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The true octave

🔗Mario Pizarro <piagui@...>

7/9/2011 8:50:22 PM

Dear Tim Reevest, I just try to confirm my primary conclusions which are firmly based. You´d better wait in silence until I tune the piano.

I might be wrong but have the right of finding why I would be wrong.

Mario

July, 09

🔗Tim Reeves <reevest360@...>

7/10/2011 7:45:19 AM

Mario

I would just add that Pyth made the observation that a tonic had a recurrence of sine wave action at 2 times the frequency...I ,too, would be interested in knowing if it isn't "exact" Are you using a particle splitter or similar device in your analysis? It does have a physical basis so who knows????
Tim

--- On Sun, 7/10/11, Mario Pizarro <piagui@...> wrote:

From: Mario Pizarro <piagui@...>
Subject: [tuning] The true octave
To: "tuning yahoogroups" <tuning@yahoogroups.com>
Cc: "Mike Battaglia" <battaglia01@...>
Date: Sunday, July 10, 2011, 3:50 AM

Dear Tim Reevest, I just try to confirm my primary conclusions which are firmly based. You´d better wait in silence until I tune the piano.

I might be wrong but have the right of finding why I would be wrong.

Mario

July, 09

🔗Mario Pizarro <piagui@...>

7/10/2011 9:38:17 AM

Tim,

First I´ll write what concerns to your message given below; after that, I will copy the message I sent to tuning this morning which you will receive too.

> Whatever the Pythagoras opinion was and with my full respect to him, I say that he was wrong. At that time the instrumentation for extremely low error measurements didn´t exist. It occurs that a modest researcher like me is correcting or perfecting one of his statements; he did a good approachment that helped to the music along centuries.

In a matter of days, you and all members of the tuning list will know the true octave value which is slightly greater than 2. No doubt that I applied a rigurous scientifical/mathematical procedure to attain the target. Thanks to the basic information given in my book I only needed about 6 weeks to get it.

Sincerely, the analysis didn´t use any splitter.(what is this?), I just availed my book data, recalled useful features of the progression of musical cells detailed in my book, excel's program, about 100 pages containing the main calculations, these were all I think. Fortunately the research of a "rowdy" electronic engineer succeded.

Yes, it has an almost hidden Physical basis.

Regards

Mario Pizarro

Lima, July 10, 2011
<<<<<<<<<<<<<<<<<<<<<<<<<<

Dear friends,

At 06:30 am, today, all the fifths of the TRUE octave keyboard were calculated. It was found that all of them have the same value and close to 3/2. That is, 12 fifths per TRUE octave. Other basic relations were also calculated.

Now I know that this finding will at least improve the musical expression everywhere.

You are the skilled people needed to extend and give out its musical properties.

I will tune the piano the coming July 16.

Full information follows.

C. Mario Pizarro

Lima, July 10, 2011

----- Original Message -----
From: Tim Reeves
To: tuning@yahoogroups.com
Sent: Sunday, July 10, 2011 9:45 AM
Subject: Re: [tuning] The true octave

Mario

I would just add that Pyth made the observation that a tonic had a recurrence of sine wave action at 2 times the frequency...I ,too, would be interested in knowing if it isn't "exact" Are you using a particle splitter or similar device in your analysis? It does have a physical basis so who knows????
Tim

--- On Sun, 7/10/11, Mario Pizarro <piagui@...> wrote:

From: Mario Pizarro <piagui@...>
Subject: [tuning] The true octave
To: "tuning yahoogroups" <tuning@yahoogroups.com>
Cc: "Mike Battaglia" <battaglia01@...>
Date: Sunday, July 10, 2011, 3:50 AM

Dear Tim Reevest, I just try to confirm my primary conclusions which are firmly based. You´d better wait in silence until I tune the piano.

I might be wrong but have the right of finding why I would be wrong.

Mario

July, 09

🔗Steve Parker <steve@...>

7/10/2011 10:26:08 AM

On 10 Jul 2011, at 17:38, Mario Pizarro wrote:

> n a matter of days, you and all members of the tuning list will know > the true octave value which is slightly greater than 2.

What are the qualities of this octave??

At the moment I'm considering announcing my new and unprecedented discovery, based on looking out of my window alone, that the earth is flat...

Steve P.

🔗Tim Reeves <reevest360@...>

7/10/2011 11:29:58 AM

Hi Mario

I accept your determination and do want to see the results...one warning that comes to mind from my own experience with excel on my pc (when finding the true value of the Pythagorean comma ) is that the program truncated the results along the way in places that i didn't want that to happen. I corrected it by using the same calculations on my mac.
Tim

--- On Sun, 7/10/11, Mario Pizarro <piagui@...> wrote:

From: Mario Pizarro <piagui@...>
Subject: Re: [tuning] The true octave
To: tuning@yahoogroups.com
Cc: "Mike Battaglia" <battaglia01@...>, "Carlos Montoya Bello" <carlosmontoyab@...>
Date: Sunday, July 10, 2011, 4:38 PM

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Tim,

First I´ll write what concerns to your message given below; after that, I will copy the message I sent to tuning this morning which you will receive too.

> Whatever the Pythagoras opinion was and with my full respect to him, I say that he was wrong. At that time the instrumentation for extremely low error measurements didn´t exist. It occurs that a modest researcher like me is correcting or perfecting one of his statements; he did a good approachment that helped to the music along centuries.

In a matter of days, you and all members of the tuning list will know the true octave value which is slightly greater than 2. No doubt that I applied a rigurous scientifical/mathematical procedure to attain the target. Thanks to the basic information given in my book I only needed about 6 weeks to get it.

Sincerely, the analysis didn´t use any splitter.(what is this?), I just availed my book data, recalled useful features of the progression of musical cells detailed in my book, excel's program, about 100 pages containing the main calculations, these were all I think. Fortunately the research of a "rowdy" electronic engineer succeded.

Yes, it has an almost hidden Physical basis.

Regards

Mario Pizarro

Lima, July 10, 2011
<<<<<<<<<<<<<<<<<<<<<<<<<<

Dear friends,

At 06:30 am, today, all the fifths of the TRUE octave keyboard were calculated. It was found that all of them have the same value and close to 3/2. That is, 12 fifths per TRUE octave. Other basic relations were also calculated.

Now I know that this finding will at least improve the musical expression everywhere.

You are the skilled people needed to extend and give out its musical properties.

I will tune the piano the coming July 16.

Full information follows.

C. Mario Pizarro

Lima, July 10, 2011

----- Original Message -----
From: Tim Reeves
To: tuning@yahoogroups.com
Sent: Sunday, July 10, 2011 9:45 AM
Subject: Re: [tuning] The true octave

--- On Sun, 7/10/11, Mario Pizarro <piagui@...> wrote:

From: Mario Pizarro <piagui@ec-red.com>
Subject: [tuning] The true octave
To: "tuning yahoogroups" <tuning@yahoogroups.com>
Cc: "Mike Battaglia" <battaglia01@...>
Date: Sunday, July 10, 2011, 3:50 AM

🔗genewardsmith <genewardsmith@...>

7/10/2011 11:40:35 AM

--- In tuning@yahoogroups.com, Steve Parker <steve@...> wrote:

> At the moment I'm considering announcing my new and unprecedented
> discovery, based on looking out of my window alone, that the earth is
> flat...

Good, because if it was round that might bring in pi and then Mike would have to ban you.

🔗Mario Pizarro <piagui@...>

7/10/2011 1:13:26 PM

Tim,

Thanks for the warning. ¿DId you derived the Pythagorean comma?. I thought that its only value is in decimals 1.01364326477 = 23.46001...cents.

Regarding excel and mac. I confess that it is a matter of cost and sensibility since my pc (NEC) is faithful until today and it was my right hand when I derived the progression of musical cells (1985 -- 1992); 624 frequencies, each one with 14 decimal digits though only 11 were printed.

It is curious that a guitarist like me has derived the true octave. I said this because I realized that most members of the list are skilled professionals on mathematics and music. I am 77, all my professional life had to deal with research not only in the area of design and manufacture of electronic equipment but putting into service complex communication equipments like the one that works in our first international airpot that is considered the best in latin America.

Twelve fifths, twelve major thirds, twelve minor fifths work in the true octave where A 440 operates in the middle octave.

Thanks

Mario

Lima, July 10, 2011

----- Original Message -----
From: Tim Reeves
To: tuning@yahoogroups.com
Sent: Sunday, July 10, 2011 1:29 PM
Subject: Re: [tuning] The true octave

Hi Mario

I accept your determination and do want to see the results...one warning that comes to mind from my own experience with excel on my pc (when finding the true value of the Pythagorean comma ) is that the program truncated the results along the way in places that i didn't want that to happen. I corrected it by using the same calculations on my mac.
Tim

--- On Sun, 7/10/11, Mario Pizarro <piagui@...> wrote:

Tim,

First I´ll write what concerns to your message given below; after that, I will copy the message I sent to tuning this morning which you will receive too.

Yes, it has an almost hidden Physical basis.

Regards

Mario Pizarro

Lima, July 10, 2011
<<<<<<<<<<<<<<<<<<<<<<<<<<

Dear friends,

Now I know that this finding will at least improve the musical expression everywhere.

You are the skilled people needed to extend and give out its musical properties.

I will tune the piano the coming July 16.

Full information follows.

C. Mario Pizarro

Lima, July 10, 2011

----- Original Message -----
From: Tim Reeves
To: tuning@yahoogroups.com
Sent: Sunday, July 10, 2011 9:45 AM
Subject: Re: [tuning] The true octave

Mario

--- On Sun, 7/10/11, Mario Pizarro <piagui@...> wrote:

From: Mario Pizarro <piagui@...>
Subject: [tuning] The true octave
To: "tuning yahoogroups" <tuning@yahoogroups.com>
Cc: "Mike Battaglia" <battaglia01@...>
Date: Sunday, July 10, 2011, 3:50 AM

Dear Tim Reevest, I just try to confirm my primary conclusions which are firmly based. You´d better wait in silence until I tune the piano.

I might be wrong but have the right of finding why I would be wrong.

Mario

July, 09

🔗Tim Reeves <reevest360@...>

7/10/2011 3:05:48 PM

Hi Mario

yes I know of the cost...I had to choose a pc when I last bought a computer...more results for 1/3 the price.... i had tio use an older mac (and a TI calculator) for the high resolution math because i didn't have the money for a newer one

as far as deriving the comma, yes I did find it...and by using natural scale values! I applied a very simple added factor process and took it to extremes never expecting to find those results. it would have been very tedious to reach those levels by writing out the ratios involved, it became very easy when simple addition was involved. it (the comma) is in fact just another note in a natural scale with more notes per octave than is practical for most

the method that I used for finding the true octave is by using the typical circle of fifths process the main thing is to continue past the initial 12 steps that every music student has to learn, you know c-g-d-a-e- b- f#- c#- g#- d#- a#- f- c when you continue this process, you can't even begin to give a letter value to all the notes that appear, but every one nonetheless falls within the value of an octave when reduced.

I use A 440 as the tonic, resolving back to a very true A 880 with virtually no audible comma after 666 steps (or 665 steps of 3/2 according to someone on the list that corrected me in an earlier post). if you haven't done it already,give that a try and see what you come up with. there are other points that come before 665 that will yield a "comma less" octave...following the process beyond that point will probably yield even more pure octave results and further eliminate the comma.

contact me offline for how to use added factor scales to build natural scales...its as easy as pie---

it's good that you recognize the skill and talent of others that post here...this group is world class in many respects and many are top level scholars in both math and music.

hope you have fun in your visits here.

Tim
On Sun, 7/10/11, Mario Pizarro <piagui@...> wrote:

From: Mario Pizarro <piagui@...>
Subject: Re: [tuning] The true octave
To: tuning@yahoogroups.com
Date: Sunday, July 10, 2011, 8:13 PM

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Tim,

Thanks for the warning. ¿DId you derived the Pythagorean comma?. I thought that its only value is in decimals 1.01364326477 = 23.46001...cents.

Regarding excel and mac. I confess that it is a matter of cost and sensibility since my pc (NEC) is faithful until today and it was my right hand when I derived the progression of musical cells (1985 -- 1992); 624 frequencies, each one with 14 decimal digits though only 11 were printed.

It is curious that a guitarist like me has derived the true octave. I said this because I realized that most members of the list are skilled professionals on mathematics and music. I am 77, all my professional life had to deal with research not only in the area of design and manufacture of electronic equipment but putting into service complex communication equipments like the one that works in our first international airpot that is considered the best in latin America.

Twelve fifths, twelve major thirds, twelve minor fifths work in the true octave where A 440 operates in the middle octave.

Thanks

Mario

Lima, July 10, 2011

----- Original Message -----
From: Tim Reeves
To: tuning@yahoogroups.com
Sent: Sunday, July 10, 2011 1:29 PM
Subject: Re: [tuning] The true octave

--- On Sun, 7/10/11, Mario Pizarro <piagui@ec-red.com> wrote:

----- Original Message -----
From: Tim Reeves
To: tuning@yahoogroups.com
Sent: Sunday, July 10, 2011 9:45 AM
Subject: Re: [tuning] The true octave

--- On Sun, 7/10/11, Mario Pizarro <piagui@...> wrote:

From: Mario Pizarro <piagui@...>
Subject: [tuning] The true octave
To: "tuning yahoogroups" <tuning@yahoogroups.com>
Cc: "Mike Battaglia" <battaglia01@...>
Date: Sunday, July 10, 2011, 3:50 AM

🔗Steve Parker <steve@...>

7/10/2011 3:09:45 PM

Where else could they fall?

Could someone please explain to me the qualities of this 'true octave' if it is not a doubling by definition?

Steve P.

On 10 Jul 2011, at 23:05, Tim Reeves wrote:

> but every one nonetheless falls within the value of an octave when > reduced.

🔗Tim Reeves <reevest360@...>

7/10/2011 3:26:13 PM

steve
the true octave that i speak of in my last post is only referring to the resolution of A in the circle of fifths...i don't like the idea of a comma value arbitrarily becoming a skewed value of the octave that demands "tempering" in basic "harmony theory" I have proof that the Pythagorean comma is just another note and certainly not an octave. I would probably agree with you and Pythagoras, that an octave is the doubling of frequency. I will give Mario his chance to make his point though.

--- On Sun, 7/10/11, Steve Parker <steve@...> wrote:

From: Steve Parker <steve@...>
Subject: Re: [tuning] The true octave
To: tuning@yahoogroups.com
Date: Sunday, July 10, 2011, 10:09 PM

Where else could they fall?

Could someone please explain to me the qualities of this 'true octave' if it is not a doubling by definition?

Steve P.

On 10 Jul 2011, at 23:05, Tim Reeves wrote:

but every one nonetheless falls within the value of an octave when reduced.

🔗Mario Pizarro <piagui@...>

7/10/2011 5:37:13 PM

Tim,

I¨d better examine your paragraphs separately.

I applied a very simple added factor process and took it to extremes never expecting to find those results. it would have been very tedious to reach those levels by writing out the ratios involved, it became very easy when simple addition was involved.

IMO-- Both tools, adders or factors could be used, it depends on the purpose of the operation and the numbers involved. In South America countries during the primary and secondary basic studies we didn´t pay much attention to common fractions like 16/9 but we can use them when necessary. If we look at 16/9 we don´t see its magnitude unless the operation is done to get 1.777.....The same happens with magnitudes given in cents, i.e.: 20 cents doesn´t show its real magnitude and if I want to know it I have to take the calculator to get the log and this value has to be multiplied by 3986.3137, what a mess. If I would have calculated the 624 cells of the progression using common fractions or cents I would have died.

it (the comma) is in fact just another note in a natural scale with more notes per octave than is practical for most

IMO: If the Pyth. comma becomes a note then you are talking about an instrument that works with 50 tones per octave approx.

the method that I used for finding the true octave is by using the typical circle of fifths process the main thing is to continue past the initial 12 steps that every music student has to learn, you know c-g-d-a-e- b- f#- c#- g#- d#- a#- f- c when you continue this process, you can't even begin to give a letter value to all the notes that appear, but every one nonetheless falls within the value of an octave when reduced.

NOTE: You said, as I understand, that you got the true octave by using the circle of fifths. However, Mike Battaglia explained the reason of the negative results when using the circle of fifths. If you already know the true octave value, there must be some incongruence for there is only one musical octave and besides what for you want to get the one I derived if you have your own.

I use A 440 as the tonic, resolving back to a very true A 880 with virtually no audible comma after 666 steps (or 665 steps of 3/2 according to someone on the list that corrected me in an earlier post). if you haven't done it already,give that a try and see what you come up with. there are other points that come before 665 that will yield a "comma less" octave...following the process beyond that point will probably yield even more pure octave results and further eliminate the comma.

NOTE: The main point is that there is no doubt that I derived the real natural octave so it has no sense to follow your method, it would be a contraposition attitude. Mario, July 10

contact me offline for how to use added factor scales to build natural scales...its as easy as pie---
----- Original Message -----
From: Tim Reeves
To: tuning@yahoogroups.com
Sent: Sunday, July 10, 2011 5:05 PM
Subject: Re: [tuning] The true octave

Hi Mario

yes I know of the cost...I had to choose a pc when I last bought a computer...more results for 1/3 the price.... i had tio use an older mac (and a TI calculator) for the high resolution math because i didn't have the money for a newer one

as far as deriving the comma, yes I did find it...and by using natural scale values! I applied a very simple added factor process and took it to extremes never expecting to find those results. it would have been very tedious to reach those levels by writing out the ratios involved, it became very easy when simple addition was involved. it (the comma) is in fact just another note in a natural scale with more notes per octave than is practical for most

contact me offline for how to use added factor scales to build natural scales...its as easy as pie---

it's good that you recognize the skill and talent of others that post here...this group is world class in many respects and many are top level scholars in both math and music.

hope you have fun in your visits here.

Tim
On Sun, 7/10/11, Mario Pizarro <piagui@...> wrote:

From: Mario Pizarro <piagui@...>
Subject: Re: [tuning] The true octave
To: tuning@yahoogroups.com
Date: Sunday, July 10, 2011, 8:13 PM

Tim,

Thanks for the warning. ¿DId you derived the Pythagorean comma?. I thought that its only value is in decimals 1.01364326477 = 23.46001...cents.

Twelve fifths, twelve major thirds, twelve minor fifths work in the true octave where A 440 operates in the middle octave.

Thanks

Mario

Lima, July 10, 2011

----- Original Message -----
From: Tim Reeves
To: tuning@yahoogroups.com
Sent: Sunday, July 10, 2011 1:29 PM
Subject: Re: [tuning] The true octave

Hi Mario

--- On Sun, 7/10/11, Mario Pizarro <piagui@...m> wrote:

Tim,

First I´ll write what concerns to your message given below; after that, I will copy the message I sent to tuning this morning which you will receive too.

Yes, it has an almost hidden Physical basis.

Regards

Mario Pizarro

Lima, July 10, 2011
<<<<<<<<<<<<<<<<<<<<<<<<<<

Dear friends,

Now I know that this finding will at least improve the musical expression everywhere.

You are the skilled people needed to extend and give out its musical properties.

I will tune the piano the coming July 16.

Full information follows.

C. Mario Pizarro

Lima, July 10, 2011

----- Original Message -----
From: Tim Reeves
To: tuning@yahoogroups.com
Sent: Sunday, July 10, 2011 9:45 AM
Subject: Re: [tuning] The true octave

Mario

--- On Sun, 7/10/11, Mario Pizarro <piagui@...> wrote:

From: Mario Pizarro <piagui@...>
Subject: [tuning] The true octave
To: "tuning yahoogroups" <tuning@yahoogroups.com>
Cc: "Mike Battaglia" <battaglia01@...>
Date: Sunday, July 10, 2011, 3:50 AM

Dear Tim Reevest, I just try to confirm my primary conclusions which are firmly based. You´d better wait in silence until I tune the piano.

I might be wrong but have the right of finding why I would be wrong.

Mario

July, 09

🔗Mike Battaglia <battaglia01@...>

7/10/2011 7:30:55 PM

It's true. The only reason I didn't ban Gene just now for bringing it
up is that he'd ban me back. Nobody wants to fire the first shot when
mutual destruction is assured.

-Mike

On Sun, Jul 10, 2011 at 2:40 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Steve Parker <steve@...> wrote:
>
> > At the moment I'm considering announcing my new and unprecedented
> > discovery, based on looking out of my window alone, that the earth is
> > flat...
>
> Good, because if it was round that might bring in pi and then Mike would have to ban you.

🔗Mike Battaglia <battaglia01@...>

7/10/2011 8:10:14 PM

On Sun, Jul 10, 2011 at 1:26 PM, Steve Parker <steve@...> wrote:
>
> On 10 Jul 2011, at 17:38, Mario Pizarro wrote:
>
> n a matter of days, you and all members of the tuning list will know the true octave value which is slightly greater than 2.
>
> What are the qualities of this octave??
> At the moment I'm considering announcing my new and unprecedented discovery, based on looking out of my window alone, that the earth is flat...
> Steve P.

Alright, since Mario's post seems to be throwing everyone for a loop,
allow me to explain where he's coming from in stricter theoretical
terms.

Mario is mainly concerned with finding 12-note well-temperaments that
sound close enough to 12-equal to not be particularly "out of tune" in
any key, while still being slightly different enough to offer some
kind of subtly stimulating intonational effect. This means that his
approach so far is to find well-temperaments that deviate from 12-tet
by 6-7 cents max. While this may not personally satisfy those of us on
the bleeding edge who are exploring higher-limit systems like Orwell
and Miracle, or radically different 5-limit tunings like Porcupine and
Mavila, or generally want something -far away- from 12-equal, there's
a certain market for what he wants to accomplish and I wish him the
best of luck in his endeavor. I've encouraged him to work with
completely different tonal systems but for now this is where his
efforts are focused.

His earlier systems basically involved messing with things like
diminished[12] that are tuned slightly off from 12-equal. I think he
messed with some sort of augmented[12] variants as well. I'm not sure
what the latest incarnation of his Piagui scale is. (To Mario: I would
highly recommend, by the way, looking at the 12-note MOS scale for
diaschismatic temperament, as you might find some pretty huge
intonational improvements there.)

I believe all of his scales come out of looking at a 612 note MOS that
he constructs by treating the generators as the schisma and one other
comma, and then he finds useful 12-note subsets of that. So it looks
like what he's done this time is ditch the octave and just stack the
two generating intervals on top of one another, much like Petr's doing
with his rank-2 subgroup approach for otherwise rank-3 temperaments.
Apparently when you do this, you arrive at an octave that is
pleasantly slightly sharp, which will vibe well both with the natural
inharmonic stretch of the piano timbre, as well as the natural
preference that people have for slightly sharp octaves.

So when Mario is saying he's found the "true octave," what he's really
saying is that, above.

-Mike

PS to other regular mapping theorists - If we do the above as much as
possible, sooner or later we'll take over the world!

🔗Jake Freivald <jdfreivald@...>

7/10/2011 8:17:19 PM

> Alright, since Mario's post seems to be throwing everyone for a loop,
> allow me to explain where he's coming from in stricter theoretical
> terms.

Thanks, Mike. That helped a lot.

🔗hstraub64 <straub@...>

7/11/2011 2:36:42 AM

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Steve Parker <steve@> wrote:
>
> > At the moment I'm considering announcing my new and unprecedented
> > discovery, based on looking out of my window alone, that the earth
> > is flat...
>
> Good, because if it was round that might bring in pi and then Mike
> would have to ban you.
>

pi is going to be replaced anyway:

http://www.msnbc.msn.com/id/43581192/ns/technology_and_science-science/
--
Hans Straub

🔗Steve Parker <steve@...>

7/11/2011 3:24:34 AM

On 11 Jul 2011, at 04:10, Mike Battaglia wrote:

> So when Mario is saying he's found the "true octave," what he's really
> saying is that, above.

Which is neither new nor truer than anything else - except by definition 2/1..

So it doesn't have any more 'octaveness' in any way than 2/1? Nor beat less?

Steve P.

🔗Mario Pizarro <piagui@...>

7/11/2011 7:31:42 AM

To clarify my position I say that:

It is inconceivable the opponency of some members to be informed about the true octave. I suppose that one the targets of tuning y.g. is to promote the research on subjects that take part of the music structure. The absurd terms and ridiculous scoffs throwed by Steve Parker against my person must be rejected by any member of the list, I am here to respect and to be respected, so I ask to all of you to recommend Steve Parker to recognize that tuning yahoogroups is not a circus. At my age it is too hard to shut my mouth when somebody offends me.

As I wrote before, as soon as the piano is tuned with the true octave that is programmed to be done the coming saturday 16, I will send you the true octave data that includes the applied procedure of its attainment.

Thanks

Mario
July, 11
----- Original Message -----
From: Steve Parker
To: tuning@yahoogroups.com
Sent: Monday, July 11, 2011 5:24 AM
Subject: Re: [tuning] The true octave

On 11 Jul 2011, at 04:10, Mike Battaglia wrote:

So when Mario is saying he's found the "true octave," what he's really
saying is that, above.

Which is neither new nor truer than anything else - except by definition 2/1..

So it doesn't have any more 'octaveness' in any way than 2/1? Nor beat less?

Steve P.

🔗Jake Freivald <jdfreivald@...>

7/11/2011 7:50:50 AM

> It is inconceivable the opponency of some members to be informed
> about the true octave.

But Mario, have you published any specific information about it? I don't
think I've yet seen anything saying what the true octave *is*.

Thanks,
Jake

🔗Steve Parker <steve@...>

7/11/2011 8:43:34 AM

I've repeatedly asked what the qualities of this true octave are? What
is its definition? Why is this one true and the eminently justifiable
2/1 not true.
This list is a circus if anyone can say anything without interrogation
of substance.
It is also a circus if anyone can call anything anything.
At my age it is hard to accept snake-oil statements about the
discovery of the one true anything.
Please... tell me what is wrong with my 2/1 octave?
Even more so, tell me what is right with yours?
Either way stop calling it 'true'.
I don't need a piano tuned to it to ask questions about it.
Can someone - anyone - explain to me why I should not accept a 2/1
octave by definition?
Another tuning of the octave may sound nice, have cute mathematical
properties or some other utility, but as it stands 2/1 'defines' an
octave.
Either way stop calling it 'true'.
Is your idea as described by Mike? If not, how not?

I'm quite used to academic discourse and entirely expect it to be
robust. A discovery that the earth is in fact flat should be followed
with evidence, an actual statement
of the details of the discovery and some pretty serious questioning.....

I have made no comment about your person and would not.
I'm no fan of 12ET and will take any improvement you can make to it!

Steve P. (robustly, but with respect, interest and curiosity!)

On 11 Jul 2011, at 15:31, Mario Pizarro wrote:

>
> To clarify my position I say that:
>
> It is inconceivable the opponency of some members to be informed
> about the true octave. I suppose that one the targets of tuning y.g.
> is to promote the research on subjects that take part of the music
> structure. The absurd terms and ridiculous scoffs throwed by Steve
> Parker against my person must be rejected by any member of the list,
> I am here to respect and to be respected, so I ask to all of you to
> recommend Steve Parker to recognize that tuning yahoogroups is not a
> circus. At my age it is too hard to shut my mouth when somebody
> offends me.
>
> As I wrote before, as soon as the piano is tuned with the true
> octave that is programmed to be done the coming saturday 16, I will
> send you the true octave data that includes the applied procedure of> its attainment.
>
> Thanks
>
> Mario
> July, 11
> ----- Original Message -----
> From: Steve Parker
> To: tuning@yahoogroups.com
> Sent: Monday, July 11, 2011 5:24 AM
> Subject: Re: [tuning] The true octave
>
>
> On 11 Jul 2011, at 04:10, Mike Battaglia wrote:
>
>> So when Mario is saying he's found the "true octave," what he's
>> really
>> saying is that, above.
>
> Which is neither new nor truer than anything else - except by
> definition 2/1..
>
> So it doesn't have any more 'octaveness' in any way than 2/1? Nor
> beat less?
>
> Steve P.
>
>
>

🔗Carl Lumma <carl@...>

7/11/2011 9:01:44 AM

--- In tuning@yahoogroups.com, "hstraub64" <straub@...> wrote:
>
> pi is going to be replaced anyway:
>
> http://www.msnbc.msn.com/id/43581192/ns/technology_and_science-science/
> --
> Hans Straub

As well it should

http://www.youtube.com/watch?v=jG7vhMMXagQ

-Carl

🔗genewardsmith <genewardsmith@...>

7/11/2011 10:51:48 AM

--- In tuning@yahoogroups.com, Steve Parker <steve@...> wrote:

> Can someone - anyone - explain to me why I should not accept a 2/1
> octave by definition?
> Another tuning of the octave may sound nice, have cute mathematical
> properties or some other utility, but as it stands 2/1 'defines' an
> octave.
> Either way stop calling it 'true'.

2/1 is a JI octave by definition. Like any other JI interval, it can be detuned, either as a part of a regular temperament tuning or irregularly. If you detune it regularly, you've now got a certain fixed tuning for it, just as detunintg 3/2 to 700 cents gives you a
new fixed tuning for that. Calling the tempered octave "true" is a bit like a fervent believer in 12 equal calling 700 cents true, I suppose.

Some people like to announce the One True Tuning, which for some people can change from day to day and with other people seems fixed for their lifetime. It's just a psychological fact of life in the alternative tuning world, one which sometimes leads to friction since no one else ever seems to climb aboard the One True Tuning train of any of these proposals.

🔗genewardsmith <genewardsmith@...>

7/11/2011 11:01:18 AM

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:

> http://www.youtube.com/watch?v=jG7vhMMXagQ

Good luck with that. We're still using the gamma function, not 1/Gamma(x+1), despite the fact that the gamma argument is obviously shifted by 1 and gives totally unnecessary numeric exceptions when you calculate it, since it is not an entire function and its inverse is. Elliptic functions such as the P-function should obviously be defined as functions of two variables, but seldom are. And so it goes.

🔗Mario Pizarro <piagui@...>

7/11/2011 12:13:04 PM

Jake,

I have clearly promised that as soon I tune the piano with the true octave to be done the coming saturday 16, I will send to tuning all the data concerning the analysis, calculations and finding of the true octave. The pythagorean comma would take part of the history of the music.

It is understandable that I must verify how it sounds, my nephew (pianist) wants to take a photo with the tuner and the piano. This tuning is taking much of my time and even the calculations are disordered pages waiting for an ordained explanation. If I would be telling you "in about one month you will have the data", in that case I would be taking a wrong attitude. From now to monday 18 there are only 7 days (Saturday 16 is the tuning day).

Mario

July, 11
----- Original Message -----
From: Jake Freivald
To: tuning@yahoogroups.com
Sent: Monday, July 11, 2011 9:50 AM
Subject: Re: [tuning] The true octave

> It is inconceivable the opponency of some members to be informed
> about the true octave.

But Mario, have you published any specific information about it? I don't think I've yet seen anything saying what the true octave *is*.

Thanks,
Jake

🔗Chris Vaisvil <chrisvaisvil@...>

7/11/2011 12:18:30 PM

Mario, with all due respect - is a piano the best choice for your
demonstration?
As I remember the inharmonicity of piano strings already forces small
errors in a piano's octave when using 12 tet - I quote from this reference:

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

"The tuning described by the above beating plan will give a good
approximation of equal temperament across the range of the temperament
octave. If it were extended further, however, the actual tuning of the
instrument would become increasingly inaccurate. This is due to a factor
known as inharmonicity <http://en.wikipedia.org/wiki/Inharmonicity>, which
is present in different amounts in all piano strings. Strings' harmonic
series do not fall exactly into whole-number multiples of their fundamental
frequency; instead each harmonic runs slightly
sharp<http://en.wikipedia.org/wiki/Sharp_%28music%29>,
the sharpness increasing as higher tones in the harmonic series are reached.
This problem is mitigated by
"stretching"<http://en.wikipedia.org/wiki/Stretched_octave>the octaves
as one tunes above (and to an extent below) the temperament
region. When octaves are stretched, they are tuned, not to the lowest
coincidental overtone (second partial) of the note below, but to a higher
one (often the 4th partial). This widens all intervals equally, thereby
maintaining intervallic and tonal consistency."

Regards,

Chris

On Mon, Jul 11, 2011 at 3:13 PM, Mario Pizarro <piagui@...> wrote:

> **
>
>
> **
> Jake,
>
> I have clearly promised that as soon I tune the piano with the true octave
> to be done the coming saturday 16, I will send to tuning all the data
> concerning the analysis, calculations and finding of the true octave. The
> pythagorean comma would take part of the history of the music.
>
> It is understandable that I must verify how it sounds, my nephew (pianist)
> wants to take a photo with the tuner and the piano. This tuning is taking
> much of my time and even the calculations are disordered pages waiting for
> an ordained explanation. If I would be telling you "in about one month you
> will have the data", in that case I would be taking a wrong attitude. From
> now to monday 18 there are only 7 days (Saturday 16 is the tuning day).
>
> Mario
>
> July, 11
>
> ----- Original Message -----
> *From:* Jake Freivald <jdfreivald@...>
> *To:* tuning@yahoogroups.com
> *Sent:* Monday, July 11, 2011 9:50 AM
> *Subject:* Re: [tuning] The true octave
>
> > It is inconceivable the opponency of some members to be informed
> > about the true octave.
>
> But Mario, have you published any specific information about it? I don't
> think I've yet seen anything saying what the true octave *is*.
>
> Thanks,
> Jake
>
>
>

🔗Tim Reeves <reevest360@...>

7/11/2011 2:03:57 PM

oh come on now...who said we had to be open minded, oh wait, I did

--- On Mon, 7/11/11, genewardsmith <genewardsmith@...> wrote:

From: genewardsmith <genewardsmith@...>
Subject: [tuning] Re: The true octave
To: tuning@yahoogroups.com
Date: Monday, July 11, 2011, 5:51 PM

--- In tuning@yahoogroups.com, Steve Parker <steve@...> wrote:

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

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🔗Mario Pizarro <piagui@...>

7/11/2011 2:50:54 PM

Chris,

There is no any conection between the true octave and any kind of instrument. I don´t need the piano to demonstrate the natural validity of the true octave. As a matter of fact I already checked its exactness by using my PC. The point is this: All my group in Lima is anxious wondering to which extent the piano chords would vary once the true octave is part of it. I arrived to some conclusions; for instance all the fifths will sound brilliant because the 12 equal fifths are slightly greater than 1.5. When you use the conventional octave (2) and calculate the 12 major thirds or the 12 minor thirds, you never get 12 equal maj. and minor thirds. Should you work with the true octave you get 12 equal fifths, 12 equal major thirds and 12 equal minor thirds. Obviously I am sure that the only variant that might be appreciated is the chord harmony improvement, (probably).

If you practice some religion, your praying in the church might stop the fever I have now. This winter in Lima sent most people to bed.

Mario
July,11
----- Original Message -----
From: Chris Vaisvil
To: tuning@yahoogroups.com
Sent: Monday, July 11, 2011 2:18 PM
Subject: Re: [tuning] The true octave

Mario, with all due respect - is a piano the best choice for your demonstration?
As I remember the inharmonicity of piano strings already forces small errors in a piano's octave when using 12 tet - I quote from this reference:

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

"The tuning described by the above beating plan will give a good approximation of equal temperament across the range of the temperament octave. If it were extended further, however, the actual tuning of the instrument would become increasingly inaccurate. This is due to a factor known as inharmonicity, which is present in different amounts in all piano strings. Strings' harmonic series do not fall exactly into whole-number multiples of their fundamental frequency; instead each harmonic runs slightly sharp, the sharpness increasing as higher tones in the harmonic series are reached. This problem is mitigated by "stretching" the octaves as one tunes above (and to an extent below) the temperament region. When octaves are stretched, they are tuned, not to the lowest coincidental overtone (second partial) of the note below, but to a higher one (often the 4th partial). This widens all intervals equally, thereby maintaining intervallic and tonal consistency."

Regards,

Chris

On Mon, Jul 11, 2011 at 3:13 PM, Mario Pizarro <piagui@...> wrote:

Jake,

Mario

July, 11
----- Original Message -----
From: Jake Freivald
To: tuning@yahoogroups.com
Sent: Monday, July 11, 2011 9:50 AM
Subject: Re: [tuning] The true octave

> It is inconceivable the opponency of some members to be informed
> about the true octave.

But Mario, have you published any specific information about it? I don't think I've yet seen anything saying what the true octave *is*.

Thanks,
Jake

🔗Tim Reeves <reevest360@...>

7/11/2011 2:55:02 PM

Hey Mike,
Without holding my breath for Mario's true explanation, that seems to have covered what we are all waiting for, but who knows????
Tim

--- On Mon, 7/11/11, Mike Battaglia <battaglia01@...> wrote:

From: Mike Battaglia <battaglia01@...>
Subject: Re: [tuning] The true octave
To: tuning@yahoogroups.com
Date: Monday, July 11, 2011, 3:10 AM

Alright, since Mario's post seems to be throwing everyone for a loop,
allow me to explain where he's coming from in stricter theoretical
terms.

So when Mario is saying he's found the "true octave," what he's really
saying is that, above.

-Mike

PS to other regular mapping theorists - If we do the above as much as
possible, sooner or later we'll take over the world!

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

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

🔗Chris Vaisvil <chrisvaisvil@...>

7/11/2011 3:00:35 PM

Hi Mario,

I am sorry to hear you have taken ill.
It sounds as if you've made 12 tet equivalent to 12 JI for all practical
purposes.
That *would* be quite an accomplishment.

"Should you work with the true octave you get 12 equal fifths, 12 equal
major thirds and 12 equal minor thirds."

This sounds like a linear algebra problem - we should be able to figure it
out from this I would think.

Chris

On Mon, Jul 11, 2011 at 5:50 PM, Mario Pizarro <piagui@...> wrote:

> **
>
>
> **
> Chris,
>
> There is no any conection between the true octave and any kind of
> instrument. I don´t need the piano to demonstrate the natural validity of
> the true octave. As a matter of fact I already checked its exactness by
> using my PC. The point is this: All my group in Lima is anxious wondering to
> which extent the piano chords would vary once the true octave is part of
> it. I arrived to some conclusions; for instance all the fifths will sound
> brilliant because the 12 equal fifths are slightly greater than 1.5. When
> you use the conventional octave (2) and calculate the 12 major thirds or the
> 12 minor thirds, you never get 12 equal maj. and minor thirds. Should you
> work with the true octave you get 12 equal fifths, 12 equal major thirds and
> 12 equal minor thirds. Obviously I am sure that the only variant that might
> be appreciated is the chord harmony improvement, (probably).
>
> If you practice some religion, your praying in the church might stop the
> fever I have now. This winter in Lima sent most people to bed.
>
> Mario
> July,11
>
> ----- Original Message -----
> *From:* Chris Vaisvil <chrisvaisvil@...>
> *To:* tuning@yahoogroups.com
> *Sent:* Monday, July 11, 2011 2:18 PM
> *Subject:* Re: [tuning] The true octave
>
> Mario, with all due respect - is a piano the best choice for your
> demonstration?
> As I remember the inharmonicity of piano strings already forces small
> errors in a piano's octave when using 12 tet - I quote from this reference:
>
> http://en.wikipedia.org/wiki/Piano_tuning
>
>
> "The tuning described by the above beating plan will give a good
> approximation of equal temperament across the range of the temperament
> octave. If it were extended further, however, the actual tuning of the
> instrument would become increasingly inaccurate. This is due to a factor
> known as inharmonicity <http://en.wikipedia.org/wiki/Inharmonicity>, which
> is present in different amounts in all piano strings. Strings' harmonic
> series do not fall exactly into whole-number multiples of their fundamental
> frequency; instead each harmonic runs slightly sharp<http://en.wikipedia.org/wiki/Sharp_%28music%29>,
> the sharpness increasing as higher tones in the harmonic series are reached.
> This problem is mitigated by "stretching"<http://en.wikipedia.org/wiki/Stretched_octave>the octaves as one tunes above (and to an extent below) the temperament
> region. When octaves are stretched, they are tuned, not to the lowest
> coincidental overtone (second partial) of the note below, but to a higher
> one (often the 4th partial). This widens all intervals equally, thereby
> maintaining intervallic and tonal consistency."
>
> Regards,
>
> Chris
>
> On Mon, Jul 11, 2011 at 3:13 PM, Mario Pizarro <piagui@...> wrote:
>
>> **
>>
>>
>> **
>> Jake,
>>
>> I have clearly promised that as soon I tune the piano with the true octave
>> to be done the coming saturday 16, I will send to tuning all the data
>> concerning the analysis, calculations and finding of the true octave. The
>> pythagorean comma would take part of the history of the music.
>>
>> It is understandable that I must verify how it sounds, my nephew (pianist)
>> wants to take a photo with the tuner and the piano. This tuning is taking
>> much of my time and even the calculations are disordered pages waiting for
>> an ordained explanation. If I would be telling you "in about one month you
>> will have the data", in that case I would be taking a wrong attitude. From
>> now to monday 18 there are only 7 days (Saturday 16 is the tuning day).
>>
>> Mario
>>
>> July, 11
>>
>> ----- Original Message -----
>> *From:* Jake Freivald <jdfreivald@...>
>> *To:* tuning@yahoogroups.com
>> *Sent:* Monday, July 11, 2011 9:50 AM
>> *Subject:* Re: [tuning] The true octave
>>
>> > It is inconceivable the opponency of some members to be informed
>> > about the true octave.
>>
>> But Mario, have you published any specific information about it? I don't
>> think I've yet seen anything saying what the true octave *is*.
>>
>> Thanks,
>> Jake
>>
>>
>
>

🔗Mike Battaglia <battaglia01@...>

7/11/2011 3:04:58 PM

I'm saying that he's calling it the "true octave," but if we instead
assume the principle of charity

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

we can derive a more mainstream theoretical explanation that describes
what Mario is after. It's also worth noting that English is his second
language, so some extra-charitable interpretation is in order.

-Mike

On Mon, Jul 11, 2011 at 5:55 PM, Tim Reeves <reevest360@...> wrote:
>
> Hey Mike,
> Without holding my breath for Mario's true explanation, that seems to have covered what we are all waiting for, but who knows????
> Tim
>
> --- On Mon, 7/11/11, Mike Battaglia <battaglia01@...> wrote:
>
> From: Mike Battaglia <battaglia01@...>
> Subject: Re: [tuning] The true octave
> To: tuning@yahoogroups.com
> Date: Monday, July 11, 2011, 3:10 AM
>
> On Sun, Jul 10, 2011 at 1:26 PM, Steve Parker <steve@...> wrote:
> >
> > On 10 Jul 2011, at 17:38, Mario Pizarro wrote:
> >
> > n a matter of days, you and all members of the tuning list will know the true octave value which is slightly greater than 2.
> >
> > What are the qualities of this octave??
> > At the moment I'm considering announcing my new and unprecedented discovery, based on looking out of my window alone, that the earth is flat...
> > Steve P.
>
> Alright, since Mario's post seems to be throwing everyone for a loop,
> allow me to explain where he's coming from in stricter theoretical
> terms.
>
> Mario is mainly concerned with finding 12-note well-temperaments that
> sound close enough to 12-equal to not be particularly "out of tune" in
> any key, while still being slightly different enough to offer some
> kind of subtly stimulating intonational effect. This means that his
> approach so far is to find well-temperaments that deviate from 12-tet
> by 6-7 cents max. While this may not personally satisfy those of us on
> the bleeding edge who are exploring higher-limit systems like Orwell
> and Miracle, or radically different 5-limit tunings like Porcupine and
> Mavila, or generally want something -far away- from 12-equal, there's
> a certain market for what he wants to accomplish and I wish him the
> best of luck in his endeavor. I've encouraged him to work with
> completely different tonal systems but for now this is where his
> efforts are focused.
>
> His earlier systems basically involved messing with things like
> diminished[12] that are tuned slightly off from 12-equal. I think he
> messed with some sort of augmented[12] variants as well. I'm not sure
> what the latest incarnation of his Piagui scale is. (To Mario: I would
> highly recommend, by the way, looking at the 12-note MOS scale for
> diaschismatic temperament, as you might find some pretty huge
> intonational improvements there.)
>
> I believe all of his scales come out of looking at a 612 note MOS that
> he constructs by treating the generators as the schisma and one other
> comma, and then he finds useful 12-note subsets of that. So it looks
> like what he's done this time is ditch the octave and just stack the
> two generating intervals on top of one another, much like Petr's doing
> with his rank-2 subgroup approach for otherwise rank-3 temperaments.
> Apparently when you do this, you arrive at an octave that is
> pleasantly slightly sharp, which will vibe well both with the natural
> inharmonic stretch of the piano timbre, as well as the natural
> preference that people have for slightly sharp octaves.
>
> So when Mario is saying he's found the "true octave," what he's really
> saying is that, above.
>
> -Mike
>
> PS to other regular mapping theorists - If we do the above as much as
> possible, sooner or later we'll take over the world!
>
>
> ------------------------------------
>
> 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@...>

7/13/2011 9:45:41 AM

----- Original Message -----
From: Mario Pizarro
To: tuning yahoogroups
Cc: Mike Battaglia
Sent: Wednesday, July 13, 2011 10:51 AM
Subject: Fw: I can send it

Dear friends,

I had programmed three days for writing a paper explaining how the true octave was derived but now I see that it would take more than two weeks. Since some members of the list want to have it as soon as possible, I decided to postpone the paper and send to Mike Battaglia, via tuning yahoogroups the following:

-- The true octave (given in decimals, 11 decimal digits and cents)

-- A 12 tone scale (the piano middle true octave) that I named MPER12ET given by 11 decimal digits (C = 1, 2C = The adjusted cents to work with A = 440 Hz),

-- The 12 tone scale where 2C equals the true octave value given in decimals and cents.

-- 12 Equal fifths (decimals and cents)

-- 12 Equal major fifths (decimals and cents)

-- A brief summary of the procedure used to derive the true octave.

All the above can be sent in a message. Since I cannot send attachments to tuning, I can also send you an attached table containing the 88 piano keyboard frequencies given in decimals, cents, Hz, A = 440, to the email address stated by tuning.

I am waiting for your instructions to achieve the above.

Thanks

Mario
Lima, July 13, 2011

🔗Mario Pizarro <piagui@...>

7/16/2011 8:22:34 AM

Chris,

Thank you for your words, the fever is gone. I think that the true octave (TOctave) is a useful tool for explaining some incongruences produced by the conventional octave. You can get full information by visiting the three files I registered yesterday.

Mario
July, 16
----- Original Message -----
From: Chris Vaisvil
To: tuning@yahoogroups.com
Sent: Monday, July 11, 2011 5:00 PM
Subject: Re: [tuning] The true octave

Hi Mario,

I am sorry to hear you have taken ill.
It sounds as if you've made 12 tet equivalent to 12 JI for all practical purposes.
That *would* be quite an accomplishment.

"Should you work with the true octave you get 12 equal fifths, 12 equal major thirds and 12 equal minor thirds."

This sounds like a linear algebra problem - we should be able to figure it out from this I would think.

Chris

On Mon, Jul 11, 2011 at 5:50 PM, Mario Pizarro <piagui@...> wrote:

Chris,

If you practice some religion, your praying in the church might stop the fever I have now. This winter in Lima sent most people to bed.

Mario
July,11
----- Original Message -----
From: Chris Vaisvil
To: tuning@yahoogroups.com
Sent: Monday, July 11, 2011 2:18 PM
Subject: Re: [tuning] The true octave

Mario, with all due respect - is a piano the best choice for your demonstration?
As I remember the inharmonicity of piano strings already forces small errors in a piano's octave when using 12 tet - I quote from this reference:

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

"The tuning described by the above beating plan will give a good approximation of equal temperament across the range of the temperament octave. If it were extended further, however, the actual tuning of the instrument would become increasingly inaccurate. This is due to a factor known as inharmonicity, which is present in different amounts in all piano strings. Strings' harmonic series do not fall exactly into whole-number multiples of their fundamental frequency; instead each harmonic runs slightly sharp, the sharpness increasing as higher tones in the harmonic series are reached. This problem is mitigated by "stretching" the octaves as one tunes above (and to an extent below) the temperament region. When octaves are stretched, they are tuned, not to the lowest coincidental overtone (second partial) of the note below, but to a higher one (often the 4th partial). This widens all intervals equally, thereby maintaining intervallic and tonal consistency."

Regards,

Chris

On Mon, Jul 11, 2011 at 3:13 PM, Mario Pizarro <piagui@...> wrote:

Jake,

Mario

July, 11
----- Original Message -----
From: Jake Freivald
To: tuning@yahoogroups.com
Sent: Monday, July 11, 2011 9:50 AM
Subject: Re: [tuning] The true octave

> It is inconceivable the opponency of some members to be informed
> about the true octave.

But Mario, have you published any specific information about it? I don't think I've yet seen anything saying what the true octave *is*.

Thanks,
Jake

🔗Chris Vaisvil <chrisvaisvil@...>

7/16/2011 9:34:22 AM

Hi Mario,

I did look at the first spreadsheet and I am very keen on trying it. I have
for a long time wondered what would happen if one didn't require an octave -
or an exact one - and recently have been trying some tunings along those
lines. I will post what I play with this new system.

Chris

On Sat, Jul 16, 2011 at 11:22 AM, Mario Pizarro <piagui@...> wrote:

> **
>
>
> **
> Chris,
>
> Thank you for your words, the fever is gone. I think that the true octave
> (TOctave) is a useful tool for explaining some incongruences produced by the
> conventional octave. You can get full information by visiting the three
> files I registered yesterday.
>
> Mario
> July, 16
>
> ----- Original Message -----
> *From:* Chris Vaisvil <chrisvaisvil@...>
> *To:* tuning@yahoogroups.com
> *Sent:* Monday, July 11, 2011 5:00 PM
> *Subject:* Re: [tuning] The true octave
>
> Hi Mario,
>
> I am sorry to hear you have taken ill.
> It sounds as if you've made 12 tet equivalent to 12 JI for all practical
> purposes.
> That *would* be quite an accomplishment.
>
> "Should you work with the true octave you get 12 equal fifths, 12 equal
> major thirds and 12 equal minor thirds."
>
> This sounds like a linear algebra problem - we should be able to figure it
> out from this I would think.
>
> Chris
>
> On Mon, Jul 11, 2011 at 5:50 PM, Mario Pizarro <piagui@...> wrote:
>
>> **
>>
>>
>> **
>> Chris,
>>
>> There is no any conection between the true octave and any kind of
>> instrument. I don´t need the piano to demonstrate the natural validity of
>> the true octave. As a matter of fact I already checked its exactness by
>> using my PC. The point is this: All my group in Lima is anxious wondering to
>> which extent the piano chords would vary once the true octave is part of
>> it. I arrived to some conclusions; for instance all the fifths will sound
>> brilliant because the 12 equal fifths are slightly greater than 1.5. When
>> you use the conventional octave (2) and calculate the 12 major thirds or the
>> 12 minor thirds, you never get 12 equal maj. and minor thirds. Should you
>> work with the true octave you get 12 equal fifths, 12 equal major thirds and
>> 12 equal minor thirds. Obviously I am sure that the only variant that might
>> be appreciated is the chord harmony improvement, (probably).
>>
>> If you practice some religion, your praying in the church might stop the
>> fever I have now. This winter in Lima sent most people to bed.
>>
>> Mario
>> July,11
>>
>> ----- Original Message -----
>> *From:* Chris Vaisvil <chrisvaisvil@...>
>> *To:* tuning@yahoogroups.com
>> *Sent:* Monday, July 11, 2011 2:18 PM
>> *Subject:* Re: [tuning] The true octave
>>
>> Mario, with all due respect - is a piano the best choice for your
>> demonstration?
>> As I remember the inharmonicity of piano strings already forces small
>> errors in a piano's octave when using 12 tet - I quote from this reference:
>>
>> http://en.wikipedia.org/wiki/Piano_tuning
>>
>>
>> "The tuning described by the above beating plan will give a good
>> approximation of equal temperament across the range of the temperament
>> octave. If it were extended further, however, the actual tuning of the
>> instrument would become increasingly inaccurate. This is due to a factor
>> known as inharmonicity <http://en.wikipedia.org/wiki/Inharmonicity>,
>> which is present in different amounts in all piano strings. Strings'
>> harmonic series do not fall exactly into whole-number multiples of their
>> fundamental frequency; instead each harmonic runs slightly sharp<http://en.wikipedia.org/wiki/Sharp_%28music%29>,
>> the sharpness increasing as higher tones in the harmonic series are reached.
>> This problem is mitigated by "stretching"<http://en.wikipedia.org/wiki/Stretched_octave>the octaves as one tunes above (and to an extent below) the temperament
>> region. When octaves are stretched, they are tuned, not to the lowest
>> coincidental overtone (second partial) of the note below, but to a higher
>> one (often the 4th partial). This widens all intervals equally, thereby
>> maintaining intervallic and tonal consistency."
>>
>> Regards,
>>
>> Chris
>>
>> On Mon, Jul 11, 2011 at 3:13 PM, Mario Pizarro <piagui@...> wrote:
>>
>>> **
>>>
>>>
>>> **
>>> Jake,
>>>
>>> I have clearly promised that as soon I tune the piano with the true
>>> octave to be done the coming saturday 16, I will send to tuning all the data
>>> concerning the analysis, calculations and finding of the true octave. The
>>> pythagorean comma would take part of the history of the music.
>>>
>>> It is understandable that I must verify how it sounds, my nephew
>>> (pianist) wants to take a photo with the tuner and the piano. This tuning is
>>> taking much of my time and even the calculations are disordered pages
>>> waiting for an ordained explanation. If I would be telling you "in about one
>>> month you will have the data", in that case I would be taking a wrong
>>> attitude. From now to monday 18 there are only 7 days (Saturday 16 is the
>>> tuning day).
>>>
>>> Mario
>>>
>>> July, 11
>>>
>>> ----- Original Message -----
>>> *From:* Jake Freivald <jdfreivald@gmail.com>
>>> *To:* tuning@yahoogroups.com
>>> *Sent:* Monday, July 11, 2011 9:50 AM
>>> *Subject:* Re: [tuning] The true octave
>>>
>>> > It is inconceivable the opponency of some members to be informed
>>> > about the true octave.
>>>
>>> But Mario, have you published any specific information about it? I don't
>>> think I've yet seen anything saying what the true octave *is*.
>>>
>>> Thanks,
>>> Jake
>>>
>>>
>>
>
>

🔗Mario Pizarro <piagui@...>

7/16/2011 11:28:13 AM

Chris,

Did you see file # 3 ?.. It is also important, deals with the piano tuning to the true octave. Good look with your TOctave productions

Mario

------------------------
----- Original Message -----
From: Chris Vaisvil
To: tuning@yahoogroups.com
Sent: Saturday, July 16, 2011 11:34 AM
Subject: Re: [tuning] The true octave

Hi Mario,

I did look at the first spreadsheet and I am very keen on trying it. I have for a long time wondered what would happen if one didn't require an octave - or an exact one - and recently have been trying some tunings along those lines. I will post what I play with this new system.

Chris

On Sat, Jul 16, 2011 at 11:22 AM, Mario Pizarro <piagui@...> wrote:

Chris,

Mario
July, 16
----- Original Message -----
From: Chris Vaisvil
To: tuning@...m
Sent: Monday, July 11, 2011 5:00 PM
Subject: Re: [tuning] The true octave

Hi Mario,

I am sorry to hear you have taken ill.
It sounds as if you've made 12 tet equivalent to 12 JI for all practical purposes.
That *would* be quite an accomplishment.

"Should you work with the true octave you get 12 equal fifths, 12 equal major thirds and 12 equal minor thirds."

This sounds like a linear algebra problem - we should be able to figure it out from this I would think.

Chris

On Mon, Jul 11, 2011 at 5:50 PM, Mario Pizarro <piagui@ec-red.com> wrote:

Chris,

If you practice some religion, your praying in the church might stop the fever I have now. This winter in Lima sent most people to bed.

Mario
July,11
----- Original Message -----
From: Chris Vaisvil
To: tuning@yahoogroups.com
Sent: Monday, July 11, 2011 2:18 PM
Subject: Re: [tuning] The true octave

Mario, with all due respect - is a piano the best choice for your demonstration?
As I remember the inharmonicity of piano strings already forces small errors in a piano's octave when using 12 tet - I quote from this reference:

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

"The tuning described by the above beating plan will give a good approximation of equal temperament across the range of the temperament octave. If it were extended further, however, the actual tuning of the instrument would become increasingly inaccurate. This is due to a factor known as inharmonicity, which is present in different amounts in all piano strings. Strings' harmonic series do not fall exactly into whole-number multiples of their fundamental frequency; instead each harmonic runs slightly sharp, the sharpness increasing as higher tones in the harmonic series are reached. This problem is mitigated by "stretching" the octaves as one tunes above (and to an extent below) the temperament region. When octaves are stretched, they are tuned, not to the lowest coincidental overtone (second partial) of the note below, but to a higher one (often the 4th partial). This widens all intervals equally, thereby maintaining intervallic and tonal consistency."

Regards,

Chris

On Mon, Jul 11, 2011 at 3:13 PM, Mario Pizarro <piagui@ec-red.com> wrote:

Jake,

Mario

July, 11
----- Original Message -----
From: Jake Freivald
To: tuning@yahoogroups.com
Sent: Monday, July 11, 2011 9:50 AM
Subject: Re: [tuning] The true octave

> It is inconceivable the opponency of some members to be informed
> about the true octave.

But Mario, have you published any specific information about it? I don't think I've yet seen anything saying what the true octave *is*.

Thanks,
Jake

🔗martinsj013 <martinsj@...>

7/17/2011 1:40:23 AM

Mario,
as far as I can see, your tuning divides 81/32 into 16 equal parts.
This means that the "2/1" is slightly large; so is the "5/1" (not at all unusual) but so is the "3/1" (unusual, for common practice music anyway).

Is that right? Why are 12 of these parts the "true octave"?

Steve M.

P.S. wrt your Progression of Cells: I see that the major 3rd (i.e. 4 of the semitones) is found at cell 205; and 8 semitones is found at cell 410; and 12 (i.e. the "true octave") at cell 615.

🔗Mario Pizarro <piagui@...>

7/17/2011 6:28:48 AM

Steve,

By the fact of dividing 81/32 (= 2.53125) into 16 equal parts, anyone of these parts has a value of (2.53125 / 16) = 0.158203125. You took 12 of these parts and said that these 12 parts are the true octave. However the product 0.158203125* 12 = 1.8984375 and not 2.00678700646 = true octave. Some of your figures must be wrong ï¿½isnï¿½t?.
I didnï¿½t take any common fraction as a starting point to get the true octave, it wouldnï¿½t be a serious mathematical procedure.
Once I finish the wording of a paper that can take about three weeks, I will send you a copy of it, just wait.
As I said before, the tOctave was derived by a rigurous mathematical procedure that you will know soon.
Mario
July, 17
<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message ----- From: "martinsj013" <martinsj@...>
To: <tuning@yahoogroups.com>
Sent: Sunday, July 17, 2011 3:40 AM
Subject: [tuning] Re: The true octave

> Mario,
> as far as I can see, your tuning divides 81/32 into 16 equal parts.
> This means that the "2/1" is slightly large; so is the "5/1" (not at all > unusual) but so is the "3/1" (unusual, for common practice music anyway).
>
> Is that right? Why are 12 of these parts the "true octave"?
>
> Steve M.
>
> P.S. wrt your Progression of Cells: I see that the major 3rd (i.e. 4 of > the semitones) is found at cell 205; and 8 semitones is found at cell 410; > and 12 (i.e. the "true octave") at cell 615.
>
>
>
> ------------------------------------
>
> 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@...>

7/17/2011 6:32:33 AM

Steve,

By the fact of dividing 81/32 (= 2.53125) into 16 equal parts, anyone of
these parts has a value of (2.53125 / 16) = 0.158203125. You took 12 of
these parts and said that these 12 parts are the true octave. However the
product 0.158203125* 12 = 1.8984375 and not 2.00678700646 = true octave.
Some of your figures must be wrong ï¿½isnï¿½t?.
I didnï¿½t take any common fraction as a starting point to get the true
octave, it wouldnï¿½t be a serious mathematical procedure.
Once I finish the wording of a paper that can take about three weeks, I will
send you a copy of it, just wait.
As I said before, the tOctave was derived by a rigurous mathematical
procedure that you will know soon.
Mario
July, 17
<<<<<<<<<<<<<
----- Original Message ----- From: "martinsj013" <martinsj@...>
To: <tuning@yahoogroups.com>
Sent: Sunday, July 17, 2011 3:40 AM
Subject: [tuning] Re: The true octave

🔗Kees van Prooijen <keesvp@...>

7/17/2011 6:52:25 AM

you are mixing your arithmetic metaphors :-)
81/32 in 16 equal parts: (81/32) ^(1/16) = 1.05976223699482
12 of these: (81/32)^(12/16) = 2.00678700656709

On Sun, Jul 17, 2011 at 6:28 AM, Mario Pizarro <piagui@...> wrote:

> **
>
>
> Steve,
>
> By the fact of dividing 81/32 (= 2.53125) into 16 equal parts, anyone of
> these parts has a value of (2.53125 / 16) = 0.158203125. You took 12 of
> these parts and said that these 12 parts are the true octave. However the
> product 0.158203125* 12 = 1.8984375 and not 2.00678700646 = true octave.
> Some of your figures must be wrong ¿isn´t?.
> I didn´t take any common fraction as a starting point to get the true
> octave, it wouldn´t be a serious mathematical procedure.
> Once I finish the wording of a paper that can take about three weeks, I
> will
> send you a copy of it, just wait.
> As I said before, the tOctave was derived by a rigurous mathematical
> procedure that you will know soon.
> Mario
> July, 17
> <<<<<<<<<<<<<<<<<<<<<<<<<<<<
> ----- Original Message -----
> From: "martinsj013" <martinsj@...>
> To: <tuning@...m>
> Sent: Sunday, July 17, 2011 3:40 AM
> Subject: [tuning] Re: The true octave
>
> > Mario,
> > as far as I can see, your tuning divides 81/32 into 16 equal parts.
> > This means that the "2/1" is slightly large; so is the "5/1" (not at all
> > unusual) but so is the "3/1" (unusual, for common practice music anyway).
> >
> > Is that right? Why are 12 of these parts the "true octave"?
> >
> > Steve M.
> >
> > P.S. wrt your Progression of Cells: I see that the major 3rd (i.e. 4 of
> > the semitones) is found at cell 205; and 8 semitones is found at cell
> 410;
> > and 12 (i.e. the "true octave") at cell 615.
> >
> >
> >
> > ------------------------------------
> >
> > 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
> >
> >
> >
> >
>
>
>

🔗martinsj013 <martinsj@...>

7/17/2011 7:12:07 AM

--- In tuning@yahoogroups.com, Kees van Prooijen <keesvp@...> wrote:
> you are mixing your arithmetic metaphors :-)
> 81/32 in 16 equal parts: (81/32) ^(1/16) = 1.05976223699482
> 12 of these: (81/32)^(12/16) = 2.00678700656709

Yes, that's exactly what I meant, of course. Perhaps I misled Mario by my use of the word "dividing".

Steve M.

🔗Mario Pizarro <piagui@...>

7/17/2011 7:44:15 AM

Hey Mr. Kees Prooijen

You have omitted my name.

You are mixing your arithmetical methaphors, not I.

Unable to realize that it is not possible to foretell those parts unless you first derive the true octave?

BTW: I didn´t use any of the Steve¨s numerical parameters to derive the tOctave.

Mario Pizarro

Lima, July, 17
----- Original Message -----
From: Kees van Prooijen
To: tuning@yahoogroups.com
Sent: Sunday, July 17, 2011 8:52 AM
Subject: Re: [tuning] Re: The true octave

you are mixing your arithmetic metaphors :-)
81/32 in 16 equal parts: (81/32) ^(1/16) = 1.05976223699482
12 of these: (81/32)^(12/16) = 2.00678700656709

On Sun, Jul 17, 2011 at 6:28 AM, Mario Pizarro <piagui@...> wrote:

Steve,

By the fact of dividing 81/32 (= 2.53125) into 16 equal parts, anyone of
these parts has a value of (2.53125 / 16) = 0.158203125. You took 12 of
these parts and said that these 12 parts are the true octave. However the
product 0.158203125* 12 = 1.8984375 and not 2.00678700646 = true octave.
Some of your figures must be wrong ¿isn´t?.
I didn´t take any common fraction as a starting point to get the true
octave, it wouldn´t be a serious mathematical procedure.
Once I finish the wording of a paper that can take about three weeks, I will
send you a copy of it, just wait.
As I said before, the tOctave was derived by a rigurous mathematical
procedure that you will know soon.
Mario
July, 17
<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message -----
From: "martinsj013" <martinsj@...>
To: <tuning@yahoogroups.com>
Sent: Sunday, July 17, 2011 3:40 AM
Subject: [tuning] Re: The true octave

> Mario,
> as far as I can see, your tuning divides 81/32 into 16 equal parts.
> This means that the "2/1" is slightly large; so is the "5/1" (not at all
> unusual) but so is the "3/1" (unusual, for common practice music anyway).
>
> Is that right? Why are 12 of these parts the "true octave"?
>
> Steve M.
>
> P.S. wrt your Progression of Cells: I see that the major 3rd (i.e. 4 of
> the semitones) is found at cell 205; and 8 semitones is found at cell 410;
> and 12 (i.e. the "true octave") at cell 615.
>
>
>
> ------------------------------------
>
> 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@...>

7/17/2011 7:56:32 AM

Steve,

May be van Prooijen needs your advise on how to address to a tuning member for heï¿½s omitted my name-- Dutch!!!

BTW: As I told to the dutch man, your ratio 81/32 can enter to work if and only if the tOctave is firstly derived.

Mario
--------------------------------------
----- Original Message ----- From: "martinsj013" <martinsj@...>
To: <tuning@yahoogroups.com>
Sent: Sunday, July 17, 2011 9:12 AM
Subject: [tuning] Re: The true octave

> --- In tuning@yahoogroups.com, Kees van Prooijen <keesvp@...> wrote:
>> you are mixing your arithmetic metaphors :-)
>> 81/32 in 16 equal parts: (81/32) ^(1/16) = 1.05976223699482
>> 12 of these: (81/32)^(12/16) = 2.00678700656709
>
> Yes, that's exactly what I meant, of course. Perhaps I misled Mario by my > use of the word "dividing".
>
> 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
>
>
>
>

🔗Ryan Avella <domeofatonement@...>

7/17/2011 8:39:11 AM

> Steve,
>
> By the fact of dividing 81/32 (= 2.53125) into 16 equal parts, anyone of
> these parts has a value of (2.53125 / 16) = 0.158203125. You took 12 of
> these parts and said that these 12 parts are the true octave. However the
> product 0.158203125* 12 = 1.8984375 and not 2.00678700646 = true octave.
> Some of your figures must be wrong ¿isn´t?.
> I didn´t take any common fraction as a starting point to get the true
> octave, it wouldn´t be a serious mathematical procedure.
> Once I finish the wording of a paper that can take about three weeks, I will
> send you a copy of it, just wait.
> As I said before, the tOctave was derived by a rigurous mathematical
> procedure that you will know soon.
> Mario
> July, 17

To divide it into 16 equal parts, you don't divide by 16. You take the 16th root, which is equivalent to taking 4 square roots on a non-scientific calculator.

2.53125^(1/16) = 1.0597622

1.0597622^(12) = 2.006787 = 1205.865 cents

Though I honestly doubt this is how he derived the octave, as there is no practical motive to divide the pythagorean major tenth into 16 parts. I think it more or less involves some sort of optimum error distribution of a stretched 12-equal scale.

-Ryan

🔗genewardsmith <genewardsmith@...>

7/17/2011 8:54:15 AM

--- In tuning@yahoogroups.com, Kees van Prooijen <keesvp@...> wrote:
>
> you are mixing your arithmetic metaphors :-)
> 81/32 in 16 equal parts: (81/32) ^(1/16) = 1.05976223699482
> 12 of these: (81/32)^(12/16) = 2.00678700656709

Which is 5.865 cents sharp; that's pretty extreme for octave tempering 12.

🔗martinsj013 <martinsj@...>

7/17/2011 9:08:31 AM

--- In tuning@yahoogroups.com, "Ryan Avella" <domeofatonement@...> wrote:
> ... doubt this is how he derived the octave, as there is no practical motive to divide the pythagorean major tenth into 16 parts. ...

Agreed (but how about (5/1)^(1/16), or (3/1)^(1/19)? ).

> ... I think it more or less involves some sort of optimum error distribution of a stretched 12-equal scale.

I'd like to think this, but don't see how it could end up with the 2, 3 and 5 all being too large.

Steve.

🔗Carl Lumma <carl@...>

7/17/2011 4:55:04 PM

--- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>
> Steve,
>
> May be van Prooijen needs your advise on how to address to a
> tuning member for he´s omitted my name-- Dutch!!!
>
> BTW: As I told to the dutch man, your ratio 81/32 can enter
> to work if and only if the tOctave is firstly derived.
>
> Mario

Whoa Mario, this is way out of line! Kees is a respected
member of this community. I have no idea what you think he
omitted or how his nationality is important, but I hope
you'll regain your composure.

-Carl

🔗Mario Pizarro <piagui@...>

7/17/2011 6:21:28 PM

Carl,

You are right, I will not exactly apologize but I will tell him that I am repentant of having involved his nationality mainly because The Netherlands is my second fatherland since I lived there two years to get the postgraduated degree.(1959-1960).

Thanks

Mario
July, 17

----- Original Message ----- From: "Carl Lumma" <carl@...>
To: <tuning@yahoogroups.com>
Sent: Sunday, July 17, 2011 6:55 PM
Subject: [tuning] Re: The true octave

--- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>
> Steve,
>
> May be van Prooijen needs your advise on how to address to a
> tuning member for heï¿½s omitted my name-- Dutch!!!
>
> BTW: As I told to the dutch man, your ratio 81/32 can enter
> to work if and only if the tOctave is firstly derived.
>
> Mario

-Carl

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

🔗Mario Pizarro <piagui@...>

7/17/2011 7:09:38 PM

Dear Mr. van Prooijen,

I would appreciate it if you excuse me for the inappropiated word I used when discussing about the True Octave.

The Netherlands is my fatherland so the least I should do is sending to you this message.

Hopeful to gain your friendship

Mario Pizarro

July, 17
----- Original Message -----
From: Kees van Prooijen
To: tuning@yahoogroups.com
Sent: Sunday, July 17, 2011 8:52 AM
Subject: Re: [tuning] Re: The true octave

you are mixing your arithmetic metaphors :-)
81/32 in 16 equal parts: (81/32) ^(1/16) = 1.05976223699482
12 of these: (81/32)^(12/16) = 2.00678700656709

On Sun, Jul 17, 2011 at 6:28 AM, Mario Pizarro <piagui@...> wrote:

Steve,

By the fact of dividing 81/32 (= 2.53125) into 16 equal parts, anyone of
these parts has a value of (2.53125 / 16) = 0.158203125. You took 12 of
these parts and said that these 12 parts are the true octave. However the
product 0.158203125* 12 = 1.8984375 and not 2.00678700646 = true octave.
Some of your figures must be wrong ¿isn´t?.
I didn´t take any common fraction as a starting point to get the true
octave, it wouldn´t be a serious mathematical procedure.
Once I finish the wording of a paper that can take about three weeks, I will
send you a copy of it, just wait.
As I said before, the tOctave was derived by a rigurous mathematical
procedure that you will know soon.
Mario
July, 17
<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message -----
From: "martinsj013" <martinsj@...>
To: <tuning@yahoogroups.com>
Sent: Sunday, July 17, 2011 3:40 AM
Subject: [tuning] Re: The true octave

> Mario,
> as far as I can see, your tuning divides 81/32 into 16 equal parts.
> This means that the "2/1" is slightly large; so is the "5/1" (not at all
> unusual) but so is the "3/1" (unusual, for common practice music anyway).
>
> Is that right? Why are 12 of these parts the "true octave"?
>
> Steve M.
>
> P.S. wrt your Progression of Cells: I see that the major 3rd (i.e. 4 of
> the semitones) is found at cell 205; and 8 semitones is found at cell 410;
> and 12 (i.e. the "true octave") at cell 615.
>
>
>
> ------------------------------------
>
> 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
>
>
>
>

🔗Kees van Prooijen <keesvp@...>

7/17/2011 5:49:59 PM

Thanks Carl.

And Mario, if I have offended you in any way, please accept my apologies,
because I never intended to do that.

Kees

On Sun, Jul 17, 2011 at 4:55 PM, Carl Lumma <carl@...> wrote:

> **
>
>
> --- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
> >
> > Steve,
> >
> > May be van Prooijen needs your advise on how to address to a
> > tuning member for he´s omitted my name-- Dutch!!!
> >
> > BTW: As I told to the dutch man, your ratio 81/32 can enter
> > to work if and only if the tOctave is firstly derived.
> >
> > Mario
>
> Whoa Mario, this is way out of line! Kees is a respected
> member of this community. I have no idea what you think he
> omitted or how his nationality is important, but I hope
> you'll regain your composure.
>
> -Carl
>
>
>

🔗Mario Pizarro <piagui@...>

7/17/2011 9:57:55 PM

Kees,

When Carl opened my eyes I realized that I had to send you a message. I am happy to be your friend.

Mario
----- Original Message -----
From: Kees van Prooijen
To: tuning@yahoogroups.com
Sent: Sunday, July 17, 2011 7:49 PM
Subject: Re: [tuning] Re: The true octave

Thanks Carl.

And Mario, if I have offended you in any way, please accept my apologies, because I never intended to do that.

Kees

On Sun, Jul 17, 2011 at 4:55 PM, Carl Lumma <carl@...> wrote:

-Carl

🔗Mario Pizarro <piagui@...>

7/23/2011 7:48:53 AM

Mike,

I have added the file DERIVING THE TRUE OCTAVE.

Mario
Saturday, July, 23

🔗Mike Battaglia <battaglia01@...>

7/23/2011 8:05:37 AM

Hi Mario - Sorry, I have no time at the moment to delve into this. But in
the future you should feel free to post to the list and upload files without
my permission - no need to ask. Just make sure the files aren't too big
(like MP3s) or we'll run out of space, but something like a spreadsheet is
always fine.

-Mike

On Sat, Jul 23, 2011 at 10:48 AM, Mario Pizarro <piagui@...> wrote:

> **
> Mike,
>
> I have added the file DERIVING THE TRUE OCTAVE.
>
> Mario
> Saturday, July, 23
>

🔗Steve Parker <steve@...>

7/23/2011 10:09:34 AM

> The conventional 2 octave was probably proposed or defended by
> Pythagoras due to its acoustical
> response; however an error of (π – 2)/π) ~ 0.003 can be detected
> by ear when playing on a seven octave
> keyboard.

Can you explain this more?

Thanks,

Steve P.

🔗Mario Pizarro <piagui@...>

7/23/2011 1:43:50 PM

Steve,

((2.00678700656 - 2)/2.00678700656) = 0.00338202636245 , since the absolute error is just the difference (numerator = 0.00678700656) it is normal to express the proportion of the absolute error regarding the whole figure of 2.00678700656. This proportion equals 0.00338202636245. It means that 0.003382026.... parts of 2.00678700656 gives the absolute error; in fact: 0.00338202636245 x 2.00678700656 = 0.00678700656.

Since ratio (2.00678700656 / 2) gives 1.00339350328 = 5.865 cents, an average of ear sensibility clearly detects this interval that only corresponds to one octave. The following octaves (4.0271940897, 8.0817..., 16.2182....) keep the same relations. At the moment of writing those words I was thinking on the piano so I see now that I shouldn´t have mentioned "when playing on a seven octave keyboard". I had marked those confusing words to be corrected but forgot to do it.

Please explain this point to any member you are in contact.

Mario

July, 23

<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message -----
From: Steve Parker
To: tuning@yahoogroups.com
Sent: Saturday, July 23, 2011 12:09 PM
Subject: Re: [tuning] The true octave

The conventional 2 octave was probably proposed or defended by Pythagoras due to its acoustical
response; however an error of (π – 2)/π) ~ 0.003 can be detected by ear when playing on a seven octave
keyboard.

Can you explain this more?

Thanks,

Steve P.

🔗Steve Parker <steve@...>

7/23/2011 2:27:57 PM

Hi Mario,

This is where I don't understand. An octave 6 cents too wide isclearly noticeable to me and clearly worse-sounding than 2/1.
What is it about this octave that is 'true'? I can see what is useful
about it, but still don't get why you're claiming it is 'the' correct
octave?

Steve P.

On 23 Jul 2011, at 21:43, Mario Pizarro wrote:

>
>
> Steve,
>
> ((2.00678700656 - 2)/2.00678700656) = 0.00338202636245 , since the
> absolute error is just the difference (numerator = 0.00678700656) it
> is normal to express the proportion of the absolute error regarding
> the whole figure of 2.00678700656. This proportion equals
> 0.00338202636245. It means that 0.003382026.... parts of
> 2.00678700656 gives the absolute error; in fact: 0.00338202636245 x
> 2.00678700656 = 0.00678700656.
>
> Since ratio (2.00678700656 / 2) gives 1.00339350328 = 5.865 cents,> an average of ear sensibility clearly detects this interval that
> only corresponds to one octave. The following octaves (4.0271940897,
> 8.0817..., 16.2182....) keep the same relations. At the moment of
> writing those words I was thinking on the piano so I see now that I
> shouldn´t have mentioned "when playing on a seven octave keyboard".
> I had marked those confusing words to be corrected but forgot to do
> it.
>
> Please explain this point to any member you are in contact.
>
> Mario
>
> July, 23
>
> <<<<<<<<<<<<<<<<<<<<<<<<<
> ----- Original Message -----
> From: Steve Parker
> To: tuning@yahoogroups.com
> Sent: Saturday, July 23, 2011 12:09 PM
> Subject: Re: [tuning] The true octave
>
>> The conventional 2 octave was probably proposed or defended by
>> Pythagoras due to its acoustical
>> response; however an error of (π – 2)/π) ~ 0.003 can be detected
>> by ear when playing on a seven octave
>> keyboard. >
> Can you explain this more?
>
> Thanks,
>
> Steve P.
>
>

🔗genewardsmith <genewardsmith@...>

7/23/2011 3:53:19 PM

--- In tuning@yahoogroups.com, Steve Parker <steve@...> wrote:
>
> Hi Mario,
>
> This is where I don't understand. An octave 6 cents too wide is
> clearly noticeable to me and clearly worse-sounding than 2/1.
> What is it about this octave that is 'true'? I can see what is useful
> about it, but still don't get why you're claiming it is 'the' correct
> octave?

What about it do you see as useful?

🔗Mario Pizarro <piagui@...>

7/23/2011 5:14:04 PM

Steve,

I just sent you an email with an attachment containing the whole file (DERIVING THE TRUE OCTAVE where I corrected page # 1.

Now it is clear. I had responded to Steve Martin instead of responding to you.

Mario

July, 23
----- Original Message -----
From: Steve Parker
To: tuning@yahoogroups.com
Sent: Saturday, July 23, 2011 12:09 PM
Subject: Re: [tuning] The true octave

Can you explain this more?

Thanks,

Steve P.

🔗Mario Pizarro <piagui@...>

7/23/2011 5:55:18 PM

Steve,

Yes, it is almost 6 cents. However the truth is that whoever was the 2 octave creator (Pythagoras?), it is not the exact value of the musical octave. In the past century, a well known orchestra director and mathematician, Julián Carrillo from México, anounced that he detected by ear that the exact octave is sligtly higher than 2. He wrote a book titled SONIDO 13, and couldn´t derive its exact value. You´d better believe me. The finded octave is fantastic.

I am absolutely shure that any scale that is based on the true octave will produce full armonized chords.

Seems that you are not an open minded man. You should study the DERIVING THE TRUE OCTAVE.

The octave is a natural parameter that man forced to be a round number. Until now, I think, didn´t find a natural property whose value is a round figure.

You can send me your personal email address in order to send you attached, the corrected page # 1. You know that tuning reject attachments.

Mario

July, 23
----- Original Message -----
From: Steve Parker
To: tuning@yahoogroups.com
Sent: Saturday, July 23, 2011 4:27 PM
Subject: Re: [tuning] The true octave

Hi Mario,

This is where I don't understand. An octave 6 cents too wide is clearly noticeable to me and clearly worse-sounding than 2/1.
What is it about this octave that is 'true'? I can see what is useful about it, but still don't get why you're claiming it is 'the' correct octave?

Steve P.

On 23 Jul 2011, at 21:43, Mario Pizarro wrote:

Steve,

Please explain this point to any member you are in contact.

Mario

July, 23

<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message -----
From: Steve Parker
To: tuning@yahoogroups.com
Sent: Saturday, July 23, 2011 12:09 PM
Subject: Re: [tuning] The true octave

Can you explain this more?

Thanks,

Steve P.

🔗Mario Pizarro <piagui@...>

7/23/2011 6:06:44 PM

Gene,

You wrote:

> What about it do you see as useful?

I will copy here my reply to Steve:
<<<<<<<<<<<<<<<
Steve,

Yes, it is almost 6 cents. However the truth is that whoever was the 2 octave creator (Pythagoras?), it is not the exact value of the musical octave. In the past century, a well known orchestra director and mathematician, Juliï¿½n Carrillo from Mï¿½xico, anounced that he detected by ear that the exact octave is sligtly higher than 2. He wrote a book titled SONIDO 13, and couldnï¿½t derive its exact value. Youï¿½d better believe me. The finded octave is fantastic.

I am absolutely shure that any scale that is based on the true octave will produce full armonized chords.

Seems that you are not an open minded man. You should study the DERIVING THE TRUE OCTAVE file.

The octave is a natural parameter that man forced to be a round number. Until now, I think, didnï¿½t find a natural property whose value is a round figure, the 2 octave is a forced parameter.

You can send me your personal email address in order to send you attached, the corrected page # 1. You know that tuning reject attachments.

Mario

July, 23
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message ----- From: "genewardsmith" <genewardsmith@...>
To: <tuning@yahoogroups.com>
Sent: Saturday, July 23, 2011 5:53 PM
Subject: [tuning] Re: The true octave

> --- In tuning@yahoogroups.com, Steve Parker <steve@...> wrote:
>>
>> Hi Mario,
>>
>> This is where I don't understand. An octave 6 cents too wide is
>> clearly noticeable to me and clearly worse-sounding than 2/1.
>> What is it about this octave that is 'true'? I can see what is useful
>> about it, but still don't get why you're claiming it is 'the' correct
>> octave?
>
> What about it do you see as useful?
>
>
>
> ------------------------------------
>
> 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 <piagui@...>

7/24/2011 2:49:22 PM

Steve Parker is not an open minded member of the list . He didn´t analyze the files I posted in tuning regarding the true octave, that is why he dares to deny the clear validity of the true octave whose value is not 2 but 2.00678700656 . In the past, somebody stated the 2 octave, this wrong value is responsible of the many incongruences and imperfections we find in the music harmony. If we call & to the true octave,the basic 12 tones of a true octave scale are the following: C = 1, C# = &^(1/12), D = &^(1/6), Eb = &^(1/4), E = &^(1/3), F = &^(5/12), F# = &^(1/2), G = &^(7/12), Ab = &^(2/3), A = &^(3/4), Bb = &^(5/6), B = &^(11/12). 2C = &. By using the true octave we get 12 equal fifths, 12 equal major thirds and 12 equal minor thirds. Mario Pizarro.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, Steve Parker <steve@> wrote:
>
> > Can someone - anyone - explain to me why I should not accept a 2/1
> > octave by definition?
> > Another tuning of the octave may sound nice, have cute mathematical
> > properties or some other utility, but as it stands 2/1 'defines' an
> > octave.
> > Either way stop calling it 'true'.
>
> 2/1 is a JI octave by definition. Like any other JI interval, it can be detuned, either as a part of a regular temperament tuning or irregularly. If you detune it regularly, you've now got a certain fixed tuning for it, just as detunintg 3/2 to 700 cents gives you a
> new fixed tuning for that. Calling the tempered octave "true" is a bit like a fervent believer in 12 equal calling 700 cents true, I suppose.
>
> Some people like to announce the One True Tuning, which for some people can change from day to day and with other people seems fixed for their lifetime. It's just a psychological fact of life in the alternative tuning world, one which sometimes leads to friction since no one else ever seems to climb aboard the One True Tuning train of any of these proposals.
>

🔗Steve Parker <steve@...>

7/24/2011 3:52:01 PM

On 24 Jul 2011, at 22:49, Mario wrote:

> Steve Parker is not an open minded member of the list .

I'm not sure you know anything about me at all?

> He didn´t analyze the files I posted in tuning regarding the true octave,

I have hardly any spare time at the moment.. despite that I have spent some time studying your files and tuning to your numbers.

> that is why he dares to deny the clear validity of the true octave whose value is not 2 but 2.00678700656 .

It sounds wide to me. Also some of your other intervals end up wide, even though in 12ET they're already wide.

I wish you'd explain the attraction of this octave to me in terms like 'it beats less' or something similar.

The fact that someone else could tell by ear that 2/1 is wrong and worse than your true octave just doesn't square with my own listening.

Being open-minded does not require that I ignore my own experience and study and just believe something because you state it.

I really am trying to understand what you hear in it that you prefer?

Steve P.

🔗Mario Pizarro <piagui@...>

7/24/2011 4:34:19 PM

Steve,

The civilized next stage is to tune a piano to the scale detailed in the upper side of file # 1. Here, the middle C works with minus 4.399 cents; its true octave has 1201.466 cents. Once the piano is tuned, you can check the results to be convinced that the high chord qualities are due to the octave.

Mario
July, 24
----- Original Message -----
From: Steve Parker
To: tuning@yahoogroups.com
Sent: Sunday, July 24, 2011 5:52 PM
Subject: Re: [tuning] Re: The true octave

On 24 Jul 2011, at 22:49, Mario wrote:

Steve Parker is not an open minded member of the list .

I'm not sure you know anything about me at all?

He didn´t analyze the files I posted in tuning regarding the true octave,

I have hardly any spare time at the moment.. despite that I have spent some time studying your files and tuning to your numbers.

that is why he dares to deny the clear validity of the true octave whose value is not 2 but 2.00678700656 .

It sounds wide to me. Also some of your other intervals end up wide, even though in 12ET they're already wide.

I wish you'd explain the attraction of this octave to me in terms like 'it beats less' or something similar.

The fact that someone else could tell by ear that 2/1 is wrong and worse than your true octave just doesn't square with my own listening.

Being open-minded does not require that I ignore my own experience and study and just believe something because you state it.

I really am trying to understand what you hear in it that you prefer?

Steve P.

🔗Steve Parker <steve@...>

7/24/2011 4:51:29 PM

On 25 Jul 2011, at 00:34, Mario Pizarro wrote:

> The civilized next stage is to tune a piano to the scale detailed in the upper side of file # 1.

Hi Mario,

I've done this (in software - multiple instances of Kontakt tuned an octave each - if anyone can tell me how to do this in Kontakt with just one instantiation please spill!).
I just don't agree with your analysis of the quality of chords. In some respects worse than standard 12ET which I'm no real fan of..

I'm sorry that you think I'm being contrary. I'm just trying to find out what it is you value in your octave over a 2/1?

If you would rather I didn't post anymore I'm happy to not to?

Steve P.

🔗Carl Lumma <carl@...>

7/24/2011 5:19:02 PM

> If you would rather I didn't post anymore I'm happy to not to?
> Steve P.

I appreciate your posts! -Carl

🔗Mario Pizarro <piagui@...>

7/24/2011 6:54:30 PM

Steve,

You wrote:
----------------------------------------------------
I've done this (in software - multiple instances of Kontakt tuned an octave each - if anyone can tell me how to do this in Kontakt with just one instantiation please spill!).
I just don't agree with your analysis of the quality of chords. In some respects worse than standard 12ET which I'm no real fan of..
-----------------------------------
I understand that you have done the tuning by software and at the same time you ask information to do it in Kontakt, I am confused.

Since I am not a pianist and despite I am sensible to detecting inharmonious piano chords, the evaluations were done by two good pianists, one of them studied and practiced piano concerts in the university of Herzen, St. Petersburg. He decided to make the evaluation bringing a second piano tuned to 12 equal tempered and took 3 hours for the comparisons and another similar period the next day. Before, he asked the tuner to make a check to the equal tempered tunng. He gave his conclussions on the second afternoon saying that in all comparisons the true octave chords and coupled chords were listened much better than what were heard from the tempered piano. I had detected that since the begining.

Since I am tired of discussing this matter and affirming that those "open minded" words were only abrupt words, I will take a rest waiting for the message of a friend of mine saying that he appreciated my posts.

Mario
July, 24
----- Original Message -----
From: Steve Parker
To: tuning@yahoogroups.com
Sent: Sunday, July 24, 2011 6:51 PM
Subject: Re: [tuning] Re: The true octave

On 25 Jul 2011, at 00:34, Mario Pizarro wrote:

The civilized next stage is to tune a piano to the scale detailed in the upper side of file # 1.

Hi Mario,

I'm sorry that you think I'm being contrary. I'm just trying to find out what it is you value in your octave over a 2/1?

If you would rather I didn't post anymore I'm happy to not to?

Steve P.

🔗Steve Parker <steve@...>

7/24/2011 11:56:42 PM

On 25 Jul 2011, at 02:54, Mario Pizarro wrote:

> I understand that you have done the tuning by software and at the same time you ask information to do it in Kontakt, I am confused.

I've done it in Kontakt with 8 channels each tuned to an octave from C-B. What I don't know how to do is to do this with 1 channel rather than 8.
I can also only do it to the nearest cent. I have some experience of piano tuning and it's not possible to tune much more accurately than that and at least with Kontakt I don't have to worry about individual strings!

Steve P.

🔗Steve Parker <steve@...>

7/25/2011 12:52:22 AM

On 25 Jul 2011, at 07:56, Steve Parker wrote:

> I've done it in Kontakt with 8 channels each tuned to an octave from C-B. What I don't know how to do is to do this with 1 channel rather than 8.

now slightly more awake... I've tuned it with 2 channels..

Steve P.

🔗martinsj013 <martinsj@...>

7/25/2011 1:55:18 AM

--- In tuning@yahoogroups.com, "Mario" <piagui@...> wrote:
> ... If we call & to the true octave,the basic 12 tones of a true octave scale are the following: C = 1, C# = &^(1/12), D = &^(1/6), Eb = &^(1/4), E = &^(1/3), F = &^(5/12), F# = &^(1/2), G = &^(7/12), Ab = &^(2/3), A = &^(3/4), Bb = &^(5/6), B = &^(11/12). 2C = &. By using the true octave we get 12 equal fifths, 12 equal major thirds and 12 equal minor thirds.

Mario,
But, with the 2 octave, we have: C = 1, C# = 2^(1/12), D = 2^(1/6), Eb = 2^(1/4), E = 2^(1/3), F = 2^(5/12), F# = 2^(1/2), G = 2^(7/12), Ab = 2^(2/3), A = 2^(3/4), Bb = 2^(5/6), B = 2^(11/12). 2C = 2. So also, by using the 2 octave we get 12 equal fifths, 12 equal major thirds and 12 equal minor thirds. Have you demonstrated that & is better?

> ... the 2 octave, this wrong value is responsible of the many incongruences and imperfections we find in the music harmony. ...

Have you demonstrated that & overcomes these?

Steve M.

🔗Mario Pizarro <piagui@...>

7/25/2011 6:16:07 AM

Steve,

It is evident that every equal tempered scale like the true octave scale gives 12 equal fifths, 12 equal major and minor thirds. I mentioned this because I know that an important group of the list are lovers of the equal tempered scale so I thought that itï¿½s better to remark this property.

The true octave scale was evaluated by a brilliant pianist despite I am very sensible to slightly inharmonious chords.. It was done in two contiguous afternoons using a second piano tuned to 12 tet for comparison purposes and I was a witness of how rigurous was the pianist. At the end of the evaluation he informed that in all comparisons the true octave chords and chord progressions were much much better than 12 tet. I just phoned the pianist to tell him that one member of tuning (Steve Parker) wrote that the true octave scale sounds bad, he said that probably he (Steve) is invaded by 2 octave chords and that if he practice the true octave scale his opinion might be different.

He recommended me to tune just the following: C maj: (100.49 + 401.95 + 703.4 cents), C minor: (301.46 instead of 401.95) and separately: 1005.37 and 1004.89 for major and minor sevenths so this way by tuning only 6 piano keys we can do about a 70 % of the evaluation.

Mario
July, 25

----- Original Message ----- From: "martinsj013" <martinsj@...>
To: <tuning@yahoogroups.com>
Sent: Monday, July 25, 2011 3:55 AM
Subject: [tuning] Re: The true octave

> --- In tuning@yahoogroups.com, "Mario" <piagui@...> wrote:
>> ... If we call & to the true octave,the basic 12 tones of a true octave >> scale are the following: C = 1, C# = &^(1/12), D = &^(1/6), Eb = &^(1/4), >> E = &^(1/3), F = &^(5/12), F# = &^(1/2), G = &^(7/12), Ab = &^(2/3), A = >> &^(3/4), Bb = &^(5/6), B = &^(11/12). 2C = &. By using the true octave we >> get 12 equal fifths, 12 equal major thirds and 12 equal minor thirds.
>
> Mario,
> But, with the 2 octave, we have: C = 1, C# = 2^(1/12), D = 2^(1/6), Eb = > 2^(1/4), E = 2^(1/3), F = 2^(5/12), F# = 2^(1/2), G = 2^(7/12), Ab = > 2^(2/3), A = 2^(3/4), Bb = 2^(5/6), B = 2^(11/12). 2C = 2. So also, by > using the 2 octave we get 12 equal fifths, 12 equal major thirds and 12 > equal minor thirds. Have you demonstrated that & is better?
>
>> ... the 2 octave, this wrong value is responsible of the many >> incongruences and imperfections we find in the music harmony. ...
>
> Have you demonstrated that & overcomes these?
>
> Steve M.
>
>
>
>
>
> ------------------------------------
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🔗Steve Parker <steve@...>

7/25/2011 6:29:29 AM

Hi Mario,

I didn't write about 12 equal fifths etc..someone else.

>> probably he (Steve) is invaded by
>> 2 octave chords and that if he practice the true octave scale his opinion
>> might be different.
>>

Not sure what you mean here? I spend a lot of time with just tuning and lately 19ET and a tuning of harmonics 1-88 on C.

Unless I'm getting something wrong somewhere your scale stretches 42 cents over the piano.

The octaves and fifths beat and doubled octaves and fifths wow all over the place?

Did you listen to the files I posted?

Steve P.

On 25 Jul 2011, at 14:16, Mario Pizarro wrote:

> Steve,
>
> It is evident that every equal tempered scale like the true octave scale
> gives 12 equal fifths, 12 equal major and minor thirds. I mentioned this
> because I know that an important group of the list are lovers of the equal
> tempered scale so I thought that it´s better to remark this property.
>
> The true octave scale was evaluated by a brilliant pianist despite I am very
> sensible to slightly inharmonious chords.. It was done in two contiguous
> afternoons using a second piano tuned to 12 tet for comparison purposes and
> I was a witness of how rigurous was the pianist. At the end of the
> evaluation he informed that in all comparisons the true octave chords and
> chord progressions were much much better than 12 tet. I just phoned the
> pianist to tell him that one member of tuning (Steve Parker) wrote that the
> true octave scale sounds bad, he said that probably he (Steve) is invaded by
> 2 octave chords and that if he practice the true octave scale his opinion
> might be different.
>
> He recommended me to tune just the following: C maj: (100.49 + 401.95 +
> 703.4 cents), C minor: (301.46 instead of 401.95) and separately: 1005.37
> and 1004.89 for major and minor sevenths so this way by tuning only 6 piano
> keys we can do about a 70 % of the evaluation.
>
> Mario
> July, 25
>
> ----- Original Message -----
> From: "martinsj013" <martinsj@...>
> To: <tuning@yahoogroups.com>
> Sent: Monday, July 25, 2011 3:55 AM
> Subject: [tuning] Re: The true octave
>
> > --- In tuning@yahoogroups.com, "Mario" <piagui@...> wrote:
> >> ... If we call & to the true octave,the basic 12 tones of a true octave
> >> scale are the following: C = 1, C# = &^(1/12), D = &^(1/6), Eb = &^(1/4),
> >> E = &^(1/3), F = &^(5/12), F# = &^(1/2), G = &^(7/12), Ab = &^(2/3), A =
> >> &^(3/4), Bb = &^(5/6), B = &^(11/12). 2C = &. By using the true octave we
> >> get 12 equal fifths, 12 equal major thirds and 12 equal minor thirds.
> >
> > Mario,
> > But, with the 2 octave, we have: C = 1, C# = 2^(1/12), D = 2^(1/6), Eb =
> > 2^(1/4), E = 2^(1/3), F = 2^(5/12), F# = 2^(1/2), G = 2^(7/12), Ab =
> > 2^(2/3), A = 2^(3/4), Bb = 2^(5/6), B = 2^(11/12). 2C = 2. So also, by
> > using the 2 octave we get 12 equal fifths, 12 equal major thirds and 12
> > equal minor thirds. Have you demonstrated that & is better?
> >
> >> ... the 2 octave, this wrong value is responsible of the many
> >> incongruences and imperfections we find in the music harmony. ...
> >
> > Have you demonstrated that & overcomes these?
> >
> > 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@...>

7/25/2011 7:43:45 AM

Steve,

Steve Martin sent me the message regarding the fact that 12 equal fifths, 12 equal major and minor thirds are also a feature of 12 tet. I add that every equal tempered scale show this feature.

Thank you very very very much for the interesting posts you sent me. How can you do that ?.

I informed to the pianist who has done the true octave scale evaluation about your conclussions, it was a surprise for him to know that. I didn´t fail mathematically. The owner of the grand piano where the true octave scale is waiting for us, has invited us to join him again to study your view points since he is fully satisfied with the true octave tuning.

The tuner who tuned the piano said that after about 40 years working as a tuner he is absolutely sure that the toctave is a very nice option.

Let to God to decide.

Mario
July, 25

----- Original Message -----
From: Steve Parker
To: tuning@yahoogroups.com
Sent: Monday, July 25, 2011 8:29 AM
Subject: Re: [tuning] Re: The true octave

Hi Mario,

I didn't write about 12 equal fifths etc..someone else.

probably he (Steve) is invaded by
2 octave chords and that if he practice the true octave scale his opinion
might be different.

Not sure what you mean here? I spend a lot of time with just tuning and lately 19ET and a tuning of harmonics 1-88 on C.

Unless I'm getting something wrong somewhere your scale stretches 42 cents over the piano.

The octaves and fifths beat and doubled octaves and fifths wow all over the place?

Did you listen to the files I posted?

Steve P.

On 25 Jul 2011, at 14:16, Mario Pizarro wrote:

Steve,

It is evident that every equal tempered scale like the true octave scale
gives 12 equal fifths, 12 equal major and minor thirds. I mentioned this
because I know that an important group of the list are lovers of the equal
tempered scale so I thought that it´s better to remark this property.

The true octave scale was evaluated by a brilliant pianist despite I am very
sensible to slightly inharmonious chords.. It was done in two contiguous
afternoons using a second piano tuned to 12 tet for comparison purposes and
I was a witness of how rigurous was the pianist. At the end of the
evaluation he informed that in all comparisons the true octave chords and
chord progressions were much much better than 12 tet. I just phoned the
pianist to tell him that one member of tuning (Steve Parker) wrote that the
true octave scale sounds bad, he said that probably he (Steve) is invaded by
2 octave chords and that if he practice the true octave scale his opinion
might be different.

He recommended me to tune just the following: C maj: (100.49 + 401.95 +
703.4 cents), C minor: (301.46 instead of 401.95) and separately: 1005.37
and 1004.89 for major and minor sevenths so this way by tuning only 6 piano
keys we can do about a 70 % of the evaluation.

Mario
July, 25

----- Original Message -----
From: "martinsj013" <martinsj@...>
To: <tuning@yahoogroups.com>
Sent: Monday, July 25, 2011 3:55 AM
Subject: [tuning] Re: The true octave

> --- In tuning@yahoogroups.com, "Mario" <piagui@...> wrote:
>> ... If we call & to the true octave,the basic 12 tones of a true octave
>> scale are the following: C = 1, C# = &^(1/12), D = &^(1/6), Eb = &^(1/4),
>> E = &^(1/3), F = &^(5/12), F# = &^(1/2), G = &^(7/12), Ab = &^(2/3), A =
>> &^(3/4), Bb = &^(5/6), B = &^(11/12). 2C = &. By using the true octave we
>> get 12 equal fifths, 12 equal major thirds and 12 equal minor thirds.
>
> Mario,
> But, with the 2 octave, we have: C = 1, C# = 2^(1/12), D = 2^(1/6), Eb =
> 2^(1/4), E = 2^(1/3), F = 2^(5/12), F# = 2^(1/2), G = 2^(7/12), Ab =
> 2^(2/3), A = 2^(3/4), Bb = 2^(5/6), B = 2^(11/12). 2C = 2. So also, by
> using the 2 octave we get 12 equal fifths, 12 equal major thirds and 12
> equal minor thirds. Have you demonstrated that & is better?
>
>> ... the 2 octave, this wrong value is responsible of the many
>> incongruences and imperfections we find in the music harmony. ...
>
> Have you demonstrated that & overcomes these?
>
> 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
>
>
>
>

🔗Steve Parker <steve@...>

7/25/2011 7:52:01 AM

On 25 Jul 2011, at 15:43, Mario Pizarro wrote:

> I informed to the pianist who has done the true octave scale evaluation about your conclussions, it was a surprise for him to know that. I didn´t fail mathematically. The owner of the grand piano where the true octave scale is waiting for us, has invited us to join him again to study your view points since he is fully satisfied with the true octave tuning.
>
> The tuner who tuned the piano said that after about 40 years working as a tuner he is absolutely sure that the toctave is a very nice option.

It may just be that I'm going wrong somewhere...

Steve P.

🔗Mario Pizarro <piagui@...>

7/25/2011 8:06:02 AM

Attachments

Steve,

If you can do it, it´s worth to tune the 88 keys of the piano by following the cents data given by the attached file. That is the way of studying and attacking the beating effect.

Mario
July, 25
----- Original Message -----
From: Steve Parker
To: tuning@yahoogroups.com
Sent: Monday, July 25, 2011 1:56 AM
Subject: Re: [tuning] Re: The true octave

On 25 Jul 2011, at 02:54, Mario Pizarro wrote:

I understand that you have done the tuning by software and at the same time you ask information to do it in Kontakt, I am confused.
I've done it in Kontakt with 8 channels each tuned to an octave from C-B. What I don't know how to do is to do this with 1 channel rather than 8.
I can also only do it to the nearest cent. I have some experience of piano tuning and it's not possible to tune much more accurately than that and at least with Kontakt I don't have to worry about individual strings!

Steve P.

🔗Tim Reeves <reevest360@...>

7/25/2011 8:19:29 AM

yea Steve, it's not over yet bro

--- On Mon, 7/25/11, Carl Lumma <carl@lumma.org> wrote:

From: Carl Lumma <carl@...>
Subject: [tuning] Re: The true octave
To: tuning@yahoogroups.com
Date: Monday, July 25, 2011, 12:19 AM

> If you would rather I didn't post anymore I'm happy to not to?
> Steve P.

I appreciate your posts! -Carl

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

🔗Steve Parker <steve@...>

7/25/2011 8:22:32 AM

Hi Mario,

> If you can do it, it´s worth to tune the 88 keys of the piano by following the cents data given by the attached file. That is the way of studying and attacking the beating effect.
>
This is what I tuned to.

Steve P.

> July, 25
> ----- Original Message -----
> From: Steve Parker
> To: tuning@yahoogroups.com
> Sent: Monday, July 25, 2011 1:56 AM
> Subject: Re: [tuning] Re: The true octave
> On 25 Jul 2011, at 02:54, Mario Pizarro wrote:
>
>> I understand that you have done the tuning by software and at the same time you ask information to do it in Kontakt, I am confused.
>
> I've done it in Kontakt with 8 channels each tuned to an octave from C-B. What I don't know how to do is to do this with 1 channel rather than 8.
> I can also only do it to the nearest cent. I have some experience of piano tuning and it's not possible to tune much more accurately than that and at least with Kontakt I don't have to worry about individual strings!
>
> Steve P.
>
>

🔗Steve Parker <steve@...>

7/25/2011 10:10:14 AM

On 25 Jul 2011, at 16:06, Mario Pizarro wrote:

> If you can do it, it´s worth to tune the 88 keys of the piano by following the cents data given by the attached file. That is the way of studying and attacking the beating effect.

Hi Mario,

This is exactly what I did to tune the piano.

Steve P.

🔗genewardsmith <genewardsmith@...>

7/25/2011 10:02:53 PM

--- In tuning@yahoogroups.com, Steve Parker <steve@...> wrote:

> It may just be that I'm going wrong somewhere...

Why? I could just as well say that the zeta maximum near to 12, which is 12.0232, gives the one true and correct 1197.68 cent octave.

🔗Mario Pizarro <piagui@...>

7/26/2011 1:06:01 PM

----- Original Message ----- From: "genewardsmith" <genewardsmith@...>
To: <tuning@yahoogroups.com>
Sent: Tuesday, July 26, 2011 12:02 AM
Subject: [tuning] Re: The true octave

> --- In tuning@yahoogroups.com, Steve Parker <steve@...> wrote:
>
>> It may just be that I'm going wrong somewhere...
>
> Why? I could just as well say that the zeta maximum near to 12, which is > 12.0232, gives the one true and correct 1197.68 cent octave.
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
GENE,
Your 1197.98 cent octave gives an octave of 1.99732163073 with a semitone factor of 1.059344787.

The 12 frequency tone components too close to equal tempered form a set of useless frequencies where not even F# is part of it as we can see here:

C = 1 = 0 CENTS
C# = 1.059344787 = 99.8
D = 1,12221137774 = 199.61
Eb = 1,18880877292 = 299.42
E = 1.25935837633 = 399.23
F = 1.33409473093 = 499.03
F# =1.41326629857 = 598.04
G = 1.49713628603 = 698.65
Ab = 1.58598352 = 798.45
A = 1.68010337421 = 898.26
Bb =1.77980875109 = 998.06
B = 1.88543112232 = 1097.87
2C = 1.99732163067 = 1197.68

> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
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> Yahoo! Groups Links
>
>
>
>

🔗Steve Parker <steve@...>

7/26/2011 1:21:57 PM

> > It may just be that I'm going wrong somewhere...
>
> Why? I could just as well say that the zeta maximum near to 12, which is 12.0232, gives the one true and correct 1197.68 cent octave. __._,_._
>
>

I'm trying really hard...! I'm not hearing anything with any more logic than just declaring that 2/1 + 9/8 is the true octave and then using that as an assumption by which to judge everything else.

Steve P.