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I feel the fundation of my central octaves is based on a 2:1 and 4/2 relation, then the 6/3 is added ant I feel it as parasitic to the cleanless of my fundation, so I am not allowing the 12th to sound too much present, most often.

If you manipulate the tuning lever slow enough, you can hear the partials flowing and coupling together as a rainbow, with sort of flute/piccolo effect.

The same process can be used within unisons

Kamin:

I assume you are talking about concert grands. Do you mean to say that your central octaves are between 4:2 and 6:3? And do you mean by "not allowing the 12th to sound too much present" that your 12ths are virtually pure?

I believe these two things go together with large grands. Is that what you believe, also?

Here is some real-world data based off of two master tunings that have been used at our exam center in Tacoma Wa. The piano is a Steinway B.

In a master tuning, the notes A3 and A4 are recorded at A5. The difference in cents will refer to the size of the 4:2 octave.

Example 1: A3 = +1.8 cents. A4= =1.1 cents. difference = -.7 cents. In this master tuning the A3/A4 octave is a 4:2 octave narrow by .7 cents.

Example 2: A3 = +0.7 cents. A4 = +1.0 cents. difference = +.3 cents. In this master tuning the A3/A4 octave is a 4:2 octave wide by .3 cents.

In my opinion .3 cents is at the threshold of being a non-difference in practical terms. Often, pure sounding unisons may still measure up to .3 cents off. Just moving an ETD from one location to another can easily result in a .3 cents difference. So, a 4:2 Octave that is .3 cents wide is virtually pure.

Keep in mind that both tunings were performed by concert level technicians who spent over 3 hours nit picking the tuning before making the measurements.

Granted, 2 examples are not a large enough sample to extrapolate to the rest of the PTG. It would be interesting to average the master tuning data collected from around the country and get an average of the A3-A4 octave size. Then your claim about 4:2+ might hold up.

Ryan:

By any chance were D3 and A5 also recorded at A5? Then we could know about how the 12th and 15th turned out.

Jeff,

Yes they are. D3 shows -1.5 cents read at octave 5(D5). A5 shows +3.2
The other example shows D3 at -1.2 and A5 at +3.4.

I'd be curious to know how you would interpret this information.

Hello, No I am unsure I talk of concert grands, also this will depend of the brand hence scaling.

I just wanted to say I focus on the consonance at the upper note level, and the 3d partial is there in "extra" it can be allowed to sing more or less, but generally less.

But I agree on vertical pianos and on pianos with large iH the 6d and 3th partials are more present in the medium octaves.

I wonder how much the other partials influence our perception of beat acceleration when comparing 3d and tenth, and 17th etc.

I dont believe I aim for a pure twelve as a final result, the max consonant spot being at a slightly broke 12th (then the consonance begin to be clean/>cold then acid)

Of course unisons, can always "temper" a tuning, I belive that when tuining unisons I probably modify the final pitch perceived, pushing the envelope in the direction I feel it sound better with the bottom note(s).

For my central octaves I refer much to the slow beating intervals to confirm my octave, then the fast beating have to be in an accepeteable range of "known" speeds, and progressive.

Not being too much nit picky in the temperament zone allow to stay quiet, corrections can be added later.
I hate for instance spending time to get perfect notes one after the other, to discover in the end that the bridge have moved a little and all my notes are constrained within the octave (what may happen if more than a few cts are to be added or if the precendent tuning was done in the opposite season.

Before I used ETD I was always aiming for a final pitch different of the one I tuned initially, now I try to have that pitch fall in place by itself, which is effective up to some point.

I am happy to see that the partial match rules are not applied as intensively they may seem originally.

Without doubting of the effectiveness of the different checks relating to partial matches, I feel that way of tuning may push the ear to focus too much on one partial relation, then possibly the ear discriminates too much.

That is funny as experienced tuners tend to agree that they mostly focus on having a quiet ear, and follow their instinct, using checks in case of doubt essentially.

I have tuned in front of tuners and musicians, that where surprised that with so little checks and tuning mostly octaves, the consistency of FBI was attained. (when tuning fast, a doubt is cleared by playing a tenth or a 17 th without any comparison with other intervals, eventually a contiguous one)

Possibly in the octave I perceive how the rest of the piano is exited by my octave, this sensation occur only when the mediums of the piano begin to be in tune, but I seem to rely on it (similar as when tuning high treble if you see what I mean)

I chase for that sensation until I perceive it, as I said generally when 2 octaves and a half are tuned , unison wise, then I may apply some corrections to my central string eventually.

The basses are a different story, but with low medium and top basses well in line, the rest fall in place often naturally (strange BTW to notice that M3 conbtinue to be progressive, down and down, on indeed a good enough piano just sticking to a resonant spot and checking/avoiding too fast 6th.

The unison bring a "material" (tone) but it is based and enhanced bu the level of consonance of the tuning at large.

The tuning with ETD (mostly good pianos) for some years learned me to follow a very slow progression, stick to a tone, I have find myself with the ETD in loss of batteries and producing the same tuning than with it, so a tuning/ a tone is something a tuner learn in his ears and brain, most probably.

Some B211 can be tuned with really 2:1 type octaves in the mediums, the ones with a warm tone there ask for such treatment (and there are often very slow M3 near the break.

A more clear sounding B will accept more enlarged octaves so to hide the beat at the higher partials level.

Sure! I'll do what I can. I was really hoping for a reading on the third partial of D3, though. That, along with the first partial of A5 A4 would indicate whether the D3-A5 D3-A4 12th was wide or narrow or pure.

Example A:

A3-A4 4:2 octave is narrow at ½ bps.
A4-A5 2:1 octave is wide at 1 bps
A3-A5 4:1 double octave is wide at 1 bps

Example B:

A3-A4 4:2 octave is virtually pure
A4-A5 2:1 octave is wide at 1 bps
A3-A5 4:1 double octave is wide at 1&1/2 bps

As far as D3, being read at D5, at first glance it seems that it would be a tuning error. Extrapolating the cent values of A3, A4 and A5 (measured at A5) you would expect the cent values of D3 (measured at D5) to be at least zero, if not positive. But since this anomaly is present in both tunings, and they are both “master tunings” then scaling comes into question.

I do not have an iH curve in my database application for an S&S B, but there is a graphic one on the pscale site:



D3 is note #30. On the graphic it is just to the right of the “knee” of the iH curve. But of course the S&S B that the cent readings were taken from might be scaled differently. And also, depending on what priorities were used in tuning across the break, another tuner might place D3 differently.

Not to get off the subject, but it makes me wonder about the master tuning and the PTG exam. The master tuning might make adjustments to D3 when listening across the break, below C3, while this note would be judged before anything below C3 was tuned and no such adjustment would be made. Hmmm…

Jeff, here's something that may either clear or muddy up the waters...

These are tuning targets generated by the Verituner for 3 Steinway Bs. Of interest is not the placement of the targets, rather the relationships between the partials of each note, where you should be able to determine the range of inharmonicity for each measured string. Since this is software based measuring, there is a trade off between speed of measuring and accuracy. This makes it hard to determine if the differences between similar pianos is due to measurement variations, or actual differences between pianos...

Anyway, I thought it might be of some value to you. Verituner doesn't generate a value for the fundamental, or 1st partial of D3 - so partials 2-6 are notated. The three pianos - older one I couldn't find a serial number, then 431230 and 431570. All used the same calculation parameters for octave width(s). This would be easier in spreadsheet form, but here goes!

Piano 1
D3 none, -3.27, -2.46, -1.24, -.55, .38
A3 -2.88, -2.22, -1.3, .59, 2.08, 4.48
A4 0.00, 1.30, 5.13, 9.76
E5 1.06, 4.13, 9.6, 17.13
A5 3.32, 8.26, 16.67, 27.77

431230
D3 none, -3.55, -3.14, -2.14, -1.41, -.38
A3 -2.56, -1.33, -1.02, -.12, 1.81, 3.72
A4 0.00, .87, 4.41, 10.0
E5 .57, 3.03, 8.75, 16.63
A5 4.43, 6.86, 17.74, 29.74

431570
D3 none, -3.07, -1.66, -.75, .01, 1.19
A3 -2.29, -2.33, -.28, -.96, 2.21, 4.85
A4 0.00, 1.42, 4.97, 9.83
E5 .64, 2.96, 8.71, 16.13
A5 3.7, 8.04, 17.03, 29.33

Ron Koval

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

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

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.

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)?

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.

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.

Question:

Answer:

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)

That's a 4:2+

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..