Alfredo:

We may come to a mutual understanding yet!

You posted: “"However, when I did apply iH to Chas theoretical frequencies, the 12ths and 15ths did not beat equally."...

And what happened? Could you tell me more?”

The graphs show what happened. Even though the incremental ratio was greater than 2^1/12, it was not enough to make even the 2:1 partial matches beat wide, let alone the 4:1 partial matches to even be just. Equal beating 12ths and 15th did not happen.

And you posted: “Now you say:..."The desired beatrate is determined, and then the frequencies are calculated. Finally, if wanted, the frequency ratios can be ascertained. But they are a byproduct, not used in the calculations."

This is what I would do in practice too, I'd tune Chas form and then I would ascertain the frequencies values and ratios.”

Now you really have my interest. How did you ascertain the frequency values and ratios? If it was by using the CHAS algorithm, then this shows that the algorithm is inadequate. We have already looked at the results.

As was shown above, the CHAS theoretical frequencies, when iH is applied, do not have the expected results. In fact, even without including iH there is a problem. The CHAS model predicts that the beatrates of the 12ths and 15ths more than double each octave, but how you hear your tuning has all these intervals beating at the same rate.

I believe the truth lies in between. When tuning equal beating 12ths and 15ths the beatrates increase, but less than double each octave, until the high treble is reached when they slow down, and become beatless. I believe the simulation is accurate and this is also similar to what I hear when tuning this way. On the average the beatrate is less than 1 bps.

Alfredo:

My apologies. I miss read ”This is what I would do in practice” as ”This is what I did in practice”.

But you still have my interest! So what would you then do with the frequencies and the ratios?

Tooner,

I hope you’ll still play the Devil’s Advocate, despite our mutual understanding.

We wrote:...“However, when I did apply iH to Chas theoretical frequencies, the 12ths and 15ths did not beat equally....

And what happened? Could you tell me more?

The graphs show what happened. Even though the incremental ratio was greater than 2^1/12, it was not enough to make even the 2:1 partial matches beat wide, let alone the 4:1 partial matches to even be just. Equal beating 12ths and 15th did not happen.”...

Going back to
http://www.box.net/shared/rxb631v2yz

I could again confirm that your ET-EB simulation do make the 2:1 partial matches beat wide. True?

Then you say “Equal beating 12ths and 15th did not happen”, but you have managed to straighten 12ths and 15ths. In my opinion, to get EB 12ths and 15ths you/we may have to adjust iH.

You say:...“The CHAS model predicts that the beatrates of the 12ths and 15ths more than double each octave, but how you hear your tuning has all these intervals beating at the same rate. I believe the truth lies in between. When tuning equal beating 12ths and 15ths the beatrates increase, but less than double each octave, until the high treble is reached when they slow down, and become beatless.”...

What you are saying may well be possible. I can not be 1000 % sure about choromatic equal beating, although I trust my sense of rhythm.

...“I believe the simulation is accurate”...

I think it is accurate only to some extent. Not because of you though.

...“and this is also similar to what I hear when tuning this way.”...

You prove to be a very good Advocate, and surely you are a very good tuner.

...“On the average the beatrate is less than 1 bps.”...

Yes, I'd say between 1/2.5 and 1/3 bps.

...“But you still have my interest! So what would you then do with the frequencies and the ratios?”

I would pass you those values and invite you to point f).

Regards, a.c.

First recording (.rar) of CHAS tuning on a baby Steinway S (5’ 1”, 155 cm) at MediaFire:

http://www.mediafire.com/?sharekey=20194ca8898fecef1bee9a6e9edd9c76e04e75f6e8ebb871

CHAS Tuning MP3 (granpianoman)
http://www.box.net/shared/od0d7506cv

Alfredo:

Have no fear. Even with a mutual understanding on the relationship of frequency ratios, beat rates and inharmonicity there is plenty that we can disagree on.

The next step is to discuss the nature of iH itself. But first, since you and I have different native tongues, allow me to summarize the mutual understanding:

Frequency ratios are useful in predicting beat rates of intervals made from harmonic tones, but are not useful in predicting beat rates of intervals made from inharmonic tones.

Before we continue on the nature of inharmonicity, perhaps you could acknowledge this mutual understanding, just to be sure.

Oh, and if you choose to give me the frequencies of a tuning that produce a certain set of beat rates, please include the inharmonicity so that all other beat rates can be calculated. If the iH is not included, then it would be best to send me the frequencies on very soft paper, so that I could find some use for them�

Tooner,

You let me know about your preferencies in terms of paper and that’s ok, I understand that as being pretty original for you.

Then you say:...“The next step is to discuss the nature of iH itself.”...

For me, the next step is going back to what you/we have already stated. In fact, lots has already been written about the nature of iH and, above all, I would like to pursue my actual aim, I would like to share Chas model as a variant of ET where the octave ratio is something a little bigger than two, in the way we are actually tuning.

You wrote (11/11/09):...“I am not trying to evade your other questions.”...

So, the questions I posted on the 10th and the 12th of November are, in my opinion, quite crucial and may well represent the central issues of this discussion, better than us having different native tongues.

You say:...“Frequency ratios are useful in predicting beat rates of intervals made from harmonic tones, but are not useful in predicting beat rates of intervals made from inharmonic tones. Before we continue on the nature of inharmonicity, perhaps you could acknowledge this mutual understanding, just to be sure.”...

Instead, I think you should explain what you meant when you wrote (06/04/09):..."Because if we take the beat rates (or at least the ratio between beat rates, including equal beating) that are predicted from a frequency ratio (such as 2^1/12) that does not take into account iH, and then tune a piano with iH using the beat rates we end up with a decent tuning, but a different frequency ratio, one that is non-linear. So on the one hand, the frequency ratio is wrong, but on the other, the beat rates are correct. And since when tuning aurally, we listen to beat rates, the model works even though it is incorrect."...

And what you mean when you write (11/13/09)...“The CHAS model predicts that the beatrates of the 12ths and 15ths more than double each octave, but how you hear your tuning has all these intervals beating at the same rate.”...

Now, if frequency ratios are not useful in predicting beat rates of intervals made from inharmonic tones, why do you raise the question for Chas model? And again I ask you: how could you use 12th root of two?

You say:...“I believe the truth lies in between. When tuning equal beating 12ths and 15ths the beatrates increase, but less than double each octave, until the high treble is reached when they slow down, and become beatless.”...

Although I do not know whether you are talking about 12th root of two or what you are referring your "truth" to, I can confirm that, in my tuning form, 12ths and 15ths are opposite equal beating all along the scale. But maybe you have one more model in mind.

I asked you: “Could you also tell me more about that well scaled studio upright? Was it a real piano? Which temperament was used and how? What standard did you smooth the curve by? Do you know the approximation degrees, just to have an idea?

And I would now add a very simple question too: do you realize that, while 12th root of two ratio is a compromise between 3ds and fifths, Chas ratio is a compromise between 3ds, 5ths and octaves?

You asked for a Chas tuning example. Have you heard Granpianoman's MP3 conversion? Then we can talk about iH's effects on small pianos.

Thanks and regards, a.c.

First recording (.rar) of CHAS tuning on a baby Steinway S (5’ 1”, 155 cm) at MediaFire:

http://www.mediafire.com/?sharekey=20194ca8898fecef1bee9a6e9edd9c76e04e75f6e8ebb871

CHAS Tuning MP3 (Granpianoman)
http://www.box.net/shared/od0d7506cv

Alfredo:

Even though it was believed (and apparently still is by you) that octaves on a piano are tuned (aurally) by frequency ratios, this is not true. They are tuned by partial matches. So I just cannot contribute to a discussion about tuning with frequency ratios. I cannot pretend “the earth is flat”.

Ok, on 10 Nov you asked: ”Could you also tell me more about that well scaled studio upright? Was it a real piano? Which temperament was used and how? What standard did you smooth the curve by? Do you know the approximation degrees, just to have an idea?

The model piano is a Charles Walter upright. The length of A0 is 48 inches. A file was generously provided to me that included the frequencies of the partials of an actual tuning. Given the frequencies and the partial numbers, I was able to calculate the inharmonicity for each note, which is affected very little by the actual tuning. Unfortunately, the file included only one partial frequency for the top octave; it takes the frequencies of two partials to calculate iH. Nonlinear extrapolation was used to estimate these iH values. It really does not matter much, since only the first partial is usable in the top octave.

The resulting curve was “V” shaped on a logarithmic graph with the left arm shorter than the right. Also the left arm, being wound strings, was “squiggly”. So by taking the value of iH for note 1, note 88 and the value of the lowest iH with its note number; an idealized “V” could be constructed using logarithmic interpolation. But this would produce an uncharacteristic sharp point to the “V”. By using a computer subroutine, this sharp point was rounded off by using increasing fractions of the slope for the eight notes centered on the point of the “V”.

I am not sure how to explain the approximation degrees in terms that would be valuable. But the purpose of the simulation was to show the general effect of iH on beat rates, and the approximations made this clearer than raw values would. Any piano’s iH values would have shown the same general effect.

The temperament was as equal as I thought practical. I had to start with a slightly wide 15th, calculate what beat rate this would produce in a 12th, and adjust back and forth. When the 3rds and 6ths were progressive, I decided that this was good enough for the simulation.

And on 12 Nov you asked: ” We may as well consider one evidence: 12th root of 2 predicts zero-beating octaves, 7th root of 3/2 predicts zero-beating 5ths, 19th root of 3 predicts zero-beating 12ths. Then I may ask you: when including iH, is it of value to theorize a zero-beating ET incremental ratio? In other words, taking your latest analisys to extremes, can an infinitesimal degree of iH agree with ET theoretical zero-beating choromatic intervals?”

“Then I may ask you: when including iH, is it of value to theorize a zero-beating ET incremental ratio?” My answer is: Yes there is no value. (“Yes, we have no bananas!”) When tones are inharmonic, octaves cannot be zero-beating. If one set of coincident partials are at the same frequency, none of the others will be. At some level the octave always beats, although it may not be noticeable. This is the case regardless of the accuracy of the iH.

Now, I have defined a limit to what I am able to discuss and have answered your outstanding questions. I am going to stop here. I am hoping that you will make shorter posts and try to deal with single subjects.

Tooner, thanks for your answer.

You say:...“Even though it was believed (and apparently still is by you) that octaves on a piano are tuned (aurally) by frequency ratios, this is not true. They are tuned by partial matches.”...

I aurally tune octaves, as well as all other intervals, by beats, like all aural tuners. Beats result from partial matches, so I can not disagree with you.

You write:...“So I just cannot contribute to a discussion about tuning with frequency ratios. I cannot pretend “the earth is flat”.”...

I’m trying to share Chas ET-EB theory because it is an improved ET model, in fact it is the model that can finally compromise all intervals, octaves included, into a beating-whole. And I could tell you about the relevance of a general temperament/tuning theory (11/10/09): “...a correct and reliable temperament theory will address aural tuners towards a practicable and euphonic model...”

Thanks for telling me more about your simulation. From what you say, I understand that there might be a chance to reduce approximations. Anyway, you've done a great job.

You say:...“I am not sure how to explain the approximation degrees in terms that would be valuable. But the purpose of the simulation was to show the general effect of iH on beat rates, and the approximations made this clearer than raw values would. Any piano’s iH values would have shown the same general effect.”...

I agree.

...“The temperament was as equal as I thought practical. I had to start with a slightly wide 15th, calculate what beat rate this would produce in a 12th, and adjust back and forth. When the 3rds and 6ths were progressive, I decided that this was good enough for the simulation.”...

I hope one day we’ll be able to work directly on Chas tuning, that day we’ll also make sure that 4ths, 5ths and octaves are progressive.

I asked you: “...when including iH, is it of value to theorize a zero-beating ET incremental ratio? In other words, taking your latest analisys to extremes, can an infinitesimal degree of iH agree with ET theoretical zero-beating choromatic intervals?”

You answer: “Yes there is no value. (“Yes, we have no bananas!”) When tones are inharmonic, octaves cannot be zero-beating. If one set of coincident partials are at the same frequency, none of the others will be. At some level the octave always beats, although it may not be noticeable. This is the case regardless of the accuracy of the iH.”...

Then you may agree on one issue (I’m asking you): an infinitesimal degree of iH makes any zero-beating theory no value.

...“I am hoping that you will make shorter posts and try to deal with single subjects.”

I’ll shorten. T & R, a.c.

First recording (.rar) of CHAS tuning on a baby Steinway S (5’ 1”, 155 cm) at MediaFire:

http://www.mediafire.com/?sharekey=20194ca8898fecef1bee9a6e9edd9c76e04e75f6e8ebb871

CHAS Tuning MP3 (Granpianoman)
http://www.box.net/shared/od0d7506cv

Alfredo:

You posted: “I’m trying to share Chas ET-EB theory because it is an improved ET model, in fact it is the model that can finally compromise all intervals, octaves included, into a beating-whole. And I could tell you about the relevance of a general temperament/tuning theory (11/10/09): “...a correct and reliable temperament theory will address aural tuners towards a practicable and euphonic model...”

That’s odd. You used the word “compromise.” I remember you taking exception when I described tuning as being about compromises…

You also posted: “Then you may agree on one issue (I’m asking you): an infinitesimal degree of iH makes any zero-beating theory no value.”

Yes, and iH makes other theories invalid (of no value), also. But the word infinitesimal can mean immeasurably or incalculably small, so there is a point when iH can be so small that its effect is negligible. I don’t believe that it is this small on any string of any piano and maybe not on other string instruments either. (There is no doubt in my mind that iH effects the tuning of guitars.)

Tooner and all Colleagues,

Often we read about having to compromise in tuning. I will treasure a concept, recently expressed by an American colleague I hold in high esteem. He makes a distinction between a “compromise” - what for me means “to make the best of a bad job” - and a “superior compromise”, what for all of us may represent an “optimum”. Today I get the chance to briefly write on this, the aim being to show how 12th root of two ET model results as a compromise, while Chas EB variant of ET can represent a superior compromise.

Most of you will know about the commas conflict. Also our practical experience confirms that if we tuned a pure interval all along the scale, this would be to all other intervals detriment and here is where the bottom problem lays.

In tuning - iH tones or non-iH tones - three contiguous pure 3rds will produce a narrow octave; in the opposite way, pure 5ths produce a wide octave. We all can experience the conflict amongst octaves, 3rds and 5ths.

Then, to get a zero-beating octave we have stretched – in theory and in practice - wide 3rds and narrow 5ths. In fact, this is what 12th root of two was meant for: this theoretical model stretches 3rds (wide) and 5ths (narrow) so to get a theoretical 2:1 pure octave. The compromise is then made between two intervals, 3rds and 5ths (considering 4ths as mirror-like 5ths).

Now, say that the octave module is a shelter, and that three 3rds are the three vehicles we room under our shelter. If we wanted to room three longer vehicles, shouldn’t we lengthen our shelter first?

So, considering a single 3rd as the octave’s sub-module, the question may be: Since three contiguous 3rds make an octave and we need to stretch 3rds, shouldn’t we stretch the octave?

As I say, this is where the bottom problem lays, the conflict that theoretical 12th root of two does not resolve in its entirety. This pure-octave ET model uses one single root, i.e. the “root of two”, so making a compromise between 3rds and 5ths, but crushes our choromatic stretched 3rds in an arbitrary 2:1 zero-beating octave. This theoretical, unpracticable and arbitrary constant (zero-beating octaves) has left tuners without a fair scale’s ratio and, above all, without reference. How could we ever go back home without a reference?

Chas ET-EB model, by using the root of 3 and the root of 4, manages to stretch 3rds (wide) and 5ths (narrow) by stretching octaves. Actually, what really happens is that 3rds, 5ths, octaves and all intervals stretch each other in a multiple function. No interval and no ratio are hold dearest, all intervals “compromise” in their own favor and in favor of a sound beating-whole. Our tuning form’s reference can now be double: 12ths and 15ths opposite equal beating in what Chas can describe as the practicable, optimized ET.

T & R, a.c.

First recording (.rar) of CHAS tuning on a baby Steinway S (5’ 1”, 155 cm) at MediaFire:

http://www.mediafire.com/?sharekey=20194ca8898fecef1bee9a6e9edd9c76e04e75f6e8ebb871

CHAS Tuning MP3 (Granpianoman)
http://www.box.net/shared/od0d7506cv

Alfredo:

Very nicely written. Your thoughts came through in an orderly, understandable way. Thank you.

The basis of the 12ths root of two is the idea that this will produce a temperament with all intervals being the same width (have the same frequency ratio), and at the same time octaves that are beatless. This is only possible with harmonic tones.

Keeping the discussion to harmonic tones (for now), the 12th root of any number will produce a temperament with all intervals being the same width. However, unless the number is two, the octaves will beat.

Now to have 12ths beat narrowly and at the same time 15ths beat widely the number has to be larger than 2 but smaller than (3^(1/19))^12 or 2.0014269… The compromise that is given results in equal beating 12ths and 15ths when these intervals have a common note on the bottom.

But it is not clear why this compromise is necessary at all, let alone why a superior compromise results with this sort of equal beating. Not to mention how the roots of any other numbers are needed to calculate this compromise. In fact, they are not needed nor actually used although it could seem that way.

The argument could easily be made that the common note should be on the top, or the 15th should beat faster than the 12ths that has a common note on the bottom, but slower than the 12ths than has a common note on the top. Another argument could be made that if anything should be equal beating, it should be the single octaves beating the same as the 5ths. But then the question again arises as to why, which note should be common, or should they actually beat equally?

Things get difficult when trying to use the 12th root of any number to describe the tuning of inharmonic tones. But rather than go into the difficulties, let’s look at what actually happens when a piano, with inharmonic tones, is tuned.

Oddly enough the tendency when tuning beatless sounding octaves is that the effects of inharmonicity produce narrowly beating 12ths and widely beating 15ths throughout much of the scale. The tuning can be adjusted so that these intervals beat equally in any or all parts of the piano, or unequally in any or all parts of the piano.

This is the true value of these intervals. They are a tool that the tuner can use to make compromises that are more important than arbitrarily equal beating intervals. They can be used to make and define compromises between melodic, harmonic and musical priorities in the tuning.

Tooner, this is not very short, I must apologize.

...“The basis of the 12ths root of two is the idea that this will produce a temperament with all intervals being the same width (have the same frequency ratio),”...

Maybe you meant “semitones being the same width”. Yes. Like for any geometric progression’s term, the semitones do have the same incremental ratio but, if we were to make a staircase, each frequency value could give us the step’s depth, or lenth, and each step would proportionally differ from the next one.

...“and at the same time octaves that are beatless.”...

Yes, and this is one of The Problems. A theoretical beatless octave is a wrong assumption, although 300 years ago it was in line with the common approach to temperament theories.

You say:...“This is only possible with harmonic tones.”...

Not true. You say that also with iH tones, on single partial matchings, we may go for beatless octaves. In any case, this is only temporarly and apparently true, any beatless interval will end up beating in a beat-flow. This is not to be understood, this is to be acknowledged or, once you acknowledge it you may understand.

...“Keeping the discussion to harmonic tones (for now), the 12th root of any number will produce a temperament with all intervals being the same width. However, unless the number is two, the octaves will beat.”...

Not correct. Like any interval, octaves will beat anyway, since 12 root of two is only an abstract case. Also “purely harmonic tones” is abstract thinking, the "pure" attraction again, it is forcing an abstract zero-iH concept into a model.

...“Now to have 12ths beat narrowly and at the same time 15ths beat widely the number has to be larger than 2 but smaller than ((3^(1/19))^12 or 2.0014269…”...

Correct.

...“The compromise that is given results in equal beating 12ths and 15ths when these intervals have a common note on the bottom.”...

If you approach the scale in terms of mirror-like order, you will not need to discriminate between top and bottom anymore.

...“But it is not clear why this compromise is necessary at all,”...

I wrote about this in my previous post. This compromise is necessary in that all intervals, with their stretch, can now contribute to the tonicity of the tuning form.

...“let alone why a superior compromise results with this sort of equal beating.”...

Opposite equal beating 12ths and 15ths results in a superior compromise for three reasons: firstly because it involves all intervals, wich are now beating intervals; secondly because the set gains stability by opposing a constant counter-beat, so all intervals compromise now for determining a perfectly stable, counter-balanced beating-whole; thirdly because the 15th encloses two octaves, what is needed to gain and ensure the intermodular quality. So, from one zero-beating octave block we progress to a two octaves beating matrix.

...“Not to mention how the roots of any other numbers are needed to calculate this compromise. In fact, they are not needed nor actually used although it could seem that way.”...

Please argue this last statement and be aware that you are getting into maths details, so before I answer please confirm you will not regret.

...“The argument could easily be made that the common note should be on the top,”...

No need. Anyway, show me please how you’d build a house starting from the roof, then I’ll follow you.

...“or the 15th should beat faster than the 12ths that has a common note on the bottom, but slower than the 12ths than has a common note on the top.”...

Ok, we both may be keen on break-dance, but this is not the place.

...“Another argument could be made that if anything should be equal beating, it should be the single octaves beating the same as the 5ths. But then the question again arises as to why, which note should be common, or should they actually beat equally?...

You try then: tune EB 5ths and octaves and then tell me how you like it. If you really like it, you can still refer to Chas algorithm:

((3/2) – Δ)^(1/7) = (2 + (Δ*s))^(1/12)

s = 1

Δ = 0.001178134272…

Scale ratio = 1.05951508823057…

...“Things get difficult when trying to use the 12th root of any number to describe the tuning of inharmonic tones.”...

Thinks get difficult only if or when you expect to find the theoretical frequencies values on iH tones. As for describing, Chas model is derived from a precise beats order and therefore can faithfully describe our actual tuning.

...“The tuning can be adjusted so that these intervals (12ths and 15ths) beat equally in any or all parts of the piano, or unequally in any or all parts of the piano. This is the true value of these intervals. They are a tool that the tuner can use to make compromises that are more important than arbitrarily equal beating intervals.”...

I hope you can better understand now the value of EB-ET and why it results in a superior compromise.

And do not worry, there will always be room for melodic, harmonic and musical priorities. Instead of calling it compromise, we'll call it knowledge.

T & R, a.c.

First recording (.rar) of CHAS tuning on a baby Steinway S (5’ 1”, 155 cm) at MediaFire:

http://www.mediafire.com/?sharekey=20194ca8898fecef1bee9a6e9edd9c76e04e75f6e8ebb871

CHAS Tuning MP3 (Granpianoman)
http://www.box.net/shared/od0d7506cv

Alfredo:

So, you see the problem of equal beating octaves and 5ths as one of ascetics, that it would not sound good. But the advantage of equal beating 12ths and 15ths is that it makes a wonderful mathematical model! They both make a wonderful mathematical model, and they both can be ascetically pleasing.

But we have a bigger problem. We continue to be unable to have a productive discussion about frequency ratios, beat rates and inharmonicity. We do not agree on the same concepts. I guess I will try again.

If the semitone interval is equal (frequency ratio is equal) then all interval ratios will also be equal.

If inharmonic tones are used, and an octave partial match is tuned to be beatless for all octaves (or tuned for equal beating intervals), the semitone intervals will not be equal.

I hoped that the simulations would make these concepts clear to you. Apparently they did not.

There is another concept that we disagree on. You do not understand that beat rates are generally progressive. There can be no “mirror image.” If a 12th and 15th beat equally with the bottom being common, the 12th that is a 4th higher will have a different beat rate.

Yes, I could show you the mathematics to calculate the frequency ratio to produce equally beating 12ths and 15ths with the common note on top. But instead, let me show you a way to tune them aurally starting with any 4th. Use the example of G3-G5 15th and C4-G5 12th. We will use D#3 as a test note. This test note is used for its 5th partial which is G5 and need not be tuned precisely, only so that it produces a beat at a useable speed. G3 and C4 have already been tuned. The 12th and 15th will beat equally when the difference in beat rate between the D#3-G3 M3 and the D#3-G5 M17 has the same difference as between the D#3-C4 M6 and the D#3-G5 M17. You may want to try this test on one of your tunings to see whether your 12ths and 15ths beat as you think they do.

I am tempted to discuss your CHAS algorithm on purely mathematical terms if we can agree to limit the discussion to just the mathematics involved and not the (mis)use in tuning. But I am not sure you understand what happens with your algorithm to begin with. For instance, in the equal beating 5ths and octave calculation you obtained a delta of 0.001178134272… Do you realize that by simply adding 2 to this number, you have the octave ratio? And this octave ratio is larger than 2 but smaller than (3^(1/19))^12 or 2.0014269… and therefore will produce wide 15ths and narrow 12ths? It is not far at all from equal beating 12ths and 15ths. This small difference would probably not be discernable.

…this is only temporarily and apparently true…

Truth has a life span?

…any beatless interval will end up beating in a beat-flow…

If an interval doesn’t beat when you want it to, it just beats in a beat-flow? Like an alternative universe?

… This is not to be understood, this is to be acknowledged or, once you acknowledge it you may understand...

You are asking me to believe by faith so that I may then have an experience in order to believe this greater truth through the experience. Sorry, I do not mix religion and piano tuning.

I am wondering why I should take you seriously at all. You may be convinced of what you say or you may be knowingly misleading. (I continue to debate this with myself…) Either way it does not form a train of logic. I am going to rethink continuing this discussion with you. I may decide that it cannot be constructive.

Tooner,

On my part there is no interest in talking about ascetics, nor about philosophy or religion, but about Chas EB-ET as an improved temperament model. So far I’ve tried to explain what a model is generally meant for, how Chas comes from my practice and why ET equal beating 12ths and 15ths can be a solid and reliable reference.

I understand that you would like a model for piano tuning, a different one for pipe organs, one for guitars and, why not, one for bagpipes. I’m sorry, I can not help you.

I do not doubt about the well known iH’s effects on actual frequencies and ratios but aural tuning is about beat-control, and it is about a beat form that we – aural tuners – can possibly find again and again, no matter the usual iH's degrees. This is what I’m saying, maybe this is what Bill says talking about EBVT and his tunings, this may be what other tuners have been and are talking about when it comes to aural tuning and temperament models.

In my opinion, how you keep on mixing aural beat-control and accuracy with iH, actual frequencies values, actual ratios, ETDs issues, piano imperfections, compromises, pinblocks, rendering points and passing thunderstorms does not help you either. Above all, it does not help young people who are approaching aural tuning, people that may like to refer to the most correct and practicable model (Chas or whatever), people that do not need to be pushed towards second-rate standards.

What I think is that our different pro experiences have matured us into different tuners with two quite opposite approaches.

To a novice you choose to say “A piano being an imperfect instrument cannot be tuned perfectly. So I try to tune pianos perfectly out-of-tune”…, I’d say: I know I’m not perfect, so I tune pianos at my best. You say “at a certain point it actually sounds worse and worse to me”…, I’d say: point after point, it has to sound right. You say “The fine little imperfections come out and all I end up doing is trying to make things sound less bad”…, I’d say: I tend to refine any little imperfection and all I keep on doing is trying to make things sound at their best. You say “And then when it is played by someone else, it sounds wonderful”…, I’d say: And then when it is played by someone else, I hope he/she’ll like it too.

You ask for short posts and single subjects, so I shall stop here. But this time, I’d like to tell you more about aural tuning, maths, undiscernible small differencies, knowingly misleading ghosts, trains of logic and constructive discussions, and I shortly will. Many scaring pop-ups on Chas tuning MP3?

R, a.c.

First recording (.rar) of CHAS tuning on a baby Steinway S (5’ 1”, 155 cm) at MediaFire:

http://www.mediafire.com/?sharekey=20194ca8898fecef1bee9a6e9edd9c76e04e75f6e8ebb871

CHAS Tuning MP3 (Granpianoman)
http://www.box.net/shared/od0d7506cv

You meant "aesthetics"?

Yes, aesthetics is what I meant. A spell checker thing. It did seem odd that there was not a "h". But now I know a new word!

Really!?!?!?

The Chas model predicts 12ths and 15ths with a beat rate that doubles about every octave. You say your actual tuning does not. The simulations that I provided do not. So, the Chas model does not faithfully describe actual tuning.

What I continue to wonder is if you conveniently forget this fact or just hope that everyone else will.

Kent,

Thank you for checking. Not only there was the "h", but also the random t and e.

Tooner,

I wrote “describe”.

I didn’t write: you can use theoretical values on pianos, or for amateur simulations. What’s wrong with you? Do you still want to talk about having to apply iH on theoretical values?

Recently you wrote:...“The CHAS model predicts that the beatrates of the 12ths and 15ths more than double each octave, but how you hear your tuning has all these intervals beating at the same rate. I believe the truth lies in between. When tuning equal beating 12ths and 15ths the beatrates increase, but less than double each octave, until the high treble is reached when they slow down, and become beatless.”...

My reply: Although I do not know whether you are talking about 12th root of two or what you are referring your "truth" to, I can confirm that, in my tuning form, 12ths and 15ths are opposite equal beating all along the scale. But maybe you have one more model in mind.

More recently you wrote:...“For instance, in the equal beating 5ths and octave calculation you obtained a delta of 0.001178134272...Do you realize that by simply adding 2 to this number, you have the octave ratio? And this octave ratio is larger than 2 but smaller than (3^(1/19))^12 or 2.0014269… and therefore will produce wide 15ths and narrow 12ths? It is not far at all from equal beating 12ths and 15ths.”...

So you say “Do you realize...It is not far at all from equal beating 12ths and 15ths.”

Tooner, what can I tell you? Only what I’ve already told you: one minute you state in a sense, the minute after you negate it. To me, you may be raving on everything and its opposite.

Still today 12th root of two describes our world-wide tunings, and 19th root of three could then describe pure 12ths tuning. Maybe you prefere the way 12th root of two describes equal temperament or, refusing Chas, you may prefere ET 19th root of three, this is up to you and I will not blame you.

...“What I continue to wonder is if you conveniently forget this fact or just hope that everyone else will.”

I conveniently stick to practical Chas tuning and I have academic theoretical reasons and evidencies for hoping to share Chas EB-ET model.

R. a.c.

First recording (.rar) of CHAS tuning on a baby Steinway S (5’ 1”, 155 cm) at MediaFire:

http://www.mediafire.com/?sharekey=20194ca8898fecef1bee9a6e9edd9c76e04e75f6e8ebb871

CHAS Tuning MP3 (Granpianoman)
http://www.box.net/shared/od0d7506cv

As measured in cents, in your "tuning form", how expanded is the double-octave (in cents) and how contracted is the twelfth (in cents)?

Alfredo:

It probably seems that I am being contradictory because you do not understand the concepts that I am talking about. And I am unable to explain them to you.

After today I doubt that I will be posting for close to two weeks. Besides Thanksgiving, I will be at deer camp. When I get back I probably will not post on this Topic anymore. I don’t see how it can be productive.

Kent,

You ask: “As measured in cents, in your "tuning form", how expanded is the double-octave (in cents) and how contracted is the twelfth (in cents)?”

You may be talking about actual pitches, i.e. real Chas tuning frequencies. If it is so, I have not been able to elaborate on them, since I do not have any adequate device.

By using the conversion program linked here:

http://www.sengpielaudio.com/calculator-centsratio.htm

I have been able to elaborate only on theoretical Chas values, so I could calculate theoretical Chas semitone’s cents value = 100.0383184402... - with quite little approx., around the 10th decimal point - and the offset in cents from A4 (440 Hz) to A6. Let me know if those figures can be of some use.

I would be very happy to be able to make all sorts of measuring on the real Chas tuning form.

Tooner,

What I have understood is that, basing on iH issues, you may like a different model for every musical instrument that produces iH tones. Or maybe a specific model for pianos.

In my opinion, we can do well with tuning, both in aural and ETDs cases, referring to 12th root of two ET model, although we could never tune its pure octaves. Now we have a chance to do even better with a reliable and practicable ET model and its two tuneable constants for reference, equal beating 12ths and 15ths.

I’ll be looking forward to hearing from you and don’t think about productivity, it is more than that, it’s breathing.

Have a good time.

Regards, a.c.

First recording (.rar) of CHAS tuning on a baby Steinway S (5’ 1”, 155 cm) at MediaFire:

http://www.mediafire.com/?sharekey=20194ca8898fecef1bee9a6e9edd9c76e04e75f6e8ebb871

CHAS Tuning MP3 (Granpianoman)
http://www.box.net/shared/od0d7506cv
_________________________

Alfredo:

I can hardly even breathe. The air is so foul.

But let me try to give you and Kent a helping hand while I hold my breath.

Take the cent value of 100.0383184402. This means that each semitone is 0.0383184402 wider than theoretical. So multiplying this by 24 gives the cent deviation for 15ths and by 19 gives the cents deviation for 12ths. Rounding off, makes the 15ths 1 cent wider than theoretical and the 12ths ¾ cent wider than theoretical.

For iH tones rather than measure the deviation from theoretical, it is better to measure it from beatless intervals. This will be about 1 cent wide for 15ths and about 2 minus ¾ or 1-1/4 cents narrow from just for 12ths.

For practical, aural tuning this will change the M3-M17 4:1 15th test so that the M17 should beat as fast as the M3 one semitone higher than the test. And will change the M6-M17 3:1 12th test so that the M17 should beat as fast as the M6 one semitone lower. Or to be even more practical, with the common note on top, the M17 should beat faster than the M3, but slower than the M6. I do not think there is any practical difference between Chas and mindless octaves.

Does that mean you are going to a stag party?

In a way, but it certainly is not the stag's idea of a good time.

Be sure to bring along the correct supplies, so you can demonstrate to the to the new guy how you can tell that a deer was there by using your sense of taste!

My favorite gag is shoving a dead mouse in the toe of someone's boot. Well, I think its funny.

The other one is the fake phone on the wall. Pick it up, you get a dial tone. Dial any muber and 10 seconds later you get a busy signal. Of course the closest phone line is miles away. Designed and made the circuits myself.

Hey, careful, or we'll have another thread devolving into an "OT Paging Jerry Groot"-fest, lol.

I thought it already had!

Not even close, that one went by the 1600-post mark a while ago!

Oh, for a few minutes it was like being at a party.

Tooner, it'll be nice if you come back with some antlers pictures. a.c.