Yahoo Tuning Groups Ultimate Backup tuning Fwd: Questions,questions....for all's

--- Latchezar Dimitrov <latchezar_d@yahoo.com> a
ï¿½critï¿½: > Date: Tue, 2 Oct 2001 00:09:06 +0200 (CEST)
> De: Latchezar Dimitrov <latchezar_d@yahoo.com>
> Rï¿½pondre ï¿½: latchezar_d@yahoo.com
> Objet: Questions,questions....for all's
> ï¿½: tuning@yahoogroups.com
>
> Hi Paul :)
>
> I have some "foundamental" questions about JI !
>
> The math say :
>
> 1/1=unisson, np :)
>
> 21/20 = 1/2 ton
> 9/8 = whole ton, right ?
> But 42/20 =! 9/8 WHY ?!
>
> 6/5=minor third, or two minor thirds=? Because the
> tritonus=7/5 For example: A=440 C=(440*6)/5 =528 and
> Eb = (528*6)/5 = 633.6; But tritonus is also
> (440*7)/5=...616 !!!
>
> 5/4=major third or major third + minor third = fifth
> ?
> Will try that also, ok
> A=440 C#= 440*5/4=550 E=550*6/5=660 Youpiiii :)))
> Here all is right !
> Hum... minor third+1/2 ton = major third?
> C=528 C# must be 528*21/20=...554.4 and NOT 550, why
> ?!
>
> 4/3=forth or D= 440*4/3=586.666 ; minor third+1
> ton=forth ? But C+1 ton= 528*9/8=...594 !!!
> Other way, major third+1/2 ton= forth ?
> C#+1/2 ton =550*21/20=...577.5 It's so so ...!!!
>
> What's THE JI ?! Most of ratios are false and that's
> named "just intonation" ? :))))
>
>
> Dimitrov
>
>
>
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>

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🔗monz <joemonz@yahoo.com>

Hi Dimitrov,

> From: Latchezar Dimitrov <latchezar_d@yahoo.com>
> To: <tuning@yahoogroups.com>
> Sent: Monday, October 01, 2001 6:50 PM
> Subject: [tuning] Fwd: Questions,questions....for all's

> > I have some "foundamental" questions about JI !
> >
> > The math say :
> >
> > 1/1=unisson, np :)
> >
> > 21/20 = 1/2 ton

Be careful... 21:20 is only *one* type of "1/2 ton" or semitone!
Obviously, it can only exist in a type of extended JI which
has a limit of 7 or higher, and not in the usual 5-limit JI.

> > 9/8 = whole ton, right ?
> > But 42/20 =! 9/8 WHY ?!

There are many different possible "whole tones" with different
ratios. More on this below.

> > 6/5=minor third, or two minor thirds=? Because the
> > tritonus=7/5 For example: A=440 C=(440*6)/5 =528 and
> > Eb = (528*6)/5 = 633.6; But tritonus is also
> > (440*7)/5=...616 !!!

You are describing two different versions of the "tritone" here:
one is 5-limit (6/5 * 6/5 = 36/25), and the other is 7-limit (7/5).

Technically, 36/25 is a "diminished 5th" rather than a "tritone",
which is also called an "augmented 4th". Using letter-names,
the "tritone" above "A" should be called "D#"; in JI this would
have yet another ratio.

In the strictest meaning of the word "tritone" at the time it
was first used, it would refer to three successive 9:8 "whole tones",
or (9/8)^3 = ratio 729/512. Of course, this is a Pythagorean
(3-limit) ratio. In 5-limit JI there are several other "tritones"
available.

> > 5/4=major third or major third + minor third = fifth
> > ?
> > Will try that also, ok
> > A=440 C#= 440*5/4=550 E=550*6/5=660 Youpiiii :)))
> > Here all is right !

Yes:

5/4 * 6/5 = 3/2
A C# E

> > Hum... minor third+1/2 ton = major third?
> > C=528 C# must be 528*21/20=...554.4 and NOT 550, why
> > ?!

In 5-limit JI, the semitone ("1/2 ton") is usually considered
to be the ratio 25:24 (the "chromatic semitone"), which is
what it is here:

6/5 * 25/24 = 5/4
A C C#

> > 4/3=forth or D= 440*4/3=586.666 ; minor third+1
> > ton=forth ? But C+1 ton= 528*9/8=...594 !!!

There are two types of "whole tone" in 5-limit JI:
the larger one with ratio 9:8, and the smaller one
with ratio 10:9.

6/5 * 10/9 = 4/3
A C D

> > Other way, major third+1/2 ton= forth ?
> > C#+1/2 ton =550*21/20=...577.5 It's so so ...!!!

The other type of semitone most often encountered in
5-limit JI is the "diatonic semitone" with ratio 16:15.

5/4 * 16/15 = 4/3
A C# D

> >
> > What's THE JI ?! Most of ratios are false and that's
> > named "just intonation" ? :))))

Actually there has been a lot of debate here on this list about
exactly what is defined by the words "just intonation". Search
the archives... I recall that most of it was around December 2000.

You can get some information on a lot of these terms from my
Tuning Dictionary <http://www.ixpres.com/interval/dict/> as well.
Try looking up the following:

- JI
- whole tone
- semitone
- major 3rd
- minor 3rd
- 4th
- 5th
- tritone
- Pythagorean
- limit

love / peace / harmony ...

-monz
http://www.monz.org
"All roads lead to n^0"

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🔗Latchezar Dimitrov <latchezar_d@yahoo.com>

Hello Joe :)

Thank-you for your time !
I understand your convictions, position ect
Will try to explate mine too...

--- monz <joemonz@yahoo.com> a ï¿½critï¿½: > Hi Dimitrov,
>
>
> > > I have some "foundamental" questions about JI !
> > >
> > > The math say :
> > >
> > > 1/1=unisson, np :)
> > >
> > > 21/20 = 1/2 ton
>
>
> Be careful... 21:20 is only *one* type of "1/2 ton"
> or semitone!
> Obviously, it can only exist in a type of extended
> JI which
> has a limit of 7 or higher, and not in the usual
> 5-limit JI.
>

Ok, many many semi tones...But one piano dont have
that and every 1/2 ton there is fixed :)) When this
piano is tuned fine all is ok ! The question is -what
tunning or scala is used there for a so nice result ?

>
> > > 9/8 = whole ton, right ?
> > > But 42/20 =! 9/8 WHY ?!
>
> There are many different possible "whole tones" with
> different
> ratios. More on this below.
>

Sure...if we have different semi tones, why not
differents whole tones...hum... :)
Do we have different major and minor thirds also and
how to guess what's the good (for JI...) ?!
I'm truelly bored by one perfect octave 2/1(too
small), or one fifth 3/2(too big), one third(too
small) ect. I think that one third(major or minor)
dont must be perfect...they are'nt fully consonants
intervals...

>
> > > 6/5=minor third, or two minor thirds=? Because
> the
> > > tritonus=7/5 For example: A=440 C=(440*6)/5 =528
> and
> > > Eb = (528*6)/5 = 633.6; But tritonus is also
> > > (440*7)/5=...616 !!!
>

> You are describing two different versions of the
> "tritone" here:
> one is 5-limit (6/5 * 6/5 = 36/25), and the other is
> 7-limit (7/5).
>
> Technically, 36/25 is a "diminished 5th" rather than
> a "tritone",
> which is also called an "augmented 4th". Using
> letter-names,
> the "tritone" above "A" should be called "D#"; in JI
> this would
> have yet another ratio.
>

One more time you say different versions...What's JI
and what version of JI we use to refferance?
Technically one good ear play the same note for
diminushed 5th and augmented 4th, and one pianist dont
have other variant to play... Right ? :)

> In the strictest meaning of the word "tritone" at
> the time it
> was first used, it would refer to three successive
> 9:8 "whole tones",

Hummm...but what type (model, version ect) of whole
tone ?! Dont agree, it's not cleven...

> or (9/8)^3 = ratio 729/512. Of course, this is a
> Pythagorean
> (3-limit) ratio. In 5-limit JI there are several
> other "tritones"
> available.
>

Ok, I understand that we have several JI's...
Or it's the same=we dont know what's JI ! :)))
Only ratios and numbers...

>
> > > 5/4=major third or major third + minor third =
> fifth
> > > ?
> > > Will try that also, ok
> > > A=440 C#= 440*5/4=550 E=550*6/5=660 Youpiiii
> :)))
> > > Here all is right !
>
>
> Yes:
>

Why here the math is good?
Nobody say several perfect fifth's !
But several thirds must "produce" several fifth's...!?

> 5/4 * 6/5 = 3/2
> A C# E
>
>
> > > Hum... minor third+1/2 ton = major third?
> > > C=528 C# must be 528*21/20=...554.4 and NOT 550,
> why
> > > ?!
>

> In 5-limit JI, the semitone ("1/2 ton") is usually
> considered
> to be the ratio 25:24 (the "chromatic semitone"),
> which is
> what it is here:
>
> 6/5 * 25/24 = 5/4
> A C C#
>

JI is not ET, ok... 21/20 =! 25/24
I'm very interested by the ET tunning with 12 steps :)
Why nobody work in this direction ?

> > > 4/3=forth or D= 440*4/3=586.666 ; minor third+1
> > > ton=forth ? But C+1 ton= 528*9/8=...594 !!!
>

> There are two types of "whole tone" in 5-limit JI:
> the larger one with ratio 9:8, and the smaller one
> with ratio 10:9.
>
> 6/5 * 10/9 = 4/3
> A C D
>

JI is not one tunning system because all interval has
different types...When anybody play out of tunning I
think the same :)) He play false because he use
different type of intervals dimentions !
And when we play just and in tune, we use everytime
the same type-the true one :)))
JI is so, so false !

> > > Other way, major third+1/2 ton= forth ?
> > > C#+1/2 ton =550*21/20=...577.5 It's so so ...!!!
>
> The other type of semitone most often encountered in
> 5-limit JI is the "diatonic semitone" with ratio
> 16:15.
>
> 5/4 * 16/15 = 4/3
> A C# D
>
>
> > >
> > > What's THE JI ?! Most of ratios are false and
> that's
> > > named "just intonation" ? :))))
>
>

Now I think so...still so :))
Sorry for your efforts...

> Actually there has been a lot of debate here on this
> list about
> exactly what is defined by the words "just
> intonation". Search
> the archives... I recall that most of it was around
> December 2000.
>
>

> You can get some information on a lot of these terms
> from my
> Tuning Dictionary
> <http://www.ixpres.com/interval/dict/> as well.
> Try looking up the following:
>
> - JI
> - whole tone
> - semitone
> - major 3rd
> - minor 3rd
> - 4th
> - 5th
> - tritone
> - Pythagorean
> - limit
>

Terms, ok. Your dictionnary is very good idea !
But the tunning is more more complex and also
beautiful when is not false :)))

Thanks again !

Dimitrov

> love / peace / harmony ...
>
> -monz
> http://www.monz.org
> "All roads lead to n^0"
>
>
>
>
>
>
_________________________________________________________
> Do You Yahoo!?
> Get your free @yahoo.com address at
> http://mail.yahoo.com
>
>

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

🔗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:
>
> > I'm very interested by the ET tunning with 12
> steps :)
> > Why nobody work in this direction ?
>
> Actually, 99.99% of the Western musical world works
> with the ET
> tuning with 12 steps.

My question was why nobody do any researsh in the
domain of 12ET and no if 12Et is useful...!
And I mean not BACH's conception of 12ET...

> It was first described, with
> mathematical
> exactitude, in 1584 by Prince Chu Tsai-yï¿½ in China,
> and shorly
> thereafter in the West by Simon Stevin (1585). It is
> often attributed
> to Mersenne, who advocated it in the 17th century.
>
> But Latchezar, this is the _alternative_ tuning
> list, as you can see
> on this list's homepage. That means that our main
> focus is tuning
> systems other than the ET tuning with 12 steps.
>

Paul, do you mean that only microtonal tunning can be
considered like a alternative one ? I think that the
12Et can have lot of 12ET alternatifs !
Right?

Dimitrov

___________________________________________________________
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🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., Latchezar Dimitrov <latchezar_d@y...> wrote:
> --- Paul Erlich <paul@s...> a écrit : >
> --- In tuning@y..., Latchezar Dimitrov
> > <latchezar_d@y...> wrote:
> >
> > > I'm very interested by the ET tunning with 12
> > steps :)
> > > Why nobody work in this direction ?
> >
> > Actually, 99.99% of the Western musical world works
> > with the ET
> > tuning with 12 steps.
>
> My question was why nobody do any researsh in the
> domain of 12ET and no if 12Et is useful...!

What type of research in the domain of 12ET are you looking for?

> And I mean not BACH's conception of 12ET...

Bach used an _unequal_ temperament, Latchezar.
>
> > It was first described, with
> > mathematical
> > exactitude, in 1584 by Prince Chu Tsai-yü in China,
> > and shorly
> > thereafter in the West by Simon Stevin (1585). It is
> > often attributed
> > to Mersenne, who advocated it in the 17th century.
> >
> > But Latchezar, this is the _alternative_ tuning
> > list, as you can see
> > on this list's homepage. That means that our main
> > focus is tuning
> > systems other than the ET tuning with 12 steps.
> >
>
> Paul, do you mean that only microtonal tunning can be
> considered like a alternative one ? I think that the
> 12Et can have lot of 12ET alternatifs !
> Right?

Well, if you just mean a natural amount of stretching of the octaves,
I'm not sure if that quite qualifies as "alternative", since
stretching is rather common already . . . otherwise, I don't know
what you could mean by "12ET can have a lot of 12ET
alternatives" . . .