Yahoo Tuning Groups Ultimate Backup tuning Eleven Perfect Fifths Scale

The Eleven Perfect Fifths Scale works with 11 pure fifths and 10 perfect fourths.
With such numbers of perfect relations I cannot understand why this scale was considered as
a disastrous scale or something like that.

Miss Margo Schults wrote that the EPFS high quality was proved in a piano concert given in
Europe. It was published that its inventor Mr. Cordier had patented his invention.

Coincidently, I deduced in Perú exactly the same scale on September 17, this year. Obviously that
before I got the scale I didn´t know about the Cordier´s invention.

Perhaps Mr. A. Sparschuh would like to explain us how a scale having the highest number of perfect fifths and almost the highest number of perfect fourths per octave can be considered as an unsatisfactory scale.

Thanks

Mario Pizarro

Lima, September 27, 2008
piagui@...

🔗Carl Lumma <carl@...>

Mario- Please give your scale in cents values here so
we know what you're talking about. As George pointed out,
there is only one 12-tone scale with pure octaves and
11 pure fifths -- the Pythagorean scale of antiquity.

-Carl

--- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>
> The Eleven Perfect Fifths Scale works with 11 pure fifths and
> 10 perfect fourths. With such numbers of perfect relations I
> cannot understand why this scale was considered as a disastrous
> scale or something like that.
>
> Miss Margo Schults wrote that the EPFS high quality was proved
> in a piano concert given in Europe. It was published that its
> inventor Mr. Cordier had patented his invention.
>
> Coincidently, I deduced in Perú exactly the same scale on
> September 17, this year. Obviously that before I got the scale
> I didn´t know about the Cordier´s invention.
>
> Perhaps Mr. A. Sparschuh would like to explain us how a scale
> having the highest number of perfect fifths and almost the
> highest number of perfect fourths per octave can be considered
> as an unsatisfactory scale.
>
> Thanks
>
> Mario Pizarro
>
> Lima, September 27, 2008
> piagui@...
>

🔗Mike Battaglia <battaglia01@...>

The scale he is referring to is the 7th root of 3/2, I believe.

On Sat, Sep 27, 2008 at 4:16 PM, Carl Lumma <carl@...> wrote:
> Mario- Please give your scale in cents values here so
> we know what you're talking about. As George pointed out,
> there is only one 12-tone scale with pure octaves and
> 11 pure fifths -- the Pythagorean scale of antiquity.
>
> -Carl
>
> --- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>>
>> The Eleven Perfect Fifths Scale works with 11 pure fifths and
>> 10 perfect fourths. With such numbers of perfect relations I
>> cannot understand why this scale was considered as a disastrous
>> scale or something like that.
>>
>> Miss Margo Schults wrote that the EPFS high quality was proved
>> in a piano concert given in Europe. It was published that its
>> inventor Mr. Cordier had patented his invention.
>>
>> Coincidently, I deduced in Perú exactly the same scale on
>> September 17, this year. Obviously that before I got the scale
>> I didn´t know about the Cordier´s invention.
>>
>> Perhaps Mr. A. Sparschuh would like to explain us how a scale
>> having the highest number of perfect fifths and almost the
>> highest number of perfect fourths per octave can be considered
>> as an unsatisfactory scale.
>>
>> Thanks
>>
>> Mario Pizarro
>>
>> Lima, September 27, 2008
>> piagui@...
>>
>
>

🔗Carl Lumma <carl@...>

🔗Mario Pizarro <piagui@...>

Carl and Mike,

Thank you.

You are right, the scale I deduced on October 17 has12 perfect fifths, and not eleven. It is a stretched scale whose octave has a value of 2,00387547376, that is 1203,3514 cents.

When I was checking the perfect fifth of note B by multiplying its value by 1,5 and going back to the first octave, I divided by 2 instead of 2.003875....I didnï¿½t get the expected F# = 1,415583..... so I wrongly thougth that note B does not give a perfect fifth and that the scale has only 11 pure fifths. Thank you again my friends.

Carl, perhaps now you can respond to my message and please confirm that my stretched twelve perfect fifths scale is not the Pythagorean scale of antiquity. The scale I deduced has an octave with 1203,3514 cents

Point 2: Please give me the email address of Andreas Sparschuh; the one I have ( a_sparschuh@...) doesnï¿½t work.

Thanks

Mario

Lima, September 28
-----------------------------------------------------------------------------------------------------------------
piagui@...
----- Original Message ----- From: "Mike Battaglia" <battaglia01@...>
To: <tuning@yahoogroups.com>
Sent: Saturday, September 27, 2008 4:03 PM
Subject: Re: [tuning] Re: Eleven Perfect Fifths Scale

The scale he is referring to is the 7th root of 3/2, I believe.

On Sat, Sep 27, 2008 at 4:16 PM, Carl Lumma <carl@...> wrote:
> Mario- Please give your scale in cents values here so
> we know what you're talking about. As George pointed out,
> there is only one 12-tone scale with pure octaves and
> 11 pure fifths -- the Pythagorean scale of antiquity.
>
> -Carl
>
> --- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>>
>> The Eleven Perfect Fifths Scale works with 11 pure fifths and
>> 10 perfect fourths. With such numbers of perfect relations I
>> cannot understand why this scale was considered as a disastrous
>> scale or something like that.
>>
>> Miss Margo Schults wrote that the EPFS high quality was proved
>> in a piano concert given in Europe. It was published that its
>> inventor Mr. Cordier had patented his invention.
>>
>> Coincidently, I deduced in Perï¿½ exactly the same scale on
>> September 17, this year. Obviously that before I got the scale
>> I didnï¿½t know about the Cordierï¿½s invention.
>>
>> Perhaps Mr. A. Sparschuh would like to explain us how a scale
>> having the highest number of perfect fifths and almost the
>> highest number of perfect fourths per octave can be considered
>> as an unsatisfactory scale.
>>
>> Thanks
>>
>> Mario Pizarro
>>
>> Lima, September 27, 2008
>> piagui@...
>>
>
>

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🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>
> Carl and Mike,
>
> Thank you.
>
> You are right, the scale I deduced on October 17 has12 perfect
> fifths, and not eleven. It is a stretched scale whose octave
> has a value of 2,00387547376, that is 1203,3514 cents.
>
> When I was checking the perfect fifth of note B by multiplying
> its value by 1,5 and going back to the first octave, I divided
> by 2 instead of 2.003875....I didn´t get the expected
> F# = 1,415583..... so I wrongly thougth that note B does not
> give a perfect fifth and that the scale has only 11 pure fifths.
> Thank you again my friends.
>
> Carl, perhaps now you can respond to my message and please
> confirm that my stretched twelve perfect fifths scale is not the
> Pythagorean scale of antiquity.

Confirmed. It is the "7th root of 1.5 equal temperament".
It is a fine scale, but its triads are noticeably more harsh
than in 12-tone equal temperament, as already discussed.

> Point 2: Please give me the email address of Andreas Sparschuh;
> the one I have ( a_sparschuh@...) doesn't work.

Perhaps Andreas himself can respond; I do not have him in
my address book.

-Carl

🔗Andreas Sparschuh <a_sparschuh@...>

--- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>
Dear Mario & all others,

> The Eleven Perfect Fifths Scale works with 11 pure fifths and 10
> perfect fourths.

Ther's something wrong with yours counting:
because the number of 5ths and 4ths must be equal the same.

Hence:
11 pure 5ths of 3/2 correspond to exactly 11 pure 4ths of 4/3
and one remaining pythagorean Wolf-5th of (3/2)/PC of

1200 * ln((3/2)/(3^12)/(2^19))/ln(2) = ~678.49499...Cents

in order to conclude the full cycle of the dozen 5ths.

> With such numbers of perfect relations I cannot understand why this
> scale was considered as
> a disastrous scale or something like that.

That defect of an whole PC appears also in
http://en.wikipedia.org/wiki/Kirnberger_temperament
#1
"...tune C-G, G-D, D-A, A-E, E-B, B-Fb/, F 839;-Cb/, Cb/-Gb/ (Ab-), Ab--Eb-,
Eb--B♭, Bb--F, F-C... the new "C" will not be the same frequency as the
first. The two "C"s will have a discrepancy of about 23 cents (a
comma), which would be unacceptable. "
>
> Perhaps Mr. A. Sparschuh would like to explain us how a scale having
>the highest number of perfect fifths and almost the highest number of
>perfect fourths per octave can be considered as an unsatisfactory >scale.

http://en.wikipedia.org/wiki/Pythagorean_tuning
"In the case of Pythagorean tuning, all the fifths are 701.96 cents
wide, in the exact ratio 3:2, except the wolf fifth, which is only
678.49 cents wide, nearly a quarter of a semitone flatter."

http://www.music.sc.edu/fs/bain/atmi02/pst/index.html
http://www.medieval.org/emfaq/harmony/pyth.html

hope that links explain -better than i can do that-
how the problematically ~678Cents pythagorean-wolf
arises from 11 perfect 5ths or 4ths.

bye
A.S.