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#2008973 - 01/04/13 02:12 PM Re: Clean Sounding/Beatless Octaves [Re: Mark Davis]
RonTuner Offline
1000 Post Club Member

Registered: 01/21/04
Posts: 1618
Loc: Chicagoland
That's just my default custom stretch for Steinways - It's all user-variable, so I could customize one to fit Ryan's example too... These were saved files from a few years ago. As I've thought more about ETD tuning, I've become more careful about what I let the machine measure - seeing as so much is riding on the data that it collects!

Instead of "pure" anything, I'm more going for a balance of the two twelfths with the single and/or double octaves to set the middle framework - (D3-A4/A3-A4) (A3-E5/A3-A4), A3-A4-A5, which may lead to a different stretch than the RPT test master tuning.

Ron Koval
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@ronkoval

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#2008978 - 01/04/13 02:19 PM Re: Clean Sounding/Beatless Octaves [Re: Mark Davis]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4908
Loc: Bradford County, PA
Thanks, Ron:

I may crunch the numbers another day to extract the iH. When A4 is at 0.0 cents and the third partial of D3 is at -1.95 cents then the D3-A4 12th is pure (as you know). Your examples are all close to that value and would sound virtually pure.

Ryan's examples are similar, so I would expect that they would also have virtually pure 12ths.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#2008987 - 01/04/13 02:38 PM Re: Clean Sounding/Beatless Octaves [Re: Mark Davis]
Withindale Offline
1000 Post Club Member

Registered: 02/09/11
Posts: 1918
Loc: Suffolk, England
Jeff

When you are crunching the numbers are you able to see why your pure 12ths rule applies? Why does the stretch of the 12th tend to be the same as the inharmonicity of a note's third partial?

It's sort of obvious that it might be but the real figures in your database are needed to prove the point.
_________________________
Ian Russell
Schiedmayer & Soehne, 1925 Model 14, 55" upright
Ibach, 1922 49" upright (project piano)

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#2009386 - 01/05/13 10:51 AM Re: Clean Sounding/Beatless Octaves [Re: UnrightTooner]
Mark Cerisano, RPT Offline
1000 Post Club Member

Registered: 01/24/10
Posts: 1065
Loc: Montreal, Quebec, Canada
Originally Posted By: UnrightTooner
Originally Posted By: Mark Cerisano, RPT
Originally Posted By: UnrightTooner


I continue to disagree but will chime in anyway smile. Stacked 4:2 octaves will ALWAYS produce wide double octaves. The smaller the piano, the wider the double octaves. And they SHOULD be slightly wide. On large grands, between 4:2 and 6:3 is appropriate in the midrange. On studio sized pianos, 4:2 is more appropriate to avoid double octaves that beat too much. And for spinets and most consoles, octaves between 2:1 and 4:2 are best. Interestingly these stretch schemes naturally happen with pure 12ths.



That is not my experience. Let's see if we can agree on some things and work from there.

First, let's define some things to make discussion simpler.
Let's define an octave that is tuned between a 4:2 and a 6:3 as a 4:2+, meaning slightly wider than a 4:2, but narrower than a 6:3.

Do you agree that a 4:2+ octave produces:

very wide 2:1
wide 4:2
narrow 6:3
very narrow 8:4

where the term "very" is used to indicate only slightly more wide or narrow than just the term wide or narrow.



Sure, we can agree that a wide 4:2 produces a wider 2:1 (measured in cents) and a narrow 6:3 produces a narrower 8:4 (again, measured in cents). Whether the term VERY wide or VERY narrow is appropriate is really up to interpretation. On a concert grand there is much less difference between octave types than on a spinet.

If we can agree that the difference in octave types is dependent on iH (the size of the piano) then we can continue our discussion to include the effect of the octave type and iH on the double octave.


Hi again Jeff,

I have read the posts concerning the ETD measurements of different master tunings and Steinway scales, etc. I see some conclusions as to octave sizes based on those measurements. I have to caution about using the ETD and making assumptions from its measurements because, as I understand it, the ETD measures the inharmonicity of a sample of strings, approximates a stretch curve from that, then measures the strings you are tuning by listening to a single partial. My understanding is that some partials are easier for the ETD to hear, that is why it changes which partial it listens to. (Notice how the partial listened to goes higher as the note you are tuning gets lower.) Then of course, it changes the offset it wants you tune tune to, so the whole string is still tuned where the ETD thinks it should go. This is the problem. We do not listen to a single partial when tuning. (Yes, when we use checks we do, but only in an attempt to get a best sound from the whole octave; i.e. we always listen as a whole as well. We know that is the key to using an ETD and getting a great tuning. Anyway...)
Also, we cannot make conclusions as to the octave size if the actual partial measurements are not at the partials we are concerned with. (I think you were able in a few examples, but not all.) And finally, the stretch offsets can't be related to each other unless they are all at the same partial; they will jump around and not be continuous.

Anyway, since you agree with me in the octave qualities of a 4:2+, then we can move on. I also agree with you that the difference of the qualities is less on a large piano with low IH.

I want to also add that the inharmonicity in the mid-range up to the high treble, increases at an even pace. This, someone (you?) showed very nicely by posting an image of Tremane's graph for scaling. (I actually used that once to scale my own treble strings by hand. Very nice.) Notice the straight line band that the IH should fit into. Also, some measurements, offered by someone, of offset show this nicely too, as the upper partials are getting more and more sharp, the higher they go.

So, evenly increasing IH, sharper partials as you go up. This is a linear relationship that produces (should produce) an even relationship to each of the higher partials. Assuming that the higher partials are sharper by an even amount at each partial, then we can begin to imagine a uniform relationship to each partial where each higher partial is sharper by the same amount, or if that amount is increasing, it is increasing by the same amount.

Also, to help this point, consider the formula for IH and frequency:

F(n) = Fn(1+Bn^2)^0.5

where 
B is the IH coefficient
n is the partial number
F(n) is the frequency of the nth partial
F is the frequency of the fundamental

Consider some typical example:
B = 0.0002
F = 100

and this graph of n versus F(n) is produced:

http://mrtuner.com/Partial_Frequency.bmp

So, do you agree that, for an octave with a given IH, the upper partials' frequencies are evenly increasing (not the same difference, but evenly increasing differences), and that each octave has a similar relationship, with each higher octave interval having a higher IH by an evenly increasing amount (given by Tremane's graph)?



Edited by Mark Cerisano, RPT (01/05/13 11:01 AM)
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Mark Cerisano, RPT
www.howtotunepianos.com

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#2009409 - 01/05/13 11:38 AM Re: Clean Sounding/Beatless Octaves [Re: Mark Davis]
Mark Cerisano, RPT Offline
1000 Post Club Member

Registered: 01/24/10
Posts: 1065
Loc: Montreal, Quebec, Canada
I realize that the graph is not clear because, while the line looks straight, actually, it is not. But after regressing the data twice, by taking the difference of the difference, I got to a linear relationship. The point I am trying to make for us to agree on, is that each higher partial frequency increases in some uniform way, not haphazardly up and down.
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#2009717 - 01/05/13 09:10 PM Re: Clean Sounding/Beatless Octaves [Re: Mark Davis]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4908
Loc: Bradford County, PA
Mark:

No, nothing is linear. Everything is closer to being logarithmic. Frequencies and beatrates double about every octave. IH doubles about every eight semitones on a concert grand and about every 12 semitones on spinets. Graphs can show straight lines, but that is because the scale on the graph is logarithmic.

But, yes, the partials are not haphazard, otherwise it would be like tuning a dime store Ukelele! But then sometimes the partials of bass strings can be haphazard, and so too can the scaling across a break.


Edited by UnrightTooner (01/05/13 09:12 PM)
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#2009902 - 01/06/13 09:05 AM Re: Clean Sounding/Beatless Octaves [Re: Withindale]
Withindale Offline
1000 Post Club Member

Registered: 02/09/11
Posts: 1918
Loc: Suffolk, England
Question:
Originally Posted By: Withindale
Why does the stretch of the 12th tend to be the same as the inharmonicity of a note's third partial?

Answer:
Originally Posted By: UnrightTooner
Everything is closer to being logarithmic. Frequencies and beatrates double about every octave. IH doubles about every eight semitones on a concert grand and about every 12 semitones on spinets.
_________________________
Ian Russell
Schiedmayer & Soehne, 1925 Model 14, 55" upright
Ibach, 1922 49" upright (project piano)

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#2009974 - 01/06/13 12:35 PM Re: Clean Sounding/Beatless Octaves [Re: Mark Davis]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7178
Loc: France
Hello, On pianos with very low IH, (verticals or grands) tuning with octaves enlarged raise the speed of the 6th and the 17th to the point the piano get too clear and a little noisy.

That said it is relatively difficult to fight our natural ten,dency to push the enveloppe unltil it is really necessary.

About "pure" intervals, tempered 12 th sound almost pure, clean, and what is really noticed is when the 12ths or the 5ths are too large.

I just tuned avertical Hoffman (1991, original Langlau factory)

These pianos have a very clear tone, when you find such instruments you can suspect low iH.

I believe I tuned most of the center octaves in 2:1, and, BTW the 2:1 was really similar to 4:2 , I felt really no need to have the 4:2 relation emphased, on that piano A few checks provided me a slighly fatser 10th than the M3 may be 1 beats for 4 or 5 seconds more anyway not somethiong that can be counted and appreciated seriously (not as when you add 1/2 or 1/3 beats second.

WHat is perceived when raising in the treble, but also in the mediums, is the difference in resonance a new note tuned with an octave provide ;, I believe the resonance is due to the longer strings that react to any exitation.

I really could detect notes that where a little low, or too high, only because they did not p)roduce the same enveloppe when played with the octave, and eventually alone.

Then, sticking to the piano resonance is absolutely not a proof of justness, but for sure it is a big help, and it is very precise , way more I am suspecting usually (on a low iH piano anyway)
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Isaac OLEG - http://picasaweb.google.fr/PianoOleg pro

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#2010006 - 01/06/13 01:44 PM Re: Clean Sounding/Beatless Octaves [Re: Olek]
Mark Cerisano, RPT Offline
1000 Post Club Member

Registered: 01/24/10
Posts: 1065
Loc: Montreal, Quebec, Canada
Originally Posted By: Kamin

A few checks provided me a slighly fatser 10th than the M3


That's a 4:2+
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Mark Cerisano, RPT
www.howtotunepianos.com

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#2010075 - 01/06/13 02:58 PM Re: Clean Sounding/Beatless Octaves [Re: Mark Davis]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7178
Loc: France
Sure Mark but I am not focusing on that, the speed between M3 and M10 could be the same or approx.

Anyway I find it very uneasy to compare the speed of different intervals, at last when you compare neighbors you can focus for the speed at the same moment in time. The acceleration and slowing of those FBI make them uneasy to compare if they are not the same.

I suggest that if we wait for the beats to be quiet enough to be counted more or less precisely, it is yet late in time, the speed is changing in time due to the waving motion, the fluctuations of volume, that make those beats difficult to count precisely.

Because of that I also believe that the tuner tend to suggest himself that the beats difference is what he want to hear, when we are in so little differences plus intervals difference (that is one of the first training of the tuner to recognize the acceleration between M3 and M10, but in the end it is not precise..



Edited by Kamin (01/06/13 02:59 PM)
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#2010125 - 01/06/13 04:30 PM Re: Clean Sounding/Beatless Octaves [Re: Olek]
Mark Cerisano, RPT Offline
1000 Post Club Member

Registered: 01/24/10
Posts: 1065
Loc: Montreal, Quebec, Canada
Hi Isaac,

I appreciate your comments and I think we may be able to see eye to eye.

Originally Posted By: Kamin
Sure Mark but I am not focusing on that, the speed between M3 and M10 could be the same or approx.

You say you are not focusing on it but you mention it in your last post. The fact that you can easily determine the speeds as M3<M10, that is what you say clearly, means they are 4:2+. There is no question. Not same or approximate, clearly you say faster.

Originally Posted By: Kamin

Anyway I find it very uneasy to compare the speed of different intervals, at last when you compare neighbors you can focus for the speed at the same moment in time. The acceleration and slowing of those FBI make them uneasy to compare if they are not the same.


Since I like to use checks, I do not have the same problem; I can easily hear very small differences in speeds; I listen for tone, not actual beat speeds. I use the attack of the note, where the beats are most prominent, as you have often suggested, and I make my assessment in a fraction of a second; no time to accel or decell.

Originally Posted By: Kamin

I suggest that if we wait for the beats to be quiet enough to be counted more or less precisely, it is yet late in time, the speed is changing in time due to the waving motion, the fluctuations of volume, that make those beats difficult to count precisely.

Most heartily agree. One must make assessment quickly, and not compare beat speeds, but tonal difference. E.g. faster beating intervals have a brighter tone for me, so I compare tone.

Originally Posted By: Kamin

Because of that I also believe that the tuner tend to suggest himself that the beats difference is what he want to hear, when we are in so little differences plus intervals difference (that is one of the first training of the tuner to recognize the acceleration between M3 and M10, but in the end it is not precise..

Again agree. That is why I use multiple checks including open interval tuning, whole interval tuning. I often catch my own mistakes. But in the end I always must use 4:2+ or I cannot tune all intervals clean. I am currently discussing with Mark Davis and hope to prove this point theoretically, and then I will post recordings on different pianos. Wish me luck. I suggest those who use 2:1+ (on large grands) may be tuning 4:2+ as well.


Edited by Mark Cerisano, RPT (01/06/13 04:31 PM)
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Mark Cerisano, RPT
www.howtotunepianos.com

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#2010151 - 01/06/13 05:08 PM Re: Clean Sounding/Beatless Octaves [Re: Mark Davis]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7178
Loc: France
"Most heartily agree. One must make assessment quickly, and not compare beat speeds, but tonal difference. E.g. faster beating intervals have a brighter tone for me, so I compare tone."


Yes that's how it happens, I agree.

WHat IO state is that I dont allow my ears to focus on the 4:2 relation if this is not what the piano want as a final result. That said, we may remind that once the unison is tuned the final pitch is changing, most often for the lower, so sticking on the 4:2+ is certainly more secure than trying to attain an open 2:1 octave immediately.

In the end of the tuning, or when in small corrections, it is often unnecessary to change the pitch of the 3 strings to correct a 10th that is a little slow (hence an octave a tad compacted)

As I tune by strip muting on a large medium portion of the scale, I am obliged to enlarge a bit, despite that I keep the 23:1 resonance as my goal, may be if I follow the 4:2 this will tend to enlarge my octaves more when I'll be in the 5 th octave..

Possibly using the 2:1 is not so different in the end, simply it allow to work on the resonance level immediately in the tuning, while when tuning by FBI, the tuning is clean of course but we pay less attention to the octaves than we could.

Learning to tune with octaves beating slowly (as 1 for 5 sec) is an excellent exercise. the beat is primarily at 2:1, it helps to master all the beats at slow level.

I really agree that the beats of FBI are recognized in a pinch, that is what was unnerving me with the ETD, giving the impression I was waiting for the machine (as you dont move the pitch if you want a clear display)

Of course beats are not "counted" we learn to count ta stack of M3 when learning to tune, or to recognize the "movment" sensation provided by a correctly set M3 . Then, depending of the scale and the voicing, the speed sensation can differ a lot so hopefully slow beating intervals are also used.

I have seen also pianos tuned with some perfect FBI speed and progression, but without particular attention to the octaves nor 5ths. The evenness of progression of the FBI provided a very playable scheme, the piano did sound absolutely just and tuned, simply little of the own personality of the instrument is used then, it sound like those transparent papers that can be used to see thru... if you see what I mean.
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Isaac OLEG - http://picasaweb.google.fr/PianoOleg pro

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#2010313 - 01/06/13 11:23 PM Re: Clean Sounding/Beatless Octaves [Re: Olek]
Mark Cerisano, RPT Offline
1000 Post Club Member

Registered: 01/24/10
Posts: 1065
Loc: Montreal, Quebec, Canada
Originally Posted By: Kamin

That said, we may remind that once the unison is tuned the final pitch is changing, most often for the lower, so sticking on the 4:2+ is certainly more secure than trying to attain an open 2:1 octave immediately.

In the end of the tuning, or when in small corrections, it is often unnecessary to change the pitch of the 3 strings to correct a 10th that is a little slow (hence an octave a tad compacted)

As I tune by strip muting on a large medium portion of the scale, I am obliged to enlarge a bit, despite that I keep the 23:1 resonance as my goal, may be if I follow the 4:2 this will tend to enlarge my octaves more when I'll be in the 5 th octave..


I tune with open double unisons, no mute strip, for this reason. The unisons have already settled by the time I am listening to them. But this topic may require a new thread. I am not ready for that yet.
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Mark Cerisano, RPT
www.howtotunepianos.com

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#2010315 - 01/06/13 11:30 PM Re: Clean Sounding/Beatless Octaves [Re: Mark Cerisano, RPT]
Mark Cerisano, RPT Offline
1000 Post Club Member

Registered: 01/24/10
Posts: 1065
Loc: Montreal, Quebec, Canada
Originally Posted By: Mark Cerisano, RPT
I am currently discussing with Mark Davis and hope to prove this point theoretically, and then I will post recordings on different pianos. Wish me luck. I suggest those who use 2:1+ (on large grands) may be tuning 4:2+ as well.


The theoretical discussion is also with Jeff Deutschle, not just Mark Davis.
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Mark Cerisano, RPT
www.howtotunepianos.com

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#2010332 - 01/07/13 12:00 AM Re: Clean Sounding/Beatless Octaves [Re: Mark Cerisano, RPT]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1651
Loc: Vancouver, Canada
Originally Posted By: Mark Cerisano, RPT


Anyway, no matter which way you cut it, Reblitz lists the highest P5 in the temperament octave as beating faster than the lowest P4, so your critique is way off.

For Pete's sake, the P4 beats (approx.) 1bps while the P5 beats once in 4 seconds, that's 0.25 bps. That's a huge difference, mathematically and aurally. Sorry, your critique doesn't pass the mustard.

I usually pass gas instead of mustard, but here's the page from Reblitz. As you can see, the lowest P4 and highest P5 both beat at 0.79 according to Reblitz.

Kees

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#2010354 - 01/07/13 01:16 AM Re: Clean Sounding/Beatless Octaves [Re: DoelKees]
Mark Cerisano, RPT Offline
1000 Post Club Member

Registered: 01/24/10
Posts: 1065
Loc: Montreal, Quebec, Canada
Originally Posted By: DoelKees
Originally Posted By: Mark Cerisano, RPT


Anyway, no matter which way you cut it, Reblitz lists the highest P5 in the temperament octave as beating faster than the lowest P4, so your critique is way off.

For Pete's sake, the P4 beats (approx.) 1bps while the P5 beats once in 4 seconds, that's 0.25 bps. That's a huge difference, mathematically and aurally. Sorry, your critique doesn't pass the mustard.

I usually pass gas instead of mustard, but here's the page from Reblitz. As you can see, the lowest P4 and highest P5 both beat at 0.79 according to Reblitz.

Kees


Busted. I realized I had made that mistake when I saw the Wikipedia link but I never got around to correcting it. Thanks for bringing it up. However, the logic still applies because the Reblitz and Wikipedia both are listing theoretical data for a piano with 0 iH, no stretch. I have stated that I believe the stretch is taken up mostly by the fourth in reality. I stand by my claim that 4:2+ octaves in the mid and high range are superior but I am open to criticism. This is my experience with every piano I tune, no matter what the size. I am still trying to prove the theory.
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Mark Cerisano, RPT
www.howtotunepianos.com

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#2010417 - 01/07/13 06:00 AM Re: Clean Sounding/Beatless Octaves [Re: Mark Cerisano, RPT]
Olek Offline
7000 Post Club Member

Registered: 03/14/08
Posts: 7178
Loc: France
Originally Posted By: Mark Cerisano, RPT
Originally Posted By: Kamin

That said, we may remind that once the unison is tuned the final pitch is changing, most often for the lower, so sticking on the 4:2+ is certainly more secure than trying to attain an open 2:1 octave immediately.

In the end of the tuning, or when in small corrections, it is often unnecessary to change the pitch of the 3 strings to correct a 10th that is a little slow (hence an octave a tad compacted)

As I tune by strip muting on a large medium portion of the scale, I am obliged to enlarge a bit, despite that I keep the 23:1 resonance as my goal, may be if I follow the 4:2 this will tend to enlarge my octaves more when I'll be in the 5 th octave..


I tune with open double unisons, no mute strip, for this reason. The unisons have already settled by the time I am listening to them. But this topic may require a new thread. I am not ready for that yet.


I follow the same logic/principle ( 2 strings unison minimally necessary to know/hear the final pitch of a note) , but I am more at ease with the strip, as I said final corrections can be done most often without changing the center wire.



Edited by Kamin (01/07/13 06:08 AM)
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Isaac OLEG - http://picasaweb.google.fr/PianoOleg pro

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#2010447 - 01/07/13 07:13 AM Re: Clean Sounding/Beatless Octaves [Re: Mark Cerisano, RPT]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4908
Loc: Bradford County, PA
Originally Posted By: Mark Cerisano, RPT
Originally Posted By: DoelKees
Originally Posted By: Mark Cerisano, RPT


Anyway, no matter which way you cut it, Reblitz lists the highest P5 in the temperament octave as beating faster than the lowest P4, so your critique is way off.

For Pete's sake, the P4 beats (approx.) 1bps while the P5 beats once in 4 seconds, that's 0.25 bps. That's a huge difference, mathematically and aurally. Sorry, your critique doesn't pass the mustard.

I usually pass gas instead of mustard, but here's the page from Reblitz. As you can see, the lowest P4 and highest P5 both beat at 0.79 according to Reblitz.

Kees


Busted. I realized I had made that mistake when I saw the Wikipedia link but I never got around to correcting it. Thanks for bringing it up. However, the logic still applies because the Reblitz and Wikipedia both are listing theoretical data for a piano with 0 iH, no stretch. I have stated that I believe the stretch is taken up mostly by the fourth in reality. I stand by my claim that 4:2+ octaves in the mid and high range are superior but I am open to criticism. This is my experience with every piano I tune, no matter what the size. I am still trying to prove the theory.


Mark:

No big deal as far as I am concerned. It was just an error, a "brain-fart". It is all part of exploring a subject.

OK, you are trying to prove a theory: 4:2+ octaves in the mid and high range are superior. Starting with a clean slate, how do you intend to prove it?
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#2010451 - 01/07/13 07:21 AM Re: Clean Sounding/Beatless Octaves [Re: Withindale]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4908
Loc: Bradford County, PA
Originally Posted By: Withindale
Question:
Originally Posted By: Withindale
Why does the stretch of the 12th tend to be the same as the inharmonicity of a note's third partial?

Answer:
Originally Posted By: UnrightTooner
Everything is closer to being logarithmic. Frequencies and beatrates double about every octave. IH doubles about every eight semitones on a concert grand and about every 12 semitones on spinets.


Please do not try to put answers into my mouth. Your comparison is like apples and oranges.

I am gong to be brutally honest. I have noticed that you will hop from one side of a discussion to another just to try to get an argument started or to keep it going. For that reason I will not give you an answer. I am not interested in playing games.

It is sad, because I have much to say on the subject, and much to ask. It is not something I understand completely. If someone else starts a serious inquiry, preferable by starting a new Topic about the effect of iH and stretch on the relationship of different beatrates, I will enthusiastically join in.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#2010453 - 01/07/13 07:28 AM Re: Clean Sounding/Beatless Octaves [Re: Mark Cerisano, RPT]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4908
Loc: Bradford County, PA
Originally Posted By: Mark Cerisano, RPT
Originally Posted By: Mark Cerisano, RPT
I am currently discussing with Mark Davis and hope to prove this point theoretically, and then I will post recordings on different pianos. Wish me luck. I suggest those who use 2:1+ (on large grands) may be tuning 4:2+ as well.


The theoretical discussion is also with Jeff Deutschle, not just Mark Davis.


Thank you, Mark.

I suspect Isaac is right. The difference between aa A3-A4 2:1 octave and a 4:2 octave on a concert grand is only about one cent, or 1/4 bps. Delibrately tuning a wide 2:1 could easily result in a wide 4:2.
_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#2010471 - 01/07/13 08:31 AM Re: Clean Sounding/Beatless Octaves [Re: UnrightTooner]
Withindale Offline
1000 Post Club Member

Registered: 02/09/11
Posts: 1918
Loc: Suffolk, England
Originally Posted By: UnrightTooner
Please do not try to put answers into my mouth. Your comparison is like apples and oranges.

I am gong to be brutally honest. I have noticed that you will hop from one side of a discussion to another just to try to get an argument started or to keep it going. For that reason I will not give you an answer. I am not interested in playing games.

Jeff

We are at cross purposes again.

I asked because I was interested.

The logarithmic nature of iH, its doubling every octave or thereabouts, is what you need to know to show that the stretch of the 12th tends to be the same as the inharmonicity of a note's third partial.

You assumed I was playing games, loading the dice, on a previous occasion. I was not, and am not, but I let it rest.

I very much doubt that I hop from one side of a discussion to another for the sake of it. People take me to task for being too single minded in pursuit of an argument.

It's true I have kept the odd discussion going. Have you ever done such a thing? What is wrong with that in a forum anyway, interesting things often emerge.

No doubt I have sometimes misunderstood where you were coming from, as they say, but I am not so sure I'm alone in that.

I will leave beat rates to you and Mark but perhaps I'll ask a question about the effect of the relative strength of partials on tuning one day.


Edited by Withindale (01/08/13 06:22 AM)
Edit Reason: Quote
_________________________
Ian Russell
Schiedmayer & Soehne, 1925 Model 14, 55" upright
Ibach, 1922 49" upright (project piano)

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#2010525 - 01/07/13 10:39 AM Re: Clean Sounding/Beatless Octaves [Re: UnrightTooner]
Mark Cerisano, RPT Offline
1000 Post Club Member

Registered: 01/24/10
Posts: 1065
Loc: Montreal, Quebec, Canada
Originally Posted By: UnrightTooner
OK, you are trying to prove a theory: 4:2+ octaves in the mid and high range are superior. Starting with a clean slate, how do you intend to prove it?


Well, we have agreed that a 4:2+ octave produces:

2:1 wider (instead of very wide)
4:2 wide
6:3 narrow
8:4 narrower

and that the 2:1 and the 8:4 beat at a similar speed,
and the 4:2 and the 6:3 beat at a similar speed.

Right?

Also, you have agreed that the higher partial frequencies are increasing in difference from the theoretical, the higher up we go on any one string (from the formula) and that iH increases uniformly for the mid and high treble (from Tremane's graph).

Are we good so far?


Edited by Mark Cerisano, RPT (01/07/13 10:40 AM)
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Mark Cerisano, RPT
www.howtotunepianos.com

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#2010558 - 01/07/13 12:00 PM Re: Clean Sounding/Beatless Octaves [Re: Mark Cerisano, RPT]
UnrightTooner Offline
4000 Post Club Member

Registered: 11/13/08
Posts: 4908
Loc: Bradford County, PA
Originally Posted By: Mark Cerisano, RPT
Originally Posted By: UnrightTooner
OK, you are trying to prove a theory: 4:2+ octaves in the mid and high range are superior. Starting with a clean slate, how do you intend to prove it?


Well, we have agreed that a 4:2+ octave produces:

2:1 wider (instead of very wide)
4:2 wide
6:3 narrow
8:4 narrower

and that the 2:1 and the 8:4 beat at a similar speed,
and the 4:2 and the 6:3 beat at a similar speed.

Right?

Also, you have agreed that the higher partial frequencies are increasing in difference from the theoretical, the higher up we go on any one string (from the formula) and that iH increases uniformly for the mid and high treble (from Tremane's graph).

Are we good so far?


Are we good so far? Partly yes. The part that is no you should find useful in your proof, although in the end I think it is a matter of priority and preference.

According to Young's paper: http://www.afn.org/~afn49304/youngnew.htm the amount that any given partial is higher in cents than the theoretical frequency equals the string's iH in cents times the square of the partial number. Now according to emperical measurement, this is only approximate. But rather than resort to tabular values, as Mr. Scott's Tunelab program does (the tabular values can be found in the online manual), let's just use Young's equations for discussion.

When including the effects of iH when calculating beatrates of an interval we must remember that the first partial is also affected. This is discussed in the paper. Also remember that iH is different for each note and in a well scaled piano will be mostly logarithmic.

All that said, if you "crunch the numbers" for an octave where the 4:2 partial match beats wide at the same speed as the 6:3 partial match beats narrow, the 2:1 partial match will also beat at this exact same speed. The 8:4 partial match beats much faster, however.

So I disagree "... that the 2:1 and the 8:4 beat at a similar speed, and the 4:2 and the 6:3 beat at a similar speed." Actually the 2:1, 4:2 and 6:3 beat at a similar speed. The 8:4 beats much faster. But let's remember that the cents that an interval is wide or narrow is another thing altogether. (I have mentioned this before.)

So, Mark, you haven't mentioned how you might decide to try to "prove" that 4:2+ octaves are superior. If you were to say that your proof would be that there is a "masking effect" you would have a good point. But you should "crunch the numbers yourself." smile

_________________________
Jeff Deutschle
Part-Time Tuner
Who taught the first chicken how to peck?

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#2010701 - 01/07/13 04:49 PM Re: Clean Sounding/Beatless Octaves [Re: Mark Davis]
Mark Davis Offline
500 Post Club Member

Registered: 04/10/08
Posts: 658
Originally Posted By: Mark Cerisano, RPT
I'll send a video. Wish me luck. But even with a video, if you are focusing your hearing on the partials, you will hear a slow beat. You should be listening to the "whole octave sound" as Virgil Smith encouraged, listening more like a musician, less like a piano technician. Maybe it is an aural illusion, but one that I definitely hear and use to tune octaves, without the need to use checks.


Originally Posted By: Mark Cerisano, RPT
Again agree. That is why I use multiple checks including open interval tuning, whole interval tuning. I often catch my own mistakes. But in the end I always must use 4:2+ or I cannot tune all intervals clean. I am currently discussing with Mark Davis and hope to prove this point theoretically, and then I will post recordings on different pianos. Wish me luck. I suggest those who use 2:1+ (on large grands) may be tuning 4:2+ as well.


Mark, unfortunenately you seem to make a lot of contradicting statements as you go along, choosing to pretend and forget what you have said. I have found this throughout your writings.

I am not really sure what your whole argument is about and what you are trying to prove?

You have been threatening to post a video on many occasion and for sometime now. I think you should either just stop saying you are going to do it or just get on and post it/do it.

I tried your test m6=M17 and found it to be invalid in the middle and treble of the piano. What part of the scale are you using this check? BTW, I do use the M6/M17 check and clearly hear it.
_________________________
Mark Davis
Piano Tuner & Technician

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#2010758 - 01/07/13 05:23 PM Re: Clean Sounding/Beatless Octaves [Re: Mark Davis]
Mark Cerisano, RPT Offline
1000 Post Club Member

Registered: 01/24/10
Posts: 1065
Loc: Montreal, Quebec, Canada
Hi Mark,

Sorry for your frustration. Hopefully I can clarify for you.

Yes I said

Originally Posted By: Mark Cerisano, RPT
Maybe it is an aural illusion, but one that I definitely hear and use to tune octaves, without the need to use checks.


and

Originally Posted By: Mark Cerisano, RPT
Again agree. That is why I use multiple checks including open interval tuning, whole interval tuning.


But I didn't say I don't use checks. I said I can tune octaves "without the need to use checks". I just am more consistent with the checks.

Originally Posted By: Mark Davis

Mark, unfortunenately you seem to make a lot of contradicting statements as you go along, choosing to pretend and forget what you have said. I have found this throughout your writings.


I think I have shown that you are making assumptions about my writings and that I am not contradicting or choosing to pretend and forget. What I do know is that it is easy to become quite frustrated when someone is trying to tell you something that you don't agree with.

As I see it, you have three choices when someone is trying to convince you of something you do not agree with:

1) Ignore them and consider them to be clueless and off track with their theories. (I'm not opposed to that)

2) Consider the topic beyond your comprehension at the moment and choose to revisit it later.

3) Make a serious effort to figure out what they are talking about. (And in the process you will find holes in their argument and that will help them patch those holes and understand their own principles better. That's the thesis process.)

I hope you choose 3)

Originally Posted By: Mark Davis

I am not really sure what your whole argument is about and what you are trying to prove?


Simple, that the 4:2+ octave is superior for a fine tuning in the mid to high treble. (4:2+ being between a 4:2 and a 6:3)

Originally Posted By: Mark Davis

You have been threatening to post a video on many occasion and for sometime now. I think you should either just stop saying you are going to do it or just get on and post it/do it.


Sorry. I have some recordings but it takes time. I do have another life. I want to wait for the recordings until Jeff and I have finished our conversation.

Originally Posted By: Mark Davis

I tried your test m6=M17 and found it to be invalid in the middle and treble of the piano. What part of the scale are you using this check? BTW, I do use the M6/M17 check and clearly hear it.


Are you using the m6 BELOW the check note, for the triple octave test?
Also, I didn't say it was easy. It is difficult to compare these fast beating intervals. You must listen for tone, and match that. You can also play all three notes together and listen for beating of the beats (wah-Wah-WAh-WAH-WAh-Wah-wah-Wah...) If you hear that, they are NOT equal.

The range is starting at F3F6, and then I use it as I am going down from F3. E.g. E3E6, D#3D#6, etc, until the break. But lately I have been able to get it to work past the break.

I use the M6M17 test too and started using it about 5 years ago. Then, as I stretched out my hearing and tried to get better double octaves, etc, I was drawn to temper the 12ths by an amount that produced better double octaves and pure triple octaves. (They are probably not pure; who can really tell at those speeds? But I can hear when they are not close enough and a re-listening of the other related intervals usually smokes out a drifter/error.)
_________________________
Mark Cerisano, RPT
www.howtotunepianos.com

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#2010824 - 01/07/13 08:10 PM Re: Clean Sounding/Beatless Octaves [Re: Mark Davis]
Mark Davis Offline
500 Post Club Member

Registered: 04/10/08
Posts: 658
Originally Posted By: Mark Cerisano, RPT
Hi Mark, I think I have shown that you are making assumptions about my writings and that I am not contradicting or choosing to pretend and forget. What I do know is that it is easy to become quite frustrated when someone is trying to tell you something that you don't agree with.


Mark, here you go again. Where do you get that I am frustrated?
I may dislike certain traits of yours but I am certainly not frustrated.

Originally Posted By: Mark Cerisano, RPT
As I see it, you have three choices when someone is trying to convince you of something you do not agree with:

1) Ignore them and consider them to be clueless and off track with their theories. (I'm not opposed to that)


I do not consider you clueless at all. Though I do not agree with you on everything you have said and do not like your manner in most, if not all your posts.

Originally Posted By: Mark Cerisano, RPT
2) Consider the topic beyond your comprehension at the moment and choose to revisit it later.


What topic are you speaking about here? Your superior 4:2+ octave size?

Originally Posted By: Mark Cerisano, RPT
3) Make a serious effort to figure out what they are talking about. (And in the process you will find holes in their argument and that will help them patch those holes and understand their own principles better. That's the thesis process.)

I hope you choose 3)


Where to from here Mark? I know the 4:2 narrow, just and wide octave and tests. I tune 4:2 just and 4:2+ octaves for my temperament and treble. So what would you like me to say? That you are right that the 4:2+ octave in the middle of the piano is superior because you say so?

I would have you to re-read Ryan Sowers fine post!

Originally Posted By: rysowers
Originally Posted By: Mark

I have been tuning for 13 years, teaching tuning for 7 and am a mechanical engineer. I think I know what I'm talking about. It appears your constant opposition to my teachings show your lack of openness. How can you go against the largest and most respected piano technology association in the world (PTG) when they state the proper size of the octave in the midrange is 4:2+.

Mark, 13 years is a modest amount of experience in this field. I've been at it for 20 and am discovering new things about tuning every year. That's part of the fun of this business. I suspect in 5 years you may look back at your old thinking at realize that you didn't have it all figured out. At least that's what should happen to an open minded student of the craft.

I'm not sure what mechanical engineering has to do with teaching tuning. Maybe you can clarify that statement.

I would be careful using the PTG as an authority on tuning. The standard that the PTG promotes and tests for is a minimal standard. A tuner has to work within a 1 cent tolerance relative to the "Master Tuning" in the middle two octaves in both temperament and unisons to get a perfect score. The tolerances increase until they are at 6 cents for the lowest and highest octaves. In fact, in one case I observed an examinee get a very poor score on the temperament, (under 60 percent) yet passed the high treble with very high scores (over 90 percent). He was good at tuning octaves! As he progressed up the scale the tolerances became wide enough to give him better scores.

In PTG literature you will find differing opinions among experts. I do not believe that PTG as an organization has an "official" stand on what the right octave size is.





Edited by Mark Davis (01/07/13 08:17 PM)
Edit Reason: minor correction
_________________________
Mark Davis
Piano Tuner & Technician

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#2010868 - 01/07/13 09:40 PM Re: Clean Sounding/Beatless Octaves [Re: UnrightTooner]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1651
Loc: Vancouver, Canada
Originally Posted By: UnrightTooner
if you "crunch the numbers" for an octave where the 4:2 partial match beats wide at the same speed as the 6:3 partial match beats narrow, the 2:1 partial match will also beat at this exact same speed.

Could you please demonstrate this surprising (and not well-known) fact?

If not I will, but I learned this from you...

Kees

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#2010869 - 01/07/13 09:42 PM Re: Clean Sounding/Beatless Octaves [Re: Mark Davis]
Mark Cerisano, RPT Offline
1000 Post Club Member

Registered: 01/24/10
Posts: 1065
Loc: Montreal, Quebec, Canada
Mark, I do not like the tone of your posts. They are verging on an attack of my personality and I believe that is against the forum rules.

My reason for continuing these posts is to prove "my superior 4:2+ octaves" But, they are not just mine. Read what you posted by Bill Bremmer:

Originally Posted By: Mark Davis quoting Bill Bremmer

In other words, the test for a 4:2 octave should reveal a slightly faster F3-A4 M10 than F3-A3 M3 and the test for a 6:3 octave should reveal a slightly slower C4-A4 M6 than A3-C4 m3. When you have found the spot for A3 which reveals this slight discrepancy between the 4:2 and 6:3 tests, you will hear that the A3-A4 octave has a very slow beat to it, about one beat in every two seconds. This is now considered the optimum width for the initial A3-A4 octave in Equal Temperament and what is used by
most CTE’s to set up the Master Tuning for the Tuning Exam.


That's the 4:2+.

So, if you want to know why it is superior, keep reading the posts. Otherwise, stop attacking me please.


Edited by Mark Cerisano, RPT (01/07/13 09:52 PM)
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Mark Cerisano, RPT
www.howtotunepianos.com

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#2010878 - 01/07/13 10:04 PM Re: Clean Sounding/Beatless Octaves [Re: Mark Cerisano, RPT]
DoelKees Offline
1000 Post Club Member

Registered: 05/01/10
Posts: 1651
Loc: Vancouver, Canada
Originally Posted By: Mark Cerisano, RPT
Mark, I do not like the tone of your posts. They are verging on an attack of my personality and I believe that is against the forum rules.

People get upset when you mention 13 y experience and having a degree in Mechanical Engineering to support your arguments, that's all. I've got similar reactions when mentioning my PhD.

I think Jeff hit the nail on the theoretical mustard with the observation about the 2:1, 4:2, and 6:3 beatrates being equal when tuning equal beating 6:3/4:2 octaves in the mid-upper range. Something like killing 3 birds with one stone. This may be the reason for the 4:2+ being the best.

Of course, the proof is in the mustard. smile


Kees

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#2010948 - 01/08/13 01:46 AM Re: Clean Sounding/Beatless Octaves [Re: Mark Davis]
Mark Cerisano, RPT Offline
1000 Post Club Member

Registered: 01/24/10
Posts: 1065
Loc: Montreal, Quebec, Canada
Ok, so I finally managed to upload a video of a piano I tuned with pure triple octaves using the P4 window and the pure triple octave test.

Please be kind. It took me over an hour to upload and add subtitles. The piano was not a good one and it was a pitch raise, so there is a mis-matched bichord and some unison drifting. But before the drift, I thought it sounded pretty good.

I just put my phone face down on the piano, so you don't see anything, and I didn't talk because I was tuning at a customer's home. I think the subtitles make it easier to listen and appreciate.

Note: You have to turn on the subtitles to read what's going on.

http://www.youtube.com/watch?v=9Eci3cwlVEM



Edited by Mark Cerisano, RPT (01/08/13 01:47 AM)
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Mark Cerisano, RPT
www.howtotunepianos.com

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