Yahoo Tuning Groups Ultimate Backup tuning Re : temperament equal (new?)

Mr. Dimitrov:

> I have the book of Mr Cordier before...1985 !
> Now I dont approve the TEQJ...

I'm not convinced either, not in theory, but from what I heard. I heard a
classical piece in a major key and it sounded very harsh for all the major
thirds were even higher than in 12-tet.

> Yes ! "My" octave is larger(2/1), my fifth is smaler
> 660 if the A=440 and i applie my consept when
> according my violin and when I play also :))

660 Hz if A=440 Hz means a perfect fifth (3/2 or 702 cents). If your fifths
are smaller than this, how comes that the octave is still larger?

> The humain ear evaluate the hight frequency less than
> the value physic and the bass sounds highter !

So that means that stretching (in french: étirer, élargir, allonger) helps
the ear to perceive what it thinks is the right frequency. I think we agree
on that.
>
>> Interesting enough, Mr. Cordier published a book 'Le
>> piano et la justesse
>> orchestrale'. I haven't red this book yet, but I can
>> immediately imagine one
>> aspect: the tuning of all the strings in the
>> orchestra, from double-bass to
>> violin, is based on a cumulation of perfect fifths.
>
> Not so perfects ;)) Because all musicians with the
> instruments lice violoncells or contrabasses use
> harmonics octaves when they verify yours strings !!!
> And they accorde himselfs highter...

That's good to know. Can you explain this in detail?

> Also today nobody accord the piano like...

Actually, there should be quite a lot Cordier-tuned pianos in France, since
I spontaneously found two of them, independent from each other and I'm not
even a pianist.

> For me the half tones are like the letters in the
> alphabet-they must be free of engagements harmonic or
> melodic out of any context musical...

>
>> Or do the string-players in an orchestra still
>> slightly temper their open
>> string fifths to prevent especially the low C being
>> too low?
>>
> Never :)) They according all the time...

While they're playing they can't tune the open string anymore, so how
exactly do they set them before playing starts?
>
>> After the equal division of the octave and the equal
>> division of the fifth,
>> the next step could be the equal division of the
>> major third into 4 steps
>> (4th root of 1.25) and simply forget about the
>> octave as an imposing
>> interval.
>
> Why evry time we must have one IMPOSING interval ?!
> That's the question ;P

The octave *is* imposing itself, since we hear it immediately on any
instrument producing harmonics, especially the violin. Could you reply to
the question: why *should* we abandon the octave? Or the fifth, or the
third?

Bien à vous,

Wim Hoogewerf

🔗Latchezar Dimitrov <latchezar_d@yahoo.com>

--- Wim Hoogewerf <wim.hoogewerf@fnac.net> a ï¿½critï¿½:
>
>
> ----------
> >Deï¿½:
> >ï¿½ : tuning@yahoogroups.com
> >
>
> > --- Paul Erlich <paul@stretch-music.com> a
> ï¿½critï¿½: >
> > --- In tuning@y..., jacky_ligon@y... wrote:
> >>
> >> > Sounds beautiful!!!
> >> >
> >> > I love making music with ths sort of thing.
> >> Especially favor a
> >> > stretched octave.
> >> >
> >> > Just days ago I wrote a wedding piece for piano
> >> and it had perfect
> >> > fifths and a 10 cents wide octave
> >>
> >> Bob Wendell, look out! :)
> >>
> > Please, +10 cents = 2.0038754/1 ? :))
> >
> > Dimitrov
>
> Should'n that be 2.0115857/1?
>
> Wim Hoogewerf
>
Dear Mr Hoogewerf,

Why 2.0115857 ? You must do 12 degree of the 7th root
of 1.5, ok ?
The half tone in (12_ET) a equal temperament must be
only between 12th root of 2(smallest possible) and
7th root of 1.5(biggest)! Can you explate me your
number, pls ?

Dimitrov

___________________________________________________________
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🔗Wim Hoogewerf <wim.hoogewerf@fnac.net>

----------
>De :
>À : tuning@yahoogroups.com
>

> --- Wim Hoogewerf <wim.hoogewerf@fnac.net> a écrit :
>> genewardsmith@juno.com
>>
>> > --- In tuning@y..., "Paul Erlich" <paul@s...>
>> wrote:
>> >> --- In tuning@y..., "Wim Hoogewerf"
>> <wim.hoogewerf@f...> wrote:
>> >
>> >> > After the equal division of the octave and the
>> equal division of
>> >> the fifth,
>> >> > the next step could be the equal division of
>> the major third into
>> > 4
>> >> steps
>> >> > (4th root of 1.25) and simply forget about the
>> octave as an
>> > imposing
>> >> > interval.
>> >
>> >> Watch out -- the octaves in this system would be
>> 41 cents flat!
>> > Ouch!
>> >
>> > I think it would make much more sense to take
>> 5^(1/28) as basic; then
>> > 3/2 ~ 5^(1/4) is 5.4 cents flat and 2 ~ 5^(3/7) is
>> 5.9 cents flat.
>> >
>> > If we are seeking after the bizarre, we could tune
>> to intervals
>> > derived from zeros of the Riemann Zeta function on
>> the critical line
>> > in the hope that this might represent some
>> condition of maximum
>> > perversity. The tunings nearest the 12-et are
>> 11.8226, 18 cents
>> > sharp, and 12.2485, 25 cents flat.
>>
>> I simply mentioned this possibility as a sort of
>> answer to Mr. Dimitrov.
>> It's pure phantasy/theory. First the octave, then
>> the fifth, next comes the
>> major third. Right?
>>
>> -Wim Hoogewerf
> Not :)) Because this order is very similar to the
> order of...harmonics !!! Fyrst harmonic=octave,
> second=octave+fifth and the 3th ? Octave+octave and
> not the major third...
>
> Mr Dimitrov

Great idea! Let's do this first. Split up a double-octave into 24 equal
parts (24th root of 4). Strange, this reminds me of something. :)

-Wim

🔗Latchezar Dimitrov <latchezar_d@yahoo.com>

-Hi :))

Ok, I will try to responding below...

--- Wim Hoogewerf <wim.hoogewerf@fnac.net> a ï¿½crit :
>
>
> Mr. Dimitrov:
>
> > I have the book of Mr Cordier before...1985 !
> > Now I dont approve the TEQJ...
>
> I'm not convinced either, not in theory, but from
> what I heard. I heard a
> classical piece in a major key and it sounded very
> harsh for all the major
> thirds were even higher than in 12-tet.
>

Each third , major or minor depend of the fifth in the
triad ! If this fifth is (very little)tempered the
third dont sounded so harsh...

> > Yes ! "My" octave is larger(2/1), my fifth is
> smaler
> > 660 if the A=440 and i applie my consept when
> > according my violin and when I play also :))
>
> 660 Hz if A=440 Hz means a perfect fifth (3/2 or 702
> cents). If your fifths
> are smaller than this, how comes that the octave is
> still larger?
>

:)))) Sorry for my laught, but this question is very
funny...
7th root of 1.5(K2) is larger that 12th root of 2(K1)
!
If you use K2 you will produce (extremly!)wide octave
when multiply the reference frequency 12 times with...
We have lots of intermediate values(K) when the fifth
is smaller(3/2) but still the octave is larger(Bach
octave) or= no one perfect interval is in use !
And this sound better that TEQJ !!!

> > The humain ear evaluate the hight frequency less
> than
> > the value physic and the bass sounds highter !
>
> So that means that stretching (in french: ï¿½tirer,
> ï¿½largir, allonger) helps
> the ear to perceive what it thinks is the right
> frequency. I think we agree
> on that.
> >

Yes, that's right for all here:))

> >> Interesting enough, Mr. Cordier published a book
> 'Le
> >> piano et la justesse
> >> orchestrale'. I haven't red this book yet, but I
> can
> >> immediately imagine one
> >> aspect: the tuning of all the strings in the
> >> orchestra, from double-bass to
> >> violin, is based on a cumulation of perfect
> fifths.
> >
> > Not so perfects ;)) Because all musicians with the
> > instruments like violoncells or contrabasses use
> > harmonics octaves when they verify yours strings
> !!!
> > And they accorde himselfs highter...
>
> That's good to know. Can you explain this in detail?
>
The harmonic of one string dont have harmonics
himselfs, ok ? :)) Or- the ear hear too down one sound
with less harmonics... If one violoncelist use the
first harmonic to compare the A from hautbois when
according - the octave (first harmonic)is too short =
the string is accorded too hight !!!

> > Also today nobody accord the piano like...
>

In the pratice I mean...

> Actually, there should be quite a lot Cordier-tuned
> pianos in France, since
> I spontaneously found two of them, independent from
> each other and I'm not
> even a pianist.

Actually I think that TEQJ is a extreme solution and
inusable in the pratice...
One PC modern is powerfull to prove that !
See multipistes section of Cool Edit Pro and produce 8
consecutive octaves in TEQJ...

>
> > For me the half tones are like the letters in the
> > alphabet-they must be free of engagements harmonic
> or
> > melodic out of any context musical...
>
> >

Like the seconds in time mesure ! If I'm stressed the
time feel to me different but that dont change the
real time...

> The octave *is* imposing itself, since we hear it
> immediately on any
> instrument producing harmonics, especially the
> violin. Could you reply to
> the question: why *should* we abandon the octave? Or
> the fifth, or the
> third?

Because the music is the live show :))
One perfect octave or fifth are dead intervals !
We need to hear little beat in EACH interval having
never one perfect there, who impose to divide
different the scale ! It's only my last opinion :))

Mr Dimitrov

___________________________________________________________
Do You Yahoo!? -- Un e-mail gratuit @yahoo.fr !
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🔗Latchezar Dimitrov <latchezar_d@yahoo.com>

--- Wim Hoogewerf <wim.hoogewerf@fnac.net> a ï¿½critï¿½:
>
>
> ----------
> >Deï¿½:
> >ï¿½ : tuning@yahoogroups.com
> >
>
> > --- Wim Hoogewerf <wim.hoogewerf@fnac.net> a
> ï¿½critï¿½:
> >> genewardsmith@juno.com
> >>
> >> > --- In tuning@y..., "Paul Erlich" <paul@s...>
> >> wrote:
> >> >> --- In tuning@y..., "Wim Hoogewerf"
> >> <wim.hoogewerf@f...> wrote:
> >> >
> >> >> > After the equal division of the octave and
> the
> >> equal division of
> >> >> the fifth,
> >> >> > the next step could be the equal division of
> >> the major third into
> >> > 4
> >> >> steps
> >> >> > (4th root of 1.25) and simply forget about
> the
> >> octave as an
> >> > imposing
> >> >> > interval.
> >> >
> >> >> Watch out -- the octaves in this system would
> be
> >> 41 cents flat!
> >> > Ouch!
> >> >
> >> > I think it would make much more sense to take
> >> 5^(1/28) as basic; then
> >> > 3/2 ~ 5^(1/4) is 5.4 cents flat and 2 ~ 5^(3/7)
> is
> >> 5.9 cents flat.
> >> >
> >> > If we are seeking after the bizarre, we could
> tune
> >> to intervals
> >> > derived from zeros of the Riemann Zeta function
> on
> >> the critical line
> >> > in the hope that this might represent some
> >> condition of maximum
> >> > perversity. The tunings nearest the 12-et are
> >> 11.8226, 18 cents
> >> > sharp, and 12.2485, 25 cents flat.
> >>
> >> I simply mentioned this possibility as a sort of
> >> answer to Mr. Dimitrov.
> >> It's pure phantasy/theory. First the octave, then
> >> the fifth, next comes the
> >> major third. Right?
> >>
> >> -Wim Hoogewerf
> > Not :)) Because this order is very similar to the
> > order of...harmonics !!! Fyrst harmonic=octave,
> > second=octave+fifth and the 3th ? Octave+octave
> and
> > not the major third...
> >
> > Mr Dimitrov
>
> Great idea! Let's do this first. Split up a
> double-octave into 24 equal
> parts (24th root of 4). Strange, this reminds me of
> something. :)
>
> -Wim

Great remark, Wim :)) But I never mind to respect the
octave, the fifth or the double octave !!!
My idea is to not have any interval to respecting, and
this is a NEW idea here... No ?

Mr Dimitrov

___________________________________________________________
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🔗jacky_ligon@yahoo.com

🔗Latchezar Dimitrov <latchezar_d@yahoo.com>

--- jacky_ligon@yahoo.com a ï¿½critï¿½: > --- In
tuning@y..., Latchezar Dimitrov
> <latchezar_d@y...> wrote:
>
> > One perfect octave or fifth are dead intervals !
> > We need to hear little beat in EACH interval
> having
> > never one perfect there, who impose to divide
> > different the scale ! It's only my last opinion
> :))
> >
> > Mr Dimitrov
>
> Now your speaking my language Mr Dimitrov!!!
>
> YES! I'm with you!
>
> Jacky Ligon
>
>
Thank-you for your support ! :)
(But my english is still bad and wrong...)

I would be able to contact Mr Cordier for discute with
him in french :)) He dont surf here and I sorry for
that...

Dimitrov

___________________________________________________________
Do You Yahoo!? -- Un e-mail gratuit @yahoo.fr !
Yahoo! Courrier : http://fr.mail.yahoo.com

🔗Wim Hoogewerf <wim.hoogewerf@fnac.net>

Dimitrov wrote:

----------
>De :
>À : tuning@yahoogroups.com
>

> --- Wim Hoogewerf <wim.hoogewerf@fnac.net> a écrit :
>>
>>
>> ----------
>> >De :
>> >À : tuning@yahoogroups.com
>> >
>>
>> > --- Paul Erlich <paul@stretch-music.com> a
>> écrit : >
>> > --- In tuning@y..., jacky_ligon@y... wrote:
>> >>
>> >> > Sounds beautiful!!!
>> >> >
>> >> > I love making music with ths sort of thing.
>> >> Especially favor a
>> >> > stretched octave.
>> >> >
>> >> > Just days ago I wrote a wedding piece for piano
>> >> and it had perfect
>> >> > fifths and a 10 cents wide octave
>> >>
>> >> Bob Wendell, look out! :)
>> >>
>> > Please, +10 cents = 2.0038754/1 ? :))
>> >
>> > Dimitrov
>>
>> Should'n that be 2.0115857/1?
>>
>> Wim Hoogewerf
>>
> Dear Mr Hoogewerf,
>
> Why 2.0115857 ? You must do 12 degree of the 7th root
> of 1.5, ok ?

I do not know how Jacky Ligon comes to a 10 cents wide octave.
He's talking about a simular tuning, not exactly Cordier.

> The half tone in (12_ET) a equal temperament must be
> only between 12th root of 2(smallest possible) and
> 7th root of 1.5(biggest)! Can you explate me your
> number, pls ?
>
> Dimitrov

To raise a frequency or ratio by one cent, as you know, you multiplie by
1.0005778 (1200th root of 2). So I simply added 10 cens to the octave.
Was that your question?

Your name never appears on the list in my mail-box. Could you please...?

-- Wim

🔗jpehrson@rcn.com

--- In tuning@y..., Latchezar Dimitrov <latchezar_d@y...> wrote:

/tuning/topicId_27561.html#27569

> Great remark, Wim :)) But I never mind to respect the
> octave, the fifth or the double octave !!!
> My idea is to not have any interval to respecting, and
> this is a NEW idea here... No ?
>
> Mr Dimitrov
>

Hello Mr. Dimitrov!

Well, of course, we have discussed here the idea of using "intervals
of equivalance" other than the octave... such as the 12th of the
Bohlen-Pierce scale (3:1) as advocated by Heinz Bohlen, who is a
participant on this very list!

However, generally speaking, there is always *one* "interval of
equivalence" for any given tuning.

Are you suggesting that the "interval of equivalence" CHANGE during
the course of a piece... something that could be done "adaptively"
with synthesizers and the like (??)

By the way, I think you can include some French in your messages...
some of us can read through it, and actually it would be just as easy
for us as your English! :) :)

___________ _________ ________
Joseph Pehrson

🔗jacky_ligon@yahoo.com

🔗Latchezar Dimitrov <latchezar_d@yahoo.com>

Salut, Joseph :))

Ca ma fait rigoler beaucoup ta suggestion or
maintenant voici en franï¿½ais ma rï¿½ponse...

--- jpehrson@rcn.com a ï¿½critï¿½: > --- In tuning@y...,
Latchezar Dimitrov
> <latchezar_d@y...> wrote:
>
> /tuning/topicId_27561.html#27569
>
> > Great remark, Wim :)) But I never mind to respect
> the
> > octave, the fifth or the double octave !!!
> > My idea is to not have any interval to respecting,
> and
> > this is a NEW idea here... No ?
> >
> > Mr Dimitrov
> >

> Hello Mr. Dimitrov!
>
> Well, of course, we have discussed here the idea of
> using "intervals
> of equivalance" other than the octave... such as the
> 12th of the
> Bohlen-Pierce scale (3:1) as advocated by Heinz
> Bohlen, who is a
> participant on this very list!
>
> However, generally speaking, there is always *one*
> "interval of
> equivalence" for any given tuning.

C'est faux :)) On n'a pas besoin d'aucun interval et
je regrette beaucoup car je ne connais pas
Bohlen-Pierce et leur ouvrage non plus...

>
> Are you suggesting that the "interval of
> equivalence" CHANGE during
> the course of a piece... something that could be
> done "adaptively"
> with synthesizers and the like (??)
>

Non ! Il n'y a pas "d'interval d'equivalence" et tous
les demi-tones restent bien a leur place durant
l'execution ! On n'a pas besoin d'adapter rien-tout
est parfait :)

> By the way, I think you can include some French in
> your messages...
> some of us can read through it, and actually it
> would be just as easy
> for us as your English! :) :)
>
> ___________ _________ ________
> Joseph Pehrson
>

A la fin je peux expliquer un peu plus mon
invention... L'octave est elargie avec un peu plus que
2 cents et la quinte est moins qu'un cent plus petite
!
Des questions ? (en english, sure ;) )

Salutations

Latchezar Dimitrov

___________________________________________________________
Do You Yahoo!? -- Un e-mail gratuit @yahoo.fr !
Yahoo! Courrier : http://fr.mail.yahoo.com

🔗graham@microtonal.co.uk

In-Reply-To: <20010829164505.82704.qmail@web14609.mail.yahoo.com>
Latchezar ecrit:

> > However, generally speaking, there is always *one*
> > "interval of
> > equivalence" for any given tuning.
>
> C'est faux :)) On n'a pas besoin d'aucun interval et
> je regrette beaucoup car je ne connais pas
> Bohlen-Pierce et leur ouvrage non plus...

Il y a un website a <http://members.aol.com/bpsite/index.html>.

> Non ! Il n'y a pas "d'interval d'equivalence" et tous
> les demi-tones restent bien a leur place durant
> l'execution ! On n'a pas besoin d'adapter rien-tout
> est parfait :)

Le "88CET" de Gary Morrison n'a pas d'intervale d'equivalence. Tous les
"demis-tones" est 88 cents. On peut parle d'un equivalence a 11 octaves,
mais ce n'est pas importante pour la musique.

Graham

🔗jpehrson@rcn.com

--- In tuning@y..., Latchezar Dimitrov <latchezar_d@y...> wrote:

/tuning/topicId_27561.html#27582

> Salut, Joseph :))
>
> Ca ma fait rigoler beaucoup ta suggestion or
> maintenant voici en français ma réponse...
>

Language difficulities can be funny... just don't make me write in
French and we're OK... :)

> > Hello Mr. Dimitrov!
> >
> > Well, of course, we have discussed here the idea of
> > using "intervals
> > of equivalance" other than the octave... such as the
> > 12th of the
> > Bohlen-Pierce scale (3:1) as advocated by Heinz
> > Bohlen, who is a
> > participant on this very list!
> >
> > However, generally speaking, there is always *one*
> > "interval of
> > equivalence" for any given tuning.
>
> C'est faux :)) On n'a pas besoin d'aucun interval et
> je regrette beaucoup car je ne connais pas
> Bohlen-Pierce et leur ouvrage non plus...
>

Maybe so... but I thought most scales were constructed with some kind
of "interval of equivalence..." Maybe not..

Paul??

Heinz Bohlen has done a lot of work with the famous "Bohlen-Pierce"
scale, which is based upon the twelfth or 3:1 ratio. He is also on
this list! He has a whole website devoted to it, and I know your
English is good enough that you can read most of it...

http://members.aol.com/bpsite/

> >
> > Are you suggesting that the "interval of
> > equivalence" CHANGE during
> > the course of a piece... something that could be
> > done "adaptively"
> > with synthesizers and the like (??)
> >
>
> Non ! Il n'y a pas "d'interval d'equivalence" et tous
> les demi-tones restent bien a leur place durant
> l'execution ! On n'a pas besoin d'adapter rien-tout
> est parfait :)
>

Oh... If I'm getting this at all you mean the larger intervals are
built up from the smaller ones... but in the case of the fifth, you
*were* making that constant, I thought... or was that the French
technician Mr. Cordier... ?? If the fifth is constant than *that*
would be the "equivalent" interval, wouldn't it??

>
> A la fin je peux expliquer un peu plus mon
> invention... L'octave est elargie avec un peu plus que
> 2 cents et la quinte est moins qu'un cent plus petite
> !
> Des questions ? (en english, sure ;) )
>

Oh... well actually then Dave Keenan and Wim Hoogewerf were right...
you are mostly concerned with "stretched" octaves and perhaps a
generating fifth, correspondingly that is only 1 cent small from just
rather than 2 cents...

Or something like that.

Thanks for sparing us from your written, er, "English" :) :) :)

__________ _________ ______
Joseph Pehrson

🔗jpehrson@rcn.com

--- In tuning@y..., graham@m... wrote:

/tuning/topicId_27561.html#27583

> In-Reply-To: <20010829164505.82704.qmail@w...>
> Latchezar ecrit:
>
> > > However, generally speaking, there is always *one*
> > > "interval of
> > > equivalence" for any given tuning.
> >
> > C'est faux :)) On n'a pas besoin d'aucun interval et
> > je regrette beaucoup car je ne connais pas
> > Bohlen-Pierce et leur ouvrage non plus...
>
> Il y a un website a <http://members.aol.com/bpsite/index.html>.
>
> > Non ! Il n'y a pas "d'interval d'equivalence" et tous
> > les demi-tones restent bien a leur place durant
> > l'execution ! On n'a pas besoin d'adapter rien-tout
> > est parfait :)
>
> Le "88CET" de Gary Morrison n'a pas d'intervale d'equivalence.
Tous les "demis-tones" est 88 cents. On peut parle d'un equivalence
a 11 octaves, mais ce n'est pas importante pour la musique.
>
>
> Graham

Oh... got it Graham. You know, I remember this discussion from
before... with this scale that is built up basically from a defined
semi-tone. I believe the context was when I was trying to find out
why a scale would be in CET.

"Cents equal temperament." Mr. Dimitrov should know about that one...

But my question is... is this similar to a *generator* in the sense
that we had a generator for the Miracle family??

It seems as though it might be...

Thanks!

________ ________ ____
Joseph Pehrson

P.S. Nice French, Graham

🔗genewardsmith@juno.com

🔗jacky_ligon@yahoo.com

--- In tuning@y..., genewardsmith@j... wrote:
> --- In tuning@y..., jacky_ligon@y... wrote:
>
> > What I'm speaking of here is an iterated scale based on Phi as
the Interval of Equivalence.
>

> Does phi = (1+sqrt(5))/2, or is this some other number?

Gene,

The variant I commonly use is (SQRT(5)+1)/2.

> Why would you want to use it?

It is one of the possibilities for generating myriad scales with
Myhill's Property.

Even further, it is also handy for creating three, four - etc... step
size tunings as well.

My interest in this is just from an ongoing fascination with self
similarity in scale design.

The Golden Mean is only one facet of my explorations. I also enjoy
ETs and JI/RI.

The sound of Golden Tunings can be very lovely to my ears, else I
wouldn't be so interested in using it for my work. Interestingly,
they can converge on very "JI-like" intervals (if desired).

If you are able to play MP3s on your PC, and you would like to hear a
piano based example of this tuning, you may download it from the
files section of the Make Micro Music Group. You'll have to join the
group, then you can go into the folder with my name on it and
download the piece "Golden_Convergence.mp3".

/makemicromusic

While you are there you can check out a piece I wrote for
Keenan/Erlich in the Blackjack tuning:

"BlackJacky-2_Modalessence.mp3".

Best Regards,

Jacky Ligon

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., jpehrson@r... wrote:
>
> Maybe so... but I thought most scales were constructed with some
kind
> of "interval of equivalence..." Maybe not..
>
> Paul??

This is not really relevant. You misunderstood Mr. Dimitrov. He
simply thinks no interval should be exactly _just_, including the
octave.

> Oh... If I'm getting this at all you mean the larger intervals are
> built up from the smaller ones... but in the case of the fifth,
you
> *were* making that constant, I thought... or was that the French
> technician Mr. Cordier... ??

Everything is constant within each tuning system. You don't mean
constancy, you mean _justness_. Cordier wants _just_ fifths, Dimitrov
does not.

> If the fifth is constant than *that*
> would be the "equivalent" interval, wouldn't it??

Just because the fifth is _just_ doesn't mean it will function as
an "interval of equivalence". The octave is almost always the
interval of equivalence -- even animals recognize octave-equivalence.
It doesn't have to be just for this effect to take place!

🔗Latchezar Dimitrov <latchezar_d@yahoo.com>

--- graham@microtonal.co.uk a ï¿½critï¿½: > In-Reply-To:
> <20010829164505.82704.qmail@web14609.mail.yahoo.com>
> Latchezar ecrit:
>
> > > However, generally speaking, there is always
> *one*
> > > "interval of
> > > equivalence" for any given tuning.
> >
> > C'est faux :)) On n'a pas besoin d'aucun interval
> et
> > je regrette beaucoup car je ne connais pas
> > Bohlen-Pierce et leur ouvrage non plus...
>
> Il y a un website a
> <http://members.aol.com/bpsite/index.html>.
>
> > Non ! Il n'y a pas "d'interval d'equivalence" et
> tous
> > les demi-tones restent bien a leur place durant
> > l'execution ! On n'a pas besoin d'adapter
> rien-tout
> > est parfait :)
>
> Le "88CET" de Gary Morrison n'a pas d'intervale
> d'equivalence. Tous les
> "demis-tones" est 88 cents. On peut parle d'un
> equivalence a 11 octaves,
> mais ce n'est pas importante pour la musique.
>
>
> Graham
>
Bien entendu, Mr Graham, c'est une demie tone hors
limites qui n'est pas appliquable car la deviation est
horrible pour l'octave, ainsi que pour la quinte !
(Voir K Bach(1.059...), K TEQJ(1.059...) car 88
cents=1.052...(K de Mr Morrison) Je suis violoniste et
je sais parfaitement de quoi je parle...Les voltiges
mathematiques ne donnent aucun resultat valable, c'est
sure !

Latchezar

___________________________________________________________
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🔗Wim Hoogewerf <wim.hoogewerf@fnac.net>

Dimitrov wrote:
>
> Ok, I will try to responding below...
>
> --- Wim Hoogewerf <wim.hoogewerf@fnac.net> a écrit :
>>
>> 660 Hz if A=440 Hz means a perfect fifth (3/2 or 702
>> cents). If your fifths
>> are smaller than this, how comes that the octave is
>> still larger?
>>
>
> :)))) Sorry for my laught, but this question is very
> funny...
> 7th root of 1.5(K2) is larger that 12th root of 2(K1)
> !
> If you use K2 you will produce (extremly!)wide octave
> when multiply the reference frequency 12 times with...
> We have lots of intermediate values(K) when the fifth
> is smaller(3/2) but still the octave is larger(Bach
> octave) or= no one perfect interval is in use !
> And this sound better that TEQJ !!!

Now I understand better what you're talking about. Your fifths are somewhere
between 700 and 702 cents and the octave is slightly stretched, but not as
much as in Cordier's tuning. K1 and K2 are a sort of outer limits, right?
Like K1 for Mount Everest and K2 for ... K2? (voir 'Le Monde' depuis lundi)

>> > Not so perfects ;)) Because all musicians with the
>> > instruments like violoncells or contrabasses use
>> > harmonics octaves when they verify yours strings
>> !!!
>> > And they accorde himselfs highter...
>>
>> That's good to know. Can you explain this in detail?
>>
> The harmonic of one string dont have harmonics
> himselfs, ok ? :)) Or- the ear hear too down one sound
> with less harmonics... If one violoncelist use the
> first harmonic to compare the A from hautbois when
> according - the octave (first harmonic)is too short =
> the string is accorded too hight !!!

So that compensation is quite welcome. Otherwise the low strings in the
orchestra would be really too low. Thanks for your explanation.
>
>
>> > Also today nobody accord the piano like...
>>
>
> In the pratice I mean...
>
>> Actually, there should be quite a lot Cordier-tuned
>> pianos in France, since
>> I spontaneously found two of them, independent from
>> each other and I'm not
>> even a pianist.
>
> Actually I think that TEQJ is a extreme solution and
> inusable in the pratice...
> One PC modern is powerfull to prove that !
> See multipistes section of Cool Edit Pro and produce 8
> consecutive octaves in TEQJ...

I believe you, but a PC is not a piano, so the result won't be exactly the
same.
>
>>
>> > For me the half tones are like the letters in the
>> > alphabet-they must be free of engagements harmonic
>> or
>> > melodic out of any context musical...
>>
>> >
>
> Like the seconds in time mesure ! If I'm stressed the
> time feel to me different but that dont change the
> real time...
>
>> The octave *is* imposing itself, since we hear it
>> immediately on any
>> instrument producing harmonics, especially the
>> violin. Could you reply to
>> the question: why *should* we abandon the octave? Or
>> the fifth, or the
>> third?
>
> Because the music is the live show :))
> One perfect octave or fifth are dead intervals !
> We need to hear little beat in EACH interval having
> never one perfect there, who impose to divide
> different the scale ! It's only my last opinion :))

Merci beaucoup. Dead or alive, it's still an octave. The interval you may
give up is the 1200 cents beatless octave, which has a function as a
measurement, but can be slightly bigger in musical reality. I can agree on
that!

Bonne continuation! Wim Hoogewerf

🔗Latchezar Dimitrov <latchezar_d@yahoo.com>

--- jpehrson@rcn.com a ï¿½critï¿½: > --- In tuning@y...,
Latchezar Dimitrov
> <latchezar_d@y...> wrote:
>
> /tuning/topicId_27561.html#27582
>
> > Salut, Joseph :))
> >
> > Ca ma fait rigoler beaucoup ta suggestion or
> > maintenant voici en franï¿½ais ma rï¿½ponse...
> >
>
> Language difficulities can be funny... just don't
> make me write in
> French and we're OK... :)
>
>
> > > Hello Mr. Dimitrov!
> > >
> > > Well, of course, we have discussed here the idea
> of
> > > using "intervals
> > > of equivalance" other than the octave... such as
> the
> > > 12th of the
> > > Bohlen-Pierce scale (3:1) as advocated by Heinz
> > > Bohlen, who is a
> > > participant on this very list!
> > >
> > > However, generally speaking, there is always
> *one*
> > > "interval of
> > > equivalence" for any given tuning.
> >
> > C'est faux :)) On n'a pas besoin d'aucun interval
> et
> > je regrette beaucoup car je ne connais pas
> > Bohlen-Pierce et leur ouvrage non plus...
> >
>
> Maybe so... but I thought most scales were
> constructed with some kind
> of "interval of equivalence..." Maybe not..
>
> Paul??
>
> Heinz Bohlen has done a lot of work with the famous
> "Bohlen-Pierce"
> scale, which is based upon the twelfth or 3:1 ratio.
> He is also on
> this list! He has a whole website devoted to it,
> and I know your
> English is good enough that you can read most of
> it...
>
>
> http://members.aol.com/bpsite/
>
>
> > >
> > > Are you suggesting that the "interval of
> > > equivalence" CHANGE during
> > > the course of a piece... something that could be
> > > done "adaptively"
> > > with synthesizers and the like (??)
> > >
> >
> > Non ! Il n'y a pas "d'interval d'equivalence" et
> tous
> > les demi-tones restent bien a leur place durant
> > l'execution ! On n'a pas besoin d'adapter
> rien-tout
> > est parfait :)
> >
>
> Oh... If I'm getting this at all you mean the larger
> intervals are
> built up from the smaller ones... but in the case
> of the fifth, you
> *were* making that constant, I thought... or was
> that the French
> technician Mr. Cordier... ?? If the fifth is
> constant than *that*
> would be the "equivalent" interval, wouldn't it??
>
>
> >
> > A la fin je peux expliquer un peu plus mon
> > invention... L'octave est elargie avec un peu plus
> que
> > 2 cents et la quinte est moins qu'un cent plus
> petite
> > !
> > Des questions ? (en english, sure ;) )
> >
>
> Oh... well actually then Dave Keenan and Wim
> Hoogewerf were right...
> you are mostly concerned with "stretched" octaves
> and perhaps a
> generating fifth, correspondingly that is only 1
> cent small from just
> rather than 2 cents...
>
> Or something like that.
>
> Thanks for sparing us from your written, er,
> "English" :) :) :)
>
> __________ _________ ______
> Joseph Pehrson
>
>

C'etait quoi la question ? :))
Pour moi quand les demi-tones sont egales alors tous
les autres intervales le sont aussi !
Tous les quintes sont privï¿½s disons de 0.8 cents, ok ?
Et les octaves sont plus grandes avec 2.3 cents...
N'oublions pas que chez Mr Cordier les quintes sont
justes !
Est -ce qu'il y a encore quelque chose pas clair ?

L. Dimitrov

___________________________________________________________
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🔗Latchezar Dimitrov <latchezar_d@yahoo.com>

--- Paul Erlich <paul@stretch-music.com> a ï¿½critï¿½: >
--- In tuning@y..., jacky_ligon@y... wrote:
> > --- In tuning@y..., Latchezar Dimitrov
> <latchezar_d@y...> wrote:
> >
> > > One perfect octave or fifth are dead intervals !
> > > We need to hear little beat in EACH interval
> having
> > > never one perfect there, who impose to divide
> > > different the scale ! It's only my last opinion
> :))
> > >
> > > Mr Dimitrov
> >
> > Now your speaking my language Mr Dimitrov!!!
> >
> > YES! I'm with you!
> >
> > Jacky Ligon
>
> Jacky -- I'm shocked! This from you, the staunch
> defender of JI??!!
>
My UT12 has never been any JI temperament, sorry !
Paul, do you understand me anytime or ...
I write better in french, ok :)

Latchezar

___________________________________________________________
Do You Yahoo!? -- Un e-mail gratuit @yahoo.fr !
Yahoo! Courrier : http://fr.mail.yahoo.com

🔗jpehrson@rcn.com

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., Latchezar Dimitrov <latchezar_d@y...> wrote:
> --- Paul Erlich <paul@s...> a écrit : >
> --- In tuning@y..., jacky_ligon@y... wrote:
> > > --- In tuning@y..., Latchezar Dimitrov
> > <latchezar_d@y...> wrote:
> > >
> > > > One perfect octave or fifth are dead intervals !
> > > > We need to hear little beat in EACH interval
> > having
> > > > never one perfect there, who impose to divide
> > > > different the scale ! It's only my last opinion
> > :))
> > > >
> > > > Mr Dimitrov
> > >
> > > Now your speaking my language Mr Dimitrov!!!
> > >
> > > YES! I'm with you!
> > >
> > > Jacky Ligon
> >
> > Jacky -- I'm shocked! This from you, the staunch
> > defender of JI??!!
> >
> My UT12 has never been any JI temperament, sorry !

Exactly. No interval is just in your temperament. I like that!

> Paul, do you understand me anytime or ...

I think I understand you very well, non?

> I write better in french, ok :)
>
Mon francais est tres pauvre.

🔗Latchezar Dimitrov <latchezar_d@yahoo.com>

--- Paul Erlich <paul@stretch-music.com> a ï¿½critï¿½: >
--- In tuning@y..., Latchezar Dimitrov
> <latchezar_d@y...> wrote:
> > --- Paul Erlich <paul@s...> a ï¿½critï¿½: >
> > --- In tuning@y..., jacky_ligon@y... wrote:
> > > > --- In tuning@y..., Latchezar Dimitrov
> > > <latchezar_d@y...> wrote:
> > > >
> > > > > One perfect octave or fifth are dead
> intervals !
> > > > > We need to hear little beat in EACH interval
> > > having
> > > > > never one perfect there, who impose to
> divide
> > > > > different the scale ! It's only my last
> opinion
> > > :))
> > > > >
> > > > > Mr Dimitrov
> > > >
> > > > Now your speaking my language Mr Dimitrov!!!
> > > >
> > > > YES! I'm with you!
> > > >
> > > > Jacky Ligon
> > >
> > > Jacky -- I'm shocked! This from you, the staunch
> > > defender of JI??!!
> > >
> > My UT12 has never been any JI temperament, sorry !
>
> Exactly. No interval is just in your temperament. I
> like that!
>
> > Paul, do you understand me anytime or ...
>
> I think I understand you very well, non?
>
> > I write better in french, ok :)
> >
> Mon francais est tres pauvre.
>
Paul,
I'm so confused...the mistake is in the word
"staunch"...
By the way JT=12ET ?
Latchezar

___________________________________________________________
Do You Yahoo!? -- Un e-mail gratuit @yahoo.fr !
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🔗Paul Erlich <paul@stretch-music.com>

🔗Latchezar Dimitrov <latchezar_d@yahoo.com>

--- Paul Erlich <paul@stretch-music.com> a ï¿½critï¿½: >
--- In tuning@y..., Latchezar Dimitrov
> <latchezar_d@y...> wrote:
> > >
> > Paul,
> > I'm so confused...the mistake is in the word
> > "staunch"...
>
> staunch = strong, determined . . .
>
> > By the way JT=12ET ?
>
> Oh no! Just Tuning means everything can be described
> with simple
> ratios.
>
Thank-you!
I'm really choked ...JT is like the communisme in the
East countries :)))
Utopie of the inalphabet peuple,ok...
I know, to not know english is little different;)
But I know also in each temperament respecting more
one interval is ...absurd position !
JT is one hymere ?
Why we use it more?
JT is one ideal who never can existing?
I thing that JT is bad formuled...
At the beguinning :)

Hope to read you more...

Mr Dimitrov

___________________________________________________________
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🔗jpehrson@rcn.com

🔗genewardsmith@juno.com

--- In tuning@y..., jacky_ligon@y... wrote:

> > Why would you want to use it?

> It is one of the possibilities for generating myriad scales with
> Myhill's Property.

It seems to me that could be said about anything. Is part of the
attraction that powers of phi tend toward integers?

> The sound of Golden Tunings can be very lovely to my ears, else I
> wouldn't be so interested in using it for my work. Interestingly,
> they can converge on very "JI-like" intervals (if desired).

An interesting property of phi is that it is the least well-
approximated number by rational approximations, so we have ratios of
relatively small integers clustered near it--3/2, 5/3, 8/5 and 13/8
etc. are all in the neighborhood.

Since you like phi, you might be interested in the number r = 1.3247..
which is defined as the real root of r^3 - r - 1. It is the
smallest "PV number", which are certain numbers having phi-like
properties. For instance, powers of r tend towards integer values,
and there are recurrence relationships associated to it like the
Fibonacci recurrence.

I think it would be interesting to experiment with timbres which have
overtones satisfing such a recurrence relationship--for instance,
something which had partial tones only at the Fibonacci numbers
1,2,3,5,8,13... . The idea is that these might have unusual
consonance/dissonance properties when several tones with such timbres
are played together, because of the lack of overlap on critical bands
in some sizes of interval. Since r at about 486.8 cents is smaller
than phi, it might be even better in some ways for such a project.

> If you are able to play MP3s on your PC, and you would like to hear
a
> piano based example of this tuning, you may download it from the
> files section of the Make Micro Music Group. You'll have to join
the
> group, then you can go into the folder with my name on it and
> download the piece "Golden_Convergence.mp3".

Thanks. I haven't gotten a sound card yet, but I could convert these
to wav files and burn a CD.