Yahoo Tuning Groups Ultimate Backup tuning The True Octave

Mario,

I've been learning about alternative tunings for less than a year. I have
limited capabilities for retuning, but I've done some experimentation. I
read what people write, and I listen to music that they compose, but please
understand that I'm new to this.

Sometimes, I will listen to a piece in an alternate tuning and think, "Those
major thirds are very flat," or "Those fifths are so sharp that they buzz a
little bit," or "I love the sound of that septimal minor third."

Then I'll read the composer's words about these pieces, and they'll say, "I
like these submajor thirds because they howl," or "I used fifths that sound
active to me," or "The 7/6 feels more restful to me than the 6/5 does."

This is very helpful: The words I read correspond to what I hear.

This is how I'm trying to understand what you've done with the true octave.
Unfortunately, I'm not reading any words that show me why this octave is the
true one. I don't know why you think it sounds better, or how it was
derived, or what you want to do with it.

It would be helpful if you could tell us that sort of thing.

Regards,
Jake

🔗Steve Parker <steve@...>

🔗Mario Pizarro <piagui@...>

To Jake Freivald,

Jake,

In the past century, Mr. Julián Carrillo, from Mexico, a well known musician who directed an orchestra, anounced that he detected by ear the real musical octave which is slightly higher than 2 but he couldn´t get its value, instead he wrote the book titled "Sonido 13". Time and the undefined range of the octave are deleting his declaration.

I trust to the Progression of Musical Cells, a set of 624 cell frequencies within the range 1 up to (9/8)^6 = 2.02728652954, I derived in the past century. To do a clear explanation I copy here its final 15 cells:

The first column gives the commas J = 1.001131371103, M = 1.00112915039. The third column gives the cell frequency. The third comma of groups JMM, MMJ used along the progression signaled all the tones of Pythagoras and JI extended scales so cell # 612 is signaled by M that is the third comma of the group J M M. Who derived the 2 octave? Nobody knows that. It is a natural parameter, and all natural parameters like the gravity acceleration constant are not given by round numbers. Cell # 615, the third cell of group MMJ was the suspected value of the true octave, some reasoning and calculations confimed it.

<Unfortunately, I'm not reading any words that show me why this octave is the true one. I don't know why you think it sounds better, or how it was derived, or what you want to do with it.>

Should you study the attached files, I filed a few days ago, you will read about this subject and know how it was derived. I think it sounds better because that is what I perceive. I don´t know what can I do with it.

You can complete the explanation by reading the attached file, feel free to ask some additional information you need. Mario

J 610
1.99549103682

M
611
1.99774424631

M
612
2.00000000000-(2 octave)

M
613
2.00225830078

M
614
2.00451915152

J
615
2.00678700656 (True octave)

J
616
2.00905742738

M
617
2.01132595536

M
618
2.01359704486

M
619
2.01587069874

M
620
2.01814691994

J
621
2.02043019304

J
622
2.02271604938

M
623
2.02500000000

M
624
2.02728652954

.= (9/8)^6

The third cell

----- Original Message -----
From: Jake Freivald
To: tuning@yahoogroups.com
Sent: Sunday, July 24, 2011 10:59 PM
Subject: [tuning] The True Octave

Mario,

I've been learning about alternative tunings for less than a year. I have limited capabilities for retuning, but I've done some experimentation. I read what people write, and I listen to music that they compose, but please understand that I'm new to this.

Sometimes, I will listen to a piece in an alternate tuning and think, "Those major thirds are very flat," or "Those fifths are so sharp that they buzz a little bit," or "I love the sound of that septimal minor third."

Then I'll read the composer's words about these pieces, and they'll say, "I like these submajor thirds because they howl," or "I used fifths that sound active to me," or "The 7/6 feels more restful to me than the 6/5 does."

This is very helpful: The words I read correspond to what I hear.

This is how I'm trying to understand what you've done with the true octave. Unfortunately, I'm not reading any words that show me why this octave is the true one. I don't know why you think it sounds better, or how it was derived, or what you want to do with it.

It would be helpful if you could tell us that sort of thing.

Regards,
Jake

🔗Steve Parker <steve@...>

🔗Mario Pizarro <piagui@...>

Jake,

If you want, I can send you the Progression of Musical Cells (About 700 KB). I would need your personal email address for the attachment.

Mario
July, 25
----- Original Message -----
From: Jake Freivald
To: tuning@yahoogroups.com
Sent: Sunday, July 24, 2011 10:59 PM
Subject: [tuning] The True Octave

Mario,

I've been learning about alternative tunings for less than a year. I have limited capabilities for retuning, but I've done some experimentation. I read what people write, and I listen to music that they compose, but please understand that I'm new to this.

Sometimes, I will listen to a piece in an alternate tuning and think, "Those major thirds are very flat," or "Those fifths are so sharp that they buzz a little bit," or "I love the sound of that septimal minor third."

Then I'll read the composer's words about these pieces, and they'll say, "I like these submajor thirds because they howl," or "I used fifths that sound active to me," or "The 7/6 feels more restful to me than the 6/5 does."

This is very helpful: The words I read correspond to what I hear.

This is how I'm trying to understand what you've done with the true octave. Unfortunately, I'm not reading any words that show me why this octave is the true one. I don't know why you think it sounds better, or how it was derived, or what you want to do with it.

It would be helpful if you could tell us that sort of thing.

Regards,
Jake

🔗Mario Pizarro <piagui@...>

Steve,

You wrote:
<It is the half-string - in this sense it is clear that it should be a round number - 1/2.>

Since the string lenght measurement necessarily includes an error considering the toctave range of 2.00678700656, your arguing cannot be applied. I cannot imagine what kind of measuring device might be used to reduce the error to 0 %.

BTW: I still don´t find an abnormal chord or not desirable effect on the Brahms piece played on the piano tuned to the toctave. Where is the failed part of it?. Instead, when single notes going up in frequency are listened, they sound fine.

Mario
July, 25

----- Original Message -----
From: Steve Parker
To: tuning@yahoogroups.com
Sent: Monday, July 25, 2011 12:42 PM
Subject: Re: [tuning] The True Octave

On 25 Jul 2011, at 18:32, Mario Pizarro wrote:

Nobody knows that. It is a natural parameter, and all natural parameters like the gravity acceleration constant are not given by round numbers.

It is the half-string - in this sense it is clear that it should be a round number - 1/2.

Steve P.

🔗Steve Parker <steve@...>

Hi Mario,

> <It is the half-string - in this sense it is clear that it should be a round number - 1/2.>
>
> Since the string lenght measurement necessarily includes an error considering the toctave range of 2.00678700656, your arguing cannot be applied. I cannot imagine what kind of measuring device might be used to reduce the error to 0 %.
>

But it is not a measurement problem, it is a logic problem..

If there is a true octave slightly further along the string than half way and slightly higher than 2/1, then there is another true octave on the other (almost) half of the string slightly *lower* than 2/1.

Your arguments can't assume your conclusions.

> BTW: I still don´t find an abnormal chord or not desirable effect on the Brahms piece played on the piano tuned to the toctave.

All is bad, but have a listen from 0:33!

http://soundcloud.com/eisik/brahms-marios-tuning

It is the same tuning as this:

http://soundcloud.com/eisik/mario-pizarro-chords

Are you suggesting it is not severely beating at say 0:18?

Will your concert pianist in Russia play a standard ticketed concert with this tuning?

Steve P.

🔗Tim Reeves <reevest360@...>

Hi Mario,

Without elaborating, I'll go out on a limb and say Steve is right about the question of logic. Without even going into heterodynamics and sinusuidol wave motion (the foundation of harmony) I'd have to ask...what is that ticket price and which conductor will risk his reputation with the symphony and patrons of the art with your pianist? John Cage????
Tim

--- On Tue, 7/26/11, Steve Parker <steve@...> wrote:

From: Steve Parker <steve@...>
Subject: Re: [tuning] The True Octave
To: tuning@yahoogroups.com
Date: Tuesday, July 26, 2011, 8:16 AM

Hi Mario,

<It is the half-string - in this sense it is clear that it should be a round number - 1/2.>

Since the string lenght measurement necessarily includes an error considering the toctave range of 2.00678700656, your arguing cannot be applied. I cannot imagine what kind of measuring device might be used to reduce the error to 0 %.

But it is not a measurement problem, it is a logic problem..

Your arguments can't assume your conclusions.

BTW: I still don´t find an abnormal chord or not desirable effect on the Brahms piece played on the piano tuned to the toctave.

All is bad, but have a listen from 0:33!

http://soundcloud.com/eisik/brahms-marios-tuning

It is the same tuning as this:

http://soundcloud.com/eisik/mario-pizarro-chords

Are you suggesting it is not severely beating at say 0:18?

Will your concert pianist in Russia play a standard ticketed concert with this tuning?

Steve P.

🔗Mario Pizarro <piagui@...>

Steve,

Last night I was thinking on your 1/2 string lenght and arrived to these conclussions:

-- Physics established different chapters each having its own rules. The rules of string mechanical vibrations depend on uniform density strings, acceptable elasticity, not a gram of weight.....If these conditions are satisfied then the Mechanics Chapter of Physics rules the inverse relation between lenght and vibration frequency.

-- The Acoustic Chapter of Physics rules the sound. No density, no elasticity, no weight. It is unquestionable that one rule that governs the string vibrations cannot govern any type of sound processes like its frequency.
---------------------------------------------
IMPORTANT:

About the piano used to record Brahms piece and chords:
There is a 99.99 % of probability that the piano is far to be tuned to toctave tuning because :

-- Even in the case that you used file # 3 (THE PIANO TUNED TO THE TRUE OCTAVE), where the middle A frequency equals 440 Hz, the resulted tuning probably is not the toctave tuning. Here in Lima, the tuner also made adjustments to compensate the imperfection of the ear. The correction was a small correction thanks to the fact that the true octave took the most part of the correction or may be all of it.

Before the correction process, just at the end of the tuning with file # 3, There are some points to check:

-- The highest frequenccy (key # 88 -- 64C) should be 8742.521 cents while the lowest one is minus 3923.460 cents.

-- At low frequencies, the tuner has to make a gradual frequency deduction in order to get "ear octaves" with respect to keys with higher than 440 Hz.

Should you do the above, you will get the real true octave tuning.

I WOULD BE HAPPY + HAPPY TO HEAR AT LEAST TWO CLASSIC WORKS PLAYED ON A PIANO TUNED TO THE TRUE OCTAVE.

Mario
July, 26
----- Original Message -----
From: Steve Parker
To: tuning@yahoogroups.com
Sent: Tuesday, July 26, 2011 3:16 AM
Subject: Re: [tuning] The True Octave

Hi Mario,

But it is not a measurement problem, it is a logic problem..

Your arguments can't assume your conclusions.

BTW: I still don´t find an abnormal chord or not desirable effect on the Brahms piece played on the piano tuned to the toctave.

All is bad, but have a listen from 0:33!

http://soundcloud.com/eisik/brahms-marios-tuning

It is the same tuning as this:

http://soundcloud.com/eisik/mario-pizarro-chords

Are you suggesting it is not severely beating at say 0:18?

Will your concert pianist in Russia play a standard ticketed concert with this tuning?

Steve P.

🔗Steve Parker <steve@...>

🔗genewardsmith <genewardsmith@...>

🔗Steve Parker <steve@...>

🔗genewardsmith <genewardsmith@...>

🔗Mario Pizarro <piagui@...>

Steve,

I see that you didn´t notice that in file # 3, I wrote the following (one of the head lines): NO ADJUSTMENTS FOR THE EAR IMPERFECTION.

SHEET # 3 of 3

THE PIANO TUNED TO THE TRUE OCTAVE [1 True octave = (1.05976223699^12) = 2.00678700656]

NO ADJUSTMENTS FOR THE EAR IMPERFECTION. (1 semitone = 100.488749859 cents = Ratio = 1.05976223699)

1 TRUEOCTAVE = 1201.466 minus (- 4.399) = 1205.865 cents. (A = 440 Hz)-

KEY #
NOTE
TONE FREQUENCY

TRUE OCTAVE:

2.00678700646
CENTS
Hz
KEY

#
NOTE
TONE FREQUENCY

TRUE OCTAVE:

1205.865 cents
CENTS
Hz

----- Original Message -----
From: Steve Parker
To: tuning@yahoogroups.com
Sent: Tuesday, July 26, 2011 11:42 AM
Subject: Re: [tuning] The True Octave

Hi Mario,

Even in the case that you used file # 3 (THE PIANO TUNED TO THE TRUE OCTAVE), where the middle A frequency equals 440 Hz, the resulted tuning probably is not the toctave tuning.
Are you saying that the frequencies in this file are not correct?
I tuned to the frequencies in this file. BUT DIDN´T PAY ATTENTION TO THAT WARNING

Here in Lima, the tuner also made adjustments to compensate the imperfection of the ear. The correction was a small correction thanks to the fact that the true octave took the most part of the correction or may be all of it.

Can you quantify in cents the degree of correction?
I SUGGEST YOU TO ANALYZE THE RAILSBACK CURVE THAT I WILL TRY TO INSERT HERE.
The Railsback curve

The Railsback curve, indicating the deviation between normal piano tuning and an equal-tempered scale.

The Railsback curve, first measured by O.L. Railsback, expresses the difference between normal piano tuning and an equal-tempered scale (one in which the frequencies of successive notes are related by a constant ratio, equal to the twelfth root of two). For any given note on the piano, the deviation between the normal pitch of that note and its equal-tempered pitch is given in cents (hundredths of a semitone).

As the Railsback curve shows, octaves are normally stretched on a well-tuned piano. That is, the high notes are higher, and the low notes lower, than they are in an equal-tempered scale. Not all octaves are equally stretched: the middle octaves are barely stretched at all, whereas the octaves on either end of the piano are stretched considerably.

Railsback discovered that pianos were typically tuned in this manner not because of a lack of precision, but because of inharmonicity in the strings. Ideally, the overtone series of a note consists of frequencies that are integer multiples of the note's fundamental frequency. Inharmonicity causes the successive overtones to be higher than they "should" be.

At low frequencies, the tuner has to make a gradual frequency deduction in order to get "ear octaves" with respect to keys with higher than 440 Hz.

Are you saying that the frequencies are ignored and the piano ends up being tuned by ear??
ONCE YOU COMPLETE THE TOCTAVE TUNING WITH THOSE FREQUENCIES YOU CAN DO THE CORRECTIONS THIS
WAY YOU HAVE GOOD REFERENCES TO SHAPE A SIMILAR CURVE. THE EAR OCTAVES PROBABLY WON´T REQUIRE MUCH ADDERS TO SHAPE BOTH SIDES OF THE CURVE. THE MIDDLE OCTAVE CONTAINING THE TOCTAVE FREQUENCIES GIVEN BY FILE # 3 SHOULD NOT BE MODIFIED.
THE WHOLE 88 KEYS COMPRISES 8742.521 CENTS BEFORE THE CORRECTIONS. GOOD LUCK
MARIO---------JULY 26

Steve P.

🔗Carl Lumma <carl@...>

🔗Steve Parker <steve@...>

On 26 Jul 2011, at 21:02, Carl Lumma wrote:

> --- In tuning@yahoogroups.com, Steve Parker <steve@...> wrote:
>
> > I'm not so sure, especially in software.
> > The stretch involved in tuning is minute, Mario's true octave
> > is wider than 2/1 by nearly 6 cents.
> > Inharmonicity will neither explain nor mitigate that..
>
> You'll see inharmonicity greater than that depending on
> the register and instrument. A gigasampler like Kontakt
> will recreate this too. It varies string by string,
> instrument by instrument, and this is why Gene's right
> about the piano being a bad testbed for tunings with
> tempered octaves. -C.
>
I have some Kontakt pianos that have been sampled stretched.

The one I used has non-beating octaves that show on a tuner as frequency doubled.
I used Mario's cent deviations from that.

I'm not being facetious in asking where I may be going wrong.. but the possibilities for screw-up that I can see currently are not of the same magnitude as the deviation from 12ET of Mario's tuning.
A 6 cent wide octave is not subtle - I'd just like to understand if anyone really hears that as beating less than 2/1 or else if it has any quality that makes it preferable for anything, let alone 'true'.

The curve that Mario linked to of nearly a semitone stretch over a keyboard is not my experience.

Steve P.

🔗Carl Lumma <carl@...>

Steve Parker <steve@...> wrote:

> The curve that Mario linked to of nearly a semitone stretch
> over a keyboard is not my experience.

On a professional-quality grand, stretch is not uniform and
is practically zero in the middle 3 octaves, but may be a
quarter tone or more over the whole keyboard.

I'm not defending Mario's tuning, which I haven't studied.
If you want a good piano tuning, I believe I've got a
definitive picture of the subject. Summary:

* With only 12 tones/oct, temperament is useless in the
13-limit, and ideal tunings are made of superposed harmonic
series segments, such as those due to George Secor and
David Canright.

* In the 7-limit, rank-3 temperament is possible by
treating 225:224 as a unison, where scales by Wilson, Hahn,
myself, and Dave Keenan come to the fore. However, giving
up a few tetrads to get more 3:2s is sometimes preferred,
and here all roads seem to point to Kraig Grady's "centaur"
scale (very similar to Other Music's 12-tone scale and
independently discovered by myself).

* 7-limit rank-2 and equal temperament points to a flat
octave (e.g. Dominant[12]). As far as I know, I'm the only
person to tune real pianos with flat-octave tunings.
There happens to be one with synchronous-beating trines
(power chords) and an octave very near Gene's zeta octave.
I've also come up with a series of flat-octave well
temperaments. The stretch based on the timbre of the
instrument can be added to the theoretical (flat) octave.

* 5-limit tuning starts with 12-tone Fokker blocks, and
Gene has done a comprehensive survey of these. Meantone
quickly follows, with Paul Erlich's TOP meantone being
optimal (and providing a tiny amount of endemic octave
stretch).

* Further tempering leads to 1/5th- and 1/6th-comma
well temperaments. Among these, I've studied the chains
that avoid the most discordant major thirds. There's also
the possibility for "rational well-tempered" versions of
these, and I've algorithmically found the VRWT with the
greatest number of 17-limit concordances. RWTs also lead
to triads with simple "beat ratios", where Bob Wendell's
"natural synchronous well" remains king. However,
investigations by myself and others showed that extended
rationals and simple beat ratios provide little if any
benefit in musical settings where well temperaments are
typically used.

* For the 3-limit, equal divisions of 3:2 or 3:1 can be
used, and will provide a modest amount of endemic stretch.

In the end, the following conclusions are reached:

- For Renaissance and early baroque music, TOP meantone
is barely better than the quarter-comma tuning in common
use since that time.

- For Baroque and early Classical music, slight improvement
may be found by using one of my 'more equal' 1/5th- or 1/6th-
comma well temperaments.

- For 20th century Russian music, equal division of 3:1 or
even 3:2 makes an interesting choice.

- For certain kinds of jazz (e.g. Oscar Peterson) or
Romantic music (Brahms), a flat-octave equal or well
temperament may provide modest benefit over 12-ET.

- For new music, certain 7-, 11- or 13-limit scales can be
tried, though the Halberstadt keyboard is far from ideal
for such purposes.

In all, very little advantage is to be found over common
keyboard tuning & practice. Nevertheless, if any of the
above strikes your fancy, let me know which bit and I can
provide more info,

-Carl

🔗genewardsmith <genewardsmith@...>

🔗Carl Lumma <carl@...>

🔗martinsj013 <martinsj@...>

Mario,

--- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
> In the past century, Mr. Julián Carrillo, from Mexico, a well known musician who directed an orchestra, anounced that he detected by ear the real musical octave which is slightly higher than 2 but he couldn´t get its value, instead he wrote the book titled "Sonido 13".

I looked up Carrillo and Sonido 13, and could find no mention of the octave being higher than 2; I could only find mention of dividing the tone into 8 or 16 equal parts (NB - I mean taking the 8th or 16th root of the ratio!) i.e. for 48 EDO or 96 EDO. Can you give a reference?

> I trust to the Progression of Musical Cells, a set of 624 cell frequencies within the range 1 up to (9/8)^6 = 2.02728652954, I derived in the past century. ...
> ... Should you study the attached files, I filed a few days ago, you will read about this subject and know how it was derived. I think it sounds better because that is what I perceive. I don´t know what can I do with it.

I have to agree with Steve P that the files do not explain "why"; they explain "what" (2.006787...), and maybe "how" (i.e. "choose cell 615 of the progression") but not "why". May I ask, why cell 615, but not 614 or 616, or 612?

Steve M.

🔗Mario Pizarro <piagui@...>

Steve Martins,

In 1985/1986 I got copies of some chapters of books that deal with music. One of them was "Teorï¿½a de la Mï¿½sica"
written by Joaquï¿½n Zamaï¿½ois. I formed two groups of pages, from page # 134/#156 and from X/Z (By trying to find this
second group I fell down and now I am taking pills for the pain). Probably the information regarding the higher than
2 octave anounced by Juliï¿½n Carrillo figures in this pages. My assistance will continue the searching.

Three are the foundations of the true octave (Cell # 615 = 2.00678700656 = 1205.865 cents)
Tomorrow I will explain you one of them. This is the first time I do that, will also explain you why the
toctave is not less than 2.

Since the foundation to be explained requires an ordained exposition, the wording will take one or two days.
Do you still have the progression of cells?. The one I have now is somewhat different, I will only use two or
three groups of cells.

I faced hard moments listening to some members how easily abandon the respect to somebody that just informed
about his conclussions.

Mario
July, 27

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

----- Original Message ----- From: "martinsj013" <martinsj@...>
To: <tuning@yahoogroups.com>
Sent: Wednesday, July 27, 2011 11:33 AM
Subject: [tuning] Re: The True Octave

Mario,

--- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
> In the past century, Mr. Juliï¿½n Carrillo, from Mexico, a well known > musician who directed an orchestra, anounced that he detected by ear the > real musical octave which is slightly higher than 2 but he couldnï¿½t get > its value, instead he wrote the book titled "Sonido 13".

> I trust to the Progression of Musical Cells, a set of 624 cell frequencies > within the range 1 up to (9/8)^6 = 2.02728652954, I derived in the past > century. ...
> ... Should you study the attached files, I filed a few days ago, you will > read about this subject and know how it was derived. I think it sounds > better because that is what I perceive. I donï¿½t know what can I do with > it.

Steve M.

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🔗Steve Parker <steve@...>

🔗Tim Reeves <reevest360@...>

Buenos Dias guys,

Here's a link that might lighten things up around here...
http://www.time.com/time/magazine/article/0,9171,884120,00.html

Note that this article is from 1940

All you 'tuners that can't get to beach for a conch shell, run to the kitchen for your pots and pans and join the orchestra. Johnny Reinhardt can bring his trombone.

But wait...can anyone put the sounds of the natural pentatonic from the Indian's shell under careful observation to see the exact frequencies that were produced?

--- On Thu, 7/28/11, Steve Parker <steve@...> wrote:

From: Steve Parker <steve@...>
Subject: Re: [tuning] Re: The True Octave
To: tuning@yahoogroups.com
Date: Thursday, July 28, 2011, 8:22 AM

Hi Mario,
I have never shown you lack of respect. Criticism of ideas is not the same as lack of respect.
If I write I expect my words to be given the most uncharitable reading and criticised on that basis.
It also would be different if you announced that you had a new tempering of the octave that sounds better, approximates x/y better etc., rather than announcing the *true* octave.

1206 cents beats

1200 doesn't

You still have to explain why a beating octave is better than a non-beating one.

Steve P.

On 28 Jul 2011, at 03:13, Mario Pizarro wrote:

I faced hard moments listening to some members how easily abandon the
respect to somebody that just informed
about his conclussions.

🔗Mario Pizarro <piagui@...>

Steve,

My GOD, what is happening to you Steve. Didn´t you realize that I always try to give you extra information I download from internet?. I do that because I am seeing you as a brother. Never, Never I said a word against you. The hard moments I faced were created by other members of the list whose names I prefer to forget now for I hope some day they reconsider their positions and conduct. I would be a child if I did something against you even inadvertently. My parents taught me how I have to respect to everybody. Regarding the "true octave", despite the fact that there are clear reasons for calling it that way, since a couple of weeks I am also using the short "toctave". Since Steve Martin is a correct man and just yesterday I sent him a message where I referred to those hard moments, somebody has injected you poisson against me, that is clear.

Regarding beating on the toctave, some wrong step might have done when tuning.

Don´t feel bad if I tell you are acting as a boy. I will forget this problem.

Mario
July, 28
--------------------------------------------------
----- Original Message -----
From: Steve Parker
To: tuning@yahoogroups.com
Sent: Thursday, July 28, 2011 3:22 AM
Subject: Re: [tuning] Re: The True Octave

1206 cents beats

1200 doesn't

You still have to explain why a beating octave is better than a non-beating one.

Steve P.

On 28 Jul 2011, at 03:13, Mario Pizarro wrote:

I faced hard moments listening to some members how easily abandon the
respect to somebody that just informed
about his conclussions.

🔗Steve Parker <steve@...>

> My GOD, what is happening to you Steve. Didn´t you realize that I always try to give you extra information I download from internet?. I do that because I am seeing you as a brother. Never, Never I said a word against you. The hard moments I faced were created by other members of the list whose names I prefer to forget now for I hope some day they reconsider their positions and conduct.

Ah, I thought because I was *still* going it must refer to me..

> Regarding the "true octave", despite the fact that there are clear reasons for calling it that way,

This is where I don't think you're being forthcoming - I have read every word of everything you've sent and haven't seen a hint of a clear reason.
A clear method I've seen, but no clear reason.

> Since Steve Martin is a correct man and just yesterday I sent him a message where I referred to those hard moments, somebody has injected you poisson against me, that is clear.

No one has - purely my own misunderstanding..

> Regarding beating on the toctave, some wrong step might have done when tuning.

No mistake. 1206 cents beats anywhere for anyone, have you tried it?

Steve P.

🔗Mario Pizarro <piagui@...>

Steve,
-------------------------------------------------------
This is where I don't think you're being forthcoming - I have read every word of everything you've sent and haven't seen a hint of a clear reason.
A clear method I've seen, but no clear reason.
--------------------------------------
You have not seen it because I didn´t send them yet. I don´t remember you have specifically ask it. If instead of claiming that the toctave produce beating you and all those who almost insulted me you would be fully informed and convinced that toctave is the only solution. As regards to the beating perhaps the tuner could accept to send you an email saying that he didn´t face any beating at all. Steve Martin asked me to explain HOW I got the toctave. I will add why any other value is not valid.
Mario
July, 28

Regarding beating on the toctave, some wrong step might have done when tuning.

No mistake. 1206 cents beats anywhere for anyone, have you tried it?

----- Original Message -----
From: Steve Parker
To: tuning@yahoogroups.com
Sent: Thursday, July 28, 2011 9:45 AM
Subject: Re: [tuning] Re: The True Octave

Ah, I thought because I was *still* going it must refer to me..

Regarding the "true octave", despite the fact that there are clear reasons for calling it that way,

This is where I don't think you're being forthcoming - I have read every word of everything you've sent and haven't seen a hint of a clear reason.
A clear method I've seen, but no clear reason.

Since Steve Martin is a correct man and just yesterday I sent him a message where I referred to those hard moments, somebody has injected you poisson against me, that is clear.

No one has - purely my own misunderstanding..

Regarding beating on the toctave, some wrong step might have done when tuning.

No mistake. 1206 cents beats anywhere for anyone, have you tried it?

Steve P.

🔗Steve Parker <steve@...>

Hi Mario,

I have asked for a reason for it, or how it is useful, or what qualities it has..
It isn't a 'claim' that it beats. Have you tuned an octave to 1206 cents??

1206 is 1206.. there isn't more than one version of it..

I'm interested to hear why any value is not valid?

You still need to set out your goals with this tuning?
Is it to tune common practise material, baroque keyboard works, serialism?
I've played music without any 2/1 at all and *that* is still valid.
As is my own music with 2/1, 5/4, 27/16 24/25 etc....

Steve P.

On 28 Jul 2011, at 17:20, Mario Pizarro wrote:

>
> Steve,
> -------------------------------------------------------
> This is where I don't think you're being forthcoming - I have read every word of everything you've sent and haven't seen a hint of a clear reason.
> A clear method I've seen, but no clear reason.
> --------------------------------------
> You have not seen it because I didn´t send them yet. I don´t remember you have specifically ask it. If instead of claiming that the toctave produce beating you and all those who almost insulted me you would be fully informed and convinced that toctave is the only solution. As regards to the beating perhaps the tuner could accept to send you an email saying that he didn´t face any beating at all. Steve Martin asked me to explain HOW I got the toctave. I will add why any other value is not valid.
> Mario
> July, 28
>
>
>> Regarding beating on the toctave, some wrong step might have done when tuning.
>
>
> No mistake. 1206 cents beats anywhere for anyone, have you tried it?
>
> ----- Original Message -----
> From: Steve Parker
> To: tuning@yahoogroups.com
> Sent: Thursday, July 28, 2011 9:45 AM
> Subject: Re: [tuning] Re: The True Octave
> My GOD, what is happening to you Steve. Didn´t you realize that I always try to give you extra information I download from internet?. I do that because I am seeing you as a brother. Never, Never I said a word against you. The hard moments I faced were created by other members of the list whose names I prefer to forget now for I hope some day they reconsider their positions and conduct.
>
> Ah, I thought because I was *still* going it must refer to me..
>
>
>> Regarding the "true octave", despite the fact that there are clear reasons for calling it that way,
>
> This is where I don't think you're being forthcoming - I have read every word of everything you've sent and haven't seen a hint of a clear reason.
> A clear method I've seen, but no clear reason.
>
>
>> Since Steve Martin is a correct man and just yesterday I sent him a message where I referred to those hard moments, somebody has injected you poisson against me, that is clear.
>
> No one has - purely my own misunderstanding..
>
>
>> Regarding beating on the toctave, some wrong step might have done when tuning.
>
> No mistake. 1206 cents beats anywhere for anyone, have you tried it?
>
> Steve P.
>
>
>

🔗Mario Pizarro <piagui@...>

Steve,

First of all, the message I will send to Steve Martin where I will categorically demonstrate that Cell # 615 is the only valid octave,
will be addressed to both Steves, (S. Martin and S. Parker).

I have asked for a reason for it, or how it is useful, or what qualities it has..
It isn't a 'claim' that it beats. Have you tuned an octave to 1206 cents??

If you mean why I proposed the toctave. All of us have the duty of giving out any abnormal value of a musical parameter.
Once the octave is inserted, either 2 or other one, its utility is in hands of the instruments, players and composers. I might confirm that I am not an acceptable musician since I don´t understand how an octave can show quality A or B or C....

1206 is 1206.. there isn't more than one version of it.. OK

I'm interested to hear why any value is not valid?. You will see it in my message. There you will verify that only Cell # 615 generates one of the tone frequencies.

You still need to set out your goals with this tuning? I am not looking for personal triumphs.
Is it to tune common practise material, baroque keyboard works, serialism? Perhaps
I've played music without any 2/1 at all and *that* is still valid. I realize that "valid" was not the right word.
As is my own music with 2/1, 5/4, 27/16 24/25 etc....The use of the toctave implies some changes.

Mario
July,28
----- Original Message -----
From: Steve Parker
To: tuning@yahoogroups.com
Sent: Thursday, July 28, 2011 12:11 PM
Subject: Re: [tuning] Re: The True Octave

Hi Mario,

I have asked for a reason for it, or how it is useful, or what qualities it has..
It isn't a 'claim' that it beats. Have you tuned an octave to 1206 cents??

1206 is 1206.. there isn't more than one version of it..

I'm interested to hear why any value is not valid?

Steve P.

On 28 Jul 2011, at 17:20, Mario Pizarro wrote:

Regarding beating on the toctave, some wrong step might have done when tuning.

No mistake. 1206 cents beats anywhere for anyone, have you tried it?

----- Original Message -----
From: Steve Parker
To: tuning@yahoogroups.com
Sent: Thursday, July 28, 2011 9:45 AM
Subject: Re: [tuning] Re: The True Octave
My GOD, what is happening to you Steve. Didn´t you realize that I always try to give you extra information I download from internet?. I do that because I am seeing you as a brother. Never, Never I said a word against you. The hard moments I faced were created by other members of the list whose names I prefer to forget now for I hope some day they reconsider their positions and conduct.

Ah, I thought because I was *still* going it must refer to me..

Regarding the "true octave", despite the fact that there are clear reasons for calling it that way,

This is where I don't think you're being forthcoming - I have read every word of everything you've sent and haven't seen a hint of a clear reason.
A clear method I've seen, but no clear reason.

Since Steve Martin is a correct man and just yesterday I sent him a message where I referred to those hard moments, somebody has injected you poisson against me, that is clear.

No one has - purely my own misunderstanding..

Regarding beating on the toctave, some wrong step might have done when tuning.

No mistake. 1206 cents beats anywhere for anyone, have you tried it?

Steve P.

🔗Ryan Avella <domeofatonement@...>

🔗Mike Battaglia <battaglia01@...>

🔗Ryan Avella <domeofatonement@...>

🔗Steve Parker <steve@...>

🔗Mike Battaglia <battaglia01@...>

On Tue, Jul 26, 2011 at 5:53 PM, Carl Lumma <carl@...> wrote:
>
> I'm not defending Mario's tuning, which I haven't studied.
> If you want a good piano tuning, I believe I've got a
> definitive picture of the subject. Summary:
>
> * With only 12 tones/oct, temperament is useless in the
> 13-limit, and ideal tunings are made of superposed harmonic
> series segments, such as those due to George Secor and
> David Canright.

Unless you're willing to use 11 tones/oct, at which point the 11-note
MOS from machine temperament is probably the victor:

http://x31eq.com/cgi-bin/pregular.cgi?limit=2.7.9.11&error=5.0
http://x31eq.com/cgi-bin/pregular.cgi?limit=2.7.9.11.13&error=5.0

It's #1 for the 2.7.9.11 subgroup, where it has a complexity of 0.440,
or little over half of meantone. If you add 13 in there, you end up
with a complexity of 0.656, still less than meantone. 3\17 is a good
tuning for the generator.

If you don't care about the 13-limit, you can always just tune 11 of
the 12 notes to 11-equal, which gives you 4:7:9:11 chords that are as
accurate as 22's by definition. You of course have 12 notes on a
piano, not 11, so you could always make one of the notes a 3/2 or 5/4
over the root if you want.

You could always try the 65/64-tempered 13-limit extension of flattone as well.

-Mike

🔗Mario Pizarro <piagui@...>

Ryan,

Just to inform you about a numeric error. Since in your example you assumed 220 HZ as one of the frequencies and wrote:
220 x 1.006787 = 441.49314 and 441.49354 - (220 x 2 ) = 1.49354 beats/sec.--------- Since A = 440,one toctave below gives (440/ 2.00678700656) = 219.2559 Hz instead of 220 so the corrected beating gives 1.4882 Hz = 89.292 beats/ minute.

On a toctave piano key # 88 works with 4819.06 cents and key # 1 at minus 3923.46 cents (No adjustments for the ear imperfection)

Mario
July, 28
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message ----- From: "Ryan Avella" <domeofatonement@...>
To: <tuning@yahoogroups.com>
Sent: Thursday, July 28, 2011 5:43 PM
Subject: [tuning] Re: The True Octave

> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>> Perhaps Mario is referring to the stretched octave of the piano timbre >> here?
>>
>> -Mike
>>
>
> I highly doubt it, because when tuning an octave for inharmonic > instruments such as pianos, the value of the octave is not constant. In > the middle register the octave may be around 1202 cents, while in the > upper and lower registers it could be as sharp as 1225 cents.
>
> The toctave Mario is referring to was derived using some sort of > progression of cells involving commas, and isn't at all related to > inharmonicity.
>
> By the way, I realized I did my math wrong. The correct answer should be > twice the beating frequency I gave in my last message, so about 1.5 hertz > or 89.6 beats per minute.
>
>
> Ryan
>
>
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
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> Yahoo! Groups Links
>
>
>
>

🔗Ryan Avella <domeofatonement@...>

🔗Mario Pizarro <piagui@...>

Steve,

Seems that I know now why here in Lima didn´t detected any beating. By using the same relations used Ryan to get 1.49 Hz beating that neither man nor the dogs can ear and considering that we are not dogs, the new follows:

Ryan is correct when says that beating goes up when the high frequency keys are played, however this happens on 2 octave tunings, Going to the numbers:

Let us take key # 85 ( A = 3556 Hz) to get the beating frequency:

3556 x 2.00678700656 ------------= 7136.13 Hz (key # 86) ------ Final key # 88
3556 x 2 ---------------------------------- 7112
Difference ------------------------------- 24.13 Hz (the dogs might listen this frequency)

Ryan: Please check the above. I just used your relations ( 220 x 2.006787 = 441.49314)
----------------------------------------------------------------------minus 220 x 2 ----------------= 440.0000
---------------------------------------------------------------------- Beating ------------------------ = 1.49 Hz

Thanks

Mario

July 28
----- Original Message -----
From: Steve Parker
To: tuning@yahoogroups.com
Sent: Thursday, July 28, 2011 6:12 PM
Subject: Re: [tuning] Re: The True Octave

On 28 Jul 2011, at 23:43, Ryan Avella wrote:

while in the upper and lower registers it could be as sharp as 1225 cents

I saw the graph on this..
It really is not my experience... is it anyone else's that inharmonicity leads to such stretch?

Steve P.

🔗Mike Battaglia <battaglia01@...>

Hi Mario,

The beating envelope is not a tone at a certain frequency, but
reflects the process of amplitude modulation taking place over the
tones. Man and dog and probably yak too can hear a 1.49 Hz beating
envelope because it doesn't require anyone to hear an actual 1.49 Hz
pitch, just to hear the volume of the existing tones changing 3 times
per second.

-Mike

On Thu, Jul 28, 2011 at 9:34 PM, Mario Pizarro <piagui@...> wrote:
>
> Steve,
>
> Seems that I know now why here in Lima didn´t detected any beating. By using the same relations used Ryan to get 1.49 Hz beating that neither man nor the dogs can ear and considering that we are not dogs, the new follows:
>
> Ryan is correct when says that beating goes up when the high frequency keys are played, however this happens on 2 octave tunings, Going to the numbers:
>
> Let us take key # 85 ( A = 3556 Hz) to get the beating frequency:
>
> 3556 x 2.00678700656 ------------= 7136.13 Hz (key # 86) ------ Final key # 88
> 3556 x 2 ---------------------------------- 7112
> Difference ------------------------------- 24.13 Hz (the dogs might listen this frequency)
>
> Ryan: Please check the above. I just used your relations ( 220 x 2.006787 = 441.49314)
> ----------------------------------------------------------------------minus 220 x 2 ----------------= 440.0000
> ---------------------------------------------------------------------- Beating ------------------------ = 1.49 Hz
>
> Thanks
>
> Mario
>
> July 28

🔗Mario Pizarro <piagui@...>

Ryan,

"Ear imperfection" are terms used by the tuner. You know that the ear response curve is about an "S" and that the response of a perfect ear is an horizontal line.

----- Original Message ----- From: "Ryan Avella" <domeofatonement@...>
To: <tuning@yahoogroups.com>
Sent: Thursday, July 28, 2011 7:54 PM
Subject: [tuning] Re: The True Octave

> --- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>>
>> Ryan,
>>
>> Just to inform you about a numeric error. Since in your example you >> assumed
>> 220 HZ as one of the frequencies and wrote:
>> 220 x 1.006787 = 441.49314 and 441.49354 - (220 x 2 ) = 1.49354
>> beats/sec.--------- Since A = 440,one toctave below gives (440/
>> 2.00678700656) = 219.2559 Hz instead of 220 so the corrected beating >> gives
>> 1.4882 Hz = 89.292 beats/ minute.
>
> Regardless of how it is done, you can see that an undesirable frequency of > beating is always detected by the ear.
>
>
>
>> On a toctave piano key # 88 works with 4819.06 cents and key # 1 at minus
>> 3923.46 cents (No adjustments for the ear imperfection)
>
> What is the "ear imperfection."?
>
>
>
> ------------------------------------
>
> 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.
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>
>
>
>

🔗Mario Pizarro <piagui@...>

Mike,

One question please:

I think the numeric relations I wrote below are wrong. Since key # 85 gives 3556 Hz, the product "3556 x 2.00678700656" means that I played key # (85 + 12 = # 97), there is no key # 97, so I made a mistake.

As I understand, when the pianist plays key # 85 (3556 HZ) two sound waves are created. Wave (a), 3556 Hz is created by the piano itself, this wave carries its first harmonics ( 2 x 3556 = 7112 Hz) with an amplitude X. I don´t know where wave (b) = 7136.13 comes from since key # 97 does not exist. Since wave (b) has a Y amplitude. Which one is having a greater amplitude?.
Thanks

Mario

-------------------------------------------------------------------------------------------------

"Let us take key # 85 ( A = 3556 Hz) to get the beating frequency:
"3556 x 2.00678700656 ------------= 7136.13 Hz (key # 86)
"3556 x 2 ---------------------------------- 7112
"Difference ------------------------------- 24.13 Hz
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message -----
From: Mario Pizarro
To: tuning@yahoogroups.com
Cc: Ryan Avella ; Mike Battaglia ; Steve Martin
Sent: Thursday, July 28, 2011 8:34 PM
Subject: Re: [tuning] Re: The True Octave

Steve,

Ryan is correct when says that beating goes up when the high frequency keys are played, however this happens on 2 octave tunings, Going to the numbers:

Let us take key # 85 ( A = 3556 Hz) to get the beating frequency:

3556 x 2.00678700656 ------------= 7136.13 Hz (key # 86) ------ Final key # 88
3556 x 2 ---------------------------------- 7112
Difference ------------------------------- 24.13 Hz

Thanks

Mario

July 28
----- Original Message -----
From: Steve Parker
To: tuning@yahoogroups.com
Sent: Thursday, July 28, 2011 6:12 PM
Subject: Re: [tuning] Re: The True Octave

On 28 Jul 2011, at 23:43, Ryan Avella wrote:

while in the upper and lower registers it could be as sharp as 1225 cents

I saw the graph on this..
It really is not my experience... is it anyone else's that inharmonicity leads to such stretch?

Steve P.

🔗Ryan Avella <domeofatonement@...>

🔗martinsj013 <martinsj@...>

🔗Mario Pizarro <piagui@...>

Steve Martin, Steve Parker, Mike Battaglia

It is important to everybody the translation of the attached declaration into the english language. It was indorsed by important authorities of the USA at the middle of the past century. Mr. JULIï¿½N CARRILLO, (Mï¿½XICO), HAS DEMONSTRATED UNDER THE WITNESS OF PHYSICISTS AND AUTHORITIES OF THE UNITED STATES
THAT THE MUSICAL OCTAVE IS SLIGHTLY SHARPER THAN 2. (> 2). I have copy of his declaration that JOHN H. CHALMERS SENT ME THIS AFTERNOON. -- Mario-- July, 29
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message ----- From: "martinsj013" <martinsj@...>
To: <tuning@yahoogroups.com>
Sent: Friday, July 29, 2011 5:48 AM
Subject: [tuning] Re: The True Octave

> --- In tuning@yahoogroups.com, "martinsj013" <martinsj@...> wrote:
>> Mario,
>> The situation Steve P is referring to is the interaction between two >> notes, e.g. key #73 and key #85. The 4th harmonic of #73 and 2nd >> harmonic of #85 are close together to produce audible beats.
>>
>> #85 x 2: 3556 x 2 ---------------------------------= 7112.00 Hz
>> #73 x 4: 3556 / 2.00678700656 x 4 ------------= 7087.95 Hz
>> Difference ----------------------------------------= 24.05 Hz
>
> Correction/Addition - I guess that the 2nd harmonic of #73 and the > fundamental of #85 will also beat, at 12.025 Hz ...
>
> (Hmm, I seem to remember that I also got it wrong the previous time I > posted about beating. I'll leave it to others from now on ...)
>
> Steve M.
>
>
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
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🔗martinsj013 <martinsj@...>

🔗Mario Pizarro <piagui@...>

Steve,
We are walking to complete in an instrument the extraordinary work done by Juliï¿½n Carrillo. Since about six months ago, I am experimenting on a "requinto" (small guitar whose open first string is tuned to A 440 Hz.- My ear is more sensible to its sound range). I tuned the original sixth string frequency of 110 Hz to a slightly higher one (> 110) that makes a clear consonance with the second fret, third string (A 220 Hz) whose original frequency was not modified. On January, this year, I started to make frequency measurements by using a High precison LG Counter. I will respond here your questions and comments.
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
> >> On a toctave piano key # 88 works with 4819.06 cents and key # 1 at > >> minus
> >> 3923.46 cents (No adjustments for the ear imperfection)

Mario, this seems ambiguous to me; do you mean "the tuner must not make any adjustments for the ear imperfection" or rather "these figures do not include any adjustments for the ear imperfection, which the tuner must make as well" ?
-----------------------------------------------------------------------------------------------------
SINCE THE TOCTAVE DELTA FREQUENCY PER 12 KEYS IS THE RATIO (2.00678700656 / 2) = 1.00339350328 = MMJ, THEN AT KEY #88 THE "NOMINAL" FREQUENCY IS 4232.352 Hz. THIS WAS THE FREQUENCY WE GOT WHEN MEASURED IN CENTS. AT THIS POINT THE PIANIST PLAYED SOME SHORT PIECES THAT SOUNDED MAGNIFICENT, THE CURIOUS THING WAS THAT ALL OF US FORGOT TO TALK ABOUT EAR ADJUSTMENTS MAINLY BECAUSE THE PIANO OWNER STARTED PLAYING CLASSIC WORKS ON THE GRAND PIANO. SINCE I WAS TIRED, I SAID GOOD BY MY BOYS. SO I DONï¿½T KNOW IF AFTER HAVING THE NOMINAL FREQUENCIES THE EAR ADJUSTMENTS SHOULD BE DONE OR NOT. BACK AT HOME I PHONED TO THE TUNER AND SAID HIM !!! MAY BE THE TOCTAVE HAS SWALLOWED YOUR ADJUSTMENTS FOR THE EAR IMPERFECTION!!!!!!!!
> "Ear imperfection" are terms used by the tuner. You know that the ear
> response curve is about an "S" and that the response of a perfect ear is > an
> horizontal line.

I am also unsure about this - do you mean the Railsback curve? YES

Steve M.

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

"In 1947 Carrillo conducted experiments at New York University examining the node law that prevailed at the time and showed that it had to be modified. His reasoning followed from the fact that a node is not a mathematical point but a physical point. If a violin string is stopped below halfway, the frequency of the bowed fraction is more than twice the frequency of its base note. He was nominated for the Nobel Prize in physics in 1950 for this work." ALMOST THE SAME WORDS I USED WHEN DISCUSSING THIS MATTER WITH STEVE PARKER, BUT HE DIDNï¿½T AGREE WITH ME.

Isn't this an example of "inharmonicity"? SOMEWHERE I HEARD THIS WORD, WHAT DOES IT MEAN AND WHAT IS ITS RELATION WITH THE CASE? --------- MARIO --- JULY 30 -- 11:30 AM

Steve.
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

----- Original Message ----- From: "martinsj013" <martinsj@...>
To: <tuning@yahoogroups.com>
Sent: Saturday, July 30, 2011 5:33 AM
Subject: [tuning] Re: The True Octave

> Mario,
> thank you for sending that - I can only grasp the outline of it at the > moment.
>
> There is a short passage about this, which I missed, in Wikipedia (also at > other sites, e.g. YouTube):
>
> "In 1947 Carrillo conducted experiments at New York University examining > the node law that prevailed at the time and showed that it had to be > modified. His reasoning followed from the fact that a node is not a > mathematical point but a physical point. If a violin string is stopped > below halfway, the frequency of the bowed fraction is more than twice the > frequency of its base note. He was nominated for the Nobel Prize in > physics in 1950 for this work."
>
> Isn't this an example of "inharmonicity"?
>
> Steve.
>
>
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
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>
>
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>

🔗Carl Lumma <carl@...>

🔗Tim Reeves <reevest360@...>

here is the facebook link to the entire article that is only partially referred to in Mario's Carillio posts. The extraordinary work that promoted him as a microtanalist probably refers to Carillio using a razor blade to find sixteen distinct tones between G and A on the 4th string of a violin. It never mentions that dividing a string into 2 equal parts produces more than an octave or "true octave" as we are coming to know it. On the other hand, it states the obvious...that dividing a string below midway produces more than an octave or more than twice the frequency. Although it does mention info about nodes, it would have been more complete to state that nodes were more than just mathematical, but in fact are also physical...what is the mystery here?
http://www.facebook.com/pages/Julian-Carrillo/144747742253619?sk=info
--- On Sat, 7/30/11, Mario Pizarro <piagui@...> wrote:

From: Mario Pizarro <piagui@...>
Subject: Re: [tuning] Re: The True Octave
To: tuning@yahoogroups.com
Cc: "Mike Battaglia" <battaglia01@...>, "John H. Chalmers" <jhchalmers@...>, "Steve Parker" <steve@...>, "Steve Martin" <martinsj@...>, "Fernando de Lucchi" <dirgen@...>, "Luis Justo" <luisjusto98@...>, "Roberto Pizarro" <roberto.pizarro@...>, rpizarro3005@...
Date: Saturday, July 30, 2011, 4:44 PM

Steve,
We are walking to complete in an instrument the extraordinary work done by
Julián Carrillo. Since about six months ago, I am experimenting on a
"requinto" (small guitar whose open first string is tuned to A 440 Hz.- My
ear is more sensible to its sound range). I tuned the original sixth string
frequency of 110 Hz to a slightly higher one (> 110) that makes a clear
consonance with the second fret, third string (A 220 Hz) whose original
frequency was not modified. On January, this year, I started to make
frequency measurements by using a High precison LG Counter. I will respond
here your questions and comments.
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
> >> On a toctave piano key # 88 works with 4819.06 cents and key # 1 at
> >> minus
> >> 3923.46 cents (No adjustments for the ear imperfection)

Mario, this seems ambiguous to me; do you mean "the tuner must not make any
adjustments for the ear imperfection" or rather "these figures do not
include any adjustments for the ear imperfection, which the tuner must make
as well" ?
-----------------------------------------------------------------------------------------------------
SINCE THE TOCTAVE DELTA FREQUENCY PER 12 KEYS IS THE RATIO (2.00678700656 /
2) = 1.00339350328 = MMJ, THEN AT KEY #88 THE "NOMINAL" FREQUENCY IS
4232.352 Hz. THIS WAS THE FREQUENCY WE GOT WHEN MEASURED IN CENTS. AT THIS
POINT THE PIANIST PLAYED SOME SHORT PIECES THAT SOUNDED MAGNIFICENT, THE
CURIOUS THING WAS THAT ALL OF US FORGOT TO TALK ABOUT EAR ADJUSTMENTS MAINLY
BECAUSE THE PIANO OWNER STARTED PLAYING CLASSIC WORKS ON THE GRAND PIANO.
SINCE I WAS TIRED, I SAID GOOD BY MY BOYS. SO I DON´T KNOW IF AFTER HAVING
THE NOMINAL FREQUENCIES THE EAR ADJUSTMENTS SHOULD BE DONE OR NOT. BACK AT
HOME I PHONED TO THE TUNER AND SAID HIM !!! MAY BE THE TOCTAVE HAS SWALLOWED
YOUR ADJUSTMENTS FOR THE EAR IMPERFECTION!!!!!!!!
> "Ear imperfection" are terms used by the tuner. You know that the ear
> response curve is about an "S" and that the response of a perfect ear is
> an
> horizontal line.

I am also unsure about this - do you mean the Railsback curve? YES

Steve M.

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

"In 1947 Carrillo conducted experiments at New York University examining the
node law that prevailed at the time and showed that it had to be modified.
His reasoning followed from the fact that a node is not a mathematical point
but a physical point. If a violin string is stopped below halfway, the
frequency of the bowed fraction is more than twice the frequency of its base
note. He was nominated for the Nobel Prize in physics in 1950 for this
work." ALMOST THE SAME WORDS I USED WHEN DISCUSSING THIS MATTER WITH STEVE
PARKER, BUT HE DIDN´T AGREE WITH ME.

Isn't this an example of "inharmonicity"? SOMEWHERE I HEARD THIS WORD, WHAT
DOES IT MEAN AND WHAT IS ITS RELATION WITH THE CASE? --------- MARIO ---
JULY 30 -- 11:30 AM

Steve.
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

----- Original Message -----
From: "martinsj013" <martinsj@...>
To: <tuning@yahoogroups.com>
Sent: Saturday, July 30, 2011 5:33 AM
Subject: [tuning] Re: The True Octave

> Mario,
> thank you for sending that - I can only grasp the outline of it at the
> moment.
>
> There is a short passage about this, which I missed, in Wikipedia (also at
> other sites, e.g. YouTube):
>
> "In 1947 Carrillo conducted experiments at New York University examining
> the node law that prevailed at the time and showed that it had to be
> modified. His reasoning followed from the fact that a node is not a
> mathematical point but a physical point. If a violin string is stopped
> below halfway, the frequency of the bowed fraction is more than twice the
> frequency of its base note. He was nominated for the Nobel Prize in
> physics in 1950 for this work."
>
> Isn't this an example of "inharmonicity"?
>
> Steve.
>
>
>
> ------------------------------------
>
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>
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>

------------------------------------

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🔗Tim Reeves <reevest360@...>

wait, I found another link that does state he proved Mario's claim...still no details of what was submitted to the Nobel Prize committee... the facebook link wasn't as thorough as the following

http://www.mexconnect.com/articles/1204-did-you-know-mexico-s-nobel-prize-nominee-and-music-revolutionary

--- On Sat, 7/30/11, Carl Lumma <carl@...> wrote:

From: Carl Lumma <carl@...>
Subject: [tuning] Re: The True Octave
To: tuning@yahoogroups.com
Date: Saturday, July 30, 2011, 9:06 PM

--- In tuning@yahoogroups.com, "martinsj013" <martinsj@...> wrote:

> "In 1947 Carrillo conducted experiments at New York University
> examining the node law that prevailed at the time and showed
> that it had to be modified. His reasoning followed from the fact
> that a node is not a mathematical point but a physical point.
> If a violin string is stopped below halfway, the frequency of
> the bowed fraction is more than twice the frequency of its base
> note. He was nominated for the Nobel Prize in physics in 1950
> for this work."
>
> Isn't this an example of "inharmonicity"?

Impossible to tell from this description (does the Nobel site
have any more info?).

-Carl

------------------------------------

🔗martinsj013 <martinsj@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> Impossible to tell from this description (does the Nobel site
> have any more info?).

I couldn't find anything despite the below which suggests it could be found in 2011 if not in 2000:

"Forms are sent to about three thousand individuals to invite them to submit nominations. The names of the nominees are never publicly announced, and neither are they told that they have been considered for the prize. Nomination records are sealed for fifty years. In practice, some nominees do become known. It is also common for publicists to make such a claim, founded or not."
http://www.answers.com/topic/nobel-prize-in-physics#ixzz1TfXvmkLq

I am increasingly confused. The paragraph I quoted seems to say nothing new, but that could be because of poor translation into English (the word "below" is the problem):

"If a violin string is stopped below halfway, the frequency of the bowed fraction is more than twice the frequency of its base note."

The site that Tim Reeves found seems clearer:
"the frequency of the note produced by halving the length of a string is actually slightly more than twice the frequency of the base note."

However, the article by Carrillo and posted here by Mario (by the way it can be found on the Internet, still in Spanish) appears not to talk of strings at all (I only have automatic translation to work with). The main points are that Carrillo became convinced that "the octave was larger than 2/1"; the example he quotes is of army trumpeters playing "el toque mañanero" (which BTW one site translated as "morning tap" and the others were even more bizarre). Then the experiments at New York were with an oboist overblowing the octave.

Can these be as accurate as working with a monochord? Surely it is subject to human factors and in any case may be a different phenomenon?

Then, the comment of the New York professor seems to be that the octave is exceeded "by five cycles" and it has been repeated many times; it doesn't say that different notes/ranges were used, but this could indicate the octave size is not constant.

Finally, the sites all speak of "the node('s) law" which seems translated from "La ley del nodo" - what would this normally be called in English? (searching for "node law" only finds Kirchhoff's law).

Steve M.

🔗martinsj013 <martinsj@...>

--- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
> ... I tuned the original sixth string
> frequency of 110 Hz to a slightly higher one (> 110) that makes a clear
> consonance with the second fret, third string (A 220 Hz) whose original
> frequency was not modified.

Mario, have you made a mistake above - then you would have tuned an octave slightly narrow?

> ... "inharmonicity" ... SOMEWHERE I HEARD THIS WORD, WHAT
> DOES IT MEAN AND WHAT IS ITS RELATION WITH THE CASE?

My understanding is: Inharmonicity means the phenomenon that, although the frequencies of the harmonics (i.e. the different modes of vibration) of a string are mathematically supposed to be in exact numerical ratios, in actual measurements they are found not to be. This is particularly noticeable in the piano, such that a piano tuned with 2/1 octaves sounds less good than expected. The Railsback curve shows the average adjustments made by a tuner to compensate for this (although each piano - and no doubt each tuner! - is different).

Thank you for your other answers, which I am still thinking about.

Steve M.

🔗Mario Pizarro <piagui@...>

TOCTAVE FOUNDATION

This article gives information regarding the derivation of the toctave, that is slightly higher than the 2 octave.
The last group of 18 cells of the progression ends on (9/8)^6 = 2.02728652954 and contains the 2 octave
as well as other cells having close frequencies like 2.00678700656 = Cell # 615, called toctave. The whole
progression comprises 624 cells.

The twelfth root of the toctave gives the semitone factor that determines the tone frequencies of an equal
tempered scale detailed below; more information is found in file # 1 which is available in folder
/tuning/files/MarioPizarro/, we get the scale you have below:

THE TOCTAVE SCALE The Progression is formed by 6 equal groups of cells, each containing 104
FREQUENCY cells which comprises six segments ordained as follows: QRQQRQ.
IN DECIMALS CENTS Set Q comprises 18 cells while Set R works with 16 so (4 x 18) + (2 x 16)
C 1 0 .= 104 cells are contained in any of the 6 segments. Since the progression
C# 1.05976223699 100.49 comprises 6 groups, the total number of cells equals 104 x 6 = 624 cells
D 1.12309599895 200.98
Eb 1.19021472820 301.47 If we take cell # 608 as the octave of a twelve tone equal tempered scale,
E 1.26134462286 401.96 the frequency of note F# will be the square root of cell # 608 that gives
F 1.33672539913 502.44 1.411022114 as shown in the table below. Similarly, by taking cell # 612
F# 1.41661109923 602.93 .= 2 as the octave of a second scale, note F# equals 2^(1/2), it is worth to
G 1.50127094746 703.42 remind that all the octaves we choose in the Segment Q column are
Ab 1.59099025761 803.91 common numbers. However, the third frequency of either the group MMJ
A 1.68607139444 904.40 or JJM coincide with classic cells of the progression like 3/2, 2^0.5, 45/32,
Bb 1.78683479269 1004.89 4/3, 32/27, ..etc, so the recommended octave would be one of the three
B 1.89362003704 1105.38 frequencies signaled by the red commas.
? 2.00678700656 1205.87
. = Toctave = Cell # 615 In the period of 1947 to 1967, Juliï¿½n Carrillo has demonstrated that the
?C# 2.12671708713 1306.35 physical octave is not 2 but a slightly higher than 2 ratio.
?D 2.25381445770 1406.84
?Eb 2.38850745145 1507.33 Therefore, the correct octave is given by cell # 615 = 2.00678700656
?E 2.53125000000 1607.82 .= 1205.865 cents
?F 2.68252316238 1708.31
Cell # SEGMENT Q SQ. ROOT
M 607 1.98873782210 1.41022615991
M 608 1.99098340619 1.41102211400
J 609 1.99323594728 1.41182008318
J 610 1.99549103682 1.41261850364
M 611 1.99774424631 1.41341580800
M 612 2 1.41421356237
M 613 2.00225830078 1.41501176701
M 614 2.00451915152 1.41581042217
J 615 2.00678700656 1.41661109926
J 616 2.00905742738 1.41741222916
M 617 2.01132595536 1.41821223918
M 618 2.01359704486 1.41901270074
M 619 2.01587069874 1.41981361408
M 620 2.01814691994 1.42061497949
J 621 2.02043019304 1.42141837368
J 622 2.02271604938 1.42222222222
M 623 2.02500000000 1.42302494708
M 624 2.02728652954 1.42382812500
.= (9/8)^6

----- Original Message ----- From: "martinsj013" <martinsj@...>
To: <tuning@yahoogroups.com>
Sent: Sunday, July 31, 2011 4:01 AM
Subject: [tuning] Re: The True Octave

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> Impossible to tell from this description (does the Nobel site
> have any more info?).

I couldn't find anything despite the below which suggests it could be found in 2011 if not in 2000:

I am increasingly confused. The paragraph I quoted seems to say nothing new, but that could be because of poor translation into English (the word "below" is the problem):

"If a violin string is stopped below halfway, the frequency of the bowed fraction is more than twice the frequency of its base note."

The site that Tim Reeves found seems clearer:
"the frequency of the note produced by halving the length of a string is actually slightly more than twice the frequency of the base note."

However, the article by Carrillo and posted here by Mario (by the way it can be found on the Internet, still in Spanish) appears not to talk of strings at all (I only have automatic translation to work with). The main points are that Carrillo became convinced that "the octave was larger than 2/1"; the example he quotes is of army trumpeters playing "el toque maï¿½anero" (which BTW one site translated as "morning tap" and the others were even more bizarre). Then the experiments at New York were with an oboist overblowing the octave.

Can these be as accurate as working with a monochord? Surely it is subject to human factors and in any case may be a different phenomenon?

Steve M.

------------------------------------

🔗Mario Pizarro <piagui@...>

TOCTAVE FOUNDATION

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message ----- From: "martinsj013" <martinsj@...>
To: <tuning@yahoogroups.com>
Sent: Sunday, July 31, 2011 5:30 AM
Subject: [tuning] Re: The True Octave

> --- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>> ... I tuned the original sixth string
>> frequency of 110 Hz to a slightly higher one (> 110) that makes a clear
>> consonance with the second fret, third string (A 220 Hz) whose original
>> frequency was not modified.
>
> Mario, have you made a mistake above - then you would have tuned an octave > slightly narrow?
>
>> ... "inharmonicity" ... SOMEWHERE I HEARD THIS WORD, WHAT
>> DOES IT MEAN AND WHAT IS ITS RELATION WITH THE CASE?
>
> My understanding is: Inharmonicity means the phenomenon that, although the > frequencies of the harmonics (i.e. the different modes of vibration) of a > string are mathematically supposed to be in exact numerical ratios, in > actual measurements they are found not to be. This is particularly > noticeable in the piano, such that a piano tuned with 2/1 octaves sounds > less good than expected. The Railsback curve shows the average > adjustments made by a tuner to compensate for this (although each piano - > and no doubt each tuner! - is different).
>
> Thank you for your other answers, which I am still thinking about.
>
> Steve M.
>
>
>
> ------------------------------------
>
> 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
>
>
>
>

🔗Mario Pizarro <piagui@...>

12T Equal temp 1.00000000000 Semitone factor M X M X J : Cmaj
1.05946309435 1.05946309435 1.05946309435 1.00339350328 1
1.12246204830 1.12627112694 1.06305838585 1.26419659610
1.18920711500 1.19324269324 1.05946309436 1.49830707687
1.25992104989 1.26419659610 1.05946309436
1.33483985416 1.33936963759 1.05946309436 C# Maj
1.41421356237 1.41901270073 1.05946309436 1.05946309435 1
1.49830707687 1.49830707687 1.05587996224 1.33936963759 1.264196596
1.58740105196 1.58740105196 1.05946309436 1.58740105196 1.498307077
1.68179283050 1.68179283050 1.05946309436
1.78179743628 1.78179743628 1.05946309436 Dmaj
1.88774862536 1.88774862536 1.05946309436 STEVE: 1.12627112694 1
2.00000000000 2.00678700656 1.06305838585 1.41901270073 1.259921050
Since the 1st string of the requinto is note A 44O, the 6th string 1.68179283050 1.493239763
(open) is two octaves below, that is, 110 Hz. I slightly raised
this frequency until detecting consonance with original A of 3d Eb maj
string (2d fret). I also raised the 1st tring to equalize with the 6th. 1.19324269324 1
E 220 given by 2d fret, 4th string had to be raised too.The strings 1.49830707687 1.255659964
that maintained their original freq. Are the 2d, the 3d and the 5th. 1.78179743628 1.493239763

THE RESULT WAS A FANTASTIC HARMONY ON ALL CHORDS WHERE IT WAS POSSIBLE
TO MAKE THEM

Mario - July 31