consonant to me than for instance 1/1 5/4
> 3/2 16/9 or 1/1 5/4 3/2 225/128 or 1/1 5/4 3/2 9/5.
> It seems logical to me that 1/1 5/4 3/2 225/128 gets it consonance from
> beeing so close to 1/1 5/4 3/2 7/4.
> But perhaps consonance in this way isn't relevant to actual music.
> And this consonance of just one chord is countered by the dissonant
> modulations and interval steps the 7th gives.
> Perhaps music is a 3 dimensional form. Primes 2, 3 and 5 making the
> structure and the 7th has no musical function and is only a harmonic
> overtone?
> I'm not trying to get anybody off their faith or use of the 7th with this
> message.
> I'm really only trying to find it out for myself, openminded and would
> really like a contructive discussion on this.
> Thanks!
> Marcel
>

Hi Mike,

> I know what you're talking about. It takes a certain musical context
> for 7-limit JI to work. Sometimes 4:5:6:7 just doesn't work as a
> dominant 7 chord.
>
> It's a question I've been asking myself for a while. I've gotten it to
> work in the string quartet I'm writing. I'm not sure what causes it
> yet.
>

Can you give me a short example?

I think it has something to do with the fact that we've gotten used to
> upper structure triads in chords, like a C major 9 chord - C E G B D.
> That GBD rings out in its own way, and it's very colorful. I'm not
> sure how it relates to phantom fundamentals or harmonic entropy, but I
> do know that the approach where you just keep adding overtones of C
> creates one possible sound for C.
>

Yes I've tried to look at it this way too, but my ear seems to allways see
the 7-limit overtones as 5-limit when used in actual music, and then the
7-limit interval is percieved as out of tune and gives problems when
changing to the next chord for instance.
Mind you, only when used in a musical context.
I do perceive them as overtones when playing nothing else.

Then again, go screw around with some neutral 11 triads and you'll
> realize that if they have use, 7-limit harmony must too. And I
> personally think neutral triads are beautiful - it's like we've added
> gray and brown to a musical palette that previously consisted only of
> bright, bold colors.
>

I have my own ideas about neutral triads and they work for me in 5-limit.
But I'd like to really try to keep this thread about the 7th harmonic, not
any higher harmonics.Just so this thread doesn't derail too much, as I find
it a very important topic.

Marcel

Just a side-note....
   Virtually all the chords you have can be expressed as X/16 and/or something like X/15 which is very very close. 
   I don't know much to help you with 7-limit, but I do recommend at least trying to see what you can do to match these chords using the "16th harmonic" IE common denominator of 16 IE o-tonal on 16, as I understand it.  You might want to try that as an alternative way of expressing those chords in JI.

-Michael

--- On Thu, 2/12/09, Marcel de Velde <m.develde@...> wrote:

From: Marcel de Velde <m.develde@...>
Subject: [tuning] 5-limit JI vs 7-limit JI
To: tuning@yahoogroups.com
Date: Thursday, February 12, 2009, 7:36 PM

I'm havind a very hard time finding confirmation 7-limit JI is valid.

I've been looking and looking every which way to confirm for instance 1/1 5/4 7/4 is a valid chord in music but I can't find it.Every instance I'm looking at a 7-limit chord or interval and work things out in a musical context it allways turns out it should actually be a 5-limit chord or interval.

I'm not prejudiced against 7-limit.Infact I really want the harmonic 7th to be valid!I started out a few years ago expecting music to be based on the harmonic overtones.
First tried to make things work and make sense of all harmonics, making scales which used up to the 31th overtone.Gradually as I worked things out more I received at a theory which makes me expect the 11th harmonic and higher are not relevant to music. (this is not what I wish to discuss here now)
But the 7th harmonic is still a little bit open, though I'm allmost ready to see the 7th as an overtone only and not part of the musical structure.So without getting into higher harmonics, can anybody give me a musical JI example of the 7th harmonic?
Preferably 2 chords played one after another of which 1 contains the 7th, preferably linked to a key/mode.
Up till now I had a little bit of hope for 8/5 2/1 12/5 14/5 -> 3/2 15/8 9/8 3/1
But everywhich way I look it looks like it should be 8/5 2/1 12/5 45/16 -> 3/2 15/8 9/8 3/1Transposed down by 3/2 it is: 16/15 4/3 8/5 15/8 -> 1/1 5/4 3/2 2/1Making the 7th chord 1/1 5/4 3/2 225/128
Mode is what I call an extended mode. 1/1 16/15 5/4 4/3 3/2 8/5 15/8 2/1 (subset)Which is made up of 2 of either the following base modes one transposed by 4/3:harmonic minor: 1/1 9/8 6/5 4/3 3/2 8/5 15/8 2/1
and/or: 1/1 9/8 5/4 4/3 3/2 8/5 15/8 2/1
Other examples I've confirmed of not beeing the 7th harmonic are:3/2 15/8 9/8 8/3 -> 1/1 3/2 2/1 5/2dominant 7th here is 1/1 5/4 3/2 16/9
mode is major: 1/1 9/8 5/4 4/3 3/2 5/3 15/8or: 1/1 9/8 5/4 4/3 3/2 8/5 15/8
Another example I've confirmed that is not constructed with the harmonic 7th is the diminished 7th chord which is:
1/1 6/5 45/32 27/16
There's another reason I distrust the 7th harmonic now.The most basic keys / modes are 5-limit for sure.Harmony can be seen as arising by playing 2 or more melodies against eachother in what is called counterpoint.
This way it seems impossible to me that a 7 limit harmony can arise from playing several 5-limit melodies at once.I don't think one can distort the melodies for the benefit of more harmonious 7-limit harmony.
So either the melodies or atleast one of the melodies of the counterpoint has to be a 7-limit melody.The only other possibility i see is that all are 5-limi melodies but 1 of the melodies is constantly in a 7th harmonic relation to the other 5-limit melodies.
So no 7th in normal classical music it seems from the above?
I also thought I'd need the 7th intervals in arabic music, but I find I can explain it perfectly within 5-limit. (I'll dedicate a new thread to this soon)
Also expected it to explain chromatic note sequences but now see the way this can be contructed from 5-limit much better.So why should the 7th harmonic have a place in the structure of music and in musical tuning?

Yes 1/1 5/4 3/2 7/4 does seem more consonant to me than for instance 1/1 5/4 3/2 16/9 or 1/1 5/4 3/2 225/128 or 1/1 5/4 3/2 9/5.It seems logical to me that 1/1 5/4 3/2 225/128 gets it consonance from beeing so close to 1/1 5/4 3/2 7/4.
But perhaps consonance in this way isn't relevant to actual music.And this consonance of just one chord is countered by the dissonant modulations and interval steps the 7th gives.Perhaps music is a 3 dimensional form. Primes 2, 3 and 5 making the structure and the 7th has no musical function and is only a harmonic overtone?

I'm not trying to get anybody off their faith or use of the 7th with this message.I'm really only trying to find it out for myself, openminded and would really like a contructive discussion on this.
Thanks!
Marcel

Also, try some parallel 4:5:6:7 chords, a la debussy... That stuff
definitely works.
-Mike

What 12 tet notes would aproximate that chord in any key you want to use?
Sent via BlackBerry from T-Mobile

-----Original Message-----
From: Mike Battaglia <battaglia01@...>

Date: Thu, 12 Feb 2009 23:19:46
To: <tuning@yahoogroups.com>
Subject: Re: [tuning] 5-limit JI vs 7-limit JI

Also, try some parallel 4:5:6:7 chords, a la debussy... That stuff
definitely works.
-Mike

You can't. I've been setting two keyboards up on top of each other,
using midi so they both control the same patch, and tuning one 32
cents flat. Then you can get a pure 7, but the 5 is still a little bit
sharp... but it's useful for just screwing around.

Someday, when I get my terpstra.... ;)

-Mike

On Thu, Feb 12, 2009 at 11:26 PM, <chrisvaisvil@...> wrote:
> What 12 tet notes would aproximate that chord in any key you want to use?
>
> Sent via BlackBerry from T-Mobile
>
> ________________________________
> From: Mike Battaglia
> Date: Thu, 12 Feb 2009 23:19:46 -0500
> To: <tuning@yahoogroups.com>
> Subject: Re: [tuning] 5-limit JI vs 7-limit JI
>
> Also, try some parallel 4:5:6:7 chords, a la debussy... That stuff
> definitely works.
> -Mike
>
>

>
> Also, try some parallel 4:5:6:7 chords, a la debussy... That stuff
> definitely works.
>

Yes you're right.
Thanks for the example.
As long as the parallel chords move by 5-limit intervals.
In a counterpoint way this makes the 7th harmonic a 5-limit melody that is
allways in 7-limit relation to the other 5-limit melodies.
But this will also work with a 5-limit 7th. Also the 7th has no real musical
function here.
I wish I could but I can't see this as evidence yet for the validity of the
7th harmonic in music.

Marcel

Well first off, what do you mean by validity... whether or not it's
possible to do anything with 7-limit intervals?
-Mike

On Thu, Feb 12, 2009 at 11:55 PM, Marcel de Velde <m.develde@...> wrote:
>> Also, try some parallel 4:5:6:7 chords, a la debussy... That stuff
>> definitely works.
>
> Yes you're right.
> Thanks for the example.
> As long as the parallel chords move by 5-limit intervals.
> In a counterpoint way this makes the 7th harmonic a 5-limit melody that is
> allways in 7-limit relation to the other 5-limit melodies.
> But this will also work with a 5-limit 7th. Also the 7th has no real musical
> function here.
> I wish I could but I can't see this as evidence yet for the validity of the
> 7th harmonic in music.
> Marcel
>

>
> Well first off, what do you mean by validity... whether or not it's
> possible to do anything with 7-limit intervals?
>

Ah I'm not sure.
I guess I mean many things.
I mean if 7-limit has a musical function.
I mean that if the 7-limit is required to make certain music, to play it
just.
I mean that I think music is perfect and has a JI base which contains all
logic of music, and I'm searching if 7-limit has a role in this.
I mean I'm searching for musical things / structures that come from / follow
logically from the 7th harmonic.
At first such structures seem very logical but after investigating I find
I'm allways looking at 5-limit structures.
Except for your above example which does not allow me to say it can't be
7-limit (untill you start to do different things with that 7th)

Marcel

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
>
> I'm havind a very hard time finding confirmation 7-limit JI is
> valid. I've been looking and looking every which way to confirm
> for instance 1/1 5/4 7/4 is a valid chord in music but I can't
> find it. Every instance I'm looking at a 7-limit chord or
> interval and work things out in a musical context it allways
> turns out it should actually be a 5-limit chord or interval.

You're familiar with Barbershop quartet singing?

> I'm not prejudiced against 7-limit.
> Infact I really want the harmonic 7th to be valid!

I would suggest you avoid words that imply a value judgment,
like "valid".

> Gradually as I worked things out more I received at a theory
> which makes me expect the 11th harmonic and higher are not
> relevant to music.

If I offer you a piece of 11-limit music that many people
enjoy, would that be a counterexample? Or, if Marcel de Velde
does not enjoy it, does that alone suffice to make it
"irrelevant to music"?

-Carl

>
> You're familiar with Barbershop quartet singing?
>

Yes, but not very well.
Do you have an example of chords / melodies that they sing from which I can
deduce the 7th harmonic when I put it in JI?

> I'm not prejudiced against 7-limit.
> > Infact I really want the harmonic 7th to be valid!
>
> I would suggest you avoid words that imply a value judgment,
> like "valid".
>

I like to use this word as it's what it is about for me.

> Gradually as I worked things out more I received at a theory
> > which makes me expect the 11th harmonic and higher are not
> > relevant to music.
>
> If I offer you a piece of 11-limit music that many people
> enjoy, would that be a counterexample? Or, if Marcel de Velde
> does not enjoy it, does that alone suffice to make it
> "irrelevant to music"?
>

Please I have asked twice allready to keep this about 7-limit.
Not higher primes like 11.
I'll ignore the other remark.
If you wish to constructively contribute to this discussion you could for
instance submit an example for 7-limit like I suggested in the first post.

Marcel

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
>
> I mean that I think music is perfect and has a JI base which
> contains all logic of music, and I'm searching if 7-limit has
> a role in this.

Maybe it would help if you qualified "music". For example, I
don't think the music of Harry Partch would conform to a
5-limit JI logic. Maybe you should say "Western music" or
"common-practice music" or "music I like". -Carl

>> > Gradually as I worked things out more I received at a theory
>> > which makes me expect the 11th harmonic and higher are not
>> > relevant to music.
>>
>> If I offer you a piece of 11-limit music that many people
>> enjoy, would that be a counterexample? Or, if Marcel de Velde
>> does not enjoy it, does that alone suffice to make it
>> "irrelevant to music"?
>
> Please I have asked twice allready to keep this about 7-limit.
> Not higher primes like 11.
> I'll ignore the other remark.
> If you wish to constructively contribute to this discussion you could for
> instance submit an example for 7-limit like I suggested in the first post.
> Marcel

http://www.akjmusic.com/audio/lost_in_appalachia.mp3

>
> Maybe it would help if you qualified "music". For example, I
> don't think the music of Harry Partch would conform to a
> 5-limit JI logic. Maybe you should say "Western music" or
> "common-practice music" or "music I like".
>

Ok I'll qualify it as common practice music.

Although Harry Partch could well be 5-limit, I can't tell.
It's mostly beyond analysis with musical structures.

Marcel

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:

> Up till now I had a little bit of hope for 8/5 2/1 12/5 14/5 ->
> 3/2 15/8 9/8 3/1
> But everywhich way I look it looks like it should be
> 8/5 2/1 12/5 45/16 -> 3/2 15/8 9/8 3/1
> Transposed down by 3/2 it is: 16/15 4/3 8/5 15/8 -> 1/1 5/4 3/2 2/1
> Making the 7th chord 1/1 5/4 3/2 225/128

That is a perfectly 7-limit chord. The 225/224 does not
prevent this; it can be ignored, or tempered out as in
miracle temperament.

> I also thought I'd need the 7th intervals in arabic music,
> but I find I can explain it perfectly within 5-limit.

I don't see how it can make sense to characterize maqam
music as being of any harmonic "limit", 5 or otherwise.

-Carl

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:

> > You're familiar with Barbershop quartet singing?
>
> Yes, but not very well.
> Do you have an example of chords / melodies that they sing
> from which I can deduce the 7th harmonic when I put it in JI?

Yes, I believe so. See subsequent post.

> > I would suggest you avoid words that imply a value judgment,
> > like "valid".
>
> I like to use this word as it's what it is about for me.

It's what it's _about_ for him, ladies and gentlemen.
We got served!

> > If I offer you a piece of 11-limit music that many people
> > enjoy, would that be a counterexample? Or, if Marcel de Velde
> > does not enjoy it, does that alone suffice to make it
> > "irrelevant to music"?
>
> Please I have asked twice allready to keep this about 7-limit.

Newsflash: You don't control what's discussed here.

-Carl

>
> http://www.akjmusic.com/audio/lost_in_appalachia.mp3

Sounds out of tune to me. And one could do it with the same colour in
5-limit.
But it's not relevant as it's 11-limit?
Also it would be more helpfull if we posted a short example in JI interval
notation.
Simply sending an mp3 like this doesn't help this discussion I think.

Marcel

http://www.akjmusic.com/audio/melancholic.mp3
Also that one. That one is mainly 5-limit, but some subtle 7-limit
stuff comes in later on... see if you can spot the subminor 6 chords.

-Mike

On Fri, Feb 13, 2009 at 12:41 AM, Mike Battaglia <battaglia01@...> wrote:
>>> > Gradually as I worked things out more I received at a theory
>>> > which makes me expect the 11th harmonic and higher are not
>>> > relevant to music.
>>>
>>> If I offer you a piece of 11-limit music that many people
>>> enjoy, would that be a counterexample? Or, if Marcel de Velde
>>> does not enjoy it, does that alone suffice to make it
>>> "irrelevant to music"?
>>
>> Please I have asked twice allready to keep this about 7-limit.
>> Not higher primes like 11.
>> I'll ignore the other remark.
>> If you wish to constructively contribute to this discussion you could for
>> instance submit an example for 7-limit like I suggested in the first post.
>> Marcel
>
> http://www.akjmusic.com/audio/lost_in_appalachia.mp3
>

On Fri, Feb 13, 2009 at 12:47 AM, Marcel de Velde <m.develde@...> wrote:
>> http://www.akjmusic.com/audio/lost_in_appalachia.mp3
>
> Sounds out of tune to me. And one could do it with the same colour in
> 5-limit.

Sounds in tune to me.

> But it's not relevant as it's 11-limit?

Is it? Even so, if music with the 7th harmonic and the 11th harmonic
can exist in functional harmony, then music with the 7th harmonic can
exist in functional harmony.

> Also it would be more helpfull if we posted a short example in JI interval
> notation.
> Simply sending an mp3 like this doesn't help this discussion I think.
> Marcel

Good luck finding that.

>
> That is a perfectly 7-limit chord. The 225/224 does not
> prevent this; it can be ignored, or tempered out as in
> miracle temperament.
>

No it's defenately NOT a 7-limit chord!!
How can you say this??
1/1 5/4 3/2 225/128 is a 5-limit chord. It does not equal 7/4.
Just as 75/64 does NOT equal 7/6.
Just as 15/8 does not equal 28/15.
etc.

> > I also thought I'd need the 7th intervals in arabic music,
> > but I find I can explain it perfectly within 5-limit.
>
> I don't see how it can make sense to characterize maqam
> music as being of any harmonic "limit", 5 or otherwise.
>

Well I'll save that for a next post as I can perfectly characterize maqam
music with extended 5-limit modes.

Marcel

>
> Yes, I believe so. See subsequent post.
>

Ok thanks.

> > I would suggest you avoid words that imply a value judgment,

> > > like "valid".
> >
> > I like to use this word as it's what it is about for me.
>
> It's what it's _about_ for him, ladies and gentlemen.
> We got served!
>

Yes, I would like to know how valid the 7th harmonic is in musical harmony /
melody/ structure.
If it is correct to use the 7th or if when i'm using a 7-limit interval i'm
actually playing an out of tune 5-limit interval.

> > > If I offer you a piece of 11-limit music that many people
> > > enjoy, would that be a counterexample? Or, if Marcel de Velde
> > > does not enjoy it, does that alone suffice to make it
> > > "irrelevant to music"?
> >
> > Please I have asked twice allready to keep this about 7-limit.
>
> Newsflash: You don't control what's discussed here.
>

No offcourse not. But I hope people will see this is a very interesting
discussion and we have plenty to discuss about the 7th.
A lot of discussions here get derailed because of arguments over irrelevant
things.
Surely one does not need to invoke the 11th harmonic to explain the 7th
harmonic.

Marcel

On Fri, Feb 13, 2009 at 12:50 AM, Marcel de Velde <m.develde@...> wrote:
>> That is a perfectly 7-limit chord. The 225/224 does not
>> prevent this; it can be ignored, or tempered out as in
>> miracle temperament.
>
> No it's defenately NOT a 7-limit chord!!
> How can you say this??
> 1/1 5/4 3/2 225/128 is a 5-limit chord. It does not equal 7/4.
> Just as 75/64 does NOT equal 7/6.
> Just as 15/8 does not equal 28/15.
> etc.

225/128 is 8 cents away from 7/4. I'd be surprised if it made that
much difference.

An equal tempered major third is closer to a lot of things than 5/4,
but it can be used to approximate 5/4.

>
> > Also it would be more helpfull if we posted a short example in JI
> interval
> > notation.
> > Simply sending an mp3 like this doesn't help this discussion I think.
> > Marcel
>
> Good luck finding that.

I just ment something like 1/1 5/4 3/2 7/4 -> 15/8 75/64 45/32 15/8 or
something like that with an explanation on why it should be a 7-limit
interval.

Marcel

>
> http://www.akjmusic.com/audio/melancholic.mp3
> Also that one. That one is mainly 5-limit, but some subtle 7-limit
> stuff comes in later on... see if you can spot the subminor 6 chords.

Some notes sound off to me.
But I'm not sure if those are 7-limit or 5-limit intervals.
I can't tell the difference between for instance 75/64 and 7/6 in music.
That's why a written example is perhaps better as it will allow people to
study it much better.

Marcel

>
> 225/128 is 8 cents away from 7/4. I'd be surprised if it made that
> much difference.
>
> An equal tempered major third is closer to a lot of things than 5/4,
> but it can be used to approximate 5/4.
>

Yes 225/128 is very close to 7/4 and it doesn't matter much in how it
sounds.
However i find it very important to know wether it should be a 225/128 or a
7/4 for music theory reasons.
It's a totally different structure.
And it doesn't have anything to do with tempering.

Marcel

I'll just leave it as this: just because a bunch of 5-limit, 7-limit,
and similar intervals might exist around the same cents range doesn't
mean that they're all mistunings of one interval, especially when
chords are brought into it instead of just dyads.

If you want to convince everyone that 7-limit music is impossible to
make, you're going to need to prove that the ear is biased to 5-limit
music only. Just saying that you can categorize everything in terms of
5-limit intervals doesn't mean that's how they're going to be
perceived.

It has to do with the fundamental that pops out at you. 6:7:9 has a
different character than 10:12:15. They're not mistunings of one
another. If you come up with some crazy compounded 5-limit interval to
take the place of 6:7, and I still hear that 1 pop out as if it were
6:7:9, then I'm perceiving it as though it were 6:7:9, no matter
whether you tuned it to 43905830495830/23409239042 or what not.

-Mike

On Fri, Feb 13, 2009 at 12:58 AM, Marcel de Velde <m.develde@...> wrote:
>> > Also it would be more helpfull if we posted a short example in JI
>> > interval
>> > notation.
>> > Simply sending an mp3 like this doesn't help this discussion I think.
>> > Marcel
>>
>> Good luck finding that.
>
> I just ment something like 1/1 5/4 3/2 7/4 -> 15/8 75/64 45/32 15/8 or
> something like that with an explanation on why it should be a 7-limit
> interval.
> Marcel
>

It depends on the chord you want. There's no blanket sweep rule for
both of them. If you want 4:5:6:7, go use that. And so on and so on

When you hear a helicopter overhead, and the overtones ring out, do
they sound "out of tune?"

-Mike

On Fri, Feb 13, 2009 at 1:03 AM, Marcel de Velde <m.develde@...> wrote:
>> 225/128 is 8 cents away from 7/4. I'd be surprised if it made that
>> much difference.
>>
>> An equal tempered major third is closer to a lot of things than 5/4,
>> but it can be used to approximate 5/4.
>
> Yes 225/128 is very close to 7/4 and it doesn't matter much in how it
> sounds.
> However i find it very important to know wether it should be a 225/128 or a
> 7/4 for music theory reasons.
> It's a totally different structure.
> And it doesn't have anything to do with tempering.
> Marcel
>

> Some notes sound off to me.
> But I'm not sure if those are 7-limit or 5-limit intervals.
> I can't tell the difference between for instance 75/64 and 7/6 in music.
> That's why a written example is perhaps better as it will allow people to
> study it much better.
> Marcel

What matters in the end is your perception.

-Mike

>
> I'll just leave it as this: just because a bunch of 5-limit, 7-limit,
> and similar intervals might exist around the same cents range doesn't
> mean that they're all mistunings of one interval, especially when
> chords are brought into it instead of just dyads.
>
> If you want to convince everyone that 7-limit music is impossible to
> make, you're going to need to prove that the ear is biased to 5-limit
> music only. Just saying that you can categorize everything in terms of
> 5-limit intervals doesn't mean that's how they're going to be
> perceived.
>
> It has to do with the fundamental that pops out at you. 6:7:9 has a
> different character than 10:12:15. They're not mistunings of one
> another. If you come up with some crazy compounded 5-limit interval to
> take the place of 6:7, and I still hear that 1 pop out as if it were
> 6:7:9, then I'm perceiving it as though it were 6:7:9, no matter
> whether you tuned it to 43905830495830/23409239042 or what not.
>
No you're turning it around.You're now biased and saying music is about the
fundamental.
Yes 6:7:9 has a different character than 10:12:15.
But you could also play 1/1 75/64 3/2
Or 1/1 32/27 3/2
Or 1/1 144/125 3/2
All different characters.
It may be due that part of this character is derived from it's proximity to
for instance 1/1 7/6 3/2.
But it could very well be that when making music you work with 5-limit
building blocks.
This is what I'm finding more and more evidence for and no evidence to the
contrary.

Marcel

>
> It depends on the chord you want. There's no blanket sweep rule for
> both of them. If you want 4:5:6:7, go use that. And so on and so on
>
> When you hear a helicopter overhead, and the overtones ring out, do
> they sound "out of tune?"
>
Yes but this is also what I mean.I mean there's a distinction between sound
and music.
And that it has started to seem likely to me there's an abrubt line at
5-limit that makes the distinction.
Musical structure = 5-limit. Sound is no limit.
So when you're using 7-limit in a musical structure way you may be doing out
of tune 5-limit.
Yet when you use 7-limit in a sound way or truly as a harmonic overtone
you're doing offcourse something correct.

Marcel

> No you're turning it around.
> You're now biased and saying music is about the fundamental.
> Yes 6:7:9 has a different character than 10:12:15.
> But you could also play 1/1 75/64 3/2
> Or 1/1 32/27 3/2
> Or 1/1 144/125 3/2
> All different characters.
> It may be due that part of this character is derived from it's proximity to
> for instance 1/1 7/6 3/2.
> But it could very well be that when making music you work with 5-limit
> building blocks.
> This is what I'm finding more and more evidence for and no evidence to the
> contrary.
> Marcel

If I played 6:7:9 three cents sharp, what would I perceive it as? A
chord with a similar but different character to 6:7:9? How different?

How flat can I make a fourth before I stop hearing it as a type of
fourth and hearing it as a major third? How about 9/7?

And as for that last comment, I like 7-limit music, and 11-limit
music, and 13-limit music, and 19 limit music too. You wrote off two
of my favorite pieces as sounding "off", and that's fine if they
aren't to your taste. But I've come to appreciate these new sounds for
what they are. So if you're going to take your personal taste and
somehow try to turn it into an all-encompassing theory of music,
that's crazy.

Especially when you use something as arbitrary as 5-limit music. Why 5?

And for the record, augmented 6 chords from back in the day were tuned
so that the augmented sixth was almost exactly 7/4 (in septimal
meantone, it would have been exactly 7/4.

-Mike

> Yes but this is also what I mean.
> I mean there's a distinction between sound and music.
> And that it has started to seem likely to me there's an abrubt line at
> 5-limit that makes the distinction.
> Musical structure = 5-limit. Sound is no limit.
> So when you're using 7-limit in a musical structure way you may be doing out
> of tune 5-limit.
> Yet when you use 7-limit in a sound way or truly as a harmonic overtone
> you're doing offcourse something correct.
> Marcel

Hell, let's go all the way with it and say that the only proper tuning
is pythagorean at this point. Maybe 5/4 is just interpreted as an out
of tune schismatic third! Who knows.

-Mike

For me any chord is "valid" in music context, everything can be used, just to know, how and where. Everything is allowed, besides chords, harmonic progressions, are only one part of music, just tools, used (or not used) to create music. If rules are unsatisfactory or missing, let's create new ones.

Some composers worked with natural harmonic series on brass, especially horns, try this:

http://www.hornharmonics.com/Helpful_Hints.html

http://www.compositiontoday.com/articles/natural_horn.asp

http://www.mooremusic.org.uk/nathorn/nathorn.htm

http://www.phys.unsw.edu.au/jw/brassacoustics.html#natural

http://books.google.com/books?id=jrF467sy4FkC&pg=PA104&lpg=PA104&dq=Natural+horns+%2B+7th+harmonics&source=web&ots=Ancxj4sO-P&sig=xlqD8xIc1wdaLSLaFn6Xf9_mrks&hl=en&ei=oAiVSabZBdXRkAX9nZG3Cw&sa=X&oi=book_result&resnum=5&ct=result

http://en.wikipedia.org/wiki/Alphorn

http://xenharmonic.wikispaces.com/microtonal+horn

http://books.google.com/books?id=t8oXNX2tY8AC&pg=PA234&lpg=PA234&dq=Natural+horns+%2B+7th+harmonics&source=web&ots=2WXKJSqppb&sig=3x_tMIQHucZlgDcXr49NGljyRtA&hl=en&ei=JwyVSbLMBdK6kAW3o_mdCw&sa=X&oi=book_result&resnum=3&ct=result#PPA234,M1

http://www.signandsight.com/features/1580.html

http://goliath.ecnext.com/coms2/gi_0199-6460528/The-African-matrix-in-jazz.html

and many more...

And what about Spectral Music:

http://en.wikipedia.org/wiki/Spectral_music

Daniel Forro

On 13 Feb 2009, at 12:36 PM, Marcel de Velde wrote:

> I'm havind a very hard time finding confirmation 7-limit JI is valid.
>
>
> I've been looking and looking every which way to confirm for > instance 1/1 5/4 7/4 is a valid chord in music but I can't find it.
> Every instance I'm looking at a 7-limit chord or interval and work > things out in a musical context it allways turns out it should > actually be a 5-limit chord or interval.
>
> I'm not prejudiced against 7-limit.
> Infact I really want the harmonic 7th to be valid!
> I started out a few years ago expecting music to be based on the > harmonic overtones.
> First tried to make things work and make sense of all harmonics, > making scales which used up to the 31th overtone.
> Gradually as I worked things out more I received at a theory which > makes me expect the 11th harmonic and higher are not relevant to > music. (this is not what I wish to discuss here now)
> But the 7th harmonic is still a little bit open, though I'm allmost > ready to see the 7th as an overtone only and not part of the > musical structure.
> So without getting into higher harmonics, can anybody give me a > musical JI example of the 7th harmonic?
> Preferably 2 chords played one after another of which 1 contains > the 7th, preferably linked to a key/mode.
>
> Up till now I had a little bit of hope for 8/5 2/1 12/5 14/5 -> 3/2 > 15/8 9/8 3/1
> But everywhich way I look it looks like it should be 8/5 2/1 12/5 > 45/16 -> 3/2 15/8 9/8 3/1
> Transposed down by 3/2 it is: 16/15 4/3 8/5 15/8 -> 1/1 5/4 3/2 2/1
> Making the 7th chord 1/1 5/4 3/2 225/128
> Mode is what I call an extended mode. 1/1 16/15 5/4 4/3 3/2 8/5 > 15/8 2/1 (subset)
> Which is made up of 2 of either the following base modes one > transposed by 4/3:
> harmonic minor: 1/1 9/8 6/5 4/3 3/2 8/5 15/8 2/1
> and/or: 1/1 9/8 5/4 4/3 3/2 8/5 15/8 2/1
>
> Other examples I've confirmed of not beeing the 7th harmonic are:
> 3/2 15/8 9/8 8/3 -> 1/1 3/2 2/1 5/2
> dominant 7th here is 1/1 5/4 3/2 16/9
> mode is major: 1/1 9/8 5/4 4/3 3/2 5/3 15/8
> or: 1/1 9/8 5/4 4/3 3/2 8/5 15/8
>
> Another example I've confirmed that is not constructed with the > harmonic 7th is the diminished 7th chord which is:
> 1/1 6/5 45/32 27/16
>
> There's another reason I distrust the 7th harmonic now.
> The most basic keys / modes are 5-limit for sure.
> Harmony can be seen as arising by playing 2 or more melodies > against eachother in what is called counterpoint.
> This way it seems impossible to me that a 7 limit harmony can arise > from playing several 5-limit melodies at once.
> I don't think one can distort the melodies for the benefit of more > harmonious 7-limit harmony.
> So either the melodies or atleast one of the melodies of the > counterpoint has to be a 7-limit melody.
> The only other possibility i see is that all are 5-limi melodies > but 1 of the melodies is constantly in a 7th harmonic relation to > the other 5-limit melodies.
> So no 7th in normal classical music it seems from the above?
>
> I also thought I'd need the 7th intervals in arabic music, but I > find I can explain it perfectly within 5-limit. (I'll dedicate a > new thread to this soon)
> Also expected it to explain chromatic note sequences but now see > the way this can be contructed from 5-limit much better.
> So why should the 7th harmonic have a place in the structure of > music and in musical tuning?
>
> Yes 1/1 5/4 3/2 7/4 does seem more consonant to me than for > instance 1/1 5/4 3/2 16/9 or 1/1 5/4 3/2 225/128 or 1/1 5/4 3/2 9/5.
> It seems logical to me that 1/1 5/4 3/2 225/128 gets it consonance > from beeing so close to 1/1 5/4 3/2 7/4.
> But perhaps consonance in this way isn't relevant to actual music.
> And this consonance of just one chord is countered by the dissonant > modulations and interval steps the 7th gives.
> Perhaps music is a 3 dimensional form. Primes 2, 3 and 5 making the > structure and the 7th has no musical function and is only a > harmonic overtone?
>
> I'm not trying to get anybody off their faith or use of the 7th > with this message.
> I'm really only trying to find it out for myself, openminded and > would really like a contructive discussion on this.
> Thanks!
>
> Marcel

>
> If I played 6:7:9 three cents sharp, what would I perceive it as? A
> chord with a similar but different character to 6:7:9? How different?
>
> How flat can I make a fourth before I stop hearing it as a type of
> fourth and hearing it as a major third? How about 9/7?
>

No that wasn't my point.
My point was that you indeed do hear the character of 6:7:9 or 1/1 7/6 3/2,
but mainly that you may not be hearing it as the musical structure 6:7:9 or
1/1 7/6 3/2.
And the difference is for instance that with 1/1 75/64 3/2 you have a
different structure. You can modulate to other chords. Change one of the
tones by a certain interval and you get another good chord. It lies in basic
modes etc etc

> And as for that last comment, I like 7-limit music, and 11-limit
> music, and 13-limit music, and 19 limit music too. You wrote off two
> of my favorite pieces as sounding "off", and that's fine if they
> aren't to your taste. But I've come to appreciate these new sounds for
> what they are. So if you're going to take your personal taste and
> somehow try to turn it into an all-encompassing theory of music,
> that's crazy.
>
> Especially when you use something as arbitrary as 5-limit music. Why 5?
>

I didn't make up 5. It's what I get when analysing music.
I gave several examples in my first post in this thread on why it may be so.

And for the record, augmented 6 chords from back in the day were tuned
> so that the augmented sixth was almost exactly 7/4 (in septimal
> meantone, it would have been exactly 7/4.
>

I'm not talking about meantone. And not talking about old tuning practices,
and 225/128 is close to 7/4.

Marcel

>
> If rules are unsatisfactory or
> missing, let's create new ones.
>
Yes I'm trying to do this. But in the process I'm finding the good rules
come from 5-limit.

> Some composers worked with natural harmonic series on brass,
> especially horns, try this:
>
> http://www.hornharmonics.com/Helpful_Hints.html
>
> http://www.compositiontoday.com/articles/natural_horn.asp
>
> http://www.mooremusic.org.uk/nathorn/nathorn.htm
>
> http://www.phys.unsw.edu.au/jw/brassacoustics.html#natural
>
> http://books.google.com/books?
> id=jrF467sy4FkC&pg=PA104&lpg=PA104&dq=Natural+horns+%2B+7th
> +harmonics&source=web&ots=Ancxj4sO-
> P&sig=xlqD8xIc1wdaLSLaFn6Xf9_mrks&hl=en&ei=oAiVSabZBdXRkAX9nZG3Cw&sa=X&o
> i=book_result&resnum=5&ct=result
>
> http://en.wikipedia.org/wiki/Alphorn
>
> http://xenharmonic.wikispaces.com/microtonal+horn
>
> http://books.google.com/books?
> id=t8oXNX2tY8AC&pg=PA234&lpg=PA234&dq=Natural+horns+%2B+7th
> +harmonics&source=web&ots=2WXKJSqppb&sig=3x_tMIQHucZlgDcXr49NGljyRtA&hl=
> en&ei=JwyVSbLMBdK6kAW3o_mdCw&sa=X&oi=book_result&resnum=3&ct=result#PPA2
> 34,M1
>
> http://www.signandsight.com/features/1580.html
>
> http://goliath.ecnext.com/coms2/gi_0199-6460528/The-African-matrix-in-
> jazz.html
>
> and many more...
>
> And what about Spectral Music:
>
> http://en.wikipedia.org/wiki/Spectral_music
>

Ok thanks I'm going to visit all the links now.
Marcel

>
> Hell, let's go all the way with it and say that the only proper tuning
> is pythagorean at this point. Maybe 5/4 is just interpreted as an out
> of tune schismatic third! Who knows.
>

I would not be closed to the idea. But it seems 5-limit explains all
Pythagorean makes no sense.

Marcel

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> >> http://www.akjmusic.com/audio/lost_in_appalachia.mp3
> >
> > Sounds out of tune to me. //
>
> Sounds in tune to me.

Me too.

> > But it's not relevant as it's 11-limit?
>
> Is it?

No.

-Carl

All the links you sent are apparently about using the harmonics higher than
5 as harmonic overtones.
Not in a music structural context. (not functional in chords or melodies)
More like a special sound effect. Or actually as sound in the last example?

I'm not debating this use at all.
In fact I suggested this is the correct use for the 7th and higher
harmonics.
I make the distinction 5-limit for musical structure.
No limit (all harmonics) for sound and for clear use as harmonic overtones.

Marcel

Some composers worked with natural harmonic series on brass,
> especially horns, try this:
>
> http://www.hornharmonics.com/Helpful_Hints.html
>
> http://www.compositiontoday.com/articles/natural_horn.asp
>
> http://www.mooremusic.org.uk/nathorn/nathorn.htm
>
> http://www.phys.unsw.edu.au/jw/brassacoustics.html#natural
>
> http://books.google.com/books?
> id=jrF467sy4FkC&pg=PA104&lpg=PA104&dq=Natural+horns+%2B+7th
> +harmonics&source=web&ots=Ancxj4sO-
> P&sig=xlqD8xIc1wdaLSLaFn6Xf9_mrks&hl=en&ei=oAiVSabZBdXRkAX9nZG3Cw&sa=X&o
> i=book_result&resnum=5&ct=result
>
> http://en.wikipedia.org/wiki/Alphorn
>
> http://xenharmonic.wikispaces.com/microtonal+horn
>
> http://books.google.com/books?
> id=t8oXNX2tY8AC&pg=PA234&lpg=PA234&dq=Natural+horns+%2B+7th
> +harmonics&source=web&ots=2WXKJSqppb&sig=3x_tMIQHucZlgDcXr49NGljyRtA&hl=
> en&ei=JwyVSbLMBdK6kAW3o_mdCw&sa=X&oi=book_result&resnum=3&ct=result#PPA2
> 34,M1
>
> http://www.signandsight.com/features/1580.html
>
> http://goliath.ecnext.com/coms2/gi_0199-6460528/The-African-matrix-in-
> jazz.html
>
> and many more...
>
> And what about Spectral Music:
>
> http://en.wikipedia.org/wiki/Spectral_music
>

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
>
> >
> > That is a perfectly 7-limit chord. The 225/224 does not
> > prevent this; it can be ignored, or tempered out as in
> > miracle temperament.
> >
>
> No it's defenately NOT a 7-limit chord!!
> How can you say this??
> 1/1 5/4 3/2 225/128 is a 5-limit chord. It does not equal 7/4.
> Just as 75/64 does NOT equal 7/6.
> Just as 15/8 does not equal 28/15.
> etc.

It is clearly approximating 4:5:6:7. 128:160:192:225 is too
high in the harmonic series to be recognizable.

-Carl

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:

> Surely one does not need to invoke the 11th harmonic to explain
> the 7th harmonic.
>
> Marcel

Indeed not. I'm trying to establish by what means
this "validity" will be determined, if that's what we
are trying to do here.

-Carl

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:

> I can't tell the difference between for instance 75/64 and 7/6
> in music.
> That's why a written example is perhaps better as it will allow
> people to study it much better.

Anything you're writing down ought to reflect what can be
heard, don't you think? -Carl

Modulations sound akward to me.
But I can't say if it's out of tune.
Can you post a very short part of the song in JI intervals, then we may
debate it more productively.

Marcel

> > Sounds out of tune to me. //
> >
> > Sounds in tune to me.
>
> Me too.
>
> > > But it's not relevant as it's 11-limit?
> >
> > Is it?
>
> No.
>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> Hell, let's go all the way with it and say that the only proper tuning
> is pythagorean at this point. Maybe 5/4 is just interpreted as an out
> of tune schismatic third! Who knows.
>
> -Mike

LOL!

-Carl

>
> It is clearly approximating 4:5:6:7. 128:160:192:225 is too
> high in the harmonic series to be recognizable.
>

Yes I agree it's approximating 4:5:6:7.
But recognizable I don't know. Maybe not in a consonance way.
But it does lead to an expectation on how to resolve.
And this works well in 5-limit and doesn't in 7-limit.
Also when you play it in a mode and play along a melody this chord is
allways clear to be a 5-limit chord.

Marcel

>
> Also when you play it in a mode and play along a melody this chord is
> allways clear to be a 5-limit chord.

All I'm asking is a clear example in JI notated in intervals where you can
make a good case that in your particular example it must be 7-limit and
can't be 5-limit.
Surely if the 7th is valid in a musical structural way there should be
plenty such examples?

Marcel

>
> All I'm asking is a clear example in JI notated in intervals where you can
> make a good case that in your particular example it must be 7-limit and
> can't be 5-limit.
> Surely if the 7th is valid in a musical structural way there should be
> plenty such examples?
>
That should be "surely if the 7th harmonic is valid in a musical structural
way there should be plenty such examples"

I'll post again in this thread:

What would work for this discussion is a simple example in JI like this for
instance:

3/2 15/8 9/4 8/3 -> 1/1 3/2 2/1 5/2
mode: 1/1 9/8 5/4 4/3 3/2 5/3 15/8 2/1

I hope nobody think this should be 7-limit and 3/2 15/8 9/4 21/8?

Marcel

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:

> All I'm asking is a clear example in JI notated in intervals where
> you can make a good case that in your particular example it must
> be 7-limit and can't be 5-limit.
> Surely if the 7th is valid in a musical structural way there should
> be plenty such examples?

The 7-limit is valid because people like the sound of
7-limit intervals. What other reason could there be?

-Carl

>
> The 7-limit is valid because people like the sound of
> 7-limit intervals.
>

People have a hard time discerning 75/64 from 7/6 for instance so this does
not mean it is indeed a 7-limit interval they like the sound off.

> What other reason could there be?
>

In my first post I gave several different reasons why the 7th harmonic may
not have a place in musical structure.
You have not adressed these very good reasons.

Marcel

And you apparently can't give me a single good reason besides "people seem
to like it" as the reason for the 7th harmonic in musical structure?
Marcel

On Fri, Feb 13, 2009 at 8:16 AM, Marcel de Velde <m.develde@...>wrote:

> The 7-limit is valid because people like the sound of
>> 7-limit intervals.
>>
>
> People have a hard time discerning 75/64 from 7/6 for instance so this does
> not mean it is indeed a 7-limit interval they like the sound off.
>
>
>
>> What other reason could there be?
>>
>
> In my first post I gave several different reasons why the 7th harmonic may
> not have a place in musical structure.
> You have not adressed these very good reasons.
>
> Marcel
>

On Fri, Feb 13, 2009 at 2:17 AM, Marcel de Velde <m.develde@...> wrote:
> And you apparently can't give me a single good reason besides "people seem
> to like it" as the reason for the 7th harmonic in musical structure?
>
> Marcel

What other reason could there possibly be? That someone with a Ph. D
said so? Is it in the bible if you work it out in some kind of code?

I have this theory that octaves are heard as out of tune perfect
fifths. All harmonics past 2 are unusable in music because they don't
sound like the same note. Also, the only valid timbres are triangle
waves that are 90 degrees out of phase.

-Mike

>
> The 7-limit is valid because people like the sound of
>> 7-limit intervals.
>>
>
> People have a hard time discerning 75/64 from 7/6 for instance so this does
> not mean it is indeed a 7-limit interval they like the sound off.
>

Besides this. I allready made a clear distinction between "sound off" and
actual underlying musical structure.
I agree 75/64 has in ways the "sound off" 7/6.
This does not mean it should indeed be 7/6 as explained before.

Marcel

>
> What other reason could there possibly be? That someone with a Ph. D
> said so? Is it in the bible if you work it out in some kind of code?
>
> I have this theory that octaves are heard as out of tune perfect
> fifths. All harmonics past 2 are unusable in music because they don't
> sound like the same note. Also, the only valid timbres are triangle
> waves that are 90 degrees out of phase.
>

Lol, this is so rediculous I won't even bother to reply.
I do have a nice qoute from you and carl now for every time you have another
one of your explenations of how something in music or perception works
according to you.

Marcel

Everything just is the way it is. Lets not even think about it.All is random
chaos. Darwin was wrong, physics is a big fraud blablabla
And music is just random pling plong.
Good luck with this attitude carl and mike.

Marcel

On Fri, Feb 13, 2009 at 2:19 AM, Marcel de Velde <m.develde@...> wrote:
>>> The 7-limit is valid because people like the sound of
>>> 7-limit intervals.
>>
>> People have a hard time discerning 75/64 from 7/6 for instance so this
>> does not mean it is indeed a 7-limit interval they like the sound off.
>
> Besides this. I allready made a clear distinction between "sound off" and
> actual underlying musical structure.
> I agree 75/64 has in ways the "sound off" 7/6.
> This does not mean it should indeed be 7/6 as explained before.
> Marcel

If you play a chord like this:

C G E- F# B- D#<

1 3/2 5/2 45/16 15/4 75/16:

Then I'd say it's best to tune that D#< on top as a 75/16, because
you're likely going to hear the D# as a 5/4 resonance on top of the
B-, which is going to be heard as a 3/2 resonance on top of the E-,
which is going to be heard as a 5/2 on top of the C.

On the other hand, if you play this chord:

C Eb< G
6:7:9

Then I'd say you're probably going to hear that C Eb< as a 6:7
resonance directly on top of the C.

Hope that clears things up.

-Mike

Ok thank you for your serious reply.
I'll go think about it.
It's about bedtime for me so I'll give a better reply tomorrow.

Marcel

If you play a chord like this:
>
> C G E- F# B- D#<
>
> 1 3/2 5/2 45/16 15/4 75/16:
>
> Then I'd say it's best to tune that D#< on top as a 75/16, because
> you're likely going to hear the D# as a 5/4 resonance on top of the
> B-, which is going to be heard as a 3/2 resonance on top of the E-,
> which is going to be heard as a 5/2 on top of the C.
>
> On the other hand, if you play this chord:
>
> C Eb< G
> 6:7:9
>
> Then I'd say you're probably going to hear that C Eb< as a 6:7
> resonance directly on top of the C.
>
> Hope that clears things up.
>

On Fri, Feb 13, 2009 at 2:25 AM, Marcel de Velde <m.develde@...> wrote:
> Everything just is the way it is. Lets not even think about it.
>
> All is random chaos. Darwin was wrong, physics is a big fraud blablabla
> And music is just random pling plong.
> Good luck with this attitude carl and mike.
> Marcel

It has nothing to do with that. You have a terrible attitude. You're
dealing with people who are trying to get 11-limit music and 13-limit
music and 93428-limit music to work. And you come along with these
blanket-sweep categorical decisions like as if it's up to you to
decide whether or not "7-limit music is valid".

Sure it's valid. What is it, illegal? How are you going to invent a
system that says it's invalid and then yell at everyone when we say
like it anyway? If nobody can quite figure out how to write amazing
Bach-style 7-limit counterpoint yet, why the hell would that somehow
invalidate future research into the subject?

You're also fond of these outrageous statements such as that 11-limit
music has no musical purpose. I've been experimenting with 11 and
13-limit music for a while, and it has plenty musical purpose. People
here have taken the time to post audio examples for you to listen to
them, and you bat them away with that they're "invalid."

You've also decided to discard 30 years of psychoacoustic research on
the periodicity mechanism of the brain in placing the virtual
fundamental of a signal just because you've come up with your own
hypothesis instead, and rather than test your hypothesis, you've
decided you're just right and that's that. Then you'll argue about it
when criticized.

To be honest your attitude is driving me nuts. I am an extremely
patient person, and I've tried my best to impart the stuff I've
learned so far to you. If you have your own ideas, I'd love to hear
them. I've changed my views on things considerably since I joined the
group. But when people take the time to give you examples, webpages,
and literature references to something like fundamental placement of a
harmonic series, you can't expect people to be happy if you just bat
them away with some remark about how the whole thing is "improbable"
and how we're all just so stupid that we believe what science says and
you're the only one smart enough to think differently.

-Mike

>
> It has nothing to do with that. You have a terrible attitude. You're
> dealing with people who are trying to get 11-limit music and 13-limit
> music and 93428-limit music to work. And you come along with these
> blanket-sweep categorical decisions like as if it's up to you to
> decide whether or not "7-limit music is valid".
>

No I was asking. I dying to find out myself wether 7-limit is valid for
musical structure.

Sure it's valid. What is it, illegal? How are you going to invent a
> system that says it's invalid and then yell at everyone when we say
> like it anyway? If nobody can quite figure out how to write amazing
> Bach-style 7-limit counterpoint yet, why the hell would that somehow
> invalidate future research into the subject?
>

Yes one would expect that by now bach style 7-limit counterpoint would have
been made to work.
I'd like to make it work but I simply don't see how this would be possible.
Not even simple musical structures seem right, let alone a whole
counterpoint work.

You're also fond of these outrageous statements such as that 11-limit
> music has no musical purpose. I've been experimenting with 11 and
> 13-limit music for a while, and it has plenty musical purpose. People
> here have taken the time to post audio examples for you to listen to
> them, and you bat them away with that they're "invalid."
>

You make terrible out of tune music.
Go get your ears checked.
I don't call this musical purpose.

You've also decided to discard 30 years of psychoacoustic research on
> the periodicity mechanism of the brain in placing the virtual
> fundamental of a signal just because you've come up with your own
> hypothesis instead, and rather than test your hypothesis, you've
> decided you're just right and that's that. Then you'll argue about it
> when criticized.
>

No I didn't decide this. I am testing for years allready.
And psychoacoustics research doesn't nessesarily hold the promice of solving
the music structure problem.
The fact that it hasn't yet even come close sais something.

To be honest your attitude is driving me nuts. I am an extremely
> patient person, and I've tried my best to impart the stuff I've
> learned so far to you. If you have your own ideas, I'd love to hear
> them. I've changed my views on things considerably since I joined the
> group. But when people take the time to give you examples, webpages,
> and literature references to something like fundamental placement of a
> harmonic series, you can't expect people to be happy if you just bat
> them away with some remark about how the whole thing is "improbable"
> and how we're all just so stupid that we believe what science says and
> you're the only one smart enough to think differently.
>

No you're not patient.
You have your own idea of how things should work and beleive in it like the
bible.
Now when someone comes along and says your god may not exist you get
frustrated when you can't give good enough arguments for you your god would
exist.
This seems to me to be the reason you get so extra pissed off.

Btw the previous discussion about beating has virtually nothing to do with
this discussion.

I've done some analysing on your example eventhough it was very unclear and
not the exact example i asked for.
But i'can show it should indeed be 75/64 not 7/6.
I'll post it tomorrow, i'm off to bed now.

Marcel

>> Sure it's valid. What is it, illegal? How are you going to invent a
>> system that says it's invalid and then yell at everyone when we say
>> like it anyway? If nobody can quite figure out how to write amazing
>> Bach-style 7-limit counterpoint yet, why the hell would that somehow
>> invalidate future research into the subject?
>
> Yes one would expect that by now bach style 7-limit counterpoint would have
> been made to work.
> I'd like to make it work but I simply don't see how this would be possible.
> Not even simple musical structures seem right, let alone a whole
> counterpoint work.

Where I come from, you have to prove that something couldn't possibly
exist for it to not be able to exist. You can't just try and then
decide it doesn't work because you haven't figured it out yet.

>
>> You're also fond of these outrageous statements such as that 11-limit
>> music has no musical purpose. I've been experimenting with 11 and
>> 13-limit music for a while, and it has plenty musical purpose. People
>> here have taken the time to post audio examples for you to listen to
>> them, and you bat them away with that they're "invalid."
>
> You make terrible out of tune music.
> Go get your ears checked.
> I don't call this musical purpose.

ROFL. That's probably it. If you're going to try to convince people
that 13-limit music is "out of tune," you might want to try a
different mailing list.

Those are Aaron Johnson's pieces, btw.

>> You've also decided to discard 30 years of psychoacoustic research on
>> the periodicity mechanism of the brain in placing the virtual
>> fundamental of a signal just because you've come up with your own
>> hypothesis instead, and rather than test your hypothesis, you've
>> decided you're just right and that's that. Then you'll argue about it
>> when criticized.
>
> No I didn't decide this. I am testing for years allready.
> And psychoacoustics research doesn't nessesarily hold the promice of solving
> the music structure problem.
> The fact that it hasn't yet even come close sais something.

Your tests have somehow determined that one can't hear the periodicity
of a signal?

>> To be honest your attitude is driving me nuts. I am an extremely
>> patient person, and I've tried my best to impart the stuff I've
>> learned so far to you. If you have your own ideas, I'd love to hear
>> them. I've changed my views on things considerably since I joined the
>> group. But when people take the time to give you examples, webpages,
>> and literature references to something like fundamental placement of a
>> harmonic series, you can't expect people to be happy if you just bat
>> them away with some remark about how the whole thing is "improbable"
>> and how we're all just so stupid that we believe what science says and
>> you're the only one smart enough to think differently.
>
> No you're not patient.
> You have your own idea of how things should work and beleive in it like the
> bible.

It's like I eat toast every morning for breakfast, and you come along
and start expounding on that toast is invalid for breakfast. The only
thing that's valid is bread. Whenever I eat toast, I'm really only
eating burnt bread. Then I say "I like toast" and you say "give me a
precise example in which toast functions properly in breakfast." So I
say "well, it's good if you're eating eggs." Then you go "yes, but I
can't tell if you're really eating toast or just burnt bread. Give me
a more precise example and explain precisely how the toast fits into
breakfast." So I say "well, you can use the toast to dip into the egg
yolk if it's sunny side up." And your response is always something
like "that situation will never come up. it's impossible. The egg yolk
would have to be undercooked to dip anything in it, and that's
unhealthy. You are completely lost, and probably morbidly obese from
eating so many eggs."

If I say "this whole discussion is pointless, I like eating toast, and
that's that, what other requirement could there be?" then you get on
about "that's a great attitude. Let's all just assume things work
because they work and not figure out the order and you have a bad
attitude and something about darwin and you better go get your head
examined because you must be screwed up to like toast since didn't you
hear me say a million times toast is overcooked bread?"

> Now when someone comes along and says your god may not exist you get
> frustrated when you can't give good enough arguments for you your god would
> exist.

ROFL, why should I sit here and argue about whether or not I like
something that I like? If you come along with some argument about how
it's "invalid" or "bad" or "doesn't work" or something, but I like it,
what arguments do I need to make? "I LIKE IT. IT'S GOOD. MAKE MIKE
HAPPY. GIVE WARM FUZZY FEELING ALL OVER." What are you going to say,
"no it doesn't?" "It's out of tune?" Should we just argue back and
forth over whether or not it sounds "good?"

> This seems to me to be the reason you get so extra pissed off.
> Btw the previous discussion about beating has virtually nothing to do with
> this discussion.
> I've done some analysing on your example eventhough it was very unclear and
> not the exact example i asked for.
> But i'can show it should indeed be 75/64 not 7/6.
> I'll post it tomorrow, i'm off to bed now.

I've given you examples. Other people have given you examples. If you
want to develop an appreciation for 7-limit music, try spending more
than 3 seconds with some of these songs before making snap judgments
about them. Or go write some of your own 7-limit music and then maybe
you'll be the one who figures out precisely how it works.

Perhaps also a personal servant might be useful in giving you the
exact example you want, formatted precisely to your personal needs,
without mention of any overtones higher than 7, and at your beck and
call. My example was plenty clear to me.

> Marcel

I like this. 7-limit chords seem pretty clear, but I've been wrong before.

I'd call it "pensive".

7, 11-limit pitches are valid, but different, and maybe more fragile--maybe they require more accuracy, and are more dependent on register.

On Feb 13, 2009, at 12:47 AM, Mike Battaglia wrote:

> http://www.akjmusic.com/audio/melancholic.mp3
> Also that one. That one is mainly 5-limit, but some subtle 7-limit
> stuff comes in later on... see if you can spot the subminor 6 chords.
>
> -Mike
>
> On Fri, Feb 13, 2009 at 12:41 AM, Mike Battaglia <battaglia01@...> > wrote:
> >>> > Gradually as I worked things out more I received at a theory
> >>> > which makes me expect the 11th harmonic and higher are not
> >>> > relevant to music.
> >>>
> >>> If I offer you a piece of 11-limit music that many people
> >>> enjoy, would that be a counterexample? Or, if Marcel de Velde
> >>> does not enjoy it, does that alone suffice to make it
> >>> "irrelevant to music"?
> >>
> >> Please I have asked twice allready to keep this about 7-limit.
> >> Not higher primes like 11.
> >> I'll ignore the other remark.
> >> If you wish to constructively contribute to this discussion you > could for
> >> instance submit an example for 7-limit like I suggested in the > first post.
> >> Marcel
> >
> > http://www.akjmusic.com/audio/lost_in_appalachia.mp3
> >
>
>

Well said, mike.

Agree completely.

Marcel, you can simply say "MY ear", or "it seems to me", or "I tend to prefer" and no one can disagree.

On Feb 13, 2009, at 1:03 AM, Mike Battaglia wrote:

> I'll just leave it as this: just because a bunch of 5-limit, 7-limit,
> and similar intervals might exist around the same cents range doesn't
> mean that they're all mistunings of one interval, especially when
> chords are brought into it instead of just dyads.
>
> If you want to convince everyone that 7-limit music is impossible to
> make, you're going to need to prove that the ear is biased to 5-limit
> music only. Just saying that you can categorize everything in terms of
> 5-limit intervals doesn't mean that's how they're going to be
> perceived.
>
> It has to do with the fundamental that pops out at you. 6:7:9 has a
> different character than 10:12:15. They're not mistunings of one
> another. If you come up with some crazy compounded 5-limit interval to
> take the place of 6:7, and I still hear that 1 pop out as if it were
> 6:7:9, then I'm perceiving it as though it were 6:7:9, no matter
> whether you tuned it to 43905830495830/23409239042 or what not.
>
> -Mike
>
> On Fri, Feb 13, 2009 at 12:58 AM, Marcel de Velde > <m.develde@...> wrote:
> >> > Also it would be more helpfull if we posted a short example in JI
> >> > interval
> >> > notation.
> >> > Simply sending an mp3 like this doesn't help this discussion I > think.
> >> > Marcel
> >>
> >> Good luck finding that.
> >
> > I just ment something like 1/1 5/4 3/2 7/4 -> 15/8 75/64 45/32 > 15/8 or
> > something like that with an explanation on why it should be a 7-> limit
> > interval.
> > Marcel
> >
>
>

no.

And, you appear to have a strange preoccupation with "rules" and "validity".

On Feb 13, 2009, at 1:33 AM, Marcel de Velde wrote:

>
> If rules are unsatisfactory or
> missing, let's create new ones.
>
> Yes I'm trying to do this. But in the process I'm finding the good > rules come from 5-limit.
>
> Some composers worked with natural harmonic series on brass,
> especially horns, try this:
>
> http://www.hornharmonics.com/Helpful_Hints.html
>
> http://www.compositiontoday.com/articles/natural_horn.asp
>
> http://www.mooremusic.org.uk/nathorn/nathorn.htm
>
> http://www.phys.unsw.edu.au/jw/brassacoustics.html#natural
>
> http://books.google.com/books?
> id=jrF467sy4FkC&pg=PA104&lpg=PA104&dq=Natural+horns+%2B+7th
> +harmonics&source=web&ots=Ancxj4sO-
> P> &sig> =xlqD8xIc1wdaLSLaFn6Xf9_mrks&hl=en&ei=oAiVSabZBdXRkAX9nZG3Cw&sa=X&o
> i=book_result&resnum=5&ct=result
>
> http://en.wikipedia.org/wiki/Alphorn
>
> http://xenharmonic.wikispaces.com/microtonal+horn
>
> http://books.google.com/books?
> id=t8oXNX2tY8AC&pg=PA234&lpg=PA234&dq=Natural+horns+%2B+7th
> +> harmonics> &source=web&ots=2WXKJSqppb&sig=3x_tMIQHucZlgDcXr49NGljyRtA&hl=
> en> &ei=JwyVSbLMBdK6kAW3o_mdCw&sa=X&oi=book_result&resnum=3&ct=result#PPA2
> 34,M1
>
> http://www.signandsight.com/features/1580.html
>
> http://goliath.ecnext.com/coms2/gi_0199-6460528/The-African-matrix-in-
> jazz.html
>
> and many more...
>
> And what about Spectral Music:
>
> http://en.wikipedia.org/wiki/Spectral_music
>
>
> Ok thanks I'm going to visit all the links now.
>
> Marcel
>
>

To Marcel,

let's put it this way. The harmonic series begins with an octave. Great, so we'll choose this as the period. Then there's a fifth and a fourth. Okay, let's choose this as our basis for working with scales. When you start combining and chaining these, sooner or later, you'll find an interval that is only ~21.5 cents away from the next one in the harmonic series -- i.e. 5/4. Because we want to get rid of this "out-of-tune" interval, we'll replace the "mathematically correct" 81/64 with 5/4 and, similarly, 32/27 with 6/5. So no we don't have one size of, for example, a major second, we've got two. This means there's not only one correct size of a major second, there are AT LEAST two (9/8 and 10/9). And we're not working with only 3-limit intervals anymore, we've got the 5-limit set. And now, a similar situation occurs. Combining and chaining the whole lot of 5-limit intervals which we have at our disposal, sooner or later, we'll quickly get to another interval which is just under 8 cents away from another one in the series. And, again, because we don't want this "out-of-tuneness", we'll replace 225/128 with 7/4, 45/32 with 7/5, and 75/64 with 7/6. So now we find that there is neither one, nor there are two, but AT LEAST four sizes of major seconds in JI (9/8, 10/9, 28/25, and 125/112). And we can't say that one of them is the "correct" one and the other are not, because, simply, every harmonic progression may have different requirements. If you should find 7-limit intervals "invalid for common-practice music" for the reasons you gave, then you'd have to find 5-limit intervals invalid in just the same way. -- BTW: Before you start arguing about my suggestions, please have a look at "parizek_7lqmtd2.scl" in Manuel's scale archive and try playing around with it for a while.

Petr

I'm watching with admiration as Mike hits softball after softball out of the park, here.

Yes, you are patient, Mike.

On Feb 13, 2009, at 3:54 AM, Mike Battaglia wrote:

> >> Sure it's valid. What is it, illegal? How are you going to invent a
> >> system that says it's invalid and then yell at everyone when we say
> >> like it anyway? If nobody can quite figure out how to write amazing
> >> Bach-style 7-limit counterpoint yet, why the hell would that > somehow
> >> invalidate future research into the subject?
> >
> > Yes one would expect that by now bach style 7-limit counterpoint > would have
> > been made to work.
> > I'd like to make it work but I simply don't see how this would be > possible.
> > Not even simple musical structures seem right, let alone a whole
> > counterpoint work.
>
> Where I come from, you have to prove that something couldn't possibly
> exist for it to not be able to exist. You can't just try and then
> decide it doesn't work because you haven't figured it out yet.
>
> >
> >> You're also fond of these outrageous statements such as that 11-> limit
> >> music has no musical purpose. I've been experimenting with 11 and
> >> 13-limit music for a while, and it has plenty musical purpose. > People
> >> here have taken the time to post audio examples for you to listen > to
> >> them, and you bat them away with that they're "invalid."
> >
> > You make terrible out of tune music.
> > Go get your ears checked.
> > I don't call this musical purpose.
>
> ROFL. That's probably it. If you're going to try to convince people
> that 13-limit music is "out of tune," you might want to try a
> different mailing list.
>
> Those are Aaron Johnson's pieces, btw.
>
> >> You've also decided to discard 30 years of psychoacoustic > research on
> >> the periodicity mechanism of the brain in placing the virtual
> >> fundamental of a signal just because you've come up with your own
> >> hypothesis instead, and rather than test your hypothesis, you've
> >> decided you're just right and that's that. Then you'll argue > about it
> >> when criticized.
> >
> > No I didn't decide this. I am testing for years allready.
> > And psychoacoustics research doesn't nessesarily hold the promice > of solving
> > the music structure problem.
> > The fact that it hasn't yet even come close sais something.
>
> Your tests have somehow determined that one can't hear the periodicity
> of a signal?
>
> >> To be honest your attitude is driving me nuts. I am an extremely
> >> patient person, and I've tried my best to impart the stuff I've
> >> learned so far to you. If you have your own ideas, I'd love to hear
> >> them. I've changed my views on things considerably since I joined > the
> >> group. But when people take the time to give you examples, > webpages,
> >> and literature references to something like fundamental placement > of a
> >> harmonic series, you can't expect people to be happy if you just > bat
> >> them away with some remark about how the whole thing is > "improbable"
> >> and how we're all just so stupid that we believe what science > says and
> >> you're the only one smart enough to think differently.
> >
> > No you're not patient.
> > You have your own idea of how things should work and beleive in it > like the
> > bible.
>
> It's like I eat toast every morning for breakfast, and you come along
> and start expounding on that toast is invalid for breakfast. The only
> thing that's valid is bread. Whenever I eat toast, I'm really only
> eating burnt bread. Then I say "I like toast" and you say "give me a
> precise example in which toast functions properly in breakfast." So I
> say "well, it's good if you're eating eggs." Then you go "yes, but I
> can't tell if you're really eating toast or just burnt bread. Give me
> a more precise example and explain precisely how the toast fits into
> breakfast." So I say "well, you can use the toast to dip into the egg
> yolk if it's sunny side up." And your response is always something
> like "that situation will never come up. it's impossible. The egg yolk
> would have to be undercooked to dip anything in it, and that's
> unhealthy. You are completely lost, and probably morbidly obese from
> eating so many eggs."
>
> If I say "this whole discussion is pointless, I like eating toast, and
> that's that, what other requirement could there be?" then you get on
> about "that's a great attitude. Let's all just assume things work
> because they work and not figure out the order and you have a bad
> attitude and something about darwin and you better go get your head
> examined because you must be screwed up to like toast since didn't you
> hear me say a million times toast is overcooked bread?"
>
> > Now when someone comes along and says your god may not exist you get
> > frustrated when you can't give good enough arguments for you your > god would
> > exist.
>
> ROFL, why should I sit here and argue about whether or not I like
> something that I like? If you come along with some argument about how
> it's "invalid" or "bad" or "doesn't work" or something, but I like it,
> what arguments do I need to make? "I LIKE IT. IT'S GOOD. MAKE MIKE
> HAPPY. GIVE WARM FUZZY FEELING ALL OVER." What are you going to say,
> "no it doesn't?" "It's out of tune?" Should we just argue back and
> forth over whether or not it sounds "good?"
>
> > This seems to me to be the reason you get so extra pissed off.
> > Btw the previous discussion about beating has virtually nothing to > do with
> > this discussion.
> > I've done some analysing on your example eventhough it was very > unclear and
> > not the exact example i asked for.
> > But i'can show it should indeed be 75/64 not 7/6.
> > I'll post it tomorrow, i'm off to bed now.
>
> I've given you examples. Other people have given you examples. If you
> want to develop an appreciation for 7-limit music, try spending more
> than 3 seconds with some of these songs before making snap judgments
> about them. Or go write some of your own 7-limit music and then maybe
> you'll be the one who figures out precisely how it works.
>
> Perhaps also a personal servant might be useful in giving you the
> exact example you want, formatted precisely to your personal needs,
> without mention of any overtones higher than 7, and at your beck and
> call. My example was plenty clear to me.
>
> > Marcel
>
>

Euler liked 7 limit intervals hundred of years ago. Much less the Greeks had whole school that would not settle for any semitone than the 28/27.
One of the most beautiful sounds in the world.
--

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

>
> let's put it this way. The harmonic series begins with an octave. Great, so
> we'll choose this as the period. Then there's a fifth and a fourth. Okay,
> let's choose this as our basis for working with scales. When you start
> combining and chaining these, sooner or later, you'll find an interval that
> is only ~21.5 cents away from the next one in the harmonic series -- i.e.
> 5/4. Because we want to get rid of this "out-of-tune" interval, we'll
> replace the "mathematically correct" 81/64 with 5/4 and, similarly, 32/27
> with 6/5.

I don't think it works like this.
81/64 is not replaced by 5/4.
You can play 81/64, but it has a different musical meaning. When you play
81/64 you can modulate to different things, play a different melody or do
different chord progressions.
81/64 and 5/4 are not just 2 different tunings of the same musical structure
in my opinion.
They're 2 different musical structures.
This becomes apparent mosly because of the 2 different notes lead to
different things.
Especially 32/27 is very much used in common practice music. And it is a
different note with a different musical meaning from 6/5.

> So no we don't have one size of, for example, a major second, we've got
> two. This means there's not only one correct size of a major second, there
> are AT LEAST two (9/8 and 10/9). And we're not working with only 3-limit
> intervals anymore, we've got the 5-limit set. And now, a similar situation
> occurs. Combining and chaining the whole lot of 5-limit intervals which we
> have at our disposal, sooner or later, we'll quickly get to another interval
> which is just under 8 cents away from another one in the series. And, again,
> because we don't want this "out-of-tuneness", we'll replace 225/128 with
> 7/4, 45/32 with 7/5, and 75/64 with 7/6.

Well I don't agree this is how we'd get to the 7/4 7/5 7/6 etc.
But yes I have been expecting the 7/4 7/5 7/6 to have a unique musical
function and to lead to new chord progressions etc.
But I can't find it, and can't make them to work in normal chord
progressions.

So now we find that there is neither one, nor there are two, but AT LEAST
> four sizes of major seconds in JI (9/8, 10/9, 28/25, and 125/112). And we
> can't say that one of them is the "correct" one and the other are not,
> because, simply, every harmonic progression may have different requirements.

If you're looking for the neutral seconds you'll hopefully find more logic
in 27/25 and 800/729 (making 32/27 together, either can come first).
No need to bring in 7-limit.

> If you should find 7-limit intervals "invalid for common-practice music"
> for the reasons you gave, then you'd have to find 5-limit intervals invalid
> in just the same way.

No I never said this is the way I find my 5-limit intervals.
I have a system for this which is not picking close to 12-tet or something
like that.

> -- BTW: Before you start arguing about my suggestions, please have a look
> at "parizek_7lqmtd2.scl" in Manuel's scale archive and try playing around
> with it for a while.

Here's one of my own 7-limit scales I've been playing with:
1/1 36/35 21/20 16/15 15/14 35/32 10/9 9/8 8/7 7/6 6/5 5/4 9/7 21/16 4/3
48/35 7/5 10/7 35/24 3/2 32/21 14/9
8/5 5/3 12/7 7/4 16/9 9/5 64/35 28/15 15/8 40/21 35/18 2/1
And I really do have a lot of experience with the 7th harmonic. Allways
tried to make it work and many many times thought I got it to work before
beeing dissapointed again.

Marcel

>
> f you play a chord like this:
>
> C G E- F# B- D#<
>
> 1 3/2 5/2 45/16 15/4 75/16:
>
> Then I'd say it's best to tune that D#< on top as a 75/16, because
> you're likely going to hear the D# as a 5/4 resonance on top of the
> B-, which is going to be heard as a 3/2 resonance on top of the E-,
> which is going to be heard as a 5/2 on top of the C.
>

I see you have your own way of looking at things to try to make sense of
them.
I don't suscribe to this way.

On the other hand, if you play this chord:
>
> C Eb< G
> 6:7:9
>
> Then I'd say you're probably going to hear that C Eb< as a 6:7
> resonance directly on top of the C.
>
> Hope that clears things up.
>

No it doesn't clear anything up.

Also it's not the kind of example I've asked for as you're not chinging into
another chord with the 6:7:9 or something like where it shows it should be
7/6 instead of 75/64.
Furthermore I would have been even more clear if youhad taken an exmple like
5:6:7, more consonant examples are easyer to work with.

When you see your 6:7:9 = 1/1 7/6 3/2 example and see it as 1/1 75/64 3/2 it
becomes clear the many musical things you can do with it.

For instance see it as part of the harmonic minor mode 1/1 9/8 6/5 4/3 3/2
8/5 15/8 2/1
Here 1/1 75/65 3/2 you'll find as 8/5 15/8 12/5
You could for instance play this:
8/5 15/8 12/5 -> 3/2 15/8 12/5 -> 3/2 15/8 9/8 -> 6/5 3/2 2/1
chord 1 = 1/1 75/64 3/2, chord 2 = 1/1 5/4 8/5, chord 3 = 1/1 5/4 3/2, chord
4 = 1/1 5/4 5/3
when you'd play this with 7/6 instead of 75/64 it doesn't work and you get
out of tune major chord etc.

Wether it is 1/1 7/6 3/2 or 1/1 75/64 3/2 becomes not clear from simply
playing 1 chord.
I becomes musically clear which chord it is after you DO something with that
chord, like for instance my above example.
I can't DO anything with the 7th harmonic (besides parralel chords which
never end), that's the kind of example I'm asking for, what to do with the
7th harmonic that warrants it's existence in musical structure.
No example has yet been given to me and I can't find one myself. This
doesn't look good for the 7th harmonic in musical structure to me.
This and my other concerns I made in my first post have not been answered.
They should all be able to be answered and countered were the 7th harmonic
valid for musical structure (maybe i should use a different english word for
valid but I don't know which one)

Marcel

Hi Kraig,

> Euler liked 7 limit intervals hundred of years ago. Much less the Greeks
> had whole school that would not settle for any semitone than the 28/27.
> One of the most beautiful sounds in the world.
>

Did Euler ever write any music from which I can see the way he would
actually use this 7th harmonic?
Euler did however comment on compositions by Rameau thinking several times
Rameau had used the 7th harmonic in his music.
To which Rameau answered every time that it was not the 7th harmonic but
5-limit with a specific function.

Greek music math, just like arab music math wasn't perfect.
For all I know they were thinking they liked the 28/27 while they really
liked the 25/24 or some other 5-limit interval.

If the 7th harmonic is usable in the structure of music surely it should be
easy to give an example of a chord progression using the 7th harmonic?

Marcel

In the example I posted here:

http://www.box.net/shared/m37jhti1og#2:20193246

called LifeTunnel.mp3

there is a mid-register drone on A

this is accompanied by A overtone series.

Then, the A mid-register drone continues, but the bass moves up to 8/7,

and the other pitches are now B+ (8/7 from A) harmonic series.

It's rudimentary, but it's a progression.

On Feb 13, 2009, at 11:35 AM, Marcel de Velde wrote:

>
> f you play a chord like this:
>
> C G E- F# B- D#<
>
> 1 3/2 5/2 45/16 15/4 75/16:
>
> Then I'd say it's best to tune that D#< on top as a 75/16, because
> you're likely going to hear the D# as a 5/4 resonance on top of the
> B-, which is going to be heard as a 3/2 resonance on top of the E-,
> which is going to be heard as a 5/2 on top of the C.
>
> I see you have your own way of looking at things to try to make > sense of them.
> I don't suscribe to this way.
>
>
> On the other hand, if you play this chord:
>
> C Eb< G
> 6:7:9
>
> Then I'd say you're probably going to hear that C Eb< as a 6:7
> resonance directly on top of the C.
>
> Hope that clears things up.
>
> No it doesn't clear anything up.
>
> Also it's not the kind of example I've asked for as you're not > chinging into another chord with the 6:7:9 or something like where > it shows it should be 7/6 instead of 75/64.
> Furthermore I would have been even more clear if youhad taken an > exmple like 5:6:7, more consonant examples are easyer to work with.
>
> When you see your 6:7:9 = 1/1 7/6 3/2 example and see it as 1/1 > 75/64 3/2 it becomes clear the many musical things you can do with it.
>
> For instance see it as part of the harmonic minor mode 1/1 9/8 6/5 > 4/3 3/2 8/5 15/8 2/1
> Here 1/1 75/65 3/2 you'll find as 8/5 15/8 12/5
> You could for instance play this:
> 8/5 15/8 12/5 -> 3/2 15/8 12/5 -> 3/2 15/8 9/8 -> 6/5 3/2 2/1
> chord 1 = 1/1 75/64 3/2, chord 2 = 1/1 5/4 8/5, chord 3 = 1/1 5/4 > 3/2, chord 4 = 1/1 5/4 5/3
> when you'd play this with 7/6 instead of 75/64 it doesn't work and > you get out of tune major chord etc.
>
> Wether it is 1/1 7/6 3/2 or 1/1 75/64 3/2 becomes not clear from > simply playing 1 chord.
> I becomes musically clear which chord it is after you DO something > with that chord, like for instance my above example.
> I can't DO anything with the 7th harmonic (besides parralel chords > which never end), that's the kind of example I'm asking for, what to > do with the 7th harmonic that warrants it's existence in musical > structure.
> No example has yet been given to me and I can't find one myself. > This doesn't look good for the 7th harmonic in musical structure to > me.
> This and my other concerns I made in my first post have not been > answered.
> They should all be able to be answered and countered were the 7th > harmonic valid for musical structure (maybe i should use a different > english word for valid but I don't know which one)
>
> Marcel
>
>

>
> In the example I posted here:
>
> http://www.box.net/shared/m37jhti1og#2:20193246
>
> called LifeTunnel.mp3
>
> there is a mid-register drone on A
>
> this is accompanied by A overtone series.
>
> Then, the A mid-register drone continues, but the bass moves up to 8/7,
>
> and the other pitches are now B+ (8/7 from A) harmonic series.
>
> It's rudimentary, but it's a progression.
>

Thank you.
And sorry but I find it very unclear.
Not a clear musical structure but more a wash of ambient sounds.
Can you post a clear example, not audio but just 2 or more simple chords
notated in intervals (of which one or all with a 7th harmonic) with a
progression, from which one may see that the 7th harmonic is functional?

Marcel

no, if that big chord on B+ isn't clear enough to you after my explanation, I think I see the problem.

It's A overtones to B+ 8/7 overtones--couldn't be simpler than that.

But the way out of your problem is this: 7's, 11's, 13's are different critters. They don't live in the common-practice menagerie.

caleb

On Feb 13, 2009, at 12:02 PM, Marcel de Velde wrote:

>
> In the example I posted here:
>
> http://www.box.net/shared/m37jhti1og#2:20193246
>
> called LifeTunnel.mp3
>
> there is a mid-register drone on A
>
> this is accompanied by A overtone series.
>
> Then, the A mid-register drone continues, but the bass moves up to > 8/7,
>
> and the other pitches are now B+ (8/7 from A) harmonic series.
>
> It's rudimentary, but it's a progression.
>
> Thank you.
> And sorry but I find it very unclear.
> Not a clear musical structure but more a wash of ambient sounds.
> Can you post a clear example, not audio but just 2 or more simple > chords notated in intervals (of which one or all with a 7th > harmonic) with a progression, from which one may see that the 7th > harmonic is functional?
>
> Marcel
>
>
>

>
> no, if that big chord on B+ isn't clear enough to you after my explanation,
> I think I see the problem.
>
> It's A overtones to B+ 8/7 overtones--couldn't be simpler than that.
>
> But the way out of your problem is this: 7's, 11's, 13's are different
> critters. They don't live in the common-practice menagerie.
>

Do you mean it's a parallel chord, and the chords consist of many harmonic
overtones?
I don't find such an example clear.
I find only an example of non parallel chords, with harmonics no higher than
7th harmonic, with a progression in which the 7th harmonic interval is
functional, writen in JI intervals usefull for analysis.

As I've allready stated before.
Harmonics higher than 5-limit I have no problem with when they're used as
harmonic overtones and a made audible like this.
This is different than functional in musical structure within a chord
progression like i've said before.
I've given several such examples myself in the first post, and later again
to mike for 5-limit chords and progression.
All I ask for is a similar example in 7-limit.

Marcel

Marcel wrote:

> 81/64 and 5/4 are not just 2 different tunings of the same musical structure in my opinion.
> They're 2 different musical structures.
> This becomes apparent mosly because of the 2 different notes lead to different things.
> Especially 32/27 is very much used in common practice music. And it is a different note
> with a different musical meaning from 6/5.

I think you're trying to link two things which may not necessarily have much to do with each other. This "link" started to appear in actual music, if I'm not mistaken, during the 16th century when a new element occured which was totally unknown to music before -- a "chord". But even sooner, music could quite happily contain "trines" (is that what they were called then?) like C-E-G or A-C-E. At that time, the "model" systém of intonation was still Pythagorean. Now, I don't know if there's a similar term in English, but Czech has a term of something like "tonal gender", which means the property that ordinary chords can be either major or minor -- i.e. have either a major or minor "tonal gender". Since the first serious introduction of 5-limit intervals into music, the ratios of 2 and 3 have determined the "fundamental tone" according to the theory of classical harmony, and the ratios of 5 have determined the "tonal gender". But weren't there things similar to the "tonal gender" even before 5-limit intervals were seriously in use?

> Well I don't agree this is how we'd get to the 7/4 7/5 7/6 etc.
> But yes I have been expecting the 7/4 7/5 7/6 to have a unique musical function and to lead
> to new chord progressions etc.
> But I can't find it, and can't make them to work in normal chord progressions.

If you cared more about difference tones and fundamental frequencies and similar things, you'd find that there ARE some even in quite ordinary harmonic progressions. To give an example, I'll suppose the tone of C2 to have a frequency of 64Hz (just about a quartertone lower than today's C2). Okay, let's say we want to tune a progression of two intervals in JI, E3-A#3 followed by D3-B3. According to strict 5-limit rules (with no verification by actual listening), the frequencies should be 160-225Hz (i.e. 45/32) and 144-240Hz (5/3). BUT ... Now here comes the fact that not only difference tones are important in our listening but the second order difference tones as well, particularly the lower one of the two (don't know about you, but I can often clearly, VERY clearly, spot them in sounding intervals). In the case of the augmented fourth, the proper difference tone is 65Hz and the lower second difference tone is 95Hz (you see, these two make something like a mistuned fifth). In the case of the major sixth, the proper difference tone is 96Hz and the lower second difference tone is 48Hz (an exact octave). What does this mean? First, this means that you will probably find it "harmonically convincing" if you add a fifth of C2-G2 to the E3-A#3 and also add an octave of G1-G2 to the D3-B3, which results in the augmented fourth being used in a totally different way than in, for example, dominant 7th resolutions (you see, the "fundamental tone" in dominant 7th chords would be F# according to classical harmony, but here it clearly is C). And secondly, when you want to find an "acoustically convincing" way to tune this chord progression, most probably you'll use 160-224Hz for E3-A#3 (i.e. 7/5) instead of 160-225Hz (45/32). The chord progression simply is of 7-limit origin, not 5-limit.

> If you're looking for the neutral seconds you'll hopefully find more logic in 27/25 and
> 800/729 (making 32/27 together, either can come first).
> No need to bring in 7-limit.

I was not speaking of neutral seconds or thirds at all.

And one other point. If you really want to find a different "musical" meaning for 7-limit intervals compared to 5-limit ones in a similar way 5-limit intervals have different meaning than 3-limit ones, the only option I can think of right now is to use 3D temperaments and not 2D ones. This means that you would have to také a completely new view on harmony which the classical theory of harmony had never considered (bear in mind that meantone is a 2D temperament and lots of harmonic concepts have developed from temperaments similar to that). Good examples of 3D temperaments may be, I think, the "breed" temperament (which I think Graham must have thought of among the first ones because why would it be called like that then) or the recent suggestions of mine which I was calling "anti-orwell" and "ragismatic". If you want, I can post some interval sizes and mappings for the temperaments. Maybe you would find your answer somewhere there. What're you saying?

Petr

Petr Par�zek wrote:

> And one other point. If you really want to find a different �musical� meaning > for 7-limit intervals compared to 5-limit ones in a similar way 5-limit > intervals have different meaning than 3-limit ones, the only option I can think > of right now is to use 3D temperaments and not 2D ones. This means that you > would have to tak� a completely new view on harmony which the classical theory > of harmony had never considered (bear in mind that meantone is a 2D temperament > and lots of harmonic concepts have developed from temperaments similar to that). > Good examples of 3D temperaments may be, I think, the �breed� temperament (which > I think Graham must have thought of among the first ones because why would it be > called like that then) or the recent suggestions of mine which I was calling > �anti-orwell� and �ragismatic�. If you want, I can post some interval sizes and > mappings for the temperaments. Maybe you would find your answer somewhere there. > What�re you saying?

The breed temperament (2401:2400 tempered out) was Gene's name and really Gene's idea. What I did was come up with a lattice for 11-limit harmony in miracle temperament and note that it could be used more generally. Gene wrote music with it -- I forget if it's 7- or 11-limit.

Anyway, I don't agree with your point. 2D temperaments are fine for 7-limit intervals. Perhaps meantone is too simplistic but even then there's adaptive tuning (manual or otherwise) and tempered timbres. I'm going with magic now. That's good enough for 9-limit chords to make sense. With tripod notation support in LilyPond it happens that I can experiment with 3D marvel temperament by thinking about magic temperament with correct spellings. That may improve the tuning. The view will still follow magic though.

One of the implications of magic is that you have three different triads: major, minor, and subminor. The difference in the thirds between major and minor is the same as between minor and subminor. And there's one very simple cadence where a subminor resolves onto a major with the same root. I don't like this as a standard minor to major because the step's too small.

Marvel temperament implies the relationships Marcel keeps talking about, 75:64 and so on. So I have no opinion about what the "true" logic of these intervals is. You can give the subminor triad an extended 5-limit rationalization if it appeals to you.

Graham

>
> I can't DO anything with the 7th harmonic (besides parralel chords which
> never end), that's the kind of example I'm asking for, what to do with the
> 7th harmonic that warrants it's existence in musical structure.
> No example has yet been given to me and I can't find one myself. This
> doesn't look good for the 7th harmonic in musical structure to me.
> This and my other concerns I made in my first post have not been answered.
> They should all be able to be answered and countered were the 7th harmonic
> valid for musical structure (maybe i should use a different english word for
> valid but I don't know which one)
>

I have found I can easily resolve a 4:5:6:7 chord as a dominant 7th:

9:12:15:21 -> 8:12:16:20

Similarly I have worked with resolving it as a German 6th:

16:20:24:28 -> 15:20:24:30 (minor)
16:20:24:28 -> 15:20:25:30 (major)

To do this will naturally require having different kinds of 4th degrees. The one that
functions as the 7th above the 5th degree (21/16) is a different 4th than the one that is
the root of the subdominant (4/3). That is to be expected when they are performing
different musical functions. All JI when really put into practical use ends up being
"adaptive" JI.

Billy

Hi Billy,

Thank you for your examples.
I don't the time this weekend to look into it in depth but will do so on
monday.
Btw are you sure you really mean all JI becomes adaptive JI in practical
use?
Please see here the defenition of adaptive JI:
http://www.tonalsoft.com/enc/a/adaptive-ji.aspx
I can't agree to adaptive JI, but perhaps you mean you have to use commas to
which I do agree offcourse. (commas I see as a good thing with meaning)

Marcel

> I have found I can easily resolve a 4:5:6:7 chord as a dominant 7th:
>
> 9:12:15:21 -> 8:12:16:20
>
> Similarly I have worked with resolving it as a German 6th:
>
> 16:20:24:28 -> 15:20:24:30 (minor)
> 16:20:24:28 -> 15:20:25:30 (major)
>
> To do this will naturally require having different kinds of 4th degrees.
> The one that
> functions as the 7th above the 5th degree (21/16) is a different 4th than
> the one that is
> the root of the subdominant (4/3). That is to be expected when they are
> performing
> different musical functions. All JI when really put into practical use ends
> up being
> "adaptive" JI.
>
> Billy
>

Hi Billy,

Couldn't let it go for the weekend so a short reply allready :)

I have found I can easily resolve a 4:5:6:7 chord as a dominant 7th:
>
> 9:12:15:21 -> 8:12:16:20
>

I don't see how this can ever work as the dominant 7th chord in major mode.
9/8 3/2 15/8 21/8 -> 1/1 3/2 2/1 5/2
Try playing the V chord 9/8 3/2 15/8 and then over that V chord the melody
9/4 -> 5/2 -> 21/8 -> 3/1 -> 21/8 and then the full dominant 7th chord 9/8
3/2 15/8 21/8 -> 1/1 3/2 2/1 5/2
This sounds very much out of tune to me.
I've just made the major mode into a 7-limit mode?
And played a 7-limit melody over the V chord?
I think it should be this:
Playing the V chord 9/8 3/2 15/8 and then over that V chord the melody 9/4
-> 5/2 -> 8/3 -> 3/1 -> 8/3 and then the full dominant 7th chord 9/8 3/2
15/8 8/3 -> 1/1 3/2 2/1 5/2
This one sounds 100% correct to me, and makes logical sense to me.
Or should I keep the melody 5-limit and make the last dominant 7th chord 9/8
3/2 15/8 21/8? This sounds wrong to me too.
When does it become a 7-limit chord? And how to get there?
And how can a melody become 7-limit all of a sudden? Just to make a more
consonant harmony?

>
> Similarly I have worked with resolving it as a German 6th:
>
> 16:20:24:28 -> 15:20:24:30 (minor)
> 16:20:24:28 -> 15:20:25:30 (major)
>

I'll get to these later but same problems as with the sominant 7th except
that in this case it's not 16/9 vs 7/4 but 225/128 vs 7/4.

To do this will naturally require having different kinds of 4th degrees. The
> one that
> functions as the 7th above the 5th degree (21/16) is a different 4th than
> the one that is
> the root of the subdominant (4/3). That is to be expected when they are
> performing
> different musical functions. All JI when really put into practical use ends
> up being
> "adaptive" JI.
>

I'm not sure on your defenition of adaptive JI but if it means you will make
a normal 5-limit harmony 7-limit all of a sudden just to make a 7th chord
more consonant I can't see how this is right while you have no need to do so
for other reasons.
If you define 21/16 and 4/3 as 2 different 4th degrees and don't expect
21/16 to play nice with anything other than for instance the dominant 7th
chord, and are happy to accept melodic distortions (which the ear doesn't
like) and can shift at will from 4/3 to 21/16. Then I can't argue with you
over function as you don't give any function to this 21/16 other than to
make a 7-limit chord.
I can however argue that besides this 7-limit chord which by itself sounds
nice, in actual music it doesn't sound nice with other chords and melodies.

If you mean all the above differently than I described please explain.

Marcel

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
>
> Yes 225/128 is very close to 7/4 and it doesn't matter much in how it
> sounds.
> However i find it very important to know wether it should be a 225/128 or a
> 7/4 for music theory reasons.
> It's a totally different structure.
> And it doesn't have anything to do with tempering.
>

After making a lot of just-tuned MIDI's of chord progressions, I found the dominant 7th
chord based on the 7/4 to be radically different sounding than the 16:9. The 7-limit
version has a firm locked sound that no other tuning offers. I can even remember the
striking difference in my head.

As for hearing a melody sound off when you try to tune it to 7-limit, I found a similar
experience when I created a MIDI of the 5-limit major scale. The 3rd, 6th and 7th degrees
sounded audibly flat, even though they resulted in tighter sounding triads when used to
make chords. The major scale tuned to 3-limit sounds more in tune as a single melody
line.

In the polyphonic architecture chords are the consequence of simultaneously sounding
melodies, and the chord tuning is a consequence of what melody notes happen to be
heard together. And that's most likely how harmony started. But in homophonic
architecture the tables are turned, and the melody tuning is subject to the implied
harmonies. Chances are if you were imagining these harmonies while singing the melody
unaccompanied, you would unconsciously bend your pitches to tune to the harmony that
the melody seems to describe. For instance, tuning the 4th scale degree to a 4/3 if it
sounds like the root of a subdominant chord, or tuning it to a 21/16 if it sounds like the
7th of a dominant chord.

You did describe an out-of-tune sound when 7-limit tunings are used in music. But
remember that much modern music bases its very charm on bending the pitch on purpose
(C.F. You Light Up My Life). When it comes to a capella styles that have as their basis the
formation of "locked in" chords, it is part of the very style to "bend" the notes to make the
vertical sonorities sound straight, particularly in the case of barbershop.

Now when I just sing up the scale without regard to a supporting harmony, it will most
likely follow a 3-limit tuning. For the entire 25-note chromatic scale (to include all
chromatic intervals) can be generated with just a chain of pure 5ths. But the chords
generated in that system will produce harshly wide major 3rds and 6ths. If you sing the
major scale while mentally accompanying it with the chords I-V-I-IV-I-IV-V-I, you will
most likely bend the pitches toward the 5-limit tuning.

Billy

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
>
> Hi Kraig,
>
>
> > Euler liked 7 limit intervals hundred of years ago. Much less the
Greeks
> > had whole school that would not settle for any semitone than the
28/27.
> > One of the most beautiful sounds in the world.
> >
>
> Did Euler ever write any music from which I can see the way he would
> actually use this 7th harmonic?
> Euler did however comment on compositions by Rameau thinking several
times
> Rameau had used the 7th harmonic in his music.
> To which Rameau answered every time that it was not the 7th harmonic
but
> 5-limit with a specific function.
>
> Greek music math, just like arab music math wasn't perfect.
> For all I know they were thinking they liked the 28/27 while they
really
> liked the 25/24 or some other 5-limit interval.
>
> If the 7th harmonic is usable in the structure of music surely it
should be
> easy to give an example of a chord progression using the 7th harmonic?
>
> Marcel
>

I can think of several nice chord progressions in the 7-limit:

1:
63/32--2/1
27/16--7/4
45/32--3/2
9/8----1/1
(notice the small voice-leading in the top two voices)

2: (a sort of I-IV-V-I but using the 7th harmonic)
7/4----12/7---49/32--3/2
5/4----9/7----21/16--5/4
1/1----1/1----63/32--1/1
1/1----8/7----7/4----1/1

3: (a sort of I-IV-II-V-I)
7/4----12/7---32/21--49/32--3/2
5/4----9/7----4/3----21/16--5/4
1/1----1/1----40/21--63/32--1/1
1/1----8/7----32/21--7/4----1/1

4: Anything making use of specific 7-limit structures such as the
1-3-5-7 hexany:

7/4----7/4
5/3----7/4
35/24--3/2
5/4----5/4
7/6----5/4
1/1----1/1

5: Anything making use of microtonal melodies on top, such as 16/15 10/9
9/8 8/7 7/6 6/5 128/105 or something similar

6: While not strictly 7-limit, Harry Partch's tonality flux (8/7 10/7
12/7 moving to 7/6 7/5 7/4) is a noteworthy chord progression using
7-limit intervals.

and there are several others that can be used. Besides that, there have
been several successful compositions that are written in or otherwise
imply 7-limit tuning. (As an example, La Monte Young's "Well Tuned
Piano" would probably not make much sense in 5- or 11-limit tuning,
would it?)

Dear Justin,

I fully agree with you and many others here that we can have many enchanting chord progressions in 7-limit. However, this thread is a lost case, I feel. Marcel had trouble finding 7-limit in *common practice music*.

I for one am interested in 7-limit and beyond precisely because it opens a world of new harmonic possibilities to explore beyond common practice music. It seems to me the problem Marcel has might be comparable to a problem some Early Renaissance musician might have had with 5-limit. In the conventional music before the Renaissance, 3-limit prevailed. So, if that was taken as a standard, then 5-limit music was not "valid" (to use Marcel's word) at that time. It is somewhat hopeless to argue with such an attitude... So, I suggest we close this thread.

Best
Torsten

On Feb 14, 2009, at 5:00 AM, justin_tone52 wrote:
> --- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
> >
> > Hi Kraig,
> >
> >
> > > Euler liked 7 limit intervals hundred of years ago. Much less > the Greeks
> > > had whole school that would not settle for any semitone than > the 28/27.
> > > One of the most beautiful sounds in the world.
> > >
> >
> > Did Euler ever write any music from which I can see the way he would
> > actually use this 7th harmonic?
> > Euler did however comment on compositions by Rameau thinking > several times
> > Rameau had used the 7th harmonic in his music.
> > To which Rameau answered every time that it was not the 7th > harmonic but
> > 5-limit with a specific function.
> >
> > Greek music math, just like arab music math wasn't perfect.
> > For all I know they were thinking they liked the 28/27 while they > really
> > liked the 25/24 or some other 5-limit interval.
> >
> > If the 7th harmonic is usable in the structure of music surely it > should be
> > easy to give an example of a chord progression using the 7th > harmonic?
> >
> > Marcel
> >
>
> I can think of several nice chord progressions in the 7-limit:
>
> 1:
> 63/32--2/1
> 27/16--7/4
> 45/32--3/2
> 9/8----1/1
> (notice the small voice-leading in the top two voices)
>
> 2: (a sort of I-IV-V-I but using the 7th harmonic)
> 7/4----12/7---49/32--3/2
> 5/4----9/7----21/16--5/4
> 1/1----1/1----63/32--1/1
> 1/1----8/7----7/4----1/1
>
> 3: (a sort of I-IV-II-V-I)
> 7/4----12/7---32/21--49/32--3/2
> 5/4----9/7----4/3----21/16--5/4
> 1/1----1/1----40/21--63/32--1/1
> 1/1----8/7----32/21--7/4----1/1
>
> 4: Anything making use of specific 7-limit structures such as the > 1-3-5-7 hexany:
>
> 7/4----7/4
> 5/3----7/4
> 35/24--3/2
> 5/4----5/4
> 7/6----5/4
> 1/1----1/1
>
> 5: Anything making use of microtonal melodies on top, such as 16/15 > 10/9 9/8 8/7 7/6 6/5 128/105 or something similar
>
> 6: While not strictly 7-limit, Harry Partch's tonality flux (8/7 > 10/7 12/7 moving to 7/6 7/5 7/4) is a noteworthy chord progression > using 7-limit intervals.
>
> and there are several others that can be used. Besides that, there > have been several successful compositions that are written in or > otherwise imply 7-limit tuning. (As an example, La Monte Young's > "Well Tuned Piano" would probably not make much sense in 5- or 11-> limit tuning, would it?)
>

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:

> Btw are you sure you really mean all JI becomes adaptive JI in practical
> use?
> Please see here the defenition of adaptive JI:
> http://www.tonalsoft.com/enc/a/adaptive-ji.aspx
> I can't agree to adaptive JI, but perhaps you mean you have to use commas to
> which I do agree offcourse. (commas I see as a good thing with meaning)

I really mean adaptive in the loose sense of having to make adjustments, sometimes
choosing between equally desirable alternatives. One example is the well-known puzzle of
vi-ii-V-I, which you may have mentioned. There are so many alternative solutions I get a
headache thinking about it. Among these are: keeping the chord roots on the Pythagorean
scale, allowing for a pure circle-of-fifth progressions. A variant of that idea is keeping the
fundamentals of the chords on the Pythagorean scale, which means giving minor chords a
different treatment. Either way you will be making extensive comma adjustments,
particularly in the 2nd and 6th degrees.

If you know "Five Foot Two, Eyes of Blue", this song accentuates the circle of fifths
progression. If you opt for Pythagorean root tuning to ensure a progression of pure fifths
back to the tonic on "girl", you will hear a comma adjustment in the melody at "Eyes". If
you opt for the 5-limit root tunings of the III and VI chords, this is at the expense of a
root movment of a wolf fifth to the II "anybody" chord. So either way there is no getting
out of being "adaptive". Even the definition of adaptive JI needs to be adaptive.

Billy

Hi Justin,

Thank you very much for taking the trouble to make these examples.
I have too little time today but I'll have a good look tomorrow.

Marcel

can think of several nice chord progressions in the 7-limit:
>
> 1:
> 63/32--2/1
> 27/16--7/4
> 45/32--3/2
> 9/8----1/1
> (notice the small voice-leading in the top two voices)
>
> 2: (a sort of I-IV-V-I but using the 7th harmonic)
> 7/4----12/7---49/32--3/2
> 5/4----9/7----21/16--5/4
> 1/1----1/1----63/32--1/1
> 1/1----8/7----7/4----1/1
>
> 3: (a sort of I-IV-II-V-I)
> 7/4----12/7---32/21--49/32--3/2
> 5/4----9/7----4/3----21/16--5/4
> 1/1----1/1----40/21--63/32--1/1
> 1/1----8/7----32/21--7/4----1/1
>
> 4: Anything making use of specific 7-limit structures such as the 1-3-5-7
> hexany:
>
> 7/4----7/4
> 5/3----7/4
> 35/24--3/2
> 5/4----5/4
> 7/6----5/4
> 1/1----1/1
>
> 5: Anything making use of microtonal melodies on top, such as 16/15 10/9
> 9/8 8/7 7/6 6/5 128/105 or something similar
>
> 6: While not strictly 7-limit, Harry Partch's tonality flux (8/7 10/7 12/7
> moving to 7/6 7/5 7/4) is a noteworthy chord progression using 7-limit
> intervals.
>
> and there are several others that can be used. Besides that, there have
> been several successful compositions that are written in or otherwise imply
> 7-limit tuning. (As an example, La Monte Young's "Well Tuned Piano" would
> probably not make much sense in 5- or 11-limit tuning, would it?)
>

Hi Torsten,

I fully agree with you and many others here that we can have many
> enchanting chord progressions in 7-limit. However, this thread is a
> lost case, I feel. Marcel had trouble finding 7-limit in *common
> practice music*.
>

Yes mainly in common practice music, but actually in general.
Although common practice music is easyest to analyse and see what is the
underlying structure and tuning.

I for one am interested in 7-limit and beyond precisely because it
> opens a world of new harmonic possibilities to explore beyond common
> practice music. It seems to me the problem Marcel has might be
> comparable to a problem some Early Renaissance musician might have
> had with 5-limit. In the conventional music before the Renaissance, 3-
> limit prevailed. So, if that was taken as a standard, then 5-limit
> music was not "valid" (to use Marcel's word) at that time. It is
> somewhat hopeless to argue with such an attitude... So, I suggest we
> close this thread.
>

Oh nonono.
Since just about everybody on this list beleives in 7-limit or higher and
uses it all the time, I don't think you can acuse me of following a
standard.
I too beleived in the 7th (and still have not written it off) but the more I
understand 5-limit the less sense the 7th harmonic makes to me in musical
structure.
I think it's a very interesting and important question that you can't easily
push away and don't do any justice by simply calling it a personal "hopeless
attitude".

Marcel

Marcel wrote:

> Yes mainly in common practice music, but actually in general.
> Although common practice music is easyest to analyse and see what is the underlying
> structure and tuning.

First, in my last reply to your messages, I've suggested a particular harmonic progression which is apparently 7-limit from the origin. And then, I've suggested using 3D temperaments like breed or "anti-orwell", which you could try out as well -- as I said earlier, if you wish, I can post some interval sizes and mappings for you to be able to play in these tunings.

Petr

Hi Billy,

After making a lot of just-tuned MIDI's of chord progressions, I found the
> dominant 7th
> chord based on the 7/4 to be radically different sounding than the 16:9.
> The 7-limit
> version has a firm locked sound that no other tuning offers. I can even
> remember the
> striking difference in my head.
>

Oh yes I completely agree.
The 7/4 is very different from 16/9, and I love that firm locked sound.
I do know of a tuning that also gives that sound.
It's very slightly different, but 1/1 5/4 3/2 225/128 does it for me too.
However I would use neither 7/4 or 225/128 as a V7 leading to I.
It doesn't work out for me melodically.

> As for hearing a melody sound off when you try to tune it to 7-limit, I
> found a similar
> experience when I created a MIDI of the 5-limit major scale. The 3rd, 6th
> and 7th degrees
> sounded audibly flat, even though they resulted in tighter sounding triads
> when used to
> make chords. The major scale tuned to 3-limit sounds more in tune as a
> single melody
> line.
>

Hmm I had a different experience.
For me only the 6th degree sounded too low when play the 5-limit major
scale.
But I found out why that was.
I was playing it like this 1: C 1/1, 2: D 9/8, 3: E 5/4, 4: F 4/3, 5: G
3/2, 6: A 5/3, 7: B 15/8, 8: C 2/1
Now how I was playing it was with a steady rhythm, 1 2 3 4 5 6 7 8
This rhythm I was subconsciously dividing in 1 2 3 4 1(5) 2(6) 3(7) 4(8)
When playing this way my ear was expecting 5 6 7 8 to be a perfect
repetition of 1 2 3 4.
This works on a normal piano offcourse and my guess is many people are used
to hearing the scale like this when they play it like this.
This is why the 7th degree sounded too low for me, I was expecting A 27/16.
So the way I naturally heared the major scale when playing like this was not
actually the real major scale but a scale made up of the first part of the
major scale then a modulation of 3/2 up and then again that first part.
But when I take rhythm and modulations and other things into account, I've
found that 5-limit gives exactly the perfect melodies I hear in my head and
allways heard in my head.
I don't beleive melody is 3-limit natually, and much research has been done
which shows melody is naturally at least 5-limit.

> In the polyphonic architecture chords are the consequence of simultaneously
> sounding
> melodies, and the chord tuning is a consequence of what melody notes happen
> to be
> heard together. And that's most likely how harmony started. But in
> homophonic
> architecture the tables are turned, and the melody tuning is subject to the
> implied
> harmonies. Chances are if you were imagining these harmonies while singing
> the melody
> unaccompanied, you would unconsciously bend your pitches to tune to the
> harmony that
> the melody seems to describe. For instance, tuning the 4th scale degree to
> a 4/3 if it
> sounds like the root of a subdominant chord, or tuning it to a 21/16 if it
> sounds like the
> 7th of a dominant chord.
>

Well one could see it another way.
Melody beeing 5-limit or 7-limit naturally, which gives many different
structures and possibilities that are close together.
All these different possibilities are actually different melodies with
different musical meaning.
It is when you play chords that you simply limit the number of possibilities
and therefore give clearer meaning / view to the melody.
So chords don't make the melody, they just shine a light on which melodies
are beeing played.
I'm not saying this is the way it is, only giving an alternative
explanation.
Perhaps you are right about melody beeing retuned for the sake of chords,
but it does not have to be this way it seems to me.

> You did describe an out-of-tune sound when 7-limit tunings are used in
> music. But
> remember that much modern music bases its very charm on bending the pitch
> on purpose
> (C.F. You Light Up My Life). When it comes to a capella styles that have as
> their basis the
> formation of "locked in" chords, it is part of the very style to "bend" the
> notes to make the
> vertical sonorities sound straight, particularly in the case of barbershop.
>

Well this is one way to look at it.
Another way to look at it is that in harmony the notes that are beeing
bended by a comma are actually not thesame note in the underlying harmonic
structure.
For example: when playing 1/1 5/4 3/2 -> 6/5 3/2 9/5 does 5/4 go down by
25/24 or can you say that the musical structure is so that 1/1 goes to 6/5
and 5/4 goes to 3/2 etc.
And that this still hold when playing an inversion of 6/5 3/2 9/5 like for
instance 2/1 5/2 3/1 -> 9/5 6/5 3/2.
I tend to see for instance the syntonic comma 81/80 in thesame way. The note
doesn't slide by 81/80 but another new note from a different location comes
to 81/80 off the other note (which is in itself off to a new location).
This could also explain why 1/1 5/4 3/2 -> 1/1 6/5 3/2 sounds so bad. Yet
the above example doesn't.

> Now when I just sing up the scale without regard to a supporting harmony,
> it will most
> likely follow a 3-limit tuning. For the entire 25-note chromatic scale (to
> include all
> chromatic intervals) can be generated with just a chain of pure 5ths. But
> the chords
> generated in that system will produce harshly wide major 3rds and 6ths.
>

Hmm I don't think the pure 5th chromatic scale is how music works on the
basic level you mean.

> If you sing the
> major scale while mentally accompanying it with the chords
> I-V-I-IV-I-IV-V-I, you will
> most likely bend the pitches toward the 5-limit tuning.
>

Yes agreed. But not agreed that if you don't do this you'll sing 3-limit :)

Marcel

>
> I really mean adaptive in the loose sense of having to make adjustments,
> sometimes
> choosing between equally desirable alternatives. One example is the
> well-known puzzle of
> vi-ii-V-I, which you may have mentioned. There are so many alternative
> solutions I get a
> headache thinking about it.
>

Ugh I know.

> Among these are: keeping the chord roots on the Pythagorean
> scale, allowing for a pure circle-of-fifth progressions. A variant of that
> idea is keeping the
> fundamentals of the chords on the Pythagorean scale, which means giving
> minor chords a
> different treatment. Either way you will be making extensive comma
> adjustments,
> particularly in the 2nd and 6th degrees.
>
> If you know "Five Foot Two, Eyes of Blue", this song accentuates the circle
> of fifths
> progression. If you opt for Pythagorean root tuning to ensure a progression
> of pure fifths
> back to the tonic on "girl", you will hear a comma adjustment in the melody
> at "Eyes". If
> you opt for the 5-limit root tunings of the III and VI chords, this is at
> the expense of a
> root movment of a wolf fifth to the II "anybody" chord. So either way there
> is no getting
> out of being "adaptive". Even the definition of adaptive JI needs to be
> adaptive.
>

Ah yes, this defenition of adaptive I can live with :)
And you can't live without commas (although I like them and their sound and
clarity they give)
But see my above message on why it doesn't need to be adaptive in the true
sense of the word.
I agree root progression seems to go pythagorean a lot, but I have many
examples where this is not the case.
Also it most often goes pythagorean up to a certain point, for instance till
32/27 or 81/64, but just about never 243/128 but instead 15/8.
Long story, deserves its own thread someday.

I really like our conversation btw :)

Marcel

>
> First, in my last reply to your messages, I've suggested a particular
> harmonic progression which is apparently 7-limit from the origin. And then,
> I've suggested using 3D temperaments like breed or „anti-orwell", which you
> could try out as well -- as I said earlier, if you wish, I can post some
> interval sizes and mappings for you to be able to play in these tunings.

Hi Petr,

Sorry! I missed it.
Had read it partly at first then replied to other messages then forgot which
one I had to check back on.
Too many messages.
Reading it now and tomorrow I'll have the time again to try things out and
give an answer.

Marcel

>
> Another way to look at it is that in harmony the notes that are beeing
> bended by a comma are actually not thesame note in the underlying harmonic
> structure.
> For example: when playing 1/1 5/4 3/2 -> 6/5 3/2 9/5 does 5/4 go down by
> 25/24 or can you say that the musical structure is so that 1/1 goes to 6/5
> and 5/4 goes to 3/2 etc.
> And that this still hold when playing an inversion of 6/5 3/2 9/5 like for
> instance 2/1 5/2 3/1 -> 9/5 6/5 3/2.
> I tend to see for instance the syntonic comma 81/80 in thesame way. The
> note doesn't slide by 81/80 but another new note from a different location
> comes to 81/80 off the other note (which is in itself off to a new
> location).
> This could also explain why 1/1 5/4 3/2 -> 1/1 6/5 3/2 sounds so bad. Yet
> the above example doesn't.
>

I'd like to add to this to make my reply more clear.
What I mean with this is that you said 7-limit must come to make harmony
more perfect and melody will folow.
What I ment with my above reply was that this does not need to be so
nessecarily, it depends on how you look at it.
I'm however not saying that even if my way of looking at commas etc is
correct, this would mean the 7th harmonic has no place in the structure of
music.
This is still possible, only the structure changes and other things start to
weigh more.
Merely saying that the 7th harmonic may not be nessecary or logical,
depending on how things may work on the most basic level to create harmony
and melody and how the 2 work together in music.

Marcel

Sorry if I bring down level of conversation, which is really good.

I always *assumed* that 5/4 to 6/5 sounds bad is because it is a small interval.

To some extent, each chord mushes together with the one following, making a
combination of the two chords. If that combination is tense, it doesn't sound good.

I suspect you will reject this explanation, as it is fairly primitive.

> This could also explain why 1/1 5/4 3/2 -> 1/1 6/5 3/2 sounds so > bad. Yet the above example doesn't.
>
> ...
>
> Marcel
>
>
>

Dear Marcel,

On Feb 15, 2009, at 9:47 AM, Marcel de Velde wrote:
>> Marcel had trouble finding 7-limit in *common practice music*.
>>
>
>
> Yes mainly in common practice music, but actually in general.

I am somewhat reluctant to keep posting on this matter.

Anyway, I am a bit surprised by this reply. So, what is your problem then? Do you argue that intervals like 7/4 or 6/7 are consonant? Or do you argue that when hearing 6/7 we are actually perceiving some 5-limit interval? Or do you argue that such intervals have ever been used in music?

Best
Torsten

> I am somewhat reluctant to keep posting on this matter.
>
> Anyway, I am a bit surprised by this reply. So, what is your problem
> then? Do you argue that intervals like 7/4 or 6/7 are consonant? Or
> do you argue that when hearing 6/7 we are actually perceiving some 5-
> limit interval? Or do you argue that such intervals have ever been
> used in music?
>
> Best
> Torsten

Hello Torsten,

This is an excerpt from the post that started it all:

Marcel wrote:
> I'm not prejudiced against 7-limit.
> Infact I really want the harmonic 7th to be valid!
> I started out a few years ago expecting music to be based on the harmonic overtones.
> First tried to make things work and make sense of all harmonics, making scales which used up to the 31th
> overtone.
> Gradually as I worked things out more I received at a theory which makes me expect the 11th harmonic
> and higher are not relevant to music. (this is not what I wish to discuss here now)
> But the 7th harmonic is still a little bit open, though I'm allmost ready to see the 7th as an overtone only
> and not part of the musical structure.

Do you see why it caused such a huge backlash now? I've said all I
need to say on the matter, but this notion that 7-limit and higher
intervals are musically useless didn't draw such a backlash just
because we are immature children who love to argue. For instance, it's
sort of antithetical to everything I'm trying to do with music right
now, and it seems a fairly arbitrary distinction.

The comments that AKJ writes "crappy out of tune music" because of his
use of 7-limit intervals weren't much appreciated either.

And if you want to post a 7-limit example to demonstrate, good luck,
as you'll get an insulting response and chastisement on how it's
really a mistuned 5-limit example with all of your 7/6's being "out of
tune" versions of 75/64 and so on and so forth and how you're
"completely lost."

I'm going back to lurking now, as even posting a recap of the whole
thing is irritating in and of itself.

-Mike

Hi Torsten,

Sorry to hear this topic isn't much fun to you.
If you don't wish to reply no problem I won't take it personal :)

Anyway, I am a bit surprised by this reply. So, what is your problem
> then? Do you argue that intervals like 7/4 or 6/7 are consonant? Or
> do you argue that when hearing 6/7 we are actually perceiving some 5-
> limit interval? Or do you argue that such intervals have ever been
> used in music?
>

Yes I argue that when we are hearing 7/6 we are actually hearing for
instance 75/64.
Same as for instance when you play C - Eb in 12tet you may be hearing 6/5 or
32/27 or 75/64 etc.

And I'm arguing that not only are for instance 32/27 and 75/64 often played
as 7/6 wrongly.
I'm also asking in which case does the 7/6 really does belong to be there,
as I don't know.

Marcel

Hi Petr,

Thanks for your message and sorry for the late reply!

I think you're trying to link two things which may not necessarily have much
> to do with each other. This „link" started to appear in actual music, if I'm
> not mistaken, during the 16th century when a new element occured which was
> totally unknown to music before -- a „chord". But even sooner, music could
> quite happily contain „trines" (is that what they were called then?) like
> C-E-G or A-C-E. At that time, the „model" systém of intonation was still
> Pythagorean.
>

Ah yes I agree they were tuning to pythagorean system, but I don't think
their music was pythagorean.
Just like we now use 12tet but I beleive the actual underlying way music
works is pure JI, I beleive the old music, and all music has allways been
pure JI no matter how you tune it. It's just that when you tune it
differently you're out of tune.

Now, I don't know if there's a similar term in English, but Czech has a term
> of something like „tonal gender", which means the property that ordinary
> chords can be either major or minor -- i.e. have either a major or minor
> „tonal gender". Since the first serious introduction of 5-limit intervals
> into music, the ratios of 2 and 3 have determined the „fundamental tone"
> according to the theory of classical harmony, and the ratios of 5 have
> determined the „tonal gender". But weren't there things similar to the
> „tonal gender" even before 5-limit intervals were seriously in use?
>
>
Yes I beleive there was tonal gender before the music theory progressed a
little a recognized this.
Btw I don't beleive 3/2 allways determines the fundamental tone.
It depends on the musical context.
I for instance beleive that 1/1 6/5 3/2 can have different origins.
One beeing an inversion of 1/1 5/4 5/3, where the fundamental of 1/1 6/5 3/2
is actually 6/5.
And one beeing the "mirror" of 1/1 5/4 3/2 - 1/1 6/5 3/2 which has it's
fundamental as 1/1.
They appear at different places in JI and have different meaning.

> If you cared more about difference tones and fundamental frequencies and
> similar things, you'd find that there ARE some even in quite ordinary
> harmonic progressions. To give an example, I'll suppose the tone of C2 to
> have a frequency of 64Hz (just about a quartertone lower than today's C2).
> Okay, let's say we want to tune a progression of two intervals in JI, E3-A#3
> followed by D3-B3. According to strict 5-limit rules (with no verification
> by actual listening), the frequencies should be 160-225Hz (i.e. 45/32) and
> 144-240Hz (5/3). BUT ... Now here comes the fact that not only difference
> tones are important in our listening but the second order difference tones
> as well, particularly the lower one of the two (don't know about you, but I
> can often clearly, VERY clearly, spot them in sounding intervals).
>
Ohmy, are we talking about difference tones (nonlinear distortion) or
beating here :)
I'm not getting into this discussion again haha
But I beleive I still have not heard a single difference tone, though have
heard beat notes and it's not clear how they behave in chords, beleive
someone is still investigating this on this list.

> In the case of the augmented fourth, the proper difference tone is 65Hz and
> the lower second difference tone is 95Hz (you see, these two make something
> like a mistuned fifth). In the case of the major sixth, the proper
> difference tone is 96Hz and the lower second difference tone is 48Hz (an
> exact octave). What does this mean? First, this means that you will probably
> find it „harmonically convincing" if you add a fifth of C2-G2 to the E3-A#3
> and also add an octave of G1-G2 to the D3-B3, which results in the augmented
> fourth being used in a totally different way than in, for example, dominant
> 7th resolutions (you see, the „fundamental tone" in dominant 7th chords
> would be F# according to classical harmony, but here it clearly is C). And
> secondly, when you want to find an "acoustically convincing" way to tune
> this chord progression, most probably you'll use 160-224Hz for E3-A#3 (i.e.
> 7/5) instead of 160-225Hz (45/32). The chord progression simply is of
> 7-limit origin, not 5-limit.
>
>
You make it sound nice and appear fairly logical.
But how can you get these kinds of things from difference tones or beat
notes?
Since surely when you play the above things in some inversion or transpose a
few of the notes by an octave for instance, you will get totally different
difference tones / beat notes which would imply a totally different
structure according to your reasoning above?
I don't beleive difference tones / beat notes are at the ground of music the
way you descrbe it now and I dont find it a convincing appeal for the 7th
harmonic.
Maybe you are indeed on to something relevant to music in a way, I don't
know, but the way described now doesn't make me think this is a solid
theory.

> > If you're looking for the neutral seconds you'll hopefully find more
> logic in 27/25 and
> > 800/729 (making 32/27 together, either can come first).
> > No need to bring in 7-limit.
>
> I was not speaking of neutral seconds or thirds at all.
>
> And one other point. If you really want to find a different „musical"
> meaning for 7-limit intervals compared to 5-limit ones in a similar way
> 5-limit intervals have different meaning than 3-limit ones, the only option
> I can think of right now is to use 3D temperaments and not 2D ones. This
> means that you would have to také a completely new view on harmony which the
> classical theory of harmony had never considered (bear in mind that meantone
> is a 2D temperament and lots of harmonic concepts have developed from
> temperaments similar to that). Good examples of 3D temperaments may be, I
> think, the „breed" temperament (which I think Graham must have thought of
> among the first ones because why would it be called like that then) or the
> recent suggestions of mine which I was calling „anti-orwell" and
> „ragismatic". If you want, I can post some interval sizes and mappings for
> the temperaments. Maybe you would find your answer somewhere there. What're
> you saying?
>

These are real temperaments (tempered tunings) you're referring to right?
Not pure JI?
I'm not interested in any tempered tuning, only in pure JI.
Thanks for the offer though!

I've allready experimented a lot with different pure JI 7-limit scales over
the past years, also very large scales, so this is not the issue.
As for different musical meaning for 7-limit intervals and a completely new
view on harmony (and melody).
Yes I think you may be right in this.
My original question was about both these things. It was about 7-limit not
beeing right in normal common practice music, and about if and how then the
7th harmonic should be used in music.
I don't know much about 2D and 3D. I allways figured 5-limit to be 3D in a
way with the octaves beeing 1 dimension, the 3/2 etc beeing the 2nd
dimension and the 5/4 / 6/5 etc beeing the third dimension. 7-limit would be
4D then.

Marcel

Hi Justin,

I can think of several nice chord progressions in the 7-limit:
>
> 1:
> 63/32--2/1
> 27/16--7/4
> 45/32--3/2
> 9/8----1/1
> (notice the small voice-leading in the top two voices)
>

This is the same as an earlyer example.
It is parallel chords which does not make clear any underlying musical
structure.
And it can also be
9/8 45/32 27/16 2/1 -> 1/1 5/4 3/2 16/9 for instance.

2: (a sort of I-IV-V-I but using the 7th harmonic)
> 7/4----12/7---49/32--3/2
> 5/4----9/7----21/16--5/4
> 1/1----1/1----63/32--1/1
> 1/1----8/7----7/4----1/1
>

> 3: (a sort of I-IV-II-V-I)
> 7/4----12/7---32/21--49/32--3/2
> 5/4----9/7----4/3----21/16--5/4
> 1/1----1/1----40/21--63/32--1/1
> 1/1----8/7----32/21--7/4----1/1
>

What's your reasoning behind making these 7-limit?
As this can all be played perfectly in 5-limit where it'll sound much beter
/ more natural, and make musical sense.
I'll give the 5-limit examples of the above later.

> 4: Anything making use of specific 7-limit structures such as the 1-3-5-7
> hexany:
>
> 7/4----7/4
> 5/3----7/4
> 35/24--3/2
> 5/4----5/4
> 7/6----5/4
> 1/1----1/1
>

Ok so this is 1/1 5/4 5/3 + 1/1 5/4 3/2 only shifted upwards by 7/6, then
1/1 5/4 3/2 7/4
I can't tell, may very well be 7-limit indeed.
But you could do something similar in 5-limit aswell in many different ways
for instance 1/1 32/27 5/4 40/27 5/3 16/9 -> 1/1 5/4 3/2 16/9
But both don't make much musical sense to me and sound extremely dissonant.

>
>
> 5: Anything making use of microtonal melodies on top, such as 16/15 10/9
> 9/8 8/7 7/6 6/5 128/105 or something similar
>
> 6: While not strictly 7-limit, Harry Partch's tonality flux (8/7 10/7 12/7
> moving to 7/6 7/5 7/4) is a noteworthy chord progression using 7-limit
> intervals.
>
> and there are several others that can be used. Besides that, there have
> been several successful compositions that are written in or otherwise imply
> 7-limit tuning. (As an example, La Monte Young's "Well Tuned Piano" would
> probably not make much sense in 5- or 11-limit tuning, would it?)
>

La Monte Young's well tuned piano is the way I hear it partly playing with
harmonic overtones (which I've stated before as beeing no-limit offcourse)
which I place myself more in the sound domain than in the music domain. And
some other parts it's more like sound art where I can't make any tuning of
it, and in other parts it sounds to me as if it has musical structure but
very much out of tune (so yes I do expect those parts to be 5-limit
probably)
In any case the well tuned piano doesn't strike me as a song with a strong
musical structure that has to be based on 7-limit.

Marcel

How about the obvious question: If you can't differentiate between
75/64 and 7/6 by ear, how can you reasonably say that 7/6 sounds "out
of tune" and 75/64 sounds "in tune?" For all you know, every instance
of 7/6 you've heard could really be 75/64, and as you've said
yourself, there isn't much of a way to tell.

-Mike

On Mon, Feb 16, 2009 at 2:12 AM, Marcel de Velde <m.develde@...> wrote:
> Hi Justin,
>>
>> I can think of several nice chord progressions in the 7-limit:
>>
>> 1:
>> 63/32--2/1
>> 27/16--7/4
>> 45/32--3/2
>> 9/8----1/1
>> (notice the small voice-leading in the top two voices)
>
> This is the same as an earlyer example.
> It is parallel chords which does not make clear any underlying musical
> structure.
> And it can also be
> 9/8 45/32 27/16 2/1 -> 1/1 5/4 3/2 16/9 for instance.
>
>> 2: (a sort of I-IV-V-I but using the 7th harmonic)
>> 7/4----12/7---49/32--3/2
>> 5/4----9/7----21/16--5/4
>> 1/1----1/1----63/32--1/1
>> 1/1----8/7----7/4----1/1
>>
>> 3: (a sort of I-IV-II-V-I)
>> 7/4----12/7---32/21--49/32--3/2
>> 5/4----9/7----4/3----21/16--5/4
>> 1/1----1/1----40/21--63/32--1/1
>> 1/1----8/7----32/21--7/4----1/1
>
> What's your reasoning behind making these 7-limit?
> As this can all be played perfectly in 5-limit where it'll sound much beter
> / more natural, and make musical sense.
> I'll give the 5-limit examples of the above later.
>
>>
>> 4: Anything making use of specific 7-limit structures such as the 1-3-5-7
>> hexany:
>>
>> 7/4----7/4
>> 5/3----7/4
>> 35/24--3/2
>> 5/4----5/4
>> 7/6----5/4
>> 1/1----1/1
>
> Ok so this is 1/1 5/4 5/3 + 1/1 5/4 3/2 only shifted upwards by 7/6, then
> 1/1 5/4 3/2 7/4
> I can't tell, may very well be 7-limit indeed.
> But you could do something similar in 5-limit aswell in many different ways
> for instance 1/1 32/27 5/4 40/27 5/3 16/9 -> 1/1 5/4 3/2 16/9
> But both don't make much musical sense to me and sound extremely dissonant.
>
>>
>> 5: Anything making use of microtonal melodies on top, such as 16/15 10/9
>> 9/8 8/7 7/6 6/5 128/105 or something similar
>>
>> 6: While not strictly 7-limit, Harry Partch's tonality flux (8/7 10/7 12/7
>> moving to 7/6 7/5 7/4) is a noteworthy chord progression using 7-limit
>> intervals.
>>
>> and there are several others that can be used. Besides that, there have
>> been several successful compositions that are written in or otherwise imply
>> 7-limit tuning. (As an example, La Monte Young's "Well Tuned Piano" would
>> probably not make much sense in 5- or 11-limit tuning, would it?)
>
> La Monte Young's well tuned piano is the way I hear it partly playing with
> harmonic overtones (which I've stated before as beeing no-limit offcourse)
> which I place myself more in the sound domain than in the music domain. And
> some other parts it's more like sound art where I can't make any tuning of
> it, and in other parts it sounds to me as if it has musical structure but
> very much out of tune (so yes I do expect those parts to be 5-limit
> probably)
> In any case the well tuned piano doesn't strike me as a song with a strong
> musical structure that has to be based on 7-limit.
> Marcel
>

Hi Mike,

> How about the obvious question: If you can't differentiate between
> 75/64 and 7/6 by ear, how can you reasonably say that 7/6 sounds "out
> of tune" and 75/64 sounds "in tune?" For all you know, every instance
> of 7/6 you've heard could really be 75/64, and as you've said
> yourself, there isn't much of a way to tell.
>

Well, most of the time people use a 7/4 when it should be 16/9, this is a
big difference.
Same thing for 32/27 vs 7/6.
And also when they use 7/6 when one should use 75/64, and then for instance
the root goes down by 16/15 and 75/64 will form 5/4 with 16/15 there
shouldn't be a comma, and other things like that.
And maybe I can hear it in some compositions I don't know.
But again the most obvious ones are intervals like 7/4 vs 16/9 that are off
many cents. And 7-limit modulations which are very obviously out of tune
too.
But I also hear a lot of 5-limit errors in peoples music.
Most people here don't understand how and when to use 81/80 and try their
very best to avoid this comma making everything out of tune as a result.
I can go on and on, but I don't think I've ever heard a piece of music here
that's completely in tune.
Which isn't that surprising since nobody here seems to know how JI really
works :)

Marcel

> Which isn't that surprising since nobody here seems to know how JI really
> works :)
> Marcel

You are completely obnoxious and full of yourself. If you want to stop
provoking arguments, don't post irritating statements like this.
Perhaps your objective here is to troll?

And for the record, yes, if you're trying to fit everything into a
5-limit modal structure, 7-limit intervals will likely be
comma-adjusted substitutes for what should be 5-limit intervals. If
your goal is to develop a 7-limit framework for music, try starting
with a 7-limit modal structure from the beginning.

I still think it's hilarious that you wrote off Aaron Johnson's
compositions as "crappy out of tune music." Since you're the only guy
around here who seems to be capable of writing music, why not post
some of your own compositions? I'm sure they're extremely inspired.

-Mike

>
> > Which isn't that surprising since nobody here seems to know how JI really
> > works :)
> > Marcel
>
> You are completely obnoxious and full of yourself. If you want to stop
> provoking arguments, don't post irritating statements like this.
> Perhaps your objective here is to troll?
>

Haha very funny I looked up the meaning of "to troll" and this is what I
found first:
http://en.wikipedia.org/wiki/Troll_(gay_slang)

But I guess/hope you mean the other meaning.
http://en.wikipedia.org/wiki/Troll_(Internet)

Mike, I make statements like "nobody here seems to know how JI really works"
first and foremost because I mean them.
And it bugs the hell out of me how almost a whole list seems to follow wrong
logic in how they tune.
I care for music and JI and it's a little bit frustrating to see things
leading to not much on this list.
But when I make such a statement I realise it is controversial and provoking
on this list, ye i will not not say it because of those reasons, so i say it
with a smile.
I think maybe for a very small part i also say it to build up an
expectation, as I'm excited about the music converted to JI i will post
later on this list.
I no way am I full of myself. I'm full of correct JI, I love JI and have the
highest respect for JI. You seem to mistake this for personal ego, but it's
not.

Now you on the other hand do something I really don't like.
You're calling me names, making personal attacks and trying to put me down
on a personal level.
This i really really don't like but i try not to behave back in a similar
manner.
Thinking of it perhaps this also partly provokes me in a way in making
strong statements about correct JI.

And for the record, yes, if you're trying to fit everything into a
> 5-limit modal structure, 7-limit intervals will likely be
> comma-adjusted substitutes for what should be 5-limit intervals. If
> your goal is to develop a 7-limit framework for music, try starting
> with a 7-limit modal structure from the beginning.
>

Thank you! Finally at least a little bit recognition and sense.
Nobody else here seems to accept that view.
Yes I've tried 7-limit modal structure from the beginning.
It doesn't make sense for common practice music, and I don't know how it
would work in any other way.
Everything I try I can't seem to escape the 5-limit modal stucture, unless I
use 7-limit or higher limit purely as overtones at which point there's not
much musical structure but mainly making "sound effect".
The way I started 5-limit vs 7-limit thread was truly an honest question of
which I hoped to get examples that would convince me the 7th harmonic has a
place in musical structure.

I still think it's hilarious that you wrote off Aaron Johnson's
> compositions as "crappy out of tune music." Since you're the only guy
> around here who seems to be capable of writing music, why not post
> some of your own compositions? I'm sure they're extremely inspired.

I don't remember what I said about his compositions, but I find it very
unlikely I commented on his compositional skill or called his compositions
crappy.
I may have called his tuning crappy, it's a different thing.
When I see and hear everybody is doing it wrong I should just keep my mouth
shut?

Marcel

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:

> When I see and hear everybody is doing it wrong I should just keep
>my mouth
> shut?
>
> Marcel
>

No, quite the opposite. You are making too little sound, not too
much.

By this I mean: post examples of "doing it right".

-Cameron Bobro

Though I don't think one nessecarily needs audio to talk about such things,
I do agree :)
Working on it as I write.
3 compositions in JI. GSTQ, Beethoven's Drei Equali, and Lassus Vicentino.

Marcel

No, quite the opposite. You are making too little sound, not too
> much.
>
> By this I mean: post examples of "doing it right".
>

> Mike, I make statements like "nobody here seems to know how JI really works"
> first and foremost because I mean them.
> And it bugs the hell out of me how almost a whole list seems to follow wrong
> logic in how they tune.
> I care for music and JI and it's a little bit frustrating to see things
> leading to not much on this list.
> But when I make such a statement I realise it is controversial and provoking
> on this list, ye i will not not say it because of those reasons, so i say it
> with a smile.

It's not that it's controversial. It's that the way you say it is as
though everyone is stupid. If you have a new idea about JI, feel free
to post it. If it's frustrating to you that people are making small
comma-adjustment errors, then post something about it. Sure. If you
take the attack and insult people from the getgo on the matter, people
won't be receptive.

Also, if you post anything about how it's impossible to get 7-limit JI
to form any coherent musical structure, expect a lot of dissent,
especially when a lot of us here enjoy 7 and 11-limit music, and not
just naively because we're hearing huge 5-limit modes.

For example, I particularly love the neutral 11 chord:

C Ev G Bv D F#v
Where the C-Ev dyad is 9:11 and the C-G is 3:2.

At first I heard that chord as being musically useless and out of
tune, sounding like a bastardized version of both major and minor. It
would "flip back and forth" in my mind between the two. Now, however,
I find it to be an extremely beautiful and complicated chord, and I'm
using it extensively in the string quartet I'm writing. I'm sure there
are 5-limit intervals that lie close to 9:11, but I also like the way
that 9:11 resonates. Why should I not assume those two characteristics
in tandem mean that 9:11 is the right interval for what I want? It
certainly seems to fit the bill for my uses, and it only sounds "out
of tune" if you don't like the sound of the neutral triad, which not
everyone does, as it's pretty out there.

> I think maybe for a very small part i also say it to build up an
> expectation, as I'm excited about the music converted to JI i will post
> later on this list.
> I no way am I full of myself. I'm full of correct JI, I love JI and have the
> highest respect for JI. You seem to mistake this for personal ego, but it's
> not.
> Now you on the other hand do something I really don't like.
> You're calling me names, making personal attacks and trying to put me down
> on a personal level.
> This i really really don't like but i try not to behave back in a similar
> manner.
> Thinking of it perhaps this also partly provokes me in a way in making
> strong statements about correct JI.
//
> I don't remember what I said about his compositions, but I find it very
> unlikely I commented on his compositional skill or called his compositions
> crappy.
> I may have called his tuning crappy, it's a different thing.
> When I see and hear everybody is doing it wrong I should just keep my mouth
> shut?
> Marcel

I'm responding to the two statements above at once.

Regarding personal attacks and AKJ's music: I linked you to a few of
AKJ's compositions to demonstrate the capabilities of 7-limit music.
While a few of them have some startling root movement in them, I found
that I got used to it as a while and started to like it. You listened
to it for 2 seconds and you responded with how I write "crappy out of
tune music" and how I should "get my ears checked" and that it "serves
no musical purpose". They weren't my compositions, but rather Aaron
Johnson's.

He's one of my favorite microtonal composers ever, so for me to see
you write it off like that is extremely irritating. I've learned a lot
about 7-limit structure from studying some of the stuff he's done -
his "Melancholic" was the first piece that got me into hearing the
difference between subminor triads and minor chords, and his "Lost in
Appalachia" was one of the first pieces that got me into hearing what
a 6:7:9 triad could sound like as the tonic of a piece of music.

But what irritated me more than anything was your attitude towards the
whole thing. You didn't suggest tuning something differently, and what
you did say you said in the most insulting way possible. You said he
wrote crappy out of tune music, that we were all "completely lost,"
that only you seem to know how to "do JI right", etc. These are all
personal attacks. How do you expect people to act?

I apologize for responding with a personal attack of my own. I wanted
you to see how your statements were being interpreted by others.

>> And for the record, yes, if you're trying to fit everything into a
>> 5-limit modal structure, 7-limit intervals will likely be
>> comma-adjusted substitutes for what should be 5-limit intervals. If
>> your goal is to develop a 7-limit framework for music, try starting
>> with a 7-limit modal structure from the beginning.
>
> Thank you! Finally at least a little bit recognition and sense.
> Nobody else here seems to accept that view.
> Yes I've tried 7-limit modal structure from the beginning.
> It doesn't make sense for common practice music, and I don't know how it
> would work in any other way.

Well, 7-limit intervals aren't going to fit into a 5-limit modal
structure because a 5-limit modal structure is 5-limit by definition.
Septimal intervals introduce new commas: sorting these out is a new
challenge. Common practice music does utilize some pretty "out"
5-limit structures, such as 75/64 and so on. It is mostly 5-limit
except for a few instances, and to try and substitute 7/6 in for 75/64
is simply not going to sound good.

I don't see why this means that 7/6 ALWAYS has to be 75/64.

On the other hand, try a mode like:

D E F< G< A B C< D

Where notes like F<, G<, and C< are tuned a septimal comma flat, so
that the D-C is a perfect 7/4. You can then make a chord like:

D F< A C< E G< B

Which is a bunch of stacked alternating 6:7 and 7:9 thirds.

I like that scale: it's sort of a "septimal dorian" scale. There are
some interesting sounds there, and I don't see any reason why the
7/6's there should be 75/64's. Sure, you could come up with a 5-limit
mode that has a few comma adjustments and sounds similar, but I don't
see why that should be a prerequisite for being musically valid.

Of course, at first it's going to sound like all of the minor thirds
are flat. Getting it to sound like chords that simply have a different
tonality from 6:5 chords is a sort of trick that I haven't figured out
quite how it works yet, but I'm starting to get the hang of it.

> Everything I try I can't seem to escape the 5-limit modal stucture, unless I
> use 7-limit or higher limit purely as overtones at which point there's not
> much musical structure but mainly making "sound effect".
> The way I started 5-limit vs 7-limit thread was truly an honest question of
> which I hoped to get examples that would convince me the 7th harmonic has a
> place in musical structure.

5-limit intervals were once overtones that only existed to make sound
effects. Music evolved from that. How did that happen, exactly? I
suspect the answer will provide some clues to see how a more complex
and exotic type of music could evolve from 7-limit intervals.

I think that 5-limit intervals evolve into what is commonly called
"music" once chord progressions are added - not only do we have
chords, but we've come up with a pleasing way to lead themselves into
one another. This, mixed with phenomena such as the priming effect -
that an Eb major played before a C-G dyad will cause the C-G dyad to
take on a subtle "minor" quality due to the memory of the Eb -
generally comprise what we call "music".

None of these things are really related inherently to "music" -
rather, they are psychological phenomena that we're making use of, and
the end result is something we call "music." So when you say that
7-limit intervals might have no relevance to "musical structure," I
say that musical structure is an emergent property of several
intersecting psychological and psychoacoustic phenomena, and that the
inclusion of 7-limit intervals will create its own musical structure.

Another interesting time to use 7:4: if you're landing on a major
chord, and that major chord isn't the I chord, but rather something
else - something unstable, like a bVI chord or a II chord or something
- putting a 7:4 on top of the chord to make it a 4:5:6:7 is often a
very nice effect. It causes an extremely strong fundamental to jump
out, which only makes it want to resolve even more.

I mentioned II7 because the 7/4 on top of the II7 chord will
definitely be a septimal comma flat of the tonic. Nonetheless, I hear
that as a different note - it's close in pitch to the tonic, but it
isn't the tonic. Small comma shifts can be used to extremely
interesting melodic effect.

Another thing that started to make higher-limit intervals work for my
predominantly 5-limit ear was to play them a bit softer than the rest
of the intervals in the chord - that way you get the feel of the
"quality" of this new chord without having the comma shift sticking
out at you like a sore thumb. It also puts it on a different "level"
than the rest of the harmony, which I find useful.

Note also that comma-adjusted intervals are only "out of tune" if you
don't like them - a few of the examples that you said sound "out of
tune" have grown on me over time and I now hear them as simply being
more complex.

-Mike

Hi Mike,

Thanks for taking the time and troube to write your email.

you responded with how I write "crappy out of
> tune music" and how I should "get my ears checked" and that it "serves
> no musical purpose".
>

I'm sorry for saying such things.
I guess I said it after an allready started argument after which I felt
personally attacked and not taken seriously.
But I should not have said those things like that. My apologies.

I'll give a reply to the rest of your email today as soon as I have the
time.

Marcel

Hi Marcel,

sorry for the late reply, I had lots of work at school recently.

You wrote:

> Ah yes I agree they were tuning to pythagorean system, but I don't think their music was
> pythagorean.
> Just like we now use 12tet but I beleive the actual underlying way music works is pure JI, I
> beleive the old music, and all music has allways been pure JI no matter how you tune it. It's
> just that when you tune it differently you're out of tune.

I’m not sure what you mean by „pure JI“ but please bear in mind that 14th century musicians were not thinking about the 5-limit dimmension and therefore were not considering an 81/64 to be a „mistuned“ 5/4 or whatever; because they were not considering 5-limit factors to be „valid for music“. The first ideas about 5-limit factors were mentioned during the 15th century when musicians discovered the Pythagorean diminished fourth which is just about 2 cents away from 5/4.

> I for instance beleive that 1/1 6/5 3/2 can have different origins.
> One beeing an inversion of 1/1 5/4 5/3, where the fundamental of 1/1 6/5 3/2 is actually 6/5.
> And one beeing the "mirror" of 1/1 5/4 3/2 - 1/1 6/5 3/2 which has it's fundamental as 1/1.
> They appear at different places in JI and have different meaning.

Excuse me, you are confusing „bass tone“ and „fundamental tone“. According to classical harmony, if you play C2-E3-A3-E4, then the bass tone is C and the fundamental tone is A. And if you play E2-E3-C4-A4, then the bass tone is E and the fundamental tone is also A. So the position of the fifth (no matter if it’s a falling fourth or a rising fifth) DOES determine the fundamental tone.

> But I beleive I still have not heard a single difference tone, though have heard beat notes
> and it's not clear how they behave in chords, beleive someone is still investigating this
> on this list.

You know what? Just for your experience, I’ve made a recording of two pairs of interval progressions. The two recordings are essentially the same, only the first of them is „dry“ and the second one has some reverb added. I think that you can know what I’m talking about when you listen to these examples. Here they are:
#1: www.sendspace.com/file/7linyb
#2: www.sendspace.com/file/0hgkuu

> You make it sound nice and appear fairly logical.
> But how can you get these kinds of things from difference tones or beat notes?
> Since surely when you play the above things in some inversion or transpose a few of the
> notes by an octave for instance, you will get totally different difference tones / beat notes
> which would imply a totally different structure according to your reasoning above?

Okay, in case of relative frequencies of 5 and 7, the proper difference tone is 2 and the lower second difference tone is 3. In case of 7 and 10, they are 3 and 4, respectively. Is that such a radical change?

> I don't beleive difference tones / beat notes are at the ground of music the way you descrbe
> it now and I dont find it a convincing appeal for the 7th harmonic.
> Maybe you are indeed on to something relevant to music in a way, I don't know, but the
> way described now doesn't make me think this is a solid theory.

Okay, this is where we differ significantly. I couldn’t agree with your view unless you gave me evidence why it doesn’t work. For me it has always worked perfectly and it has confirmed lots of classical harmony concepts to me. And remember, this is not something I’m making up somewhere in mi mind just to have something to say, this is my description of what I can hear.

> These are real temperaments (tempered tunings) you're referring to right?
> Not pure JI?
> I'm not interested in any tempered tuning, only in pure JI.

You are apparently not thinking about one very important fact. The only musical concept (concerning common-practice music) which has its origins in 5-limit JI is the concept of single chords as usable musical elements. But a vast majority of properties in Baroque and classical harmony has its origins in meantone temperaments, not in JI, and people would never have found them meaningful and thought of using them in music if meantone temperaments had not been known of. And then, there were many many harmonic progressions favored in romanticism which musicians would probably never have thought of if there were no circular temperaments. You can’t directly say that every harmonic progression or structure has its origin in JI because it doesn’t have. For most of Baroque and classical music, the model for harmony was the meantone temperament, which means that the comma we are tempering out here is 81/80. But you can, of course, come up with totally different models for harmonic structures, once you choose a different comma to be tempered out -- which is exactly what I did about a year ago when I made „Run Down The Whistle“ -- I think even you heard it then, didn’t you?

Petr

<<< Excuse me, you are confusing „bass tone" and „fundamental tone". According to
classical harmony, if you play C2-E3-A3-E4, then the bass tone is C and the fundamental
tone is A. And if you play E2-E3-C4-A4, then the bass tone is E and the fundamental tone is
also A. So the position of the fifth (no matter if it's a falling fourth or a rising fifth) DOES
determine the fundamental tone. >>>

The bass is just the lowest sounding note. The root is the note you're talking about that is
the "1th" degree of the chord. The fundamental in the true sense of the word refers to the
note which is in the same pitch class as the fundamental of the harmonic series that the
chord is tuned to. In the case of the C2-E3-A3-E4 tuned in 5-limit, the bass is C2 and the
root is A3, but the fundamental is actually F. If the chord is tuned differently, the
fundamental will be different. If the chord is tempered, the fundamental is undefined.

Billy

William Gard wrote:

> The fundamental in the true sense of the word refers to the
> note which is in the same pitch class as the fundamental of the harmonic series that the
> chord is tuned to. In the case of the C2-E3-A3-E4 tuned in 5-limit, the bass is C2 and the
> root is A3, but the fundamental is actually F.

Okay, here comes the fact that English is not my native language and that I had all my harmony lessons in Czech. Czech actually has to distinguish between the "acoustical" fundamental frequency and the "harmonical" fundamental tone, where the latter actually is what you meant by "root".

Petr

Hello Petr,

> I'm not sure what you mean by „pure JI" but please bear in mind that 14th
> century musicians were not thinking about the 5-limit dimmension and
> therefore were not considering an 81/64 to be a „mistuned" 5/4 or whatever;
> because they were not considering 5-limit factors to be „valid for music".
> The first ideas about 5-limit factors were mentioned during the 15th century
> when musicians discovered the Pythagorean diminished fourth which is just
> about 2 cents away from 5/4.
>

I ment that when a 14th century musician was playing the major scale for
instance, or played C E G, that even if he tuned it to 1/1 81/64 3/2 he
would probably have used it as if it were 1/1 5/4 3/2 etc, so in this
respect 81/64 would have been a mistuned 5/4. Even though they were not
aware of this themselves.
I also find it probable that people didn't tune very exact to 81/64 in that
time, and that choirs for instance would have surely sung 5/4 even though
they thought it was 81/64.

> > I for instance beleive that 1/1 6/5 3/2 can have different origins.
> > One beeing an inversion of 1/1 5/4 5/3, where the fundamental of 1/1 6/5
> 3/2 is actually 6/5.
> > And one beeing the "mirror" of 1/1 5/4 3/2 - 1/1 6/5 3/2 which has it's
> fundamental as 1/1.
> > They appear at different places in JI and have different meaning.
>
> Excuse me, you are confusing „bass tone" and „fundamental tone". According
> to classical harmony, if you play C2-E3-A3-E4, then the bass tone is C and
> the fundamental tone is A. And if you play E2-E3-C4-A4, then the bass tone
> is E and the fundamental tone is also A. So the position of the fifth (no
> matter if it's a falling fourth or a rising fifth) DOES determine the
> fundamental tone.
>
>
Yes very possible I'm confuning names as I'm not good with names.
Though I don't mean merely the bass. Maybe I mean root as Billy described
but then think E C A can have 2 functions (or more) in music, with different
roots as I described before.

> > But I beleive I still have not heard a single difference tone, though
> have heard beat notes
> > and it's not clear how they behave in chords, beleive someone is still
> investigating this
> > on this list.
>
> You know what? Just for your experience, I've made a recording of two pairs
> of interval progressions. The two recordings are essentially the same, only
> the first of them is „dry" and the second one has some reverb added. I think
> that you can know what I'm talking about when you listen to these examples.
> Here they are:
> #1: www.sendspace.com/file/7linyb
> #2: www.sendspace.com/file/0hgkuu
>
>
I'm sorry but I'm at my girlfriends house where I can only access google /
google mail but not the rest of the internet. (wireless paid internet that
lets you search google but then you have to pay to access those pages,
luckily this also allows me to see gmail.)
I will check them on sunday when I get back home.

> You make it sound nice and appear fairly logical.
> > But how can you get these kinds of things from difference tones or beat
> notes?
> > Since surely when you play the above things in some inversion or
> transpose a few of the
> > notes by an octave for instance, you will get totally different
> difference tones / beat notes
> > which would imply a totally different structure according to your
> reasoning above?
>
> Okay, in case of relative frequencies of 5 and 7, the proper difference
> tone is 2 and the lower second difference tone is 3. In case of 7 and 10,
> they are 3 and 4, respectively. Is that such a radical change?
>
> > I don't beleive difference tones / beat notes are at the ground of music
> the way you descrbe
> > it now and I dont find it a convincing appeal for the 7th harmonic.
> > Maybe you are indeed on to something relevant to music in a way, I don't
> know, but the
> > way described now doesn't make me think this is a solid theory.
>
> Okay, this is where we differ significantly. I couldn't agree with your
> view unless you gave me evidence why it doesn't work. For me it has always
> worked perfectly and it has confirmed lots of classical harmony concepts to
> me. And remember, this is not something I'm making up somewhere in mi mind
> just to have something to say, this is my description of what I can hear.
>
> > These are real temperaments (tempered tunings) you're referring to right?
> > Not pure JI?
> > I'm not interested in any tempered tuning, only in pure JI.
>
> You are apparently not thinking about one very important fact. The only
> musical concept (concerning common-practice music) which has its origins in
> 5-limit JI is the concept of single chords as usable musical elements. But a
> vast majority of properties in Baroque and classical harmony has its origins
> in meantone temperaments, not in JI, and people would never have found them
> meaningful and thought of using them in music if meantone temperaments had
> not been known of.
>
I can agree only because of practical reasons meantone has been good but
beleive the underlying way music works is JI, also for music written in
meantone.

> And then, there were many many harmonic progressions favored in romanticism
> which musicians would probably never have thought of if there were no
> circular temperaments. You can't directly say that every harmonic
> progression or structure has its origin in JI because it doesn't have. For
> most of Baroque and classical music, the model for harmony was the meantone
> temperament, which means that the comma we are tempering out here is 81/80.
>
Yes but just because they used meantone doesn't mean the reason meantone
works isn't because of JI.
Meantone I see as playing pure JI out of tune, and it has the great benefit
for the composer that he/she doesn't have to think about commas etc, making
certain music much easyer (and other music impossible, like arabic music)

> But you can, of course, come up with totally different models for harmonic
> structures, once you choose a different comma to be tempered out -- which is
> exactly what I did about a year ago when I made „Run Down The Whistle" -- I
> think even you heard it then, didn't you?
>
> Petr
>
No I didn't hear it, can you send the link, I'll be able to hear it
tomorrow.
Marcel

Marcel wrote:

> Yes but just because they used meantone doesn't mean the reason meantone works isn't
> because of JI.

If you také the often discussed example of the „C a d G C“ triads, you’ll realize that you have to temper out the syntonic comma if you want to preserve at least one common tone in consecutive chords and you don’t want to end up lower than where you started. Meanwhile, if you play major triads of „Ab C E G#“, you have to temper out the diesis of 128/125 if you don’t want to end up lower than where you started. If harmony were based on 5-limit JI, then 18th or 19th century musicians would never ever have thought of such harmonic progressions. 12-equal is usable for both of these examples because it tempers out both 81/80 and 128/125. BUT .. There are lots of other commas and dieses which aren‘t tempered out in 12-equal and therefore they can be effectively used in music only if we use a different tuning than 12-equal. For example, let’s say you want to play this chord progression in 5-limit JI and you want to always preserve at least one tone’s pitch in consecutive chords: „C A f# B g# C#“. See what’s happened? Because I’m using „meantone-like“ notation, the root is called C at the beginning and C# at the end. But in 5-limit JI, the last chord is higher than the first by 250/243, which is about a quartertone in size. If you make a temperament where this interval changes into unison (which is porcupine), then the first and last chord will be the same. But if you try to play this in 12-equal, you’ll end up one step higher than where you started.
Or let’s také a different set of triads: „Cb ab Db Bb G e A F# D# B#“. Again, because the standard notation is based on meantone, the first and last note have different names. But in 5-limit JI, in fact, the difference between the first and the last pitch is 78732/78125, which is ONLY about 13 cents in size. If you make a temperament where this small interval turns into unison (which is semisixths), the first and last chord will be the same. But if you try to play this in 12-equal, again, the last chord will be one step higher.

BTW: The piece which I made yesterday is in porcupine, and the one from last year (to which I’m sending the link now) is in semisixths: www.sendspace.com/file/bv3dvj

Petr

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:

>
> I ment that when a 14th century musician was playing the major
scale for
> instance, or played C E G, that even if he tuned it to 1/1 81/64 3/
2 he
> would probably have used it as if it were 1/1 5/4 3/2 etc, so in
this
> respect 81/64 would have been a mistuned 5/4. Even though they were
not
> aware of this themselves.
> I also find it probable that people didn't tune very exact to 81/64
in that
> time, and that choirs for instance would have surely sung 5/4 even
though
> they thought it was 81/64.

> Marcel
>

But you don't tune 81/64 by matching the 81st partial of one tone to
the 64th partial of another. In a world where C-G-D in pure fifths is
a perfect harmony (iow, in reality :-) ), "81/64" is just two pure
fifths away.

And the higher harmonics do show up one after the other as you
combine ever more colorful melodies and harmonies, even as you stick,
theoretically, to the lower prime limit. Like the aforementioned
diminished Pyth. 4th. Then check out, in 5-limit, what lies a
syntonic comma under 16/9, for example.

>
> If you také the often discussed example of the „C a d G C" triads, you'll
> realize that you have to temper out the syntonic comma if you want to
> preserve at least one common tone in consecutive chords and you don't want
> to end up lower than where you started.

There's never a need for tempering.
If I understand what you mean correctly, when you play consecutive chords
who sais they have to be in the same scale, when you play consecutive chords
you play the root along a scale for instance and the chord can move syntonic
commas or other commas from tones in the previous chord.

> Meanwhile, if you play major triads of „Ab C E G#", you have to temper out
> the diesis of 128/125 if you don't want to end up lower than where you
> started.

No you don't have to temper it out.
First of all the chord you just gave is not constucted of consecutive 5/4
intervals but of 1/1 5/4 8/5 2/1
But even if it was constructed of consecutive 5/4 intervals giving 128/125
you get the following situation.
You can either play inversions of thesame chord in which case you do indeed
end up lower but the chord changes (though doesn't make much sense as you'd
get a 128/125 interval in the chord).
Or you can follow a different scale with the root of the chord, forinstance
1/1 > 5/4 > 8/5 2/1 in which case you don't end up lower.
But if you wish to really use the chord made up out of consecutive 5/4
intervals and end up lower you can.
But normally it's 1/1 5/4 8/5 2/1 or an inversion of this.

> If harmony were based on 5-limit JI, then 18th or 19th century musicians
> would never ever have thought of such harmonic progressions.

Wether they would have thought about it and wether it is how it is are 2
different things.

> 12-equal is usable for both of these examples because it tempers out both
> 81/80 and 128/125. BUT .. There are lots of other commas and dieses which
> aren't tempered out in 12-equal and therefore they can be effectively used
> in music only if we use a different tuning than 12-equal. For example, let's
> say you want to play this chord progression in 5-limit JI and you want to
> always preserve at least one tone's pitch in consecutive chords: „C A f# B
> g# C#". See what's happened? Because I'm using „meantone-like" notation, the
> root is called C at the beginning and C# at the end. But in 5-limit JI, the
> last chord is higher than the first by 250/243, which is about a quartertone
> in size. If you make a temperament where this interval changes into unison
> (which is porcupine), then the first and last chord will be the same. But if
> you try to play this in 12-equal, you'll end up one step higher than where
> you started.
> Or let's také a different set of triads: „Cb ab Db Bb G e A F# D# B#".
> Again, because the standard notation is based on meantone, the first and
> last note have different names. But in 5-limit JI, in fact, the difference
> between the first and the last pitch is 78732/78125, which is ONLY about 13
> cents in size. If you make a temperament where this small interval turns
> into unison (which is semisixths), the first and last chord will be the
> same. But if you try to play this in 12-equal, again, the last chord will be
> one step higher.

I'm not sure which point you're making with the above.
But you can do anything you want in 5-limit JI and not run into any
problems.

Marcel

>
> But you don't tune 81/64 by matching the 81st partial of one tone to
> the 64th partial of another. In a world where C-G-D in pure fifths is
> a perfect harmony (iow, in reality :-) ), "81/64" is just two pure
> fifths away.
>
> And the higher harmonics do show up one after the other as you
> combine ever more colorful melodies and harmonies, even as you stick,
> theoretically, to the lower prime limit. Like the aforementioned
> diminished Pyth. 4th. Then check out, in 5-limit, what lies a
> syntonic comma under 16/9, for example.
>

I'm not saying 81/64 is not a usefull interval.
Was merely saying that it is usually not the correct interval in the major
triad which is usually 1/1 5/4 3/2.
A syntonic comma under 16/9 lies 225/128, very beautifull tone in the german
sixth chord if I got the name correct (can't look it up now)

Marcel

Marcel wrote:

> If I understand what you mean correctly, when you play consecutive chords who sais
> they have to be in the same scale, when you play consecutive chords you play the root
> along a scale for instance and the chord can move syntonic commas or other commas
> from tones in the previous chord.

You have completely misunderstood what I was saying. Okay, I see I’ll have to explain more. Suppose you have a C major triad where the relative frequencies are 1/1 for C, 5/4 for E, and 3/2 for G. Now let’s change it to an A minor and leave the lower two pitches the same. So the relative frequencies become 1/1, 5/4, 5/3. Now we want a D minor and we want the pitch of the A to stay the same. So we get 10/9, 4/3, 5/3. Now we want a G major and we want the D to have the same pitch as before. So we get 25/27, 10/9, 40/27. And now we want a C major and we want the G to have the same pitch as before. So we get 80/81, 100/81, 40/27. You see, the final C major is a syntonic comma lower than the initial C major. And if you don’t want this to happen, you simply have to temper out this comma, which is exactly what meantone temperaments do.

> First of all the chord you just gave is not constucted of consecutive 5/4 intervals but of 1/1
> 5/4 8/5 2/1
> But even if it was constructed of consecutive 5/4 intervals giving 128/125 you get the
> following situation.
> You can either play inversions of thesame chord in which case you do indeed end up lower
> but the chord changes (though doesn't make much sense as you'd get a 128/125 interval
> in the chord).
> Or you can follow a different scale with the root of the chord, forinstance 1/1
> 5/4 8/5 2/1 in which case you don't end up lower.

Again, you’re completely misunderstanding the meaning of what I was saying. Okay, suppose we have an Ab major triad with relative frequencies of 4/5 for Ab, 1/1 for C, and 6/5 for Eb. Now we want a C major triad and we wish to preserve the pitch of the C. So we get 3/4 for G, 1/1 for C, and 5/4 for E. Now we want an E major and we want to preserve the E from the previous chord. So we get 25/32, 15/16, 5/4. Now we want a G# major and we wish to preserve the G#. So we get 25/32, 125/128, 75/64. You see, the last triad is a diesis lower than the first one. And if you don’t want this to happen, you have to temper out the diesis, which is possible in temperaments like augmented (in the 2D field) or 12-equal (in the 1D field).

> I'm not sure which point you're making with the above.

And I don’t know what’s unclear.

Petr

>
> You have completely misunderstood what I was saying. Okay, I see I'll have
> to explain more. Suppose you have a C major triad where the relative
> frequencies are 1/1 for C, 5/4 for E, and 3/2 for G. Now let's change it to
> an A minor and leave the lower two pitches the same. So the relative
> frequencies become 1/1, 5/4, 5/3. Now we want a D minor and we want the
> pitch of the A to stay the same. So we get 10/9, 4/3, 5/3. Now we want a G
> major and we want the D to have the same pitch as before. So we get 25/27,
> 10/9, 40/27. And now we want a C major and we want the G to have the same
> pitch as before. So we get 80/81, 100/81, 40/27. You see, the final C major
> is a syntonic comma lower than the initial C major. And if you don't want
> this to happen, you simply have to temper out this comma, which is exactly
> what meantone temperaments do.
>

Aah ok I understand what you mean now.
In the case above I don't think music moves like that and the sequence you
described contains modulations.
So it will go for instance like 1/1 5/4 3/2 -> 1/1 5/4 5/3 -> 9/8 27/20
27/16 -> 9/8 3/2 15/8 -> 1/1 5/4 3/2
It's a comma pump.
There are several solutions but they all contain a modulation / are not in a
base mode.
You can write this down in 12tet with held notes so it seems that there is
no solution, but a 12tet held note can contain a JI comma shift since 12tet
tempers this out it is not modifying the composition.
The reason this doesn't work in your above example is that you're setting
12tet rules for preserving the pitch of a note in the next chord, these
rules don't work in JI / are unmusical rules.
If you absolutely must use these rules than yes you will end up lower /
higher than you started.

Again, you're completely misunderstanding the meaning of what I was saying.
> Okay, suppose we have an Ab major triad with relative frequencies of 4/5 for
> Ab, 1/1 for C, and 6/5 for Eb. Now we want a C major triad and we wish to
> preserve the pitch of the C. So we get 3/4 for G, 1/1 for C, and 5/4 for E.
> Now we want an E major and we want to preserve the E from the previous
> chord. So we get 25/32, 15/16, 5/4. Now we want a G# major and we wish to
> preserve the G#. So we get 25/32, 125/128, 75/64. You see, the last triad is
> a diesis lower than the first one. And if you don't want this to happen, you
> have to temper out the diesis, which is possible in temperaments like
> augmented (in the 2D field) or 12-equal (in the 1D field).
>

Same as above, this is a comma pump and you can solve it with a modulation
in JI.
Marcel

Marcel wrote:

> There are several solutions but they all contain a modulation / are not in a base mode.

I don't know what you mean by base mode.

> The reason this doesn't work in your above example is that you're setting 12tet rules
> for preserving the pitch of a note in the next chord, these rules don't work in JI
> / are unmusical rules.

For one thing, the requirement of preserving pitches in consecutive chords is NOT specific to 12-equal; and, for another thing, it isn't an "unmusical rule". It's a mystery to me where you've got this statement. If on one hand you want to ask about 7-limit intervals being "valid for music" but on the other hand you say that preserving pitches is an "unmusical rule", then you're against yourself and I can't comment on that because you seem to be the only person saying this. Earlier today, I gave you two example harmonic progressions where I also preserved pitches in chords and I showed you that both of them were unusable in 12-equal because the actual commas aren't tempered out in 12-equal (and that people would possibly never have thought about these progressions if they kept stuck with 12-equal), with which I meant to explain that some harmonic progressions have their origin in characteristic properties of JI and others have their origin in properties of temperaments. To that, you replied you didn't know what point I was trying to make. So I wonder if we'll ever be able to understand each other.

Petr

> For one thing, the requirement of preserving pitches in consecutive chords
> is NOT specific to 12-equal; and, for another thing, it isn't an „unmusical
> rule". It's a mystery to me where you've got this statement. If on one hand
> you want to ask about 7-limit intervals being „valid for music" but on the
> other hand you say that preserving pitches is an „unmusical rule", then
> you're against yourself and I can't comment on that because you seem to be
> the only person saying this. Earlier today, I gave you two example harmonic
> progressions where I also preserved pitches in chords and I showed you that
> both of them were unusable in 12-equal because the actual commas aren't
> tempered out in 12-equal (and that people would possibly never have thought
> about these progressions if they kept stuck with 12-equal), with which I
> meant to explain that some harmonic progressions have their origin in
> characteristic properties of JI and others have their origin in properties
> of temperaments. To that, you replied you didn't know what point I was
> trying to make. So I wonder if we'll ever be able to understand each other.
>
> Petr

Where are these two example progressions? I'd like to see them.

Marcel thinks that when we hear a quarter comma meantone major chord
we're really hearing a mistuned 4:5:6. Also that when we move from C
major to a detuned G major it's like we're hearing movement by a
mistuned 3:2. So I think he's trying to figure out the way that we'd
perceive a comma pump like Cmaj-Amin-Dmin-G7 - is it a mistuned
version of some JI progression?

Mike wrote:

> Where are these two example progressions? I'd like to see them.

Towards the end of this message (there are also links to the music I'm mentioning there): /tuning/topicId_81042.html#81692

> Marcel thinks that when we hear a quarter comma meantone major chord
> we're really hearing a mistuned 4:5:6. Also that when we move from C
> major to a detuned G major it's like we're hearing movement by a
> mistuned 3:2. So I think he's trying to figure out the way that we'd
> perceive a comma pump like Cmaj-Amin-Dmin-G7 - is it a mistuned
> version of some JI progression?

The reason why we ran into this discussion is that I�ve suggested him to try 3d temperaments if he wanted to find a possible �musical� explanation for 7-limit intervals. To that, he answered he was only interested in JI and not in temperaments. But if he doesn�t want to admit that some harmonic progressions have no equivalent in JI and their use in music is just a result of using temperaments, then, instead of having one problem, he�s got two.

Petr

Petr Par�zek wrote:

> For one thing, the requirement of preserving pitches in consecutive chords is > NOT specific to 12-equal; and, for another thing, it isn�t an �unmusical rule�. > It�s a mystery to me where you�ve got this statement. If on one hand you want to <snip>

It sounds like a "no true Scotsman" fallacy:

http://www.logicalfallacies.info/notruescotsman.html

- all music works in 5-limit JI

- your example doesn't work in 5-limit JI

- therefore your example isn't musical

Graham

>
> For one thing, the requirement of preserving pitches in consecutive chords
> is NOT specific to 12-equal; and, for another thing, it isn't an „unmusical
> rule". It's a mystery to me where you've got this statement.

Yes it is unmusical to link chords together preserving pitches from the last
chord in the way you did in your examples.
You've shown so yourself by showing this causes overall pitches to drop or
rise.

> If on one hand you want to ask about 7-limit intervals being „valid for
> music" but on the other hand you say that preserving pitches is an
> „unmusical rule", then you're against yourself and I can't comment on that
> because you seem to be the only person saying this.

I'm not contradicting myself in any way here.
And I can't imagine I'm the only person saying this.
Just about everybody who's even remotely serious about JI will know about
comma pumps and that the overall pitch shouldn't fall or rise.

> Earlier today, I gave you two example harmonic progressions where I also
> preserved pitches in chords and I showed you that both of them were unusable
> in 12-equal because the actual commas aren't tempered out in 12-equal (and
> that people would possibly never have thought about these progressions if
> they kept stuck with 12-equal), with which I meant to explain that some
> harmonic progressions have their origin in characteristic properties of JI
> and others have their origin in properties of temperaments. To that, you
> replied you didn't know what point I was trying to make. So I wonder if
> we'll ever be able to understand each other.

I still don't know what point you're making with this.
I thought your point was to convince me of using a temperament, which in
itself was a way to convince me of the way you think one should use the
prime 7 in musical structure.
What you're saying above speaks against using 12tet for certain things, to
which I can offcourse agree.
I've also told you several times I don't like temperaments. Then you tried
to convince me of why temperaments are usefull, to which I replied no you
can do those things in JI, etc etc.
But I have no idea the point you're trying to make with the chord
progressions that don't work in 12tet, and how this speaks against JI and
how this will make me want to use yet another temperament.

Infact I have no idea anymore what we're talking about.
All I asked for was a simple written JI example of why a certain chord with
a certain progression would have to have the prime 7.

Marcel

>
> Towards the end of this message (there are also links to the music I'm
> mentioning there): /tuning/topicId_81042.html#81692
>

Sorry I can't hear any music from the internet connection I have now, can
only access gmail.
Will listen tomorrow.

>
> > Marcel thinks that when we hear a quarter comma meantone major chord
> > we're really hearing a mistuned 4:5:6. Also that when we move from C
> > major to a detuned G major it's like we're hearing movement by a
> > mistuned 3:2. So I think he's trying to figure out the way that we'd
> > perceive a comma pump like Cmaj-Amin-Dmin-G7 - is it a mistuned
> > version of some JI progression?
>
> The reason why we ran into this discussion is that I've suggested him to
> try
> 3d temperaments if he wanted to find a possible „musical" explanation for
> 7-limit intervals. To that, he answered he was only interested in JI and
> not
> in temperaments. But if he doesn't want to admit that some harmonic
> progressions have no equivalent in JI and their use in music is just a
> result of using temperaments, then, instead of having one problem, he's got
> two.
>

No I don't have to admit certain harmonic progressions have no equivalent in
JI because it simply isn't true.
And this is not a problem at all.

Marcel

>
> It sounds like a "no true Scotsman" fallacy:
>
> http://www.logicalfallacies.info/notruescotsman.html
>
> - all music works in 5-limit JI
>
> - your example doesn't work in 5-limit JI
>
> - therefore your example isn't musical
>

No his example does work perfectly in 5-limit JI.
It's just that he gives a specific example in 5-limit JI that works
offcourse exactly the way he wrote it down because this is the way he wrote
it down.
If I translate what's underneath what he's saying I come to the following
conclusion.
He's writing a chord progression that works this way in 12tet.
It works that way because in 12tet you get enharmonically equivalent notes.
So when going from one chord to another chord while holding 1 of the notes
it can work.
But it will only work because in 12tet this note has one function in the
first chord and gets another function in the other chord.
In JI this doesn't work that way so the note shifts by a comma.
It does this too in 12tet in the underlying structure, but 12tet tempers out
the difference.

Marcel

> It sounds like a "no true Scotsman" fallacy:
>
> http://www.logicalfallacies.info/notruescotsman.html
>
> - all music works in 5-limit JI
>
> - your example doesn't work in 5-limit JI
>
> - therefore your example isn't musical
>

Ok to make it even more clear.
Petr gives me an example of a chord progression in pure JI where the overall
pitch drops on repetition.
He then sais, look the pitch drops.
It doesn't drop in 12tet, so this is proof JI doesn't work.

I then say, no this isn't proof this chord progression doesn't work in JI.
You gave a wrong translation of how this 12tet progression works in JI.
I then give a correct translation of this 12tet chord progression to thesame
chord progression in 5-limit JI.
And I told in addition that the way he translated the 12tet chord
progression to JI and added an additional rule that there can be no comma
shift when going from one chord to another chord, that this additional rule
is an unmisucal rule.
Clear?

Marcel

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
>
> Okay, here comes the fact that English is not my native language and that I had all my
harmony lessons in Czech. Czech actually has to distinguish between the "acoustical"
fundamental frequency and the "harmonical" fundamental tone, where the latter actually is
what you meant by "root".
>

I figured that "fundamental" might be being used here in the more musically functional
sense of the word rather than in the acoustical sense. Then in that sense you are correct.

The concept of a root in fact is more loose than the being based on the perfect 5th
interval. Even the diminished triad B-D-F, which as no perfect 5th interval, can be said to
have B as a root, since it can cadence down a fifth.

Likewise the half-diminished 7th chord can have one of three roots depending on how it is
used musically. B-D-F-A can be used as a "true" half-diminished 7th because it can
cadence down a fifth, making B the root. It can also be a minor 6th chord, making D the
root. It can also be the upper four notes of a dominant 9th chord, making G the actual
implied root.

I guess an extreme example is a single unaccompanied melody, where a note can suggest
the harmony of which it is the 5th. Thus it ends up being "chord" consisting only of one
note, the 5th, such as the "day" note in "Happy Birthday".

Billy

To Marcel,

okay, if you don't want to use temperaments, then we'll have to do something different. When I wanted to find a "model" harmonic progression which ended with the same chord as where it started, you changed it in such a way that the A moved from 5/3 to 27/16 (i.e. it fell by a full syntonic comma). But can you give me an example of a 5-limit JI harmonic progression which doesn't include any commatic shifts and where the first and last chord are the same? If you can, than maybe we are onto something and we can then try to work out some 7-limit progressions that would answer your question. But anyway, I'm still not sure how you want to find them.

Petr

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
>
> Hello Petr,

> I ment that when a 14th century musician was playing the major
> scale for instance, or played C E G, that even if he tuned it to
> 1/1 81/64 3/2 he would probably have used it as if it were
> 1/1 5/4 3/2 etc, so in this respect 81/64 would have been a
> mistuned 5/4.

But this is exactly the point. They did NOT use triads as if
they were consonances. Major 3rds were treated musically as
dissonances that had to resolve.

-Carl

>
> If you can, than maybe we are onto something and we can then try to work
> out some 7-limit progressions that would answer your question.

Ok I've just been working on chromatic 5-limit scales.
I'll use a major chomatic scale for the example without commas.

Play 1/1 5/4 3/2 and then on top of that an octave higher 1/1 16/15 9/8
32/27 5/4 4/3 64/45 3/2 128/81 5/3 16/9 15/8 2/1

Here random 5-limit chord progressions based on major and minor triads
without commas:
1/1 5/4 3/2 16/9 -> 1/1 32/27 4/3 5/3 -> 32/27 45/32 5/3 2/1 -> 4/3 3/2 16/9
32/15 -> 45/32 16/9 32/15 5/2 -> 4/3 5/3 2/1 5/2 -> 45/32 5/3 2/1 5/2 ->
4/3 3/2 15/8 9/4 -> 1/1 5/4 3/2 2/1

It's ugly nonsense, did it quickly but tried to use different chords where
people often use the 7th harmonic.

But anyway, I'm still not sure how you want to find them.

Me neither, that's why I started this thread :)
But I've seen the 7th harmonic used a lot here in common practice music
where it seems to me it should be a 5-limit interval.
Or if we're not discussing commonpractice music, we're indeed discussing
where and if the 7th harmonic is used in musical structure.
I have no idea other than to play the harmonic overtone series as a sort of
sound effect (and make it clear i'm doing so otherwise it may be
misinterpreted as out of tune actual music)

Marcel

>
> Here random 5-limit chord progressions based on major and minor triads
> without commas:
> 1/1 5/4 3/2 16/9 -> 1/1 32/27 4/3 5/3 -> 32/27 45/32 5/3 2/1 -> 4/3 3/2
> 16/9 32/15 -> 45/32 16/9 32/15 5/2 -> 4/3 5/3 2/1 5/2 -> 45/32 5/3 2/1 5/2
> -> 4/3 3/2 15/8 9/4 -> 1/1 5/4 3/2 2/1
>

Uh sorry that should be 64/45 in place of all 45/32 above.

Marcel

>
> But this is exactly the point. They did NOT use triads as if
> they were consonances. Major 3rds were treated musically as
> dissonances that had to resolve.
>

Yes because they thought they were making pythagorean music.
But the modes they were using and thought they were pythagorean modes are
actually 5-limit modes.
They had a wrong model (pythagorean) for normal 5-limit music with which i
think everybody is born.

Marcel

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:

> I have no idea other than to play the harmonic overtone series as a
sort of
> sound effect (and make it clear i'm doing so otherwise it may be
> misinterpreted as out of tune actual music)
>
> Marcel
>

Are you defining "actual music" as "5-limit JI triadic music"? :-)

My impression is that acceptence of harmonic dissonance has progressed through time. If one is singing pure intervals adaptively I do not see how any other tuning applies imho.
Sent via BlackBerry from T-Mobile

-----Original Message-----
From: Marcel de Velde <m.develde@...>

Date: Mon, 23 Feb 2009 20:16:14
To: <tuning@yahoogroups.com>
Subject: Re: [tuning] Re: 5-limit JI vs 7-limit JI

>
> But this is exactly the point. They did NOT use triads as if
> they were consonances. Major 3rds were treated musically as
> dissonances that had to resolve.
>

Yes because they thought they were making pythagorean music.
But the modes they were using and thought they were pythagorean modes are
actually 5-limit modes.
They had a wrong model (pythagorean) for normal 5-limit music with which i
think everybody is born.

Marcel

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
>
> >
> > But this is exactly the point. They did NOT use triads as if
> > they were consonances. Major 3rds were treated musically as
> > dissonances that had to resolve.
>
> Yes because they thought they were making pythagorean music.
> But the modes they were using and thought they were pythagorean
> modes are actually 5-limit modes.
> They had a wrong model (pythagorean) for normal 5-limit music
> with which is think everybody is born.

?? They weren't making "5-limit music", whether they were
born with it or not.

-Carl

>
> Are you defining "actual music" as "5-limit JI triadic music"? :-)

Possibly :-)

Not triadic though, but 5-limit yes.
I know it's a lousy defenition. And I said it while discussing possible
7-limit or no-limit.
But I see it as possible that 5-limit gives what we call music with keys
keychanges harmony melody etc.
And that possible the 7th harmonic doesn't work in this way and the only use
I'm sure of is correct for the 7th harmonic is when playing clearly the
harmonic overtone series which I see as different than common practice
music.
Ah I'm not explaining it well but I hope you understand what I mean.

Marcel

>
> They weren't making "5-limit music", whether they were
> born with it or not.
>

Well I think it's very possible / likely that they were :)

Marcel

The last bunch of postings about the subtleties of JI calculations and limits etc. demonstrate how and why many musicians are scared away by the complications of traditional JI microtuning.

Integer frequency ratios are becoming a joke;-)

On 23 Feb 2009, at 20:47, Marcel de Velde wrote:

>
> They weren't making "5-limit music", whether they were
> born with it or not.
>
> Well I think it's very possible / likely that they were :)
>
> Marcel

Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

Or not.

In other news, Tim is becoming increasingly disenchanted with Phil.

On Feb 23, 2009, at 4:10 PM, Charles Lucy wrote:

> The last bunch of postings about the subtleties of JI calculations > and limits etc. demonstrate how and why many musicians are scared > away by the complications of traditional JI microtuning.
>
>
> Integer frequency ratios are becoming a joke;-)
>
>
>
>
> On 23 Feb 2009, at 20:47, Marcel de Velde wrote:
>
>>
>> They weren't making "5-limit music", whether they were
>> born with it or not.
>>
>> Well I think it's very possible / likely that they were :)
>>
>> Marcel
>
> Charles Lucy
> lucy@...
>
> - Promoting global harmony through LucyTuning -
>
> for information on LucyTuning go to:
> http://www.lucytune.com
>
> For LucyTuned Lullabies go to:
> http://www.lullabies.co.uk
>
>
>
>
>

let me yell into the well again :-)

at what period in history do we have consistent application of accidentals,
implied or explicit, that indicate a key changes?

I think I may be in the minority here - I find it to be extrapolation on too
little data to start talking about what someone was thinking some 600+ years
ago without something to back it up. Otherwise it is just speculation.

Marcel, are you on a mission to recreate ancient music?

On Mon, Feb 23, 2009 at 3:46 PM, Marcel de Velde <m.develde@...>wrote:

> Are you defining "actual music" as "5-limit JI triadic music"? :-)
>
>
> Possibly :-)
>
> Not triadic though, but 5-limit yes.
> I know it's a lousy defenition. And I said it while discussing possible
> 7-limit or no-limit.
> But I see it as possible that 5-limit gives what we call music with keys
> keychanges harmony melody etc.
> And that possible the 7th harmonic doesn't work in this way and the only
> use I'm sure of is correct for the 7th harmonic is when playing clearly the
> harmonic overtone series which I see as different than common practice
> music.
> Ah I'm not explaining it well but I hope you understand what I mean.
>
> Marcel
>
>

>
> at what period in history do we have consistent application of accidentals,
> implied or explicit, that indicate a key changes?
>

Oh I don't know much about music history but I thought it was forever.
The way the greeks and arabs made music.

I think I may be in the minority here - I find it to be extrapolation on too
> little data to start talking about what someone was thinking some 600+ years
> ago without something to back it up. Otherwise it is just speculation.
>
What I ment is what someone was hearing 600+ or 6000+ years ago.I
specifically wasn't talking about what reasoning they were using behind
their music.
Music is based on hearing in the first place, and I was suggesting that the
way we hear music may be based on the 5-limit harmony.
As in melody is based on 5-limit harmony.
And yes it's just speculation :)

Marcel

Is there any evidence for accidentals in ancient music? I know there is some
Babylonian music recovered from tablets - this was posted a while back here.
I would look to the instruments that survive that we can still play for
evidence of chromaticism. Flutes are a good choice.

I have trouble picturing Babylonians playing blue notes.. but it could be
true.

On Mon, Feb 23, 2009 at 6:42 PM, Marcel de Velde <m.develde@...>wrote:

> at what period in history do we have consistent application of
>> accidentals, implied or explicit, that indicate a key changes?
>>
>
> Oh I don't know much about music history but I thought it was forever.
> The way the greeks and arabs made music.
>
> I think I may be in the minority here - I find it to be extrapolation on
>> too little data to start talking about what someone was thinking some 600+
>> years ago without something to back it up. Otherwise it is just speculation.
>>
> What I ment is what someone was hearing 600+ or 6000+ years ago.I
> specifically wasn't talking about what reasoning they were using behind
> their music.
> Music is based on hearing in the first place, and I was suggesting that the
> way we hear music may be based on the 5-limit harmony.
> As in melody is based on 5-limit harmony.
> And yes it's just speculation :)
>
> Marcel
>
>

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
>
> >
> > They weren't making "5-limit music", whether they were
> > born with it or not.
> >
>
> Well I think it's very possible / likely that they were :)
>
> Marcel
>

I think you wildly underestimate the people of days gone by.
Regardless, you do seem to be unaware of how strong and persistent
for such a long time the perfect fifth was, as "the" harmonic
interval.

Let me repeat: 81/64 was not a "third" as we know it in "common
practice", it was the product of pure fifths. That's why it is so
easy to tune such a "complex" interval. By the way, 81/64 is properly
called a ditone, not a major third.

Actually the pesistence of 3:2 as "the" harmony continues to this day
in Western music, if you think about it.

Margo Schulter, if she's around, could explain the history of these
things the best.

And: if you wish to speak about things like "being born with..." in
music, beware that you do not confuse a particular usage of the
harmonic series with the harmonic series itself. If you do accept the
"natural" quality of the harmonic series (hard for the sane not to,
as anyone who has measured human voices knows), you need to be honest
about it and not ignore certain things just because they sound
strange to you personally.

Given the harmonic series as the foundation, if you accept 9/4 as
"natural", but not 7/4, you might as well come straight out and state
that you're not actually basing your judgements on "nature", but on
conditioning.

-Cameron Bobro

>
> I think you wildly underestimate the people of days gone by.
> Regardless, you do seem to be unaware of how strong and persistent
> for such a long time the perfect fifth was, as "the" harmonic
> interval.
>
> Let me repeat: 81/64 was not a "third" as we know it in "common
> practice", it was the product of pure fifths. That's why it is so
> easy to tune such a "complex" interval. By the way, 81/64 is properly
> called a ditone, not a major third.
>

Yes but for the people who were not making music under the church according
to strict pythagorean tuning, would have probably tuned by a different
system often by ear making 5/4 not 81/64.
And even for those who used 81/64 when tuning in fifths, it's very easy to
use this 81/64 as an out of tune 5/4, similar to what we're doing in 12tet
with 400cents as an out of tune 5/4.

> Actually the pesistence of 3:2 as "the" harmony continues to this day
> in Western music, if you think about it.
>

Yes but this seems to me to be more likely because of a born with
likeability of 3/2.

Margo Schulter, if she's around, could explain the history of these
> things the best.
>
> And: if you wish to speak about things like "being born with..." in
> music, beware that you do not confuse a particular usage of the
> harmonic series with the harmonic series itself. If you do accept the
> "natural" quality of the harmonic series (hard for the sane not to,
> as anyone who has measured human voices knows), you need to be honest
> about it and not ignore certain things just because they sound
> strange to you personally.
>

I am allways trying to be honest. I see no sense in fooling myself.

Given the harmonic series as the foundation, if you accept 9/4 as
> "natural", but not 7/4, you might as well come straight out and state
> that you're not actually basing your judgements on "nature", but on
> conditioning.
>

No not nessecarily.
9/4 might come later in the harmonic overtone series than 9/4, but 9/4 is
based on the simpler interval of 3/2.
Have you read part of my theory of music based on harmonic interval
permutations?
9/4 comes before 7/4 if you look at it this way.
But my harmonic interval permuation theory gives 7/4 aswell, and many other
7-limit intervals.
It's me personally who doesn't know how to use them in common practice
music, and I don't know how to use them in a music form similar to common
practice music.
See my concerns in the first message of this thread.

Marcel

Marcel:

It seems like what you're after isn't just 7-limit harmonies in music,
but a 7-limit form of -tonality-, similar to the 5-limit one. Why not
mess around with 7-limit modal-sounding music instead? Then maybe
you'll start to hear the "pull" of a few chords here and there, and
then see how 7-limit tonality might expand into a greater thing.

-Mike

Hi Mike,

> It seems like what you're after isn't just 7-limit harmonies in music,
> but a 7-limit form of -tonality-, similar to the 5-limit one.
>

Yes, thank you for wording it the way I ment it! :)

> Why not
> mess around with 7-limit modal-sounding music instead? Then maybe
> you'll start to hear the "pull" of a few chords here and there, and
> then see how 7-limit tonality might expand into a greater thing.
>

Yes I've done and tried exactly this.
The only problem is that I'm just too unsure about 7-limit modes.
It's so hard to hear if I'm actually tuning correctly the way I interpret
and use the modes.
Everytime I thought I had found a good 7-limit mode I could also see it as a
5-limit mode which after comparing made more sense to me :(
I'm of the belief that for instance harmonic minor is one of the base
5-limit modes, it has the notes 3/2 8/5 15/8 2/1
Often when I thought I had found proper use for 7/6 in a mode I could also
see it as the 75/64 from 8/5 to 15/8 in the harmonic minor.
And something like 1/1 16/15 5/4 4/3 3/2 8/5 15/8 2/1 comes from this.
In the end I spent several months making 7-limit modes and trying to make
sense of them, but in the end I prefered to look at the modes I tried as
5-limit modes, just made more sense and sounds more right to my ears.
For a while I thought some arabic modes and blues modes could be 7-limit,
but then I figured out how they can be constructed with a lot of sense from
5-limit, for instance for a very simple mode 1/1 10/9 6/5 4/3 3/2 5/3 9/5
2/1, but also found other more complex modes and what are their likely
construction, found thousands of possible 5-limit modes based on a simple
and logical contrcution that include all arabic and blues modes.
So then I thought, ok the 7th harmonic is notes outside a mode, a mode is
5-limit and 7-limit makes chromatic music.
But then after working things out more I found chromatic music works
perfectly and makes perfect sense in 5-limit.
So then I posted on this list saying I don't know about the 7th harmonic
anymore, can someone give an example that shows how to use it.
Still haven't gotten an answer that makes me say a convinced yes this is the
7th harmonic in a musical structural / tonality way similar to 5-limit.
That it has been so hard for others to give a convincing example makes me
even more sombre about the 7th harmonic.

Marcel

>
> So then I thought, ok the 7th harmonic is notes outside a mode, a mode is
> 5-limit and 7-limit makes chromatic music.
> But then after working things out more I found chromatic music works
> perfectly and makes perfect sense in 5-limit.
>

Ok actually, this one I still have more hopes for.
Determine the tonality with a 5-limit mode and use 7-limit notes outside
that mode but in a different way than normal chromatic music.
So to use the 7-limit notes as more notes in thesame tonality, not
suggesting another tonal center / key /modulation or something like that.
So the 7-limit notes would kind of be like extra harmonics without any
normal function.
And once you then use notes outside the mode in a normal functional
chromatic way (5-limit) you get a comma shift.
Don't know how correct this line of thinking is.
Sorry for the terrible way of explaining it but I'm lousy with words :)

Marcel

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
>
Hi Mike,

> So then I posted on this list saying I don't know about the 7th
> harmonic anymore, can someone give an example
> that shows how to use it.

http://www.ex-tempore.org/ARCHYTAS/ARCHYTAS.html

> Still haven't gotten an answer
> that makes me say a convinced yes this is the
> 7th harmonic in a musical structural / tonality way similar to
> 5-limit.
> That it has been so hard for others to give a convincing example
> makes me even more sombre about the 7th harmonic.

But
http://plato.stanford.edu/entries/archytas/
Platon rejected everything above 3-limt:

"One genus was called the diatonic; one example of this is the
Pythagorean diatonic described above, which is built on the tetrachord
with the intervals 9 : 8, 9 : 8 and 256 : 243 and was used by
Philolaus and Plato. There is no doubt that Archytas knew of this
diatonic scale, but his own diatonic tetrachord was somewhat
different, being composed of the intervals 9 : 8, 8 : 7 and 28 : 27.
Archytas also defined scales in the two other major genera, the
enharmonic and chromatic. Archytas' enharmonic tetrachord is composed
of the intervals 5 : 4, 36 : 35 and 28 : 27 and his chromatic
tetrachord of the intervals 32 : 27, 243 : 224, and 28 : 27. There are
several puzzles about the tetrachords which Archytas adopts in each of
the genera. First, why does Archytas reject the Pythagorean diatonic
used by Philolaus and Plato?"....

http://de.wikipedia.org/wiki/Archytas_von_Tarent#Musik
"
enharmonisches Tetrachord: (28:27)(36:35)(5:4)
chromatisches Tetrachord: (28:27)(15:14)(6:5)
diatonisches Tetrachord: (28:27)(8:7)(9:8)
"

Quest:
Are you an modern
http://www.thefreedictionary.com/Platonist
that persists in barely allowing 5-limit,
but rejects "sombre" 7-limit?

bye
A.S.

carl - you were say 22 edo is close to 7 limit?

Is 5 limit essentialy 12 tet?
Sent via BlackBerry from T-Mobile

-----Original Message-----
From: Marcel de Velde <m.develde@gmail.com>

Date: Tue, 24 Feb 2009 11:38:41
To: <tuning@yahoogroups.com>
Subject: Re: [tuning] Re: 5-limit JI vs 7-limit JI

>
> So then I thought, ok the 7th harmonic is notes outside a mode, a mode is
> 5-limit and 7-limit makes chromatic music.
> But then after working things out more I found chromatic music works
> perfectly and makes perfect sense in 5-limit.
>

Ok actually, this one I still have more hopes for.
Determine the tonality with a 5-limit mode and use 7-limit notes outside
that mode but in a different way than normal chromatic music.
So to use the 7-limit notes as more notes in thesame tonality, not
suggesting another tonal center / key /modulation or something like that.
So the 7-limit notes would kind of be like extra harmonics without any
normal function.
And once you then use notes outside the mode in a normal functional
chromatic way (5-limit) you get a comma shift.
Don't know how correct this line of thinking is.
Sorry for the terrible way of explaining it but I'm lousy with words :)

Marcel

>
> http://www.ex-tempore.org/ARCHYTAS/ARCHYTAS.html
>

Thanks for the link, very intersting.
However simply because archytas wrote down 7-limit intervals doesn't mean he
did so correctly.
28/27 is for instance close enough to 25/24 to be confused with it by the
ear.
Or even 256/243 or 135/128. I've caught myself making the error of 25/24 vs
256/243 vs 135/128 a lot.

This could lead to something like this
making diatonic stepsizes 25/24 256/225 9/8 making 1/1 25/24 32/27 4/3 3/2
25/16 16/9 2/1
chromatic 25/24 32/27 25/27 making 1/1 25/24 100/81 4/3 3/2 25/16 50/27 2/1
enharmonic 25/24 128/125 5/4 making 1/1 25/24 16/15 4/3 3/2 25/16 8/5 2/1
Or enharmonic 256/243 81/80 5/4 making 1/1 256/243 16/15 4/3 3/2 128/81 8/5
2/1

I don't know, so many possibilities.
And can't find actual music written in these scales on that page.
So could be the 7th harmonic, could not be the 7th harmonic. Can't make up
from this page even though things are written down as the 7-limit.
Though it seems the greeks were arguing over the ratios amongst themselves
too, so there is not 1 tuning but many describing thesame music?
I will look at the page more later.

But
> http://plato.stanford.edu/entries/archytas/
> Platon rejected everything above 3-limt:
>
> "One genus was called the diatonic; one example of this is the
> Pythagorean diatonic described above, which is built on the tetrachord
> with the intervals 9 : 8, 9 : 8 and 256 : 243 and was used by
> Philolaus and Plato. There is no doubt that Archytas knew of this
> diatonic scale, but his own diatonic tetrachord was somewhat
> different, being composed of the intervals 9 : 8, 8 : 7 and 28 : 27.
> Archytas also defined scales in the two other major genera, the
> enharmonic and chromatic. Archytas' enharmonic tetrachord is composed
> of the intervals 5 : 4, 36 : 35 and 28 : 27 and his chromatic
> tetrachord of the intervals 32 : 27, 243 : 224, and 28 : 27. There are
> several puzzles about the tetrachords which Archytas adopts in each of
> the genera. First, why does Archytas reject the Pythagorean diatonic
> used by Philolaus and Plato?"....
>
> http://de.wikipedia.org/wiki/Archytas_von_Tarent#Musik
> "
> enharmonisches Tetrachord: (28:27)(36:35)(5:4)
> chromatisches Tetrachord: (28:27)(15:14)(6:5)
> diatonisches Tetrachord: (28:27)(8:7)(9:8)
> "

Here different step sizes than the one given on the earlyer page?

Quest:
> Are you an modern
> http://www.thefreedictionary.com/Platonist
> that persists in barely allowing 5-limit,
> but rejects "sombre" 7-limit?

Perhaps in the sense that I think music is based on a perfect system.
But I don't "barely allow" 5-limit, I could not allow 5-limit more fully.
And don't reject 7-limit but do question it's use.

Marcel

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:

> However simply because archytas wrote down 7-limit intervals
>doesn't mean he
> did so correctly.
> 28/27 is for instance close enough to 25/24 to be confused with it
>by the
> ear.
> Or even 256/243 or 135/128. I've caught myself making the error of
>25/24 vs
> 256/243 vs 135/128 a lot.

But the 28/27 isn't in isolation! It makes a 9/7 with the 4/3. On a
stringed instrument especially, the 9/7 can really leap out, too.

Tetrachords are tuned as a whole, and constructed as a whole, it's
not necessary to tune the small intervals out of the blue.

>
> But the 28/27 isn't in isolation! It makes a 9/7 with the 4/3. On a
> stringed instrument especially, the 9/7 can really leap out, too.
>
> Tetrachords are tuned as a whole, and constructed as a whole, it's
> not necessary to tune the small intervals out of the blue.
>

Yes ok but 4/3 also makes a 32/25 with 25/24 and 81/64 with 256/243 and 5/4
with 16/15.
Both 32/25 and 81/64 are much used intervals in common practice music.

Marcel

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
>
> >
> > But the 28/27 isn't in isolation! It makes a 9/7 with the 4/3. On
a
> > stringed instrument especially, the 9/7 can really leap out, too.
> >
> > Tetrachords are tuned as a whole, and constructed as a whole, it's
> > not necessary to tune the small intervals out of the blue.
> >
>
> Yes ok but 4/3 also makes a 32/25 with 25/24 and 81/64 with 256/243
and 5/4
> with 16/15.
> Both 32/25 and 81/64 are much used intervals in common practice
music.
>
> Marcel
>

So? The point is that your original point about 28/27 isn't valid. It
is NOT a mistaken 25/24, it's a perfect fourth minus a 9/7. Once
you've got a 9/7 in there, and only superparticular intervals, it is
a different thing. It is not Pythagorean tuning. Doesn't sound like
Pythagorean tuning. You really should tune these things up and listen
to them.

A burrito is not a badly made hamburger.

And you might want to study this whole thing:

http://eamusic.dartmouth.edu/~larry/published_articles/
divisions_of_the_tetrachord/index.html

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
>
> >
> > http://www.ex-tempore.org/ARCHYTAS/ARCHYTAS.html
> >
Dear Marcel,

> However simply because archytas wrote down 7-limit intervals doesn't
> mean he did so correctly.

He calculated his ratios by
http://www.ex-tempore.org/means/means.htm

Here an historically introduction of the
http://www.chrysalis-foundation.org/origins_of_length_ratios.htm
coeval critizised by Aristoxenos
http://eamusic.dartmouth.edu/~larry/published_articles/divisions_of_the_tetrachord/chapter3.pdf
and modern in the
http://www.mind-energy.net/archives/264-Against-Archytas-How-the-West-Lost-Alchemy-or-Paranormal-Complimentary-Opposite-Harmonics.html
controversy.

> 28/27 is for instance close enough to 25/24 to be confused with it
> by the ear.

The ratio intbetween both amounts

225/224 := (25/24):(28/27)

labeled
http://en.wikipedia.org/wiki/Septimal_kleisma
as used in
http://en.wikipedia.org/wiki/Septimal_meantone_temperament

> Or even 256/243 or 135/128.
that both differ even barely an

http://de.wikipedia.org/wiki/Komma_(Musik)#Schisma

> I've caught myself making the error of 25/24 vs
> 256/243 vs 135/128 a lot.

Kirnberger wrote about such calculations in his letter to Forkel
http://harpsichords.pbwiki.com/f/Kirn_1871.html#Note_1
concluding:
"
Ich muss auch ganz nicht mehr daran gedenken, weil ich viele Jahre
damit die Zeit verdorben habe. Damals, wo ich ging und standte,
rechnete ich immer: es ist eine Arbeit für einen Baugefangenen oder
für einen Menschen ohne Genie.
"
tr:
'I haven't to think about it anymore,
because I wasted many years of time by doing that.
Then, where ever I went and stood,
I was always computing: it is a work for a prisoner or
for a men without genius.'

http://mtcs.truman.edu/~thammond/history/Archytas.html
>
> This could lead to something like this
> making diatonic stepsizes 25/24 256/225 9/8

That are all 5-smooth
http://en.wikipedia.org/wiki/Smooth_number
ratios composed of
http://www.research.att.com/~njas/sequences/A051037
in nominator vs. denominator.

> making 1/1 25/24 32/27 4/3 3/2
> 25/16 16/9 2/1
> chromatic 25/24 32/27 25/27
> making 1/1 25/24 100/81 4/3 3/2 25/16 50/27 2/1

> enharmonic 25/24 128/125 5/4
> making 1/1 25/24 16/15 4/3 3/2 25/16 8/5 2/1

> Or enharmonic 256/243 81/80 5/4
> making 1/1 256/243 16/15 4/3 3/2 128/81 8/5 2/1

or restricted to
http://en.wikipedia.org/wiki/Regular_number
s
>
> I don't know, so many possibilities.

Collocated in a Hasse-diagram according
http://en.wikipedia.org/wiki/File:Regular_divisibility_lattice.svg
factorization.

> And can't find actual music written in these scales on that page.
Just try for
http://en.wikipedia.org/wiki/Music_of_ancient_Greece
the few examples in
http://www.oeaw.ac.at/kal/agm/

> So could be the 7th harmonic, could not be the 7th harmonic.
> Can't make up
> from this page even though things are written down as the 7-limit.

that 7-limit ratios
http://en.wikipedia.org/wiki/User:SharkD/Sandbox/Sortable_tables_2
consist of
http://en.wikipedia.org/wiki/Highly_composite_number
that are made of
http://www.research.att.com/~njas/sequences/A002473
fractions.

> Though it seems the greeks were arguing over the ratios amongst
> themselves
> too, so there is not 1 tuning but many describing thesame music?
right,
hence you have to care about applying
the correct tetrachord division,
as it was intended by the composer.

> But I don't "barely allow" 5-limit,
> I could not allow 5-limit more fully.
Agreed.

> And don't reject 7-limit but do question it's use.
Here you are in good company, because
http://en.wikipedia.org/wiki/Leonard_Bernstein
in
http://www.hup.harvard.edu/catalog/BERUNX.html
even casts doubts on 5-limit,
because he refused 5-smooth-ratios
when preferring the older plain pythagorean 3-limit
interval proportions.

bye
A.S.

On Tue, 2009-02-24 at 11:00 +0100, Marcel de Velde wrote:

> For a while I thought some arabic modes and blues modes could be
> 7-limit, but then I figured out how they can be constructed with a lot
> of sense from 5-limit, for instance for a very simple mode 1/1 10/9
> 6/5 4/3 3/2 5/3 9/5 2/1, but also found other more complex modes and
> what are their likely construction, found thousands of possible
> 5-limit modes based on a simple and logical contrcution that include
> all arabic and blues modes.

If you want Arabic scales, you might as well go on to 11-limit at least.
A traditional neutral second, for example, is 12/11, and raising that by
a whole tone, fourth and fifth gives you 27/22, 16/11 and 18/11. You
could also use 13-based ratios like Avicenna did.

By the way, if you haven't done so already, familiarize yourself with
Harry Partch's 43-tone scale, which is a full set of 11-limit ratios.
(Wouldn't hurt to listen to some of his music either; I bought Delusion
of the Fury a while ago and I recommend it) All but two of these (11/10
and 20/11) could be used as a rationalized 41 equal temperament scale,
and all of these could be expressed in terms of 72 equal. And if you
want to use an equal temperament as a meantone, forget 19-tone; get busy
with 31-tone. That's best for approximating 11-limit.

> So then I thought, ok the 7th harmonic is notes outside a mode, a mode
> is 5-limit and 7-limit makes chromatic music.
> But then after working things out more I found chromatic music works
> perfectly and makes perfect sense in 5-limit.
> So then I posted on this list saying I don't know about the 7th
> harmonic anymore, can someone give an example that shows how to use
> it.
> Still haven't gotten an answer that makes me say a convinced yes this
> is the 7th harmonic in a musical structural / tonality way similar to
> 5-limit.
> That it has been so hard for others to give a convincing example makes
> me even more sombre about the 7th harmonic.

It took me *years* to bust my brain out of thinking in terms of 12 equal
temperament. I still have trouble telling 7/4 from 16/9 and 9/5 and I
have perfect pitch. (12/11 from 9/8 or 10/9 is no problem.) So it's a
lot of work.

I personally use the prime 7 in a few ways:

1. as a basis for augmented intervals, if I'm in a major key or mode.
I've discussed augmented sixth chords here; a German sixth could be 1/1
5/4 3/2 7/4. Two chords could contain two 7-otonal ratios: the French
sixth would be 1/1 5/4 7/5 7/4, and a chord with an augmented fifth and
six I've seen called a "Russian sixth" would be 1/1 5/4 14/9 7/4. I've
used a mixture of augmented and major in "blues major" scales such as
1/1 7/6 5/4 4/3 3/2 7/4 15/8 2/1. Inversely, I can put seven in the
denominator as diminished intervals and call these "yellow": 1/1 16/15
6/5 9/7 3/2 8/5 9/5 27/14 9/4 12/5 could be a type of maqam Saba Zamzama
(replace 16/15 with 12/11 for regular Saba).

2. for "hollow" scales, including pentatonic. 1/1 7/6 4/3 3/2 7/4 2/1
vaguely approximates slendro, and a lot of African music is often
pentatonic. Again, this has blues connotations - blues came from Africa
after all. (So I'd recommend listening to Robert Johnson with your Harry
Partch, and also Umm Kalthoum for Arabic music and 11-limit.)

3. in the resolved seventh chord, 1/1 5/4 3/2 7/4, which is a staple of
barbershop music, which has been discussed here very recently. The
conventional dominant seventh, which has 16/9 or 9/5 on top instead, has
to resolve to something, typically a major chord on 4/3 in a V7-I
cadence. 7/4 as a seventh should be understood as a "subminor seventh"
in this context rather than an augmented sixth, so the ratio plays a
dual role.

But anyway, you just need practice, and a lot of it. It's a major sea
change from 12-tone equal, which is really a modified Pythagorean scale
and not even 5-limit.

~D.

On Tue, 2009-02-24 at 10:06 -0600, I wrote:

> And if you
> want to use an equal temperament as a meantone, forget 19-tone; get busy
> with 31-tone. That's best for approximating 11-limit.

I need to backtrack on that statement: 19-tone equal temperament is NOT
a useless tuning, if you're reading that. I've used some third-tone
progressions myself, and I still recommend 19 for beginners, at least as
something where enharmonic degrees aren't the exact same pitch.

I did once mistakenly think that 19-tone could be used for Middle
Eastern-styled music (17 is what I needed).

~D.

Hi Danny,

If you want Arabic scales, you might as well go on to 11-limit at least.
> A traditional neutral second, for example, is 12/11, and raising that by
> a whole tone, fourth and fifth gives you 27/22, 16/11 and 18/11. You
> could also use 13-based ratios like Avicenna did.
>

I find 27/25 a perfectly good neutral second. Where 27/25 + 10/9 make 6/5
And within a modulation you can make 800/729 where 27/25 + 800/729 make
32/27.

By the way, if you haven't done so already, familiarize yourself with
> Harry Partch's 43-tone scale, which is a full set of 11-limit ratios.
> (Wouldn't hurt to listen to some of his music either; I bought Delusion
> of the Fury a while ago and I recommend it) All but two of these (11/10
> and 20/11) could be used as a rationalized 41 equal temperament scale,
> and all of these could be expressed in terms of 72 equal. And if you
> want to use an equal temperament as a meantone, forget 19-tone; get busy
> with 31-tone. That's best for approximating 11-limit.
>

Well first the 7th before I'm willing to try higher primes :)

> It took me *years* to bust my brain out of thinking in terms of 12 equal
> temperament. I still have trouble telling 7/4 from 16/9 and 9/5 and I
> have perfect pitch. (12/11 from 9/8 or 10/9 is no problem.) So it's a
> lot of work.
>
> I personally use the prime 7 in a few ways:
>
> 1. as a basis for augmented intervals, if I'm in a major key or mode.
> I've discussed augmented sixth chords here; a German sixth could be 1/1
> 5/4 3/2 7/4.
>

I have really strong reasons to beleive the german sixth is 1/1 5/4 3/2
225/128.

> Two chords could contain two 7-otonal ratios: the French
> sixth would be 1/1 5/4 7/5 7/4, and a chord with an augmented fifth and
> six I've seen called a "Russian sixth" would be 1/1 5/4 14/9 7/4. I've
> used a mixture of augmented and major in "blues major" scales such as
> 1/1 7/6 5/4 4/3 3/2 7/4 15/8 2/1. Inversely, I can put seven in the
> denominator as diminished intervals and call these "yellow": 1/1 16/15
> 6/5 9/7 3/2 8/5 9/5 27/14 9/4 12/5 could be a type of maqam Saba Zamzama
> (replace 16/15 with 12/11 for regular Saba).
>
> 2. for "hollow" scales, including pentatonic. 1/1 7/6 4/3 3/2 7/4 2/1
> vaguely approximates slendro, and a lot of African music is often
> pentatonic. Again, this has blues connotations - blues came from Africa
> after all. (So I'd recommend listening to Robert Johnson with your Harry
> Partch, and also Umm Kalthoum for Arabic music and 11-limit.)
>
> 3. in the resolved seventh chord, 1/1 5/4 3/2 7/4, which is a staple of
> barbershop music, which has been discussed here very recently. The
> conventional dominant seventh, which has 16/9 or 9/5 on top instead, has
> to resolve to something, typically a major chord on 4/3 in a V7-I
> cadence. 7/4 as a seventh should be understood as a "subminor seventh"
> in this context rather than an augmented sixth, so the ratio plays a
> dual role.
>

Do you mean that the 7th here doesn't need to resolve to anywhere?
Yes I agree that if it's a true 7/4 I'd expect it to be usable as a final
chord.

But anyway, you just need practice, and a lot of it. It's a major sea

> change from 12-tone equal, which is really a modified Pythagorean scale
> and not even 5-limit.
>

Oh I really can't agree to 12tet beeing based on pythagorean :)
I see it as 5-limit.
But thanks for the advice and agree that the 7th must be a very different
thing from normal music as we're used to.

Marcel

On Tue, 2009-02-24 at 17:24 +0100, Marcel de Velde wrote:

> I find 27/25 a perfectly good neutral second. Where 27/25 + 10/9 make
> 6/5
> And within a modulation you can make 800/729 where 27/25 + 800/729
> make 32/27.

It would work, and some Iranian theorists have recommended 27/25 or
something close to it for a neutral second (Hormoz Farhat uses 135
cents). Though I think of it as a two-thirds tone rather than a
three-quarter tone, and I think Arabic and Turkish music uses a higher
pitch, somewhere between 12/11 and 10/9 depending on location.

27/25 could be called a "semi-minor second" or "minor neutral second".
But I'm using higher primes, and like you said, we'll stick to 7-limit.
11-limit is your next goal after getting the hang of 7.

35/32 is also a good neutral second in 7-limit.

> I have really strong reasons to beleive the german sixth is 1/1 5/4
> 3/2 225/128.

In 5-limit, it would be exactly that, and 1/1 5/4 45/32 225/128 for the
French sixth. My 7-limit version replaces 225/128 with 7/4, and 7/4 is
lower than 225/128 by an interval smaller than a comma, the septimal
kleisma, 225/224, or 7.71 cents. That interval is tempered out in 31,
41, 53 and 72 equal temperament, among others.

Altering pitches by 225/224 could be called "septimal substitution", or
is there a better term? I know changing complex Pythagorean ratios like
8192/6561 to 5/4 using the schisma (32805/32768) is called "schismatic
alteration"...

> 3. in the resolved seventh chord, 1/1 5/4 3/2 7/4, which is a
> staple of
> barbershop music, which has been discussed here very recently.
> The
> conventional dominant seventh, which has 16/9 or 9/5 on top
> instead, has
> to resolve to something, typically a major chord on 4/3 in a
> V7-I
> cadence. 7/4 as a seventh should be understood as a "subminor
> seventh"
> in this context rather than an augmented sixth, so the ratio
> plays a
> dual role.
>
>
> Do you mean that the 7th here doesn't need to resolve to anywhere?
> Yes I agree that if it's a true 7/4 I'd expect it to be usable as a
> final chord.

Yeah, the "barbershop seventh" is simply a chain of consecutive
harmonics, 4:5:6:7. It's as relaxed as you could possibly get with a
seventh chord, so you want to end there.

> Oh I really can't agree to 12tet beeing based on pythagorean :)
> I see it as 5-limit.
> But thanks for the advice and agree that the 7th must be a very
> different thing from normal music as we're used to.

12 equal temperament is marginally 5-limit at best. Going along the
circle of fifths in either direction, you're closer to the Pythagorean
interval as far as the major third or minor sixth (81/64 ~ 407.82 cents
versus 5/4 ~ 386.31). While a meantone, including 19 and 31 equal,
compromises the fifth in order to best approximate 5-limit JI major and
minor intervals, 12 only alters the fifth to eliminate the wolf fifth of
Pythagorean tuning without giving much consideration to intonation of
majors and minors, except the whole tone and the 16/9 minor seventh. The
fifth is technically lowered by a twelfth of a Pythagorean comma.

And yes, 12 is way off on 7, 11 and 13-limit, but it's a great
approximate of the prime 17. I think al-Farabi might've predicted 12
equal when he divided the whole tone into half (in terms of string
length on his oud) and came up with 18/17.

~D.

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
>
> Yes but for the people who were not making music under the church
> according to strict pythagorean tuning, would have probably tuned
> by a different system often by ear making 5/4 not 81/64.

Nobody's claiming strict pythagorean tuning was used. The point
is it does not matter how the thirds are tuned if they are treated
as dissonances in the music.

> Margo Schulter, if she's around, could explain the history of
> these things the best.

We're hardly wanting for explanations. You can lead a horse's
mouth to water...

-Carl

--- In tuning@yahoogroups.com, Danny Wier <dawiertx@...> wrote/reccomend:

>...familiarize yourself with
> Harry Partch's 43-tone scale, which is a full set of 11-limit ratios.

http://en.wikipedia.org/wiki/Harry_Partch's_43-tone_scale

>
> It would work, and some Iranian theorists have recommended 27/25 or
> something close to it for a neutral second (Hormoz Farhat uses 135
> cents). Though I think of it as a two-thirds tone rather than a
> three-quarter tone, and I think Arabic and Turkish music uses a higher
> pitch, somewhere between 12/11 and 10/9 depending on location.
>
> 27/25 could be called a "semi-minor second" or "minor neutral second".
> But I'm using higher primes, and like you said, we'll stick to 7-limit.
> 11-limit is your next goal after getting the hang of 7.
>

Have you tried / heard the 27/25?
To my ears it's spot on. Play for instance the sequence 3/2 5/3 9/5 2/1 9/5
5/3 3/2 45/32 6/5 10/9 1/1 10/9 6/5 45/32 3/2 etc

> 35/32 is also a good neutral second in 7-limit.
>

Yes, very close to the 800/729 i mentioned earlyer.
It looks like a strange interval but it's musically very logical in a
modulation.

> I have really strong reasons to beleive the german sixth is 1/1 5/4
> > 3/2 225/128.
>
> In 5-limit, it would be exactly that, and 1/1 5/4 45/32 225/128 for the
> French sixth. My 7-limit version replaces 225/128 with 7/4, and 7/4 is
> lower than 225/128 by an interval smaller than a comma, the septimal
> kleisma, 225/224, or 7.71 cents. That interval is tempered out in 31,
> 41, 53 and 72 equal temperament, among others.
>

Yes ok, but why replace it when this gets you into trouble when using the
interval in a normal 5-limit melody?
Surely in such a case it should still be 225/128?
When and why does it become 7/4 instead of 225/128?
I think this is probably the key of what we're discussing.

12 equal temperament is marginally 5-limit at best. Going along the
> circle of fifths in either direction, you're closer to the Pythagorean
> interval as far as the major third or minor sixth (81/64 ~ 407.82 cents
> versus 5/4 ~ 386.31). While a meantone, including 19 and 31 equal,
> compromises the fifth in order to best approximate 5-limit JI major and
> minor intervals, 12 only alters the fifth to eliminate the wolf fifth of
> Pythagorean tuning without giving much consideration to intonation of
> majors and minors, except the whole tone and the 16/9 minor seventh. The
> fifth is technically lowered by a twelfth of a Pythagorean comma.
>
> And yes, 12 is way off on 7, 11 and 13-limit, but it's a great
> approximate of the prime 17. I think al-Farabi might've predicted 12
> equal when he divided the whole tone into half (in terms of string
> length on his oud) and came up with 18/17.
>

12tet is pretty far off at times for certain step sizes, but in the overall
structure of a 5-limit scale 12tet does pretty well.
Below an in my opinion very good 5-limit scale compared to 12tet:

0: 1/1 0.000 unison, perfect prime
1: 16/15 111.731 minor diatonic semitone
2: 10/9 182.404 minor whole tone
3: 9/8 203.910 major whole tone
4: 32/27 294.135 Pythagorean minor third
5: 6/5 315.641 minor third
6: 5/4 386.314 major third
7: 4/3 498.045 perfect fourth
8: 27/20 519.551 acute fourth
9: 45/32 590.224 diatonic tritone
10: 64/45 609.776 2nd tritone
11: 40/27 680.449 grave fifth
12: 3/2 701.955 perfect fifth
13: 8/5 813.686 minor sixth
14: 5/3 884.359 major sixth, BP sixth
15: 27/16 905.865 Pythagorean major sixth
16: 16/9 996.090 Pythagorean minor seventh
17: 9/5 1017.596 just minor seventh, BP seventh
18: 15/8 1088.269 classic major seventh
19: 2/1 1200.000 octave
|
Step size is 100.0000 cents
1: 111.731: 1: 100.0000 cents diff. -0.117312 steps, -11.7313
cents
2: 182.404: 2: 200.0000 cents diff. 0.175962 steps, 17.5963
cents
3: 203.910: 2: 200.0000 cents diff. -0.039100 steps, -3.9100
cents
4: 294.135: 3: 300.0000 cents diff. 0.058650 steps, 5.8650
cents
5: 315.641: 3: 300.0000 cents diff. -0.156412 steps, -15.6413
cents
6: 386.314: 4: 400.0000 cents diff. 0.136862 steps, 13.6863
cents
7: 498.045: 5: 500.0000 cents diff. 0.019550 steps, 1.9550
cents
8: 519.551: 5: 500.0000 cents diff. -0.195512 steps, -19.5513
cents
9: 590.224: 6: 600.0000 cents diff. 0.097762 steps, 9.7763
cents
10: 609.776: 6: 600.0000 cents diff. -0.097762 steps, -9.7763
cents
11: 680.449: 7: 700.0000 cents diff. 0.195512 steps, 19.5513
cents
12: 701.955: 7: 700.0000 cents diff. -0.019550 steps, -1.9550
cents
13: 813.686: 8: 800.0000 cents diff. -0.136862 steps, -13.6863
cents
14: 884.359: 9: 900.0000 cents diff. 0.156412 steps, 15.6413
cents
15: 905.865: 9: 900.0000 cents diff. -0.058650 steps, -5.8650
cents
16: 996.090: 10: 1000.0000 cents diff. 0.039100 steps, 3.9100
cents
17: 1017.596: 10: 1000.0000 cents diff. -0.175962 steps, -17.5963
cents
18: 1088.269: 11: 1100.0000 cents diff. 0.117312 steps, 11.7313
cents
19: 1200.000: 12: 1200.0000 cents diff. 0.000000 steps, 0.0000
cents
Total absolute difference : 1.994254 steps, 199.4254 cents
Average absolute difference: 0.104960 steps, 10.4961 cents
Root mean square difference: 0.121852 steps, 12.1852 cents
Highest absolute difference: 0.195512 steps, 19.5513 cents

>
> The point
> is it does not matter how the thirds are tuned if they are treated
> as dissonances in the music.
>

Hmm this sounds as if you're implying that every interval which is used
musically as a dissonance can be tuned whatever which way the person likes
and keep the same meaning?
There's just one meaning then which is dissonance?
Don't think I can agree with this.
If I misunderstand you can you explain how you mean it?

Marcel

An answer as to the tuning of antiquity is here

"In 1986 several gudi
<http://en.wikipedia.org/wiki/Gudi_%28instrument%29>(literally "bone
flutes") were found in
Jiahu <http://en.wikipedia.org/wiki/Jiahu> in Henan Province, China. They
date to about 6,000 BC. They have between 5 and 8 holes each and were made
from the hollow bones of a bird, the red-crowned
crane<http://en.wikipedia.org/wiki/Red-crowned_crane>.
At the time of the discovery, one was found to be still playable. The bone
flute plays both the five- or seven-note scale of Xia
Zhi<http://en.wikipedia.org/w/index.php?title=Xia_Zhi&action=edit&redlink=1>and
six-note scale of Qing
Shang<http://en.wikipedia.org/w/index.php?title=Qing_Shang&action=edit&redlink=1>of
the ancient Chinese
musical system <http://en.wikipedia.org/wiki/Chinese_musical_system>."

If this is 5 limit or not I leave up to the experts.

http://en.wikipedia.org/wiki/Prehistoric_music

On Tue, Feb 24, 2009 at 1:36 PM, Marcel de Velde <m.develde@...>wrote:

> The point
>> is it does not matter how the thirds are tuned if they are treated
>> as dissonances in the music.
>>
>
> Hmm this sounds as if you're implying that every interval which is used
> musically as a dissonance can be tuned whatever which way the person likes
> and keep the same meaning?
> There's just one meaning then which is dissonance?
> Don't think I can agree with this.
> If I misunderstand you can you explain how you mean it?
>
> Marcel
>
>

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
>
> >
> > The point
> > is it does not matter how the thirds are tuned if they are treated
> > as dissonances in the music.
> >
>
> Hmm this sounds as if you're implying that every interval which
> is used musically as a dissonance can be tuned whatever which way
> the person likes and keep the same meaning?
> There's just one meaning then which is dissonance?
> Don't think I can agree with this.
> If I misunderstand you can you explain how you mean it?
>
> Marcel

The tuning of the dissonances is less important. It no doubt
works better with the a tense interval like 81/64 (and there
may be melodic reasons to choose it also), but 5/4 would work
too. The grammar of the music creates the expectation that it
must resolve, which is what musical dissonance is: an interval
that must resolve. Besides, since 3/2 is the most concordant
of all intervals, any other interval is more tense.

-Carl

>
> Ok actually, this one I still have more hopes for.
> Determine the tonality with a 5-limit mode and use 7-limit notes outside
> that mode but in a different way than normal chromatic music.
> So to use the 7-limit notes as more notes in thesame tonality, not
> suggesting another tonal center / key /modulation or something like that.
> So the 7-limit notes would kind of be like extra harmonics without any
> normal function.
> And once you then use notes outside the mode in a normal functional
> chromatic way (5-limit) you get a comma shift.
> Don't know how correct this line of thinking is.
> Sorry for the terrible way of explaining it but I'm lousy with words :)
>
> Marcel
>

Whether it's correct or not, it has a following. This is basically what happens when a
barbershop chord has the septimal 7th in a harmony part. Absent that part, you have a
just=-tuned major triad, so the 7/4 is really just along for the ride. It may be a different
matter when the lead is singing the 7th. Then the melody would have to bend and have
that out of tune sound you mention.

Billy

Marcel de Velde wrote:

> That it has been so hard for others to give a convincing example makes > me even more sombre about the 7th harmonic.

What do you expect, when all we get is one of two responses:

1) It's really a 5-limit interval (usually a more complex one), or
2) It's not music.

After enough iterations of this, why bother? You have only yourself to blame if no one takes your ideas seriously.

---What do you expect, when all we get is one of two responses:

--1) It's really a 5-limit interval (usually a more complex one), or
--2) It's not music.
      Amen!  Exactly...you can't make something truly different and mostly the same at the same time.

    I think the ONLY "problem" I see with 7-limit is that it's impossible to translate 5-limit music perfectly into it.  But it is thanks to that "problem", that 7-limit JI music is a step up from 5-limit in the first place. 
------------------
     It's like saying Mac OS can't work for users simply because it doesn't have the exact same user interface as Windows XP and they have to, say, rewrite their old XP programs to work on Mac OS.  
--------------------------
  7-limit JI, I can assure you, is capable of all the emotions 5-limit JI has.  It might not use the same exact chords or ones that have "similar musical functions"...but the net result is that slightly different chords with different emotions in 7-limit JI can be combined.

>>>>>>>>

--- On Tue, 2/24/09, Herman Miller <hmiller@...> wrote:

From: Herman Miller <hmiller@...>
Subject: Re: [tuning] Re: 5-limit JI vs 7-limit JI
To: tuning@yahoogroups.com
Date: Tuesday, February 24, 2009, 5:54 PM

Marcel de Velde wrote:

> That it has been so hard for others to give a convincing example makes

> me even more sombre about the 7th harmonic.

What do you expect, when all we get is one of two responses:

1) It's really a 5-limit interval (usually a more complex one), or

2) It's not music.

After enough iterations of this, why bother? You have only yourself to

blame if no one takes your ideas seriously.

>
> > Ok actually, this one I still have more hopes for.
> > Determine the tonality with a 5-limit mode and use 7-limit notes outside
> > that mode but in a different way than normal chromatic music.
> > So to use the 7-limit notes as more notes in thesame tonality, not
> > suggesting another tonal center / key /modulation or something like that.
> > So the 7-limit notes would kind of be like extra harmonics without any
> > normal function.
> > And once you then use notes outside the mode in a normal functional
> > chromatic way (5-limit) you get a comma shift.
> > Don't know how correct this line of thinking is.
> > Sorry for the terrible way of explaining it but I'm lousy with words :)
> >
> > Marcel
> >
>
> Whether it's correct or not, it has a following. This is basically what
> happens when a
> barbershop chord has the septimal 7th in a harmony part. Absent that part,
> you have a
> just=-tuned major triad, so the 7/4 is really just along for the ride. It
> may be a different
> matter when the lead is singing the 7th. Then the melody would have to bend
> and have
> that out of tune sound you mention.
>
> Billy

Thank you Billy!
Starting to beleive again in prime 7 for actual music :)
The more I think about it the more this seems like the right aproach.

Will experiment with this!

Marcel

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:

>
>Zhi<http://en.wikipedia.org/w/index.php?title=Xia_Zhi&action=edit&redlink=1>and
> six-note scale of Qing
>Shang<
>http://en.wikipedia.org/w/index.php?title=Qing_Shang&action=edit&redlink=1>of
> the ancient Chinese
> musicalsystem
> <http://en.wikipedia.org/wiki/Chinese_musical_system>."
>
> If this is 5 limit or not I leave up to the experts.
>

noway, but it is 1181-limit

! ShiErLue.scl
!
Old Chinese 12-tone scale, compiled by A.Sparschuh
! from the source: http://en.wikipedia.org/wiki/Shi_Er_L%C3%BC
12
!
!__________ *i; i(Huáng ZhE ng)
! that's 1/1 Yellow-bell=Fundamental-root
!
2187/2048 ! * e$'e (Dà LG) ..... 3^7/2^11
9/8 !_____! * e$*g0 (Tài Cù).... 3^2/2^3
1968/1683! *e$9i(JiáZhE ng)41*3*2^4/17/11/3^2 41-limit
81/64 !___! * e'f4 (GE+ XiGn) .... 3^4/2^5
1771/1311 ! *&#20013;e(ZhòngLG) .. 23*11*7/23*19*3=77/57=
! =(4/3)*(77/76) ~almost an PC sharper above the JI: 4/3
729/512 !__ * h$e.> (Ruí BD+n). 3^6/2^9=(9/8)^3 tritone
3/2 !______ * fi (Lín ZhE ng)... 5th
6561/4096 ! * e$7e (Yí Zé) ...... 3^8/2^12
27/16 !____ * e e (Nán LG) .... 3^3/2^4
5095/3277 ! * f e0 (Wú Yì)....1181*5/113/29 1181-limit
243/128 !__ * e:i (Yìng ZhE ng) .. 3^5/2^7
2/1
!
!

http://www.plu.edu/~youtzgl/essays/silk/Chchap9.doc

http://www.smccd.net/accounts/lapuzd/Lectures/China%20Notes.pdf

http://www.silkqin.com/02qnpu/07sqmp/sq44spwy.htm
http://www.silkqin.com/02qnpu/10tgyy/tg24hzd.htm
http://www.silkqin.com/02qnpu/05tydq/ty1c.htm

http://www.nationmaster.com/encyclopedia/Guqin-tunings

But another theory stays persisting within Pythagorean 3-limit:
http://www.hygeiasbowl.com/YellowBell.aspx

! YellowBell.scl
Chinese 12-tone scale, that stays within Pythagorean 3-limit
12
!
! Unison (doh)
! 1:1 1:1 1:1 Huang Zhon Gong (earth) Yellow-Bell fundamental-root
!
! Pythagorean Limma or Minor Diatonic Semitone (doh#) 256/243 16:15
2187/2048 ! 3^7/2^11
!
! Da Lu Major Whole Tone (re) 9:8 9:8
9/8 ! 3^2/2^3
!
! Da Cu Shang (metal) Minor Third (re#) 288:243=3^2*2^5/3^5=32/27 6:5
19683/16384 ! 3^9/2^14
!
! Jia Zhong Major Third(mi) 81:64 5:4
81/64 ! 3^4/2^5 Pyth. 3rd = Ditone (9/8)^2
!
! Gu Xian Jue (wood) Perfect Fourth (fa) 4:3 4:3
177147/131072 ! 3^11/2^17
!
! Zhong Lu qingjue Tritone (fa#) 1024/729 64:45
729/512 ! 3^6/2^11
!
! Rui Bin bianzhi Perfect Fifth (sol) 3:2 3:2
3/2
!
!Lin Zhong Zhi (fire) Minor Sixth (sol#) 768:486 8:5
6561/4096 ! 3^8/2^12
!
! Yi Ze Major Sixth (la) 27:16 5:3
27/16 ! 3^3/2^4
!
! Nan Lu Yu (water) Minor Seventh (la#) 16:9 16:9
59049/32768 ! 3^10/2^15
!
! Wu Yi run Major Seventh (ti) 243:128 15:8
243:128 ! 3^5/2^7
!
! Ying Zhong biangong Octave (doh1) 2:1 2:1 531441:262144
2/1 ! Qing Huang Zhong qing-gong (octave of Yellow-Bell)
!
!

some MP3 files
http://www.silkqin.com/06hear.htm

bye
A.S.

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, Marcel de Velde <m.develde@> wrote:
>
> > > The point
> > > is it does not matter how the thirds are tuned if they are treated
> > > as dissonances in the music.
> >
> > Hmm this sounds as if you're implying that every interval which
> > is used musically as a dissonance can be tuned whatever which way
> > the person likes and keep the same meaning?
> > There's just one meaning then which is dissonance?
> > Don't think I can agree with this.
> > If I misunderstand you can you explain how you mean it?
> >
> > Marcel
>
> The tuning of the dissonances is less important. It no doubt
> works better with the a tense interval like 81/64 (and there
> may be melodic reasons to choose it also), but 5/4 would work
> too. The grammar of the music creates the expectation that it
> must resolve, which is what musical dissonance is: an interval
> that must resolve. Besides, since 3/2 is the most concordant
> of all intervals, any other interval is more tense.
>
> -Carl
>
I think one needs a bit more theory as to what dissonances are doing
in music in the first place. If they were random dissonant sounds
whose only function was to contrast with consonant ones then indeed
the exact tuning would hardly be important, rather it would vary with
the tastes of the performers.

However in classical (post-medieval) harmony one has the rule that
*dissonances must be prepared* - meaning, of two notes sounding
dissonantly together, one must be held over from a previous
consonance. Notes that begin together must be consonant.
This means that the values of all dissonant intervals in classical
harmony are in practice determined by *differences between consonant
intervals*.
(In fact this is true in classic medieval harmony too: the 'imperfect'
consonances of thirds and sixths are determined by sums/differences of
perfect 4ths and 5ths in a more or less fixed scale. However, there is
no rule against unprepared dissonance.)

A very simple example: C-E-G -> C-D-G -> B-D-G
(common notes from one chord to the next are tied over).
The dissonance C-D is determined by the consonances C-G and D-G.

But compare C-E-G-G -> C-D-F-A -> B-D-F-G -> C-C-E-G
- now C-D is determined by the new consonances C-F, C-A and A-D: C is
the dissonance here, the new tones D-F-A must be consonant together.
So the second, as a dissonance in JI, is either 9/8 or 10/9.
(You could ask: why must C-F be consonant? - the only answer I have
is, because it's a fourth. In practice, a singer could not pitch F any
other way than as a consonant - not necessarily just! - 4th from C.)
Now in the third chord F is the dissonance - but where can the pitch
of G come from? Certainly not from holding over D, then we would end
up a comma flat (assuming JI consonances).
The 'classical' JI procedure a la Marcel would be to take G from C -
and shift D upwards such that F now makes a dissonant third with D. We
already know that tied-over *consonances* have to be shifted by commas
to keep JI on an even keel, if we accept that we would be are safe
home. One can perhaps justify shifting tied-over consonances in common
practice by thinking that the singer or player listens some newly
entered tones and adjusts the pitch to produce consonant intervals
with them.

But can tied-over dissonances always be kept exactly the same pitch,
as would be convenient for singers? Adjusting pitch, by ear, by any
controlled amount to produce a *dissonance* with new tones is more
difficult, if not impossible.
Consider
G-C-E -> F-A-E -> F-A-D -> E-G-D -> E-G-C
how, in practice, can the 4th chord be tuned from the previous one?
Marcel would no doubt want the middle part to find a G (C*3/2) which
is dissonant with all of the previous tones A,D(10/9),F, and should
cause the held-over D to get jolted up to (9/8)...

So even the classical principle that dissonant intervals are
determined by tied-over notes from previous consonances, cannot be
preserved in JI (assuming we don't accept comma-drift).
~~~T~~~

>
> G-C-E -> F-A-E -> F-A-D -> E-G-D -> E-G-C
> how, in practice, can the 4th chord be tuned from the previous one?
> Marcel would no doubt want the middle part to find a G (C*3/2) which
> is dissonant with all of the previous tones A,D(10/9),F, and should
> cause the held-over D to get jolted up to (9/8)...
>

Could be D, could be E that has the enharmonically equivalent function here.
D 10/9 9/8, E 5/4 81/64 (shifting from first to second chord)

> So even the classical principle that dissonant intervals are
> determined by tied-over notes from previous consonances, cannot be
> preserved in JI (assuming we don't accept comma-drift).
>

Yes agreed.
The classical principle doesn't make much sense anyhow, can give a zillion
JI examples where this is not the case, comma shift can just as well happen
with a dissonance as with a consonance.
Neither is any strict division between consonance and dissonance.
All rational intervals are "consonant" to some degree especially in
harmonies, and can be used in many different ways.

Marcel

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:

>... so the second, as a dissonance in JI, is either 9/8 or 10/9...

Just discern properly among that both distinct variants of
that two possible seizes, that differ 81/80 in JI.

Boethius reports about
http://en.wikipedia.org/wiki/Philolaus
"..(ca. 480 BC â€" ca. 385 BC)...
that he had subdivided the Pythagorean heptatonic-octave of
5-tones 9/8 and 2-limmata 256/243
again into

1: the 5 tones (9/8) ~204c each into 9 subparts, of about ~22.6c
2: the 2 limma (256/243) ~90c into 4 subparts, of about ~22.5c

That procedure refines the coarse 12-tone decompostion of octave
into an more precise advanced resolution of accuracy:

53commata := 45 + 8 = (5-tones)*9 + (2-limmata)*4

Then probably somewhat later in India
the legendary alleged inventor of the modern 22-shruti-scale:
http://en.wikipedia.org/wiki/Bharata_Muni
"...dated to between roughly 400 BC and 200 BC..."
tryed something simlar:
http://www.plainsound.org/pdfs/bharata.pdf
likely in 5-limit terms.
Moreover B. is supposed that he had perhaps
invented again somehow an crude 53-division acoustically,
when tuning ~by-ear~ two 26-tone
vinha-haprps that were identical in construction
by the displacement of 1-comma among both instruments
allways in reference against the fix fundamental-root sadja:

53 := 1 + 26 + 26

That works similar alike my own recent:
poppy-seed-comma 53 dyadic
using the 26 letters arranged in alphabetically order:
53 := |@| + |A...Z| + |a...z| = 1 + 26 + 26
as done in
/tuning/topicId_22165.html#81808

Eventually
http://en.wikipedia.org/wiki/Jing_Fang
~(78â€"37 BC) obtained a better one, when yielding:
"The final value he gave for the ratio between this 53rd fifth and the
original was 177147 / 176776."

So far about the ~2 millenia old (pre)history
http://en.wikipedia.org/wiki/53_equal_temperament#History

In contrast to Tom's working-hypothesis:
>...assuming we don't accept comma-drift...

Counter-proposal,
from a old physicist point of view:

Attend when performing functional modulations
I.Newton's 1664 hexachordic "commata-drifts"
fully aware with care
http://societymusictheory.org/mto/issues/mto.93.0.3/mto.93.0.3.lindley7.gif
Later did H.Helmholtz & his pupil M.Planck attend such drifts so too,
not to mention my own master Martin Vogel.

bye
A.S.

Yes 53tet is amazing.Perfect for 5-limit JI, I'd call it JI since it's so
close to JI I consider it just as good.
And you keep thesame logic and music theory as with pure 5-limit JI.
Only trouble is that it's 53 tones per octave, this is large.
But if you want to have a fixed scale where you can play everything
(5-limit) in every key 53tet is the best.

Marcel

53 is amazing indeed. I like 72 as well. Between those two all of my
needs are met.

Tunings like 19 and 22 and 31 are pretty hip as well - 41 I've never
liked though.

-Mike

On Wed, Feb 25, 2009 at 4:02 PM, Marcel de Velde <m.develde@...> wrote:
> Yes 53tet is amazing.
>
> Perfect for 5-limit JI, I'd call it JI since it's so close to JI I consider
> it just as good.
> And you keep thesame logic and music theory as with pure 5-limit JI.
> Only trouble is that it's 53 tones per octave, this is large.
> But if you want to have a fixed scale where you can play everything
> (5-limit) in every key 53tet is the best.
> Marcel
>
>

Andreas Sparschuh wrote:

> ! ShiErLue.scl
> !
> Old Chinese 12-tone scale, compiled by A.Sparschuh > ! from the source: http://en.wikipedia.org/wiki/Shi_Er_L%C3%BC

I don't trust that at all. It's a Pythagorean (implicitly schismatic?) scale rounded off to four figures. I haven't seen any Chinese sources for the rounding. I'll check your references.

Graham

Andreas Sparschuh wrote:

> http://www.silkqin.com/02qnpu/07sqmp/sq44spwy.htm
> http://www.silkqin.com/02qnpu/10tgyy/tg24hzd.htm
> http://www.silkqin.com/02qnpu/05tydq/ty1c.htm

That site gives optional JI tunings for the studs:

http://www.silkqin.com/08anal/tunings.htm

All 5-limit except for one in the 7-limit. Combine these with the instructions in your last link and I get the following scale:

1/1 20/19 45/41 6/5 5/4 4/3 24/17 3/2 30/19 5/3 30/17 15/8 2/1

The parenthetical "correct" tunings work out as:

1/1 48/37 80/71 240/203 100/79 4/3 10/7 3/2 30/19 100/59 25/14 100/53 2/1

They look like approximations to Pythagorean notes but I haven't checked them all.

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
hi Graham,
appearently the questionable alleged ratios
> > ! from the source: http://en.wikipedia.org/wiki/Shi_Er_L%C3%BC
were overtaken from the last chart at the end of the page:

http://www.wfu.edu/~moran/Cathay_Cafe/G_tar.html

Ptolemy vs. alleged Chinese
"
1 / 1 A: 1/1
16/15 A# 2187/2048
9 / 8 B: 9/8
6 / 5 C: 1968/1638
5 / 4 C# 81/64
4 / 3 D: 1771/1311
7 / 5 D# 729/512
3 / 2 E: 3/2
8 / 5 F: 6561/4096
5 / 3 F# 27/16
7 / 4 G: 5905/3277
15/ 8 G# 243/128
2 / 1 A: 2/1

Probably here the author refers to the
http://en.wikipedia.org/wiki/Tetrachord
of
"Ptolemy soft chromatic 28:27, 15:14, 6:5"

or also found too in
http://eamusic.dartmouth.edu/~larry/published_articles/divisions_of_the_tetrachord/chapter2.pdf
on p.5 #14
"28/27 15/14 6/5 PTOLEMY SOFT CHROMATIC"

http://www.absoluteastronomy.com/topics/Tetrachord

> I don't trust that at all.
Me too.

the crude ratios on C,D and G sound very dodgy in my ears.

> It's a Pythagorean (implicitly schismatic?)
Most Chinese scale do persist in keeping plain 3-limit
regardless without careing about any higher limit than Pythagorean.

> scale rounded off to four figures.

looks quite-clear fishy, especially on the 3 cases

C: 1968/1638
D: 1771/1311
A: 5905/3277

> I haven't seen any Chinese sources for the rounding.
that crude ratios appear also in the discussion forum in Feb./2007 :

http://www.pjnet.com.my/ftopic-4055-days0-orderasc-120.html

> I'll check your references.
Very probably barely guff.

Sorry for the misleading astray.

bye
A.S.

Ok, so 53TET allows virtually perfect 5-limit.
So what EDO-type tuning allows perfect 7-limit (more or less)?

--- On Wed, 2/25/09, Marcel de Velde <m.develde@...> wrote:

From: Marcel de Velde <m.develde@...>
Subject: Re: [tuning] Re: 5-limit JI vs 7-limit JI, space-resolved in 53-tone
To: tuning@yahoogroups.com
Date: Wednesday, February 25, 2009, 1:02 PM

Yes 53tet is amazing.Perfect for 5-limit JI, I'd call it JI since it's so close to JI I consider it just as good.And you keep thesame logic and music theory as with pure 5-limit JI.Only trouble is that it's 53 tones per octave, this is large.
But if you want to have a fixed scale where you can play everything (5-limit) in every key 53tet is the best.
Marcel

--- In tuning@yahoogroups.com, Michael Sheiman <djtrancendance@...> wrote:
>
> Ok, so 53TET allows virtually perfect 5-limit.
> So what EDO-type tuning allows perfect 7-limit (more or less)?

The 5-limit TOP damage of 53-ET is 0.3033. The first ET
to hit that kind of performance in the 7-limit is 99-ET, coming
in at 0.3391.

-Carl

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:

> All 5-limit except for one in the 7-limit. Combine these
> with the instructions in your last link and I get the
> following scale:
>
Hi Graham,
just consider the Pythagorean 3-limit approximations of that:

1/1
20/19 = (256/243)(1215/1216)Erasthostenes 19-limit approx of the limma
45/41 = (9/8)(40/41)
6/5 = (32/27)(81/80)
5/4 = (81/64)(80/81)
4/3
24/17 = (729)(4096/4131) = (7/5)(120/119)
3/2
30/19 = (128/81)(1215/1216)
5/3 = (27/16)(80/81)
30/17 = (16/9)(135/136)
15/8 = (243/128)(80/81)
2/1
>
> The parenthetical "correct" tunings work out as:
>
> 1/1 48/37 80/71 240/203 100/79 4/3 10/7 3/2 30/19 100/59
> 25/14 100/53 2/1
>
> They look like approximations to Pythagorean notes but I
> haven't checked them all.
>
in deed,
here my own check vs. the ordinary 3-limit intervals:

1/1
48/37 ??? ~450.6 cents, hence none semi-tone, wrong ratio ???
80/71 = (9/8)(640/639)
240/203 = (32/27)(405/406)
100/79 = (81/64)(6400/6399) = (5/4)(80/79)
4/3
10/7 = (729/512)(5120/5103)
3/2
30/19 = (128/81)(1215/1216)
100/59 = (27/16)(1600/1593)
25/14 = (16/9)(225/224)
100/53 = (243/128)(12800/12879)
2/1

What do you think about:
http://www.silkqin.com/08anal/tunings.htm
"
2. Background: Modern standard note frequencies in Hertz
(Hz [= vib/sec])
Note the following approximate modern concert pitch levels of a
chromatic scale beginning one octave below A = 440 Hz. Some qin
players today insist that the first (lowest) string on a qin should be
tuned to this modern concert C (262 Hz on this chart). However, there
is no historical evidence to support this claim."

Pitch
220 A
233 A#
247 B
262 C
277 C#
294 D
311 D#
330 E
349 F
370 F#
392 G
415 G#
440 A
"

hmm, that sounds similar as my own old piano:

525 c" tenor-C5
555 #"
588 d"
624 #"
658 e"
702 f"
740 #"
786 g"
880 a" := 2 * 440Hz
936 #"
987 b"
1050c''' sopran-C6

obtained from the 5ths-circle

A: 110 220 440Hz
E: 329 (<330)
B: 987
F# 185 370 740 1480 2960 (<2961)
C# 555
G# 13 ... 416 832 1664 (<1665)
D# 39
A# 117
F: (175 350 <) 351
C: (131 262 524 <) 525 = 7*5*5 hence within 7-smooth-limit
G: (7*7 = 49 98 196 392 <) 393 from Werckmeister's "Septenarius"
D: 147
A: 440 (< 441 = 7^2*3^2)

! Sparschuh12.scl
!
Sparschuh's old piano @ c"=575Hz & a"=880Hz in 'Septenarian' style
12
!
37/35 !_! C#
196/175 ! D
208/175 ! D#
94/75 !_! E
234/175 ! F
148/105 ! F#
262/175 ! G
832/525 ! G#
176/105 ! A
312/175 ! A#
47/25 !_! B
2/1
!
!

bye
A.S.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
Hi Mike & Marcel,

> 53 is amazing indeed.
due to wide gap within 53-EDO and 200-EDO that appears in

http://www.research.att.com/~njas/sequences/A060528

> I like 72 as well
but in the
http://en.wikipedia.org/wiki/72_equal_temperament
the 5ths the same ~-1.96..C off as in 12-EDO,
as critizised in:

http://anaphoria.com/mjm1.pdf
in the pdf-file on
p.20
Janko:
http://en.wikipedia.org/wiki/Paul_von_Janko
the inverntor of
http://en.wikipedia.org/wiki/Janko_keyboard
"...the 5ths must be better than the one found in 12-tone equal
temperament"
p.21 in the pdf:
Partch:
http://en.wikipedia.org/wiki/Harry_Partch
footnote 37
...even 2-Cents is an excessive alteration: Ref:
"A heared 2-Cents discrepancy is a sensible difference in
simutaneous soundings"

For this reason P. opposes against 12-edo by his own
http://en.wikipedia.org/wiki/Harry_Partch%27s_43-tone_scale

In my own view
tempered 5ths can tolerate well an deviation of maximal:
/tuning/topicId_22165.html#81808

" 53: B+ 1 ... 2048 (< 2049)"
or
1200 Cents * ln(2049/2048)/ln(2) = ~0.845...Cents off,

as there in ultimate 53th concluding step, when retuning
back home to the fundamental root C\\ = 1/1.

All the 52 other 5ths before that last one
depart even less than the difference 2049/2048.

> Tunings like 19 and 22 and 31 are pretty hip as well

The 5ths errors versus the JI 3/2=1.5
amount for pure quintes in that crude 19, 22 & 31 EDOs

http://en.wikipedia.org/wiki/19_equal_temperament
~ -7.218...Cents
http://en.wikipedia.org/wiki/22_equal_temperament
~ +7.14...Cents
http://en.wikipedia.org/wiki/31_equal_temperament
~ -5.19...Cents

Result:
All the 3 turn out in the 5ths even worser than in 12-EDO,
hence refused, at least in my ears.

>- 41 I've never liked though.
Ok, let's consider:
http://en.wikipedia.org/wiki/41_equal_temperament
~ +0.48...Cents for the 5ths is well,
but i do agree with you, that the
"major third 5:4" located @ ~386.31...Cents,
deviates with ~-5.83...Cents difference to much flattend off.

Marcel wrote:
> > Yes 53tet is amazing.
> >
> > Perfect for 5-limit JI,
> > I'd call it JI since it's so close to JI I consider
> > it just as good.
Fully agreed.
> > And you keep the same logic and music theory
> > as with pure 5-limit JI.
An real significant advantage.

> > Only trouble is that it's 53 tones per octave, this is large.
No problem, if you can handle playing in that:
http://www.cortex-design.com/body-project-terpstra-1.htm

> > But if you want to have a fixed scale where you can play
> > everything
> > (5-limit) in every key 53tet is the best.
as for instance realized in an appropriate layout alike
http://www.cortex-design.com/body-project-terpstra-3.htm
There you can even distinct inbetween 53-enharmonics,
when separating

E// ~ F\\ and B// ~ C\\

that are usually identically in 53,
due to compensating the
http://en.wikipedia.org/wiki/Mercator%27s_comma
3^53/2^84 ~3.615...c
over 53 more or less tempered 5ths.

bye
A.S.

Andreas Sparschuh wrote:

> What do you think about:
> http://www.silkqin.com/08anal/tunings.htm
> "
> 2. Background: Modern standard note frequencies in Hertz > (Hz [= vib/sec])
> Note the following approximate modern concert pitch levels of a
> chromatic scale beginning one octave below A = 440 Hz. Some qin
> players today insist that the first (lowest) string on a qin should be
> tuned to this modern concert C (262 Hz on this chart). However, there
> is no historical evidence to support this claim."

<snip>
> hmm, that sounds similar as my own old piano:
<snip>
> obtained from the 5ths-circle

Yes, probably. Theoretical Chinese tunings have been Pythagorean for a long time now. The imperial authorities specified Pythagorean tuning and you can understand that theorists weren't going to openly disagree with it. There may be clues to other tunings buried in the literature but I don't know if there's any insight to be gained in digging them out. Actual intonation, especially in folk music, is frequently a long way from Pythagorean, and has probably always been so. There are plenty of flexible-pitch instruments (including the guqin) and the bureaucrats probably didn't know and didn't care what noises they made.

This is an interesting page:

http://www.silkqin.com/08anal/intn.htm

The author plainly knows what he's talking about, knows about just intonation, and has studied the primary sources. Maybe he places too much emphasis on fixed intonation, but never mind that. If anybody wants to study more there are references and more explanations on the site. There's written music going back to the Ming Dynasty, and some more recent notation with exact pitch specifications. Plenty to analyze.

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> Maybe he places too much emphasis on fixed intonation, but
> never mind that.

hi Graham,

but

http://www.colorado.edu/MCDB/MCDB3650/DeutschAbsolutePitch.pdf
http://www.mmk.e-technik.tu-muenchen.de/persons/ter/top/absolute.html

"...It is said that - in Europe and USA - about 3% of the population
are AP possessors. When one selects persons who are professional or
semi-professional musicians (e.g., students at music conservatories),
about 8% AP possessors are found in that group [57], [62]. Most
remarkably, however, in Japan nearly 70% of students at music
conservatories are AP possessors..."

so in China it is more common than in the western-world
http://www.colorado.edu/MCDB/MCDB3650/DeutschAbsolutePitch.pdf

http://www.apa.org/monitor/feb05/pitch.html

alike all Indian scales refer to the
absolute basic-root pitch: 'SA'
http://www.chandrakantha.com/articles/scales.html
http://www.batish.com/archives/arcgloss.html
"Shadaja - First musical note (Sa). A. k. a. Kharaja"
http://en.wikipedia.org/wiki/Hindustani_classical_music
"Sa (Shadaj) = Do"
http://en.wikipedia.org/wiki/%C5%9Aruti_(music)

so does the Chinese refer all other pitches to the:

Huang-Zhong ( engl. Yellow-Bell)

http://www.smccd.net/accounts/lapuzd/Lectures/China%20Notes.pdf
http://cicm.mshparisnord.org/ColloqueXenakis/papers/Jones,%20Wong.pdf
http://www.tagg.org/xpdfs/origins3.pdf
http://music.chosta.net/details/126.html
". From the principal tone huang zhong ("yellow bell") eleven
additional pitches were derived using intervals of fourths and fifths.
This fundamental tone is said to have mystical powers. It is the
eternal principle of the universe and the fundament for the well-being
of the state. Different dynasties used complicated systems of
measurement to arrive at "their" fundamental tone. A sensitive ear was
thus vital for the development of Chinese music."

bye
A.S.

I also read somewhere that historically the musical pitch was also used as the basis of the weights and measurement system, rather like the meter in Paris is used for the metric system.

Do you happen to have any more info on this?

On 28 Feb 2009, at 20:54, Andreas Sparschuh wrote:

> --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
> >
> > Maybe he places too much emphasis on fixed intonation, but
> > never mind that.
>
> hi Graham,
>
> but
>
> http://www.colorado.edu/MCDB/MCDB3650/DeutschAbsolutePitch.pdf
> http://www.mmk.e-technik.tu-muenchen.de/persons/ter/top/absolute.html
>
> "...It is said that - in Europe and USA - about 3% of the population
> are AP possessors. When one selects persons who are professional or
> semi-professional musicians (e.g., students at music conservatories),
> about 8% AP possessors are found in that group [57], [62]. Most
> remarkably, however, in Japan nearly 70% of students at music
> conservatories are AP possessors..."
>
> so in China it is more common than in the western-world
> http://www.colorado.edu/MCDB/MCDB3650/DeutschAbsolutePitch.pdf
>
> http://www.apa.org/monitor/feb05/pitch.html
>
> alike all Indian scales refer to the
> absolute basic-root pitch: 'SA'
> http://www.chandrakantha.com/articles/scales.html
> http://www.batish.com/archives/arcgloss.html
> "Shadaja - First musical note (Sa). A. k. a. Kharaja"
> http://en.wikipedia.org/wiki/Hindustani_classical_music
> "Sa (Shadaj) = Do"
> http://en.wikipedia.org/wiki/%C5%9Aruti_(music)
>
> so does the Chinese refer all other pitches to the:
>
> Huang-Zhong ( engl. Yellow-Bell)
>
> http://www.smccd.net/accounts/lapuzd/Lectures/China%20Notes.pdf
> http://cicm.mshparisnord.org/ColloqueXenakis/papers/Jones,%20Wong.pdf
> http://www.tagg.org/xpdfs/origins3.pdf
> http://music.chosta.net/details/126.html
> ". From the principal tone huang zhong ("yellow bell") eleven
> additional pitches were derived using intervals of fourths and fifths.
> This fundamental tone is said to have mystical powers. It is the
> eternal principle of the universe and the fundament for the well-being
> of the state. Different dynasties used complicated systems of
> measurement to arrive at "their" fundamental tone. A sensitive ear was
> thus vital for the development of Chinese music."
>
> bye
> A.S.
>
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

Charles Lucy wrote:
> I also read somewhere that historically the musical pitch was also used as the > basis of the weights and measurement system, rather like the meter in Paris is > used for the metric system.
> > Do you happen to have any more info on this?

Yes, it's in one of the references of the message you top-quoted:

>> http://www.tagg.org/xpdfs/origins3.pdf

'An Imperial Office of Music (Yuefu) was founded under the Emperor Wu (141-87 BP)
for standardising pitch, supervising music and building up musical archives. The
Chinese had long previously recognised the relationship of musical pitch to the
length and capacity of a tube and so it was that this organisation was attached to the
Office of Weights and Measures� (Crossley-Holland 1959:48).
�The basic lu pipe preserved in this office was also used as a standard measurement
for length and weight. Thus, the music office was a bureau of the Office of Weights
and Measurements and remained so through many dynasties� (Malm 1977:152).

In think "BP" means "BC". Maybe part of the conspiracy to keep the Chinese from learning what the "C" stands for. This link claims "Before Present" from a vantage point of 1950 AD (whoever he was):

http://highered.mcgraw-hill.com/sites/0767430220/student_view0/glossary.html

But they're plainly talking about this Emperor Wu:

http://en.wikipedia.org/wiki/Emperor_Wu_of_Han

Graham

Graham,
 
Please correct your statement that:  "In think "BP" means "BP".

--- On Sat, 2/28/09, Graham Breed <gbreed@...> wrote:

From: Graham Breed <gbreed@...>
Subject: Re: [tuning] Old chinese 1181-limit 12-tone ratios, was Re: 5-limit JI vs 7-limit JI
To: tuning@yahoogroups.com
Date: Saturday, February 28, 2009, 5:26 PM

Charles Lucy wrote:
> I also read somewhere that historically the musical pitch was also used as
the
> basis of the weights and measurement system, rather like the meter in
Paris is
> used for the metric system.
>
> Do you happen to have any more info on this?

Yes, it's in one of the references of the message you
top-quoted:

>> http://www.tagg.org/xpdfs/origins3.pdf

'An Imperial Office of Music (Yuefu) was founded under the
Emperor Wu (141-87 BP)
for standardising pitch, supervising music and building up
musical archives. The
Chinese had long previously recognised the relationship of
musical pitch to the
length and capacity of a tube and so it was that this
organisation was attached to the
Office of Weights and Measures’ (Crossley-Holland 1959:48).
‘The basic lu pipe preserved in this office was also used as
a standard measurement
for length and weight. Thus, the music office was a bureau
of the Office of Weights
and Measurements and remained so through many dynasties’
(Malm 1977:152).

In think "BP" means "BC". Maybe part of the conspiracy to
keep the Chinese from learning what the "C" stands for.
This link claims "Before Present" from a vantage point of
1950 AD (whoever he was):

http://highered.mcgraw-hill.com/sites/0767430220/student_view0/glossary.html

But they're plainly talking about this Emperor Wu:

http://en.wikipedia.org/wiki/Emperor_Wu_of_Han

Graham

------------------------------------

You can configure your subscription by sending an empty email to one
of these addresses (from the address at which you receive the list):
tuning-subscribe@yahoogroups.com - join the tuning group.
tuning-unsubscribe@yahoogroups.com - leave the group.
tuning-nomail@yahoogroups.com - turn off mail from the group.
tuning-digest@yahoogroups.com - set group to send daily digests.
tuning-normal@yahoogroups.com - set group to send individual emails.
tuning-help@yahoogroups.com - receive general help information.
Yahoo! Groups Links

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> Charles Lucy wrote:
> > I also read somewhere that historically
> > the musical pitch was also used as the
> > basis of the weights and measurement system,....

Hi Charles & Graham,
that ancient pitches are preserved in bronze-bells and
sounding-stones:

http://www.chinesemusic.net/book_instruments_trends.php
http://www.chinesemusic.net/feature_jasmine_blossom.php

some examples with pics:
http://arts.cultural-china.com/en/94Arts1438.html
http://www.cultural-china.com/chinaWH/html/en/28Arts1438.html
http://www.arts.cornell.edu/Knight_institute/publicationsprizes/discoveries/discoveriesspring2006/07du.pdf
http://www.uh.edu/engines/epi175.htm
http://www.china.org.cn/english/features/FbiCh/78450.htm
http://www.uh.edu/engines/epi1676.htm
http://www.cuhk.edu.hk/ics/amm/acquisition/bronze_3e.htm
in a set:
http://www.gochinaadventure.com/public/ebbs/Disbbs.asp?boardid=1&replyid=17&ID=17&Page=1
here an modern reproduction of that
http://www.vases.biz/bianzhong.htm

A scientific pitch determiantion:
http://www.gochinaadventure.com/public/ebbs/Disbbs.asp?boardid=1&replyid=17&ID=17&Page=1

Museum with 47-ton bell:
http://www.travelpod.com/ad/Big_Bell_Temple_Da_Zhong_Si-Beijing
http://www.frommers.com/destinations/beijing/A19174.html
http://travel.ciao.co.uk/Big_Bell_Temple_Da_Zhong_Si_Beijing__6246909
>

Graham replied:
> Yes, it's in one of the references of the message you
> top-quoted:
>
> >> http://www.tagg.org/xpdfs/origins3.pdf
>
attend:
in that article the questionable author
confuses there wrongly the originally 5-limit Indian

http://en.wikipedia.org/wiki/%C5%9Aruti_(music)
http://www.22shrutiharmonium.com/research_topic_31.asp
/tuning/topicId_74961.html#74973
http://www.22shrutiharmonium.com/research_topic_32.asp
(&ct...then click several times the <NEXT-TOPIC> button)

with the Bosanquet's modern invention of

http://en.wikipedia.org/wiki/22_equal_temperament

as probably faulty overtaken
from overaged British 19-th century obsolete view:
http://www.geocities.com/threesixesinarow/hindoo.htm
that meanwhile got outdated for explaining the 22 shrutis.

bye
A.S.

Andreas Sparschuh wrote:
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>> Charles Lucy wrote:
>>> I also read somewhere that historically >>> the musical pitch was also used as the >>> basis of the weights and measurement system,....
> > Hi Charles & Graham,
> that ancient pitches are preserved in bronze-bells and
> sounding-stones:

Yes, we know that. What about the basis of weights and measures?

> some examples with pics:
<snip>
> http://www.uh.edu/engines/epi1676.htm
<snip>

This is the only one that answers the question, but it's vague:

"Once historians began piecing the record together, they realized these strange bells played a role beyond music-making. For consistency of tone, they were all tuned against a standard string. The consistency of their shape made them a standard of volumetric measure. The amount of bronze in each was so carefully controlled as to provide weight standard. Each set of bells was a mini-bureau of standards in ancient China."

> A scientific pitch determiantion:
> http://www.gochinaadventure.com/public/ebbs/Disbbs.asp?boardid=1&replyid=17&ID=17&Page=1

No scientific pitch determination that I can see.

> Museum with 47-ton bell:
> http://www.travelpod.com/ad/Big_Bell_Temple_Da_Zhong_Si-Beijing
> http://www.frommers.com/destinations/beijing/A19174.html
> http://travel.ciao.co.uk/Big_Bell_Temple_Da_Zhong_Si_Beijing__6246909

Is this something we're supposed to care about?

> Graham replied:
>> Yes, it's in one of the references of the message you >> top-quoted:
>>
>> >> http://www.tagg.org/xpdfs/origins3.pdf
>>
> attend:
> in that article the questionable author > confuses there wrongly the originally 5-limit Indian
>
> http://en.wikipedia.org/wiki/%C5%9Aruti_(music)
> http://www.22shrutiharmonium.com/research_topic_31.asp
> /tuning/topicId_74961.html#74973
> http://www.22shrutiharmonium.com/research_topic_32.asp
> (&ct...then click several times the <NEXT-TOPIC> button)

None of these deal with the origins in an adequate way. These are better:

http://www.plainsound.org/pdfs/srutis.pdf

http://www.plainsound.org/pdfs/bharata.pdf

But they still don't prove an explicitly 5-limit system, rather than a schismatic one.

> with the Bosanquet's modern invention of
> > http://en.wikipedia.org/wiki/22_equal_temperament

So, back to the issue, where are you saying the author confused 5-limit JI with 22-equal, and what does it have to do with Chinese music?

Graham

Andreas Sparschuh wrote:
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>> Maybe he places too much emphasis on fixed intonation, but >> never mind that. > > hi Graham,
> > but
> > http://www.colorado.edu/MCDB/MCDB3650/DeutschAbsolutePitch.pdf
> http://www.mmk.e-technik.tu-muenchen.de/persons/ter/top/absolute.html
> > "...It is said that - in Europe and USA - about 3% of the population
> are AP possessors. When one selects persons who are professional or
> semi-professional musicians (e.g., students at music conservatories),
> about 8% AP possessors are found in that group [57], [62]. Most
> remarkably, however, in Japan nearly 70% of students at music
> conservatories are AP possessors..." Not the best of quotes because it doesn't mention China.

> so in China it is more common than in the western-world
> http://www.colorado.edu/MCDB/MCDB3650/DeutschAbsolutePitch.pdf
> > http://www.apa.org/monitor/feb05/pitch.html

Yes, so what does it have to do with the issue at hand? How does having absolute pitch stop a musician from stopping a string at the position he wants to stop it, instead of retuning the string so that it sounds right if he stops it at the theoretically correct position?

> alike all Indian scales refer to the
> absolute basic-root pitch: 'SA'
> http://www.chandrakantha.com/articles/scales.html
> http://www.batish.com/archives/arcgloss.html
> "Shadaja - First musical note (Sa). A. k. a. Kharaja"
> http://en.wikipedia.org/wiki/Hindustani_classical_music
> "Sa (Shadaj) = Do"
> http://en.wikipedia.org/wiki/%C5%9Aruti_(music)

All scales by definition refer to a root pitch. The Indian system is mainly about relative pitch. At least, none of your references have convinced me otherwise.

> so does the Chinese refer all other pitches to the:
> > Huang-Zhong ( engl. Yellow-Bell)

Yes, we know about that. But what does it mean to a practicing musician? Chinese musical notations have always been relative to the tonic, like with jianpu (which isn't itself Chinese). We know there were 12 note scales defined with fixed, precise pitches. Did musicians really care about that precision? And why does it matter?

> http://www.smccd.net/accounts/lapuzd/Lectures/China%20Notes.pdf
> http://cicm.mshparisnord.org/ColloqueXenakis/papers/Jones,%20Wong.pdf

This is good because although not much it has some interesting factoids.

"Evidence of the use of just intonation emerges in the 6th century CE, in surviving performance
indications for the ancient Qin (7-stringed zither) that reveals a use of harmonics befitting just intonation.
It is assumed, though, that the revered blind musician-sages of antiquity would have been able to manage
their tuning by ear without needing to resort to visible markings. There is evidence for the de facto
existence of equal temperament in fretted instruments as far back as the 2nd century BCE, but no actual
theory of equal temperament was promulgated until 1584 [9]."

And under "Multiple Temperaments" they talk about a feature of Chinese music that's often overlooked:

"""
Characteristic of the music of Ancient China and contemporary Chinese folk ensembles is the
simultaneous use in performance of tunings derived from the open cycle of fifths, just intonation, equal
temperament, and the higher overtone series. To a western listener this �sweet-and-sour� combination is
bewildering, and even distressing, but it is consistent with the broader axioms of Chinese thought in its
appreciation of what to a western mind are contradictory positions. Chinese musicologist Liang Mingyue
observes: �This poly-temperament phenomenon is an important trait in Chinese music, providing an �out-
of-tune� flavor. It is as essential an ingredient in Chinese music as spice is to its cuisine.� [4: 23]
"""

What this says is that the instruments are out of tune with each other. I'd like to see the evidence for just intonation and equal temperament.

> http://www.tagg.org/xpdfs/origins3.pdf

This is the one you've since repudiated.

> http://music.chosta.net/details/126.html
> ". From the principal tone huang zhong ("yellow bell") eleven
> additional pitches were derived using intervals of fourths and fifths.
> This fundamental tone is said to have mystical powers. It is the
> eternal principle of the universe and the fundament for the well-being
> of the state. Different dynasties used complicated systems of
> measurement to arrive at "their" fundamental tone. A sensitive ear was
> thus vital for the development of Chinese music."

That's an advert for a CD. Hardly a reliable source. But still, it's about mysticism and astrology. Theoretical ideas applied to music not coming from it.

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:

Graham asked:
> What about the basis of weights and
> measures?

http://www.ihns.ac.cn/English/journals/shns/abstracts/2006/200603.htm
"Research on the Xian Qin Huangzhong Pipe: An Attempt to Calculate the Inside Diameter of Huangzhong Pipe with Modern Acoustic Formula...
... states that the Huangzhong pitch pipe has a length of 3.9 cun,whereas according to the literature of Han Dynasty,it is 9 cun long. The authors made a comprehensive survey to find out the real length of the pipe. It is the Qing Huangzhong pipe that is recorded in Lshi Chunqiu. And its pitch is octachord of 9 cun Huangzhong pipe. Using the currently accepted acoustic formula, it can be inferred that the inside diameter of the Xian Qin bamboo pipe must be about 0.71 cun. This paper also argues that the 8.1 cun pipe hypothesis and the 8.71 cun pipe hypothesis are groundless."

http://www.plu.edu/~youtzgl/essays/silk/Chchap9.doc

http://books.google.de/books?id=Lgs4AAAAIAAJ&pg=PA119&lpg=PA119&dq=huang-zhong+pitch+japan&source=bl&ots=RoNdOrzz9C&sig=RPRXJcu5oQIrcTeCbdKfCyXpBdg&hl=de&ei=uFuuSabCKczD_gbZjsTPBg&sa=X&oi=book_result&resnum=10&ct=result#PPA121,M1

But the far-east musicologist: Britten Dean wrote about that in his
comments on:
"Mr. Gi's Music-Book"
'An Annotated Translation of Gi Shimei's Gi-shi Gakufu,
by Britten Dean Monumenta Nipponica XXXVII,3 p. 317-322 © 1982
http://www.jstor.org/stable/2384388?seq=13
Quote, p.329, footnote 40:
"HUANG-ZHONG was the absolute pitch in the Chinese system,
and it varied over the dynastiese between c#' and a';
it was also the name of the mode based on this pitch....
....For a convenient summary of these tonal systems,
see (author) Ongaku Jitzen {some Hanzi-characters}
Heibonza, 1955-1957, v, pp.28-31."

there had been also sone other cultural changes
https://eprints.soas.ac.uk/2987/1/ARC_to_Japanese_Music_Ch1_for_RAE.pdf
over the dynasties, when the preferred taste had changed within time.

http://www.zoeybot.com/soswp/wp/g/Guqin.htm
"...There are more than 20 different tunings used in qin music, out of which only between two and four are commonly used. Some of these, however, are actually alternate names for the same tuning. A single tuning can have several different names depending on which system the composer was taught and used; an additional confusion is caused by the fact that two different tunings can share the same name. For example, huangzhong diao ci;ih*?/i;;ih0c could mean either "lower first string and tighten fifth string" (e.g. Shenqi Mipu, etc), "lower third string" (e.g. Qinxue Lianyao), or normal tuning (e.g. Mei'an Qinpu). Another potentially confusing problem is the naming of some of the tunings which may have misleading names, like the ruibin tuning. Ruibin is the name of the Chinese pitch which Western equivalent is "Fb/", but that note does not appear or is used in the tuning, and so it is difficult to explain the logic in the naming...."

bye
A.S.

Andreas Sparschuh wrote:
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:

>> What about the basis of weights and >> measures?
> > http://www.ihns.ac.cn/English/journals/shns/abstracts/2006/200603.htm
> "Research on the Xian Qin Huangzhong Pipe: An Attempt to Calculate the Inside Diameter of Huangzhong Pipe with Modern Acoustic Formula...
> ... states that the Huangzhong pitch pipe has a length of 3.9 cun,whereas according to the literature of Han Dynasty,it is 9 cun long. The authors made a comprehensive survey to find out the real length of the pipe. It is the Qing Huangzhong pipe that is recorded in Lshi Chunqiu. And its pitch is octachord of 9 cun Huangzhong pipe. Using the currently accepted acoustic formula, it can be inferred that the inside diameter of the Xian Qin bamboo pipe must be about 0.71 cun. This paper also argues that the 8.1 cun pipe hypothesis and the 8.71 cun pipe hypothesis are groundless."

And that's all we have -- the abstract. Nothing to say why they care so much about the length of the pipe, or the original chinese names. Nothing about the pipe being the *basis* for weights and measures, as Charles originally asked.

> http://www.plu.edu/~youtzgl/essays/silk/Chchap9.doc

This is a proprietary format.

> http://books.google.de/books?id=Lgs4AAAAIAAJ&pg=PA119&lpg=PA119&dq=huang-zhong+pitch+japan&source=bl&ots=RoNdOrzz9C&sig=RPRXJcu5oQIrcTeCbdKfCyXpBdg&hl=de&ei=uFuuSabCKczD_gbZjsTPBg&sa=X&oi=book_result&resnum=10&ct=result#PPA121,M1

I don't have page 122 and I don't see anything relevant in the neighboring pages.

> But the far-east musicologist: Britten Dean wrote about that in his
> comments on:
> "Mr. Gi's Music-Book"
> 'An Annotated Translation of Gi Shimei's Gi-shi Gakufu,
> by Britten Dean Monumenta Nipponica XXXVII,3 p. 317-322 � 1982 > http://www.jstor.org/stable/2384388?seq=13
> Quote, p.329, footnote 40:
> "HUANG-ZHONG was the absolute pitch in the Chinese system,
> and it varied over the dynastiese between c#' and a';
> it was also the name of the mode based on this pitch....
> ....For a convenient summary of these tonal systems,
> see (author) Ongaku Jitzen {some Hanzi-characters}
> Heibonza, 1955-1957, v, pp.28-31."

What of it?

> there had been also sone other cultural changes
> https://eprints.soas.ac.uk/2987/1/ARC_to_Japanese_Music_Ch1_for_RAE.pdf
> over the dynasties, when the preferred taste had changed within time.

That's about Japan, as the URL suggests. Is it news that tastes change in any random country?

> http://www.zoeybot.com/soswp/wp/g/Guqin.htm
> "...There are more than 20 different tunings used in qin music, out of which only between two and four are commonly used. Some of these, however, are actually alternate names for the same tuning. A single tuning can have several different names depending on which system the composer was taught and used; an additional confusion is caused by the fact that two different tunings can share the same name. For example, huangzhong diao 〈黃鐘調/黄钟调〉 could mean either "lower first string and tighten fifth string" (e.g. Shenqi Mipu, etc), "lower third string" (e.g. Qinxue Lianyao), or normal tuning (e.g. Mei'an Qinpu). Another potentially confusing problem is the naming of some of the tunings which may have misleading names, like the ruibin tuning. Ruibin is the name of the Chinese pitch which Western equivalent is "F♯", but that note does not appear or is used in the tuning, and so it is difficult to explain the logic in th
e naming...."

That looks like a Wikipedia copy. So we're back to guqin tunings.

Graham

I have looked back to attempt to find my exact references for this
"Kung" also called "Huang Kuang" from more than 20 years ago, and
remember that I had found this information in a book which I had
borrowed from the Westminster Music Library which was about ancient
Chinese inventions. I don't have the title to hand, but what I wrote
at the time was:

"Kung (also called Huang Kuang)
A reference pitch from which all other pitches were aligned in ancient
Chinese music. Kung was believed to be the foundation of divine will,
and was reassessed by each incoming ruler. The value was also used to
determine all the other standards of measurement including weight and
distance. Our present standard which corresponds to Kung is A4 equal
440 Hertz. The use of other tunings were believed to be indications of
political subversion and therefore suppressed within the rulers' domain.
The final Chinese dynasty Kung was believed, by musicologist van Aalst
in 1884 to have been somewhere around 601.5 Hz."

I don't know if this might help in tracking down this concept.

On 4 Mar 2009, at 12:32, Graham Breed wrote:

> Andreas Sparschuh wrote:
> > --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> >> What about the basis of weights and
> >> measures?
> >
> > http://www.ihns.ac.cn/English/journals/shns/abstracts/
> 2006/200603.htm
> > "Research on the Xian Qin Huangzhong Pipe: An Attempt to Calculate
> the Inside Diameter of Huangzhong Pipe with Modern Acoustic Formula...
> > ... states that the Huangzhong pitch pipe has a length of 3.9
> cun,whereas according to the literature of Han Dynasty,it is 9 cun
> long. The authors made a comprehensive survey to find out the real> length of the pipe. It is the Qing Huangzhong pipe that is recorded
> in Lshi Chunqiu. And its pitch is octachord of 9 cun Huangzhong
> pipe. Using the currently accepted acoustic formula, it can be
> inferred that the inside diameter of the Xian Qin bamboo pipe must
> be about 0.71 cun. This paper also argues that the 8.1 cun pipe
> hypothesis and the 8.71 cun pipe hypothesis are groundless."
>
> And that's all we have -- the abstract. Nothing to say why
> they care so much about the length of the pipe, or the
> original chinese names. Nothing about the pipe being the
> *basis* for weights and measures, as Charles originally asked.
>
> > http://www.plu.edu/~youtzgl/essays/silk/Chchap9.doc
>
> This is a proprietary format.
>
> > http://books.google.de/books?id=Lgs4AAAAIAAJ&pg=PA119&lpg=PA119&dq=huang-zhong+pitch+japan&source=bl&ots=RoNdOrzz9C&sig=RPRXJcu5oQIrcTeCbdKfCyXpBdg&hl=de&ei=uFuuSabCKczD_gbZjsTPBg&sa=X&oi=book_result&resnum=10&ct=result#PPA121,M1
>
> I don't have page 122 and I don't see anything relevant in
> the neighboring pages.
>
> > But the far-east musicologist: Britten Dean wrote about that in his
> > comments on:
> > "Mr. Gi's Music-Book"
> > 'An Annotated Translation of Gi Shimei's Gi-shi Gakufu,
> > by Britten Dean Monumenta Nipponica XXXVII,3 p. 317-322 © 1982
> > http://www.jstor.org/stable/2384388?seq=13
> > Quote, p.329, footnote 40:
> > "HUANG-ZHONG was the absolute pitch in the Chinese system,
> > and it varied over the dynastiese between c#' and a';
> > it was also the name of the mode based on this pitch....
> > ....For a convenient summary of these tonal systems,
> > see (author) Ongaku Jitzen {some Hanzi-characters}
> > Heibonza, 1955-1957, v, pp.28-31."
>
> What of it?
>
> > there had been also sone other cultural changes
> > https://eprints.soas.ac.uk/2987/1/ARC_to_Japanese_Music_Ch1_for_RAE.pdf
> > over the dynasties, when the preferred taste had changed within
> time.
>
> That's about Japan, as the URL suggests. Is it news that
> tastes change in any random country?
>
> > http://www.zoeybot.com/soswp/wp/g/Guqin.htm
> > "...There are more than 20 different tunings used in qin music,
> out of which only between two and four are commonly used. Some of
> these, however, are actually alternate names for the same tuning. A
> single tuning can have several different names depending on which
> system the composer was taught and used; an additional confusion is
> caused by the fact that two different tunings can share the same
> name. For example, huangzhong diao ci;ih*?/
> i;ih0c could mean either "lower first
> string and tighten fifth string" (e.g. Shenqi Mipu, etc), "lower
> third string" (e.g. Qinxue Lianyao), or normal tuning (e.g. Mei'an
> Qinpu). Another potentially confusing problem is the naming of some
> of the tunings which may have misleading names, like the ruibin
> tuning. Ruibin is the name of the Chinese pitch which Western
> equivalent is "Fb/", but that note does not appear or is used
> in the tuning, and so it is difficult to explain the logic in th
> e naming...."
>
> That looks like a Wikipedia copy. So we're back to guqin
> tunings.
>
> Graham
>
>

Charles Lucy
lucy@lucytune.com

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
..
> > ... states that the Huangzhong pitch pipe has a length of 3.9
> > cun,whereas according to the literature of Han Dynasty,it is 9 cun > > long. The authors made a comprehensive survey to find out the real > > length of the pipe. It is the Qing Huangzhong pipe that is
> > recorded in Lshi Chunqiu....
>
> And that's all we have -- the abstract.

Sorry, but I have no access to the full text version,
for impeaching the lack of credibility of the statement,
due to my doubts about the alleged numbers.

> Nothing to say why
> they care so much about the length of the pipe,

Competing with that, a Vietnamese source
http://honque.com/HQ018/bKhao_tqHai018.htm
claims about the old Chinese gauge:
"The first and basic tube (Huang Zhong) reproduces the FA (Gong tonic). This FA is close to the FA sharp of the physics scale with its 708.76 vibrations per second."

That alleged pitch designation resides inbetween todays
http://en.wikipedia.org/wiki/Piano_key_frequencies
"
58 fb/b2b2/gb-b2b2 Fb/5/Gb-5 739.989 and
57 fb2b2 F5 698.456
"
~about an quarter 12EDO-semitone ~25Cents above f"=F5,
or when more precisely computed:

1200Cents * ln(708.76 / 698.456)) / ln(2) = ~25.35...Cents

> or the original chinese names.
Please consult for that information the references on the pages.

> Nothing about the pipe being the
> *basis* for weights and measures, as Charles originally asked.

"The author has carried out experimental research in the presence of overtones in Yoga. The result of his three-year study was presented at the International Congress of Yoga in France in 2002 .
According to his research, the fundamental of voice should be at 150Hz "

How about to contact that author himself
about his personal hypothesis?

http://tranquanghai.info/index.php?cat=24
Email: tranquanghai@...

> > http://www.plu.edu/~youtzgl/essays/silk/Chchap9.doc
> This is a proprietary format.
Google converts that to HTML
http://209.85.129.132/search?q=cache:jOsFmTCAR9MJ:www.plu.edu/~youtzgl/essays/silk/Chchap9.doc+http://www.plu.edu/~youtzgl/essays/silk/Chchap9.doc&hl=en&ct=clnk&cd=1&gl=de

> http://books.google.de/books?id=Lgs4AAAAIAAJ&pg=PA119&lpg=PA119&dq=huang-zhong+pitch+japan&source=bl&ots=RoNdOrzz9C&sig=RPRXJcu5oQIrcTeCbdKfCyXpBdg&hl=de&ei=uFuuSabCKczD_gbZjsTPBg&sa=X&oi=book_result&resnum=10&ct=result#PPA121,M1
> I don't have page 122 and I don't see anything relevant in
> the neighboring pages.
It reports about the difficulties
due to lost of information over the centuries.

> > see (author) Ongaku Jitzen {some Hanzi-characters}
> > Heibonza, 1955-1957, v, pp.28-31."
>
> What of it?
It refers to an recommended standard review article
on the requested topic.

> That's about Japan, as the URL suggests.

There, in the more isolated island Japan survied some
unxticted old Chinese traditional music,
that was already lost by dieing out
in the formerly producing country of origin.

> Is it news that
> tastes change in any random country?
Noway!

But consider the counterexample of
http://en.wikipedia.org/wiki/A440
That convention remained stabil,
since the acoustican
Johann Heinrich Scheibler advocated
just that absolute
http://en.wikipedia.org/wiki/Pitch_(music)
in 1834 as international standard.
Since then that etalon persists more or less independent
from other proposals in taste for the reference normal-tone.

> That looks like a Wikipedia copy.
It's deed only a clone of:
http://en.wikipedia.org/wiki/Guqin

> So we're back to guqin tunings.
Right:
http://en.wikipedia.org/wiki/Guqin#Tuning

Forum:
http://www.chinahistoryforum.com/index.php?showtopic=3549&mode=threaded&pid=4712473

Charles Lucy wrote:
> I have looked back to attempt to find my exact references for this "Kung" also > called "Huang Kuang" from more than 20 years ago, and remember that I had found > this information in a book which I had borrowed from the Westminster Music > Library which was about ancient Chinese inventions. I don't have the title to > hand, but what I wrote at the time was:

I think Huang Kua?ng is 黄宫 or Huang Gong. There's a definition here:

http://cd.kdd.cc/5/6Y1/

http://www.zdic.net/cd/ci/11/ZdicE9ZdicBBZdic84316511.htm

(Looks like the same translation on both pages.) It says it's one of the 12 lv and short for Huang Zhong zhi Gong. Gong is the first note of the pentatonic scale. The other term is Huang Zhong (黄种) or "yellow bell" which refers to the absolute pitch.

> "Kung (also called Huang Kuang)
> A reference pitch from which all other pitches were aligned in ancient Chinese > music. Kung was believed to be the foundation of divine will, and was reassessed > by each incoming ruler. The value was also used to determine all the other > standards of measurement including weight and distance. Our present standard > which corresponds to Kung is A4 equal 440 Hertz. The use of other tunings were > believed to be indications of political subversion and therefore suppressed > within the rulers' domain.
> The final Chinese dynasty Kung was believed, by musicologist van Aalst in 1884 > to have been somewhere around 601.5 Hz."
> > I don't know if this might help in tracking down this concept.

It tells us the things we already knew really :-S

Could one of these have been your reference?

CROSSLEY-HOLLAND, PETER. `Non-Western Music'. The Pelican History of Music, 1. London, 1959: 13-135.

MALM, WILLIAM P (1977). Music Cultures of the Pacific, the Near East, and Asia. Englewood Cliffs, 1977.

They're the citations "origins3.pdf" gives. Neither are particularly good because they're generalist works. This is starting to look like a wild goose chase, but maybe we'll get a reliable reference.

I can believe that the Yuefu (which is 乐/樂府: the PDF does give it) was attached to the weights and measures office but not that it had this central power. References to it are all about the arts. It's in my dictionary as a school of poetry.

Graham

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:

> The final Chinese dynasty Kung was believed,
> by musicologist van Aalst
> in 1884 to have been somewhere around 601.5 Hz."
>
Hi Charles,

that's -if halfway reasonable?- inbetween the
http://en.wikipedia.org/wiki/Piano_key_frequencies

key# 55 Eb5 622.254 and
key# 54 D_5 587.330 Hz

against
http://honque.com/HQ018/bKhao_tqHai018.htm
" This FA is close to the FA sharp of the physics scale with its 708.76 vibrations per second. "

Yielding an alleged decrease of about nearly an minor-3rd:

1200Cents * ln(708.76 / 601.5) / ln(2) = ~284.08...Cents

over the average of all dynasties during a few millenia.

bye
A.S.

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
>
> http://cd.kdd.cc/5/6Y1/
Wehn converted into Google's pidgin-"English
http://translate.google.de/translate?u=http%3A%2F%2Fcd.kdd.cc%2F5%2F6Y1%2F&sl=zh-CN&tl=en&hl=en&ie=UTF-8
>
> http://www.zdic.net/cd/ci/11/ZdicE9ZdicBBZdic84316511.htm
and also
http://translate.google.de/translate?u=http%3A%2F%2Fwww.zdic.net%2Fcd%2Fci%2F11%2FZdicE9ZdicBBZdic84316511.htm&sl=zh-CN&tl=en&hl=en&ie=UTF-8
>
it
> (Looks
in deed
> like the same
gobbledygook
> translation on both pages.)

bye
A.S.

Andreas Sparschuh wrote:
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
> hi Graham,
> appearently the questionable alleged ratios
>>> ! from the source: http://en.wikipedia.org/wiki/Shi_Er_L%C3%BC
> were overtaken from the last chart at the end of the page:
> > http://www.wfu.edu/~moran/Cathay_Cafe/G_tar.html
> > Ptolemy vs. alleged Chinese > "
> 1 / 1 A: 1/1
> 16/15 A# 2187/2048 > 9 / 8 B: 9/8 > 6 / 5 C: 1968/1638 > 5 / 4 C# 81/64 > 4 / 3 D: 1771/1311 > 7 / 5 D# 729/512 > 3 / 2 E: 3/2
> 8 / 5 F: 6561/4096 > 5 / 3 F# 27/16 > 7 / 4 G: 5905/3277 > 15/ 8 G# 243/128 > 2 / 1 A: 2/1

Notice that the Chinese Wikipedia has more details than the English one, including the Pythagorean derivation of the lv:

http://zh.wikipedia.org/wiki/十二律

Of course, any sufficiently long Pythagorean chain can be interpreted schismatically. I've yet to find any evidence for how this might relate to Chinese musical practice.

Graham

Andreas Sparschuh wrote:
> --- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:

>>> http://www.plu.edu/~youtzgl/essays/silk/Chchap9.doc
>> This is a proprietary format.
> Google converts that to HTML
> http://209.85.129.132/search?q=cache:jOsFmTCAR9MJ:www.plu.edu/~youtzgl/essays/silk/Chchap9.doc+http://www.plu.edu/~youtzgl/essays/silk/Chchap9.doc&hl=en&ct=clnk&cd=1&gl=de

I can't see the point of your other references, so I've cut them out. This one is another reasonably good introduction to Chinese music. It mentions some primary sources under "Philosophical Roots". They're all on Wikisources and here:

http://chinese.dsturgeon.net/text.pl?node=3925&if=en

Note that the Shu Jing comes out as "尚書 - Shang Shu" and Tso Zhuan as "春秋左傳 - Chun Qiu Zuo Zhuan".

Further down, "The Li Ji- the Han dynasty reconstruction of the Zhou Dynasty 'Book of Rites,' describes the transposition of these two scales to any of the 12 notes of the Lu-Lu system." This book is also online, with an English translation, but I can't find the details that quote suggests. This is the most promising chapter:

http://chinese.dsturgeon.net/text.pl?node=10113&if=en

While I'm here, you may remember this page has a quote from Guangzi that describes Pythagorean tuning by string division:

http://www.silkqin.com/08anal/tunings.htm

It's in context as paragraph 7 here:

http://chinese.dsturgeon.net/text.pl?node=48689

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:

> > http://www.wfu.edu/~moran/Cathay_Cafe/G_tar.html
> >
> > Ptolemy vs. alleged Chinese
> > "
> > 1 / 1 A: 1/1
> > 16/15 A# 2187/2048
> > 9 / 8 B: 9/8
> > 6 / 5 C: 1968/1638
> > 5 / 4 C# 81/64
> > 4 / 3 D: 1771/1311
> > 7 / 5 D# 729/512
> > 3 / 2 E: 3/2
> > 8 / 5 F: 6561/4096
> > 5 / 3 F# 27/16
> > 7 / 4 G: 5905/3277
> > 15/ 8 G# 243/128
> > 2 / 1 A: 2/1
>
> Of course, any sufficiently long Pythagorean chain can be
> interpreted schismatically. I've yet to find any evidence
> for how this might relate to Chinese musical practice...

Hi Graham,

how about that alleged ancient chinese
http://www.microtonal-synthesis.com/scale_china_lu.html
but pseudo-'Pythagorean' approximation by 43, 19, & 17-limits?

bye
A.S.

Andreas Sparschuh wrote:

> how about that alleged ancient chinese > http://www.microtonal-synthesis.com/scale_china_lu.html
> but pseudo-'Pythagorean' approximation by 43, 19, & 17-limits?

The primary source is "Huai-nan-dsi" which I take to be the 《淮南子 - Huainanzi》 given here:

http://chinese.dsturgeon.net/text.pl?node=3022&if=en

It'll take a while to get through, though.

There's an interesting page here:

http://www.emus.cn/?9087/viewspace-6443.html

which is showing ratios relating to it. You can try the Google translation, and note that lv (律) translates as "law".

This page has a lot of information that I haven't been through:

http://www1.ihns.ac.cn/members/dainianz/yueli.htm

This summary:

http://scholar.ilib.cn/A-ISSN~1003-0042(2003)01-0102-07.html

mentions 360 lv as well as the commonly given 60 lv. I don't know how to get the full article.

There are other hits in Google. I'll see if I can get somebody with better Chinese to go through them.

Graham

Andreas Sparschuh wrote:

> how about that alleged ancient chinese > http://www.microtonal-synthesis.com/scale_china_lu.html
> but pseudo-'Pythagorean' approximation by 43, 19, & 17-limits?

I've extracted the following table from http://chinese.dsturgeon.net/text.pl?node=3054&if=en which is a modern copy of a Western Han text, Huainanzi, probably the one indirectly cited in your link. (Proportional spacing with wide characters as 2 positions helps.)

黃鍾大呂太蔟夾鍾姑洗仲呂蕤賓林鍾夷則南呂無射無射
nov dec jan feb mar apr may jun jul aug sep oct
81 76 72 68 64 60 57 54 51 48 45 42
1 8 3 10 5 11 7 2 9 4 11 6

It shows, for each of the twelve lv, a month of the year, a number, and a sequential order. The months give a pitch ordering. The ordering in the text looks like the spiral of fifths. The numbers I take as string lengths.

As http://www.emus.cn/?9087/viewspace-6443.html states, there are two subharmonic series fragments in these string lengths. 76:72:68:60 simplifies as 19:18:17:16:15 and 60:57:54:51:48:45:42 simplifies as 20:19:18:17:16:15:14. The whole scale as reduced fractions relative to huang zhong would be

1/1
81/76
9/8
81/68
81/64
27/20
27/19
3/2
27/17
27/16
9/5
27/14
2/1

That's interesting, but clearly not the same as the scale in the original link. Even if the tonic's different I don't see a 43. Note however there are some numbers here linked to the Qin dynasty, with a 43 where Huaninazi has a 42:

http://www1.ihns.ac.cn/members/dainianz/yueli.htm

Here's the original text with some words translated. The character 主 means "own/to host/master/lord/primary" so this is the relationship between a note and a month. The character 數 could be "to count/number/figure/to calculate/several/frequently/repeated" so ths describes the numbers (presumably string lengths). 下生, for what looks like progression by fifths, could be "born under". All this is modern Chinese -- I don't have a historical dictionary.

故黃鍾位子 huangzhong
其數八十一 81
主十一月 november
下生林鍾 leads to linzhong
林鍾之數五十四 linzhong 54
主六月 june
上生太蔟 leads to taicu
太蔟之數七十二 taicu 72
主正月 january
下生南呂 leads to nanlv
南呂之數四十八 nanlv 48
主八月 august
上生姑洗 leads to guxi
姑洗之數六十四 gixi 64
主三月 march
下生應鍾 leads to yingzhong
應鍾之數四十二 yingzhong 42
主十月 october
上生蕤賓 leads to ruibin
蕤賓之數五十七 ruibin 57
主五月 may
上生大呂 leads to dalv
大呂之數七十六 dalv 76
主十二月 december
下生夷則 leads to yize
夷則之數五十一 yize 51
主七月 july
上生夾鍾 leads to jiazhong
夾鍾之數六十八 jiazhong 68
主二月 february
下生無射 leads to wushe
無射之數四十五 wushe 45
主九月 september
上生仲呂 leads to zhonglv
仲呂之數六十 zhonglv 60
主四月 april

Earlier in the same paragraph there's a description of a pentatonic scale in terms of the lv

黃鍾為宮 huangzhong gives gong
太蔟為商 taicu gives shang
姑洗為角 guxxi gives jiao
林鍾為徵 linzhong gives zhi
南呂為羽 nanlv gives yu

If we call huangzhong C, this is C D E G A, which is a scale I've seen a lot in traditional Chinese music. I don't have a full translation of the text and the Chinese people I asked say it's difficult to understand. Still the information extracted above is clear, because it's only names and numbers.

Graham