Defining the method for determining the final distribution of elements.

Mike,

By taking six contiguous cells of the progression which embrace the ratio (1.75 = 7/4) whose condition of consonant or disonant is to be known and calculating the difference between the ratio 1.75 and the cell whose frequency is close approximated to the 1.75 ratio: 1.75 - 1.749887 = 0.000112 . Since this difference is lower than reference 0.0005, ratio 7/4 is consonant.

...........For a ratio of 1.75
M- 493- 1.74791410141
M- 494- 1.74988775930
J- 495- 1.75186753174
J- 496- 1.75384954404
M- 497- 1.75582990393
M- 498- 1.7578125
..........................................
493 ---1.75 - 1.747914 = 0.002086
494 ---1.75 - 1.749887 = 0.000112 .
495 ---1.75 - 1.751867 = 0.001867
496 --- > .......................................
497 --- >> .....................................
498 --- >>> ...................................
--------------------------------------------------
For a ratio of 1.375
M 279 1.37151045250
M 280 1.37305909407
J 281 1.37461253344
J 282 1.37616773034
U 283 1.37783798031
U 284 1.37951025746

1.375 minus cell # 281 = 0.0003874 < 0.000500, then
11/8 = 1.375 is also consonant.
Similar operations are applied for other ratios .

Mario

January, 7

<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message -----
From: "John H. Chalmers" <jhchalmers@...>
To: "Mario Pizarro" <piagui@...>
Sent: Saturday, January 07, 2012 3:04 PM
Subject: Re: A useful tool to recognize consonance.

> Mario: J 281 and J 282 are so close to 1.375 that I doubt in music
> performance, one could hear the difference between either of them and
> 11/8. Likewise, M493, M494 and J495 are so close to 7/4, that the
> difference wouldn't matter.
>
> As I said in my previous post, consonance is a very complex phenomenon
> that depends upon context, timbre, register, loudness, style and prior
> experience. Close approximations to consonant intervals are perceived as
> consonant also--for thirds, some people actually prefer slightly mistuned
> intervals, perhaps because of their experience with 12-tone equal
> temperament or because they like the richer and dynamic sound of the
> tempered intervals. If these perceptual findings weren't true, meantone
> and equal temperament would never have been adopted in Western music.
>
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

--- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>
> Mike,
>
> By taking six contiguous cells of the progression which embrace the ratio (1.75 = 7/4) whose condition of consonant or disonant is to be known and calculating the difference between the ratio 1.75 and the cell whose frequency is close approximated to the 1.75 ratio: 1.75 - 1.749887 = 0.000112 . Since this difference is lower than reference 0.0005, ratio 7/4 is consonant.
>
> ...........For a ratio of 1.75
> M- 493- 1.74791410141
> M- 494- 1.74988775930
> J- 495- 1.75186753174
> J- 496- 1.75384954404
> M- 497- 1.75582990393
> M- 498- 1.7578125
> ..........................................
> 493 ---1.75 - 1.747914 = 0.002086
> 494 ---1.75 - 1.749887 = 0.000112 .
> 495 ---1.75 - 1.751867 = 0.001867
> 496 --- > .......................................
> 497 --- >> .....................................
> 498 --- >>> ...................................
> --------------------------------------------------
> For a ratio of 1.375
> M 279 1.37151045250
> M 280 1.37305909407
> J 281 1.37461253344
> J 282 1.37616773034
> U 283 1.37783798031
> U 284 1.37951025746
>
>
> 1.375 minus cell # 281 = 0.0003874 < 0.000500, then
> 11/8 = 1.375 is also consonant.
> Similar operations are applied for other ratios .

If so, then it seems like there are a LOT of intervals that fit your definition of consonance!

Tell me: if I pick an interval uniformly at random between 0 cents and 1200 cents, what is the probability that it is consonant?

Keenan

If so, then it seems like there are a LOT of intervals that fit your definition of consonance!

Tell me: if I pick an interval uniformly at random between 0 cents and 1200 cents, what is the probability that it is consonant?

Keenan

In tunin@yahoogroups.com "Keenan Pepper" keenanpepper@... wrote

----- Original Message ----- From: "Keenan Pepper" <keenanpepper@...>
To: <tuning@yahoogroups.com>
Sent: Sunday, January 08, 2012 10:54 AM
Subject: [tuning] Re: Defining the method for determining the final distribution of elements.

> --- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>>
>> Mike,
>>
>> By taking six contiguous cells of the progression which embrace the ratio >> (1.75 = 7/4) whose condition of consonant or disonant is to be known and >> calculating the difference between the ratio 1.75 and the cell whose >> frequency is close approximated to the 1.75 ratio: 1.75 - 1.749887 = >> 0.000112 . Since this difference is lower than reference 0.0005, ratio >> 7/4 is consonant.
>>
>> ...........For a ratio of 1.75
>> M- 493- 1.74791410141
>> M- 494- 1.74988775930
>> J- 495- 1.75186753174
>> J- 496- 1.75384954404
>> M- 497- 1.75582990393
>> M- 498- 1.7578125
>> ..........................................
>> 493 ---1.75 - 1.747914 = 0.002086
>> 494 ---1.75 - 1.749887 = 0.000112 .
>> 495 ---1.75 - 1.751867 = 0.001867
>> 496 --- > .......................................
>> 497 --- >> .....................................
>> 498 --- >>> ...................................
>> --------------------------------------------------
>> For a ratio of 1.375
>> M 279 1.37151045250
>> M 280 1.37305909407
>> J 281 1.37461253344
>> J 282 1.37616773034
>> U 283 1.37783798031
>> U 284 1.37951025746
>>
>>
>> 1.375 minus cell # 281 = 0.0003874 < 0.000500, then
>> 11/8 = 1.375 is also consonant.
>> Similar operations are applied for other ratios .
>
> If so, then it seems like there are a LOT of intervals that fit your > definition of consonance!
>
> Tell me: if I pick an interval uniformly at random between 0 cents and > 1200 cents, what is the probability that it is consonant?
>
> Keenan
>
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

Keenan,

Consonance implies the interaction of two sinusoidal waves if we want to get clear the idea.

If two pure tones: D = 1.125 and G = 1.5 are accompanied by the following overtones: A = 1.6875, A# = 1.40625, B = 1.875. The two roots (D and G) and their partials settle the dissonance, that is, the inverse of the consonance. Other partials work as reinforcing elements.

I will assume that when you pick intervals at random and to catch a lot of consonances you have to operate with two sources of tones, with a range 0 cents to 1200.

You want to know the probab�lity that the at random measurements give all consonant results in N1 case, partial results in N2 case and NONE in N3 case.

Sadness, for not beeing possible to calculate that probability. Nobody in this planet can do it. Even the number of complex variables is a previous big problem.

If I would have a mathematician enemy, a child killer, I would put him in jail for the period of time he takes for the solution of that probability problem.

I am tempted to send this message to your personal email, a fine reply that would correspond to your fine joke.

Thanks

Mario

January, 8

--- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
> You want to know the probabílity that the at random measurements give all
> consonant results in N1 case, partial results in N2 case and NONE in N3
> case.

I did not ask about three cases. I asked what is the probability that an interval is consonant. I don't see how that question implies the existence of three cases.

> Sadness, for not beeing possible to calculate that probability. Nobody in
> this planet can do it. Even the number of complex variables is a previous
> big problem.

Even assuming you can't calculate it exactly, you can always approximate it by the Monte Carlo method. If you have a mathematical definition of "consonant", then it's possible to write a computer program to output "consonant" or "not consonant" for any input interval. With such a program you can run it on very many randomly chosen intervals and get an estimate for the probability.

> If I would have a mathematician enemy, a child killer, I would put him in
> jail for the period of time he takes for the solution of that probability
> problem.
>
> I am tempted to send this message to your personal email, a fine reply that
> would correspond to your fine joke.

My question was not a joke at all. It was a serious question about your definition of consonance.

Keenan

Keenan,

I am not convinced that theoretical basis of probability is really a useful matter that deserves to be included in the universitary studies. Time ago somebody insisted on calculating the probability that a handful of pins when thrown to the floor describes the greek PI letter.

Honestly I say that I am the last human for devoting time in probability calculations no matter that in this case the problem was not stated properly. I am really sorry for setting aside your petition and I avail this contact to congratulate you for the deep knowledges you have in music.

However, I think the referred method only gives relative information regarding scale tones consonances if the references 5000, 2000, 1000, 500 are applied according to the consonance magnitude. I don�t discard that the method take us to incoherent conclusions, maybe not.

Have a good time.

Mario

January, 9
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message ----- From: "Keenan Pepper" <keenanpepper@...>
To: <tuning@yahoogroups.com>
Sent: Monday, January 09, 2012 3:10 AM
Subject: [tuning] Re: Defining the method for determining the final distribution of elements.

--- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
> You want to know the probab�lity that the at random measurements give all
> consonant results in N1 case, partial results in N2 case and NONE in N3
> case.

I did not ask about three cases. I asked what is the probability that an interval is consonant. I don't see how that question implies the existence of three cases.

> Sadness, for not beeing possible to calculate that probability. Nobody in
> this planet can do it. Even the number of complex variables is a previous
> big problem.

Even assuming you can't calculate it exactly, you can always approximate it by the Monte Carlo method. If you have a mathematical definition of "consonant", then it's possible to write a computer program to output "consonant" or "not consonant" for any input interval. With such a program you can run it on very many randomly chosen intervals and get an estimate for the probability.

> If I would have a mathematician enemy, a child killer, I would put him in
> jail for the period of time he takes for the solution of that probability
> problem.
>
> I am tempted to send this message to your personal email, a fine reply > that
> would correspond to your fine joke.

My question was not a joke at all. It was a serious question about your definition of consonance.

Keenan

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Mario,

Probability is in inherently included in the scientific method. All theoretical models are evaluated based on whether they succeed with greater frequency than random chance (or than a competing model) at fitting established experimental data. To become an accepted theory, a model must fit established data and successfully predict new data points more effectively than random chance or any competing models. In other words, your model needs to be shown to have a higher probability of predicting consonance and dissonance than random chance, as well as a higher probability than any of the competing models (like harmonic entropy, critical band dissonance, Sethares' sensory dissonance model, etc.). If you reject probability out-of-hand, then your model and theory will similarly be rejected out-of-hand by any scientific community. If you refuse to evaluate your model against competing models and/or random chance, then all of your claims about the superiority of your model will appear to any rational human being as "unfounded" and "faith-based", the result of the worst kind of confirmation bias.

Also, your hostile and antagonistic response to those who criticize or challenge your results or ideas is unnecessary and unprofessional. If you cannot communicate with civility, do not expect to be taken seriously.

-Igliashon

--- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>
> Keenan,
>
> I am not convinced that theoretical basis of probability is really a useful
> matter that deserves to be included in the universitary studies. Time ago
> somebody insisted on calculating the probability that a handful of pins when
> thrown to the floor describes the greek PI letter.

Igliashon,
Keenan,

I didn�t explain well my position regarding the study of probability in the university. In my country we get the diploma of electronic- electrical engineer after 5 or 6 years of studies. Along these years we are extremely busy with the courses where the course of probability is not included but is attended in an Institute where graduated EE engineers can continue their studies.

About 20 % of the electrical engineers enter to this Institute, I did not. I studied at home some basic information on this topic.
Since the inclusion of this course in the university would affect the operation of the Institute it is advisable that its theoretical basis don�t be part of the universitary studies.

The explanation given above was the reason of the two lines that follows. Obviously, "really a useful matter....." are not the correct words since all the courses are useful in the university but time is a limiting factor.

>> I am not convinced that theoretical basis of probability is really a >> useful
>> matter that deserves to be included in the universitary studies.

Best regards

Mario

January, 9.
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message ----- From: "cityoftheasleep" <igliashon@...>
To: <tuning@yahoogroups.com>
Sent: Monday, January 09, 2012 12:32 PM
Subject: [tuning] Re: Defining the method for determining the final distribution of elements.

> Mario,
>
> Probability is in inherently included in the scientific method. All > theoretical models are evaluated based on whether they succeed with > greater frequency than random chance (or than a competing model) at > fitting established experimental data. To become an accepted theory, a > model must fit established data and successfully predict new data points > more effectively than random chance or any competing models. In other > words, your model needs to be shown to have a higher probability of > predicting consonance and dissonance than random chance, as well as a > higher probability than any of the competing models (like harmonic > entropy, critical band dissonance, Sethares' sensory dissonance model, > etc.). If you reject probability out-of-hand, then your model and theory > will similarly be rejected out-of-hand by any scientific community. If > you refuse to evaluate your model against competing models and/or random > chance, then all of your claims about the superiority of your model will > appear to any rational human being as "unfounded" and "faith-based", the > result of the worst kind of confirmation bias.
>
> Also, your hostile and antagonistic response to those who criticize or > challenge your results or ideas is unnecessary and unprofessional. If you > cannot communicate with civility, do not expect to be taken seriously.
>
> -Igliashon
>
> --- In tuning@yahoogroups.com, "Mario Pizarro" <piagui@...> wrote:
>>
>> Keenan,
>>
>> I am not convinced that theoretical basis of probability is really a >> useful
>> matter that deserves to be included in the universitary studies. Time ago
>> somebody insisted on calculating the probability that a handful of pins >> when
>> thrown to the floor describes the greek PI letter.
>
>
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
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> tuning-unsubscribe@yahoogroups.com - leave the group.
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>
>
>
>

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> Mario,
>
> Probability is in inherently included in the scientific method. All theoretical models are evaluated based on whether they succeed with greater frequency than random chance (or than a competing model) at fitting established experimental data. To become an accepted theory, a model must fit established data and successfully predict new data points more effectively than random chance or any competing models. In other words, your model needs to be shown to have a higher probability of predicting consonance and dissonance than random chance, as well as a higher probability than any of the competing models (like harmonic entropy, critical band dissonance, Sethares' sensory dissonance model, etc.). If you reject probability out-of-hand, then your model and theory will similarly be rejected out-of-hand by any scientific community. If you refuse to evaluate your model against competing models and/or random chance, then all of your claims about the superiority of your model will appear to any rational human being as "unfounded" and "faith-based", the result of the worst kind of confirmation bias.

I agree with this 100%. (Haha, I love wordplay.)

> Also, your hostile and antagonistic response to those who criticize or challenge your results or ideas is unnecessary and unprofessional. If you cannot communicate with civility, do not expect to be taken seriously.

I wasn't even trying to criticize. I was just asking a question.

I think it's an important question for anyone who wants to compare intervals based on consonance, or compare scales based on the numbers of consonant intervals they have.

All the time people are saying "Look how many consonant intervals this scale has! It's amazing!". But if your definition of "consonant" is, for example, anything within 10 cents of a 13-odd-limit ratio, then already over 60% of intervals fit that criterion. (I just calculated that myself, and I did not, in fact, use the Monte Carlo method. To more decimal places it's 60.483448670%.) Consonance is only a remarkable property if it is sufficiently rare. I was simply wondering how rare Mario Pizarro's consonance property is.

BTW, if anyone does hold the extreme opinion that probability is a useless concept, you can reformulated it as "length of the interval continuum that is covered by consonant intervals" rather than "probability that an interval is consonant". I doubt many people think that the concept of length is useless or suspect...

Keenan

On Mon, Jan 9, 2012 at 3:49 PM, Keenan Pepper <keenanpepper@...> wrote:
>
> All the time people are saying "Look how many consonant intervals this scale has! It's amazing!". But if your definition of "consonant" is, for example, anything within 10 cents of a 13-odd-limit ratio, then already over 60% of intervals fit that criterion. (I just calculated that myself, and I did not, in fact, use the Monte Carlo method. To more decimal places it's 60.483448670%.) Consonance is only a remarkable property if it is sufficiently rare. I was simply wondering how rare Mario Pizarro's consonance property is.

I just want to know which intervals in 12-EDO are consonant, really.

-Mike

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:

> BTW, if anyone does hold the extreme opinion that probability is a useless concept, you can reformulated it as "length of the interval continuum that is covered by consonant intervals" rather than "probability that an interval is consonant". I doubt many people think that the concept of length is useless or suspect...

It's all measure theory anyway from the point of view of pure math. "Probability" is an interpretation.

Hi Mario,

Interesting an engineering degree does not include probability. My degree
in Chemistry required not only using the concepts of probability to compute
the error of analytical measurements and various physical chemical
attributes in p-chem it also included taking probability as a mathematics
course besides - along with algebra, calculus and differential equations.
As I remember probability entered into college level physics too.

Not saying anything bad about your course work - its just interesting to
know the differences.

Have a good day,

Chris

On Mon, Jan 9, 2012 at 3:49 PM, Mario Pizarro <piagui@...> wrote:

> **
>
>
> Igliashon,
> Keenan,
>
> I didn´t explain well my position regarding the study of probability in
> the
> university. In my country we get the diploma of electronic- electrical
> engineer after 5 or 6 years of studies. Along these years we are extremely
> busy with the courses where the course of probability is not included but
> is
> attended in an Institute where graduated EE engineers can continue their
> studies.
>
>