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Thanks for continuing to update.

Looking forward to testing. I did notice today that the note switching was odd - even on "off", it was jumping notes and when I went to chromatic up or down it still wanted to jump away from the note I was playing. When using full auto note switching, it worked better. There was some kind of background 'hum' in the room that might have been interfering.

Kimball console - 100-150 cents flat (It's been my week for these...) I greatly enjoy the "play the notes" for the pitch raise parameters. Easy to play, then use the slider to put it on the right note. Thanks for that!

The top stretched higher than I like in the last octave or so. I do know that many of these Kimball pianos have high inharmonicity, (difficult scales at the best of times) so trying to match the wider intervals will often leave the upper notes strident when octaves are played. I've seen all the custom stretch parameters, but didn't play with them at the piano - perhaps just pulling down the extra treble stretch slider would've been enough.

Ron Koval

Sorry for this. I introduced a regression with the last build. It should be fixed again with build 499.


You're welcome. It was your idea


I would like to analyze this. Do you still have the pianoscope tuning document? If so, please send it to support@pianoscope.app .

I have just released build 499 with a handful of new features for configuring the look and behaviour of the tuning view.

- You can now set the strobe contrast to "very high".
- There is a new contour setting for the strobe. With it you can replace the blurry edges of the strobe with a sharp contour.
- You can now define activation thresholds for the line indicator and the strobe in the settings. With them you can for example show the strobe only when you are less than 5 cents from the tuning target and the indicator otherwise.
- There is a new setting to always hide the scale, or to dynamically only show it if the line indicator is visible.
- There is a new setting to hide the keyboard.
- The keyboard can be toggled by double-tapping on the red note name label.

I also updated the manual to describe the new options.
I hope these new features help you all to configure pianoscope to your needs.

Done.

The treble ended up with around 55 cents offset for C. I preferred it around 40, but lowered pitches starting around G6 or so to get there? It could just be personal preference, I tend to aim for "sweeter" rather than "sparkle" up there...

Ron Koval

Looking back at the file this morning, I realize I didn't take full inharmonicity readings in the treble - maybe that had something to do with it?

Ron Koval

Frank - another idea for a small improvement.

If you're in the mode where the partials display is on, but the keyboard is off, often times the partials don't show up because there's an implicit assumption that the keyboard would be there aligned with the display where it was last put. This means that sometimes no partials show - you have to scroll the invisible keyboard until you're in the right range. It would be good if the 1st partial could automatically be left-aligned so you don't have to scroll to find them.

Paul.

Paul, actually I regard it as a bug, that the partials area is not hidden together with the keyboard view, as the keyboard is the main pitch reference for it. I fixed this in the latest build 522. If you really need the partials indicator without the keyboard, I can rethink this.

I have just released build 522 of pianoscope with the following changes:

- Attack detection in the high treble should now be more reliable.
- You can now manually switch notes in tuning view via the keyboard or swiping while a tone is sounding. The view will now adjust accordingly.
- The automatic note selection in the inharmonicity view now allows to easily re-measure consecutive notes without having to delete all measurements.

Please let me know if you should encounter any regressions in the note detection.

The other day, a beta tester sent me an interesting question via e-mail. He asked whether it is necessary to re-measure the inharmonicity for fine tuning after pitch raising a piano that was 20 cents flat. As I haven't made any measurements yet on the relation between string tension and inharmonicity, I have tried to derive an answer from theory. I find the result quite interesting, so I want to share it with you. The deduction is using some math. I hope this doesn't scare anyone away.


The Fletcher model describes inharmonicity as:

B = Pi^2 * Q * S * K^2 / (T * l^2)

Q being the Young's modulus of the string, S its cross sectional area, K the gyration radius, T the string tension and l its length.
For a single string, we can simply pack most string parameters into a single constant C and only keep the tension T. Then we get

B = C / T

The fundamental frequency f of a string can be described by:

f = (1/(2 * l)) * sqrt(T/mu)

With l again being string length and mu being the linear string density. We again combine some parameters into another constant D and get.

f = D sqrt(T)

When we combine both equations by eliminating the tension T, we get:

B = C / (f^2 * D^2)

If we now raise the frequency by c cents, we get a new frequency f':

f' = f * 2^(c/1200)

With this we also get a new inharmonicity:

B' = C / (f'^2 * D^2) = C / (f^2 * 2^(c/600) * D^2) = B / 2^(c/600)

This is our result:

B' / B = 2^(-c/600)

If you raise a string by c cents, you will change the inharmonicity by a factor of 2^(-c/600)

So lets put some numbers into this formula:

For a 20 cents raise, we get a factor of 0.98 or a decrease of 2% in inharmonicity.
For a 50 cents raise, we get a factor of 0.94 or a decrease or 6% in inharmonicity.
For a 100 cents raise, we get a factor of 0.89 or a decrease of 11% in inharmonicity.
For a 200 cents raise, we get a factor of 0.79 or a decrease of 21% in inharmonicity.

In the interesting region, the formula is actually nearly linear.

So we can easily estimate the inharmonicity change with ~ -1% per every 10 cents of pitch raise.

The measurement error of pianoscope for inharmonicities is about 2-3%, especially when measuring unmuted unisons. So one could see a small effect when remeasuring after a pitch raise of 20 cents, but most of it will be within the margin of error. For larger pitch raises >50 cents however, I would recommend to remeasure the inharmonicity before a fine tuning pass if one wants to get the best result.

I hope I correctly deduced this result. If you spot an error or if this result contradicts your experience please let me know.

Great analysis! I would add that, continuing to use Fletcher's model, the shifts in the harmonic frequencies vary with the square root of the inharmonicity B. Specifically, Fn = n*F0*sqrt(1+B*n^2) where n is the harmonic number (1,2,3,..), F0 is the fundamental frequency, and Fn is the frequency of the nth harmonic. So an error of 6% in the inharmonicity constant B would only translate into a 3% error in the calculated harmonic frequencies. I don't have data to back this up, but I suspect that errors due to pianos not conforming exactly to Fletcher's model would be more significant than this.

I don't think that is quite right. The formula quoted shows the frequency varies with the square root of (1+B*n^2). The thing under that square root is not proportional to B because of the "1+..". The formula I am familiar with is that

log2(Fn/(n*F0)) = 1200*B*n^2

which implies

Fn/(n*F0) = 2^(1200*B*n^2)

For typical small values of B, this differs from 1.000 by an amount that is approximately proportional to B.

But I too am very interested to hear the results of empirical studies on how a pitch raise affects inharmonicity.

You're right. Looking at it again, I think I should have used the "binomial approximation" where sqrt(1+B*n^2) ≈ 1+(B*n^2)/2. (That only works if B*n^2 is small compared to 1, which is usually true.) Oddly the error still gets halved.


I'm not familiar with that formula but it's very suggestive of working in cents rather than frequency. I just spent 10 minutes trying to get from Fletcher's formula to this one, but it's too late at night for that right now.

Target is indicated under the red note symbol. In the settings, you can choose to display in hertz, cents, hertz along with cents. It would be nice to add the ability to completely disable information in this block, add the None item in the settings. It makes no sense to make the adjustment scale from -100 cents to +100 cents, quite enough from -50 to +50. A scale of -50 to +50 increases the sensitivity of the pitch bend display.

I have just released build 565 of pianoscope with a couple of new features:

- You can now start a pitch raise without having to measure the inharmonicity first. If no prior inharmonicity measurement is available, the inharmonicity is recorded alongside the pitches during the pitch raise setup. This should further speed up the process of preparing a pitch raise. By swiping up or down in the chart, you can switch to show the measured inharmonicities.

- You can now show pitch information in the inharmonicity view. Simply swipe up or down in the chart to switch between the inharmonicity and pitch charts. The pitch chart also contains the pitches you have measured during tuning.

- The more menu in the tuning curve view now also offers an option to show the actual pitches measured during tuning.

- You can disable showing the target pitch altogether in the general settings.

I hope you enjoy these new features.

In build 565 I have added a "none" setting as you requested.


I think a scale from -100 to +100 can provide some orientation when pitch raising very flat instruments. But I could however make the range configurable.

When measuring disharmony, the Fine Tuning mode is suggested first. Better if Coarse Tuning was the default. Thanks for the prompt changes.

I have just released build 569 which now allows you to change the range of the tuning scale. It can now cover either ±100 cents or only ±50 cents. You can switch between both ranges via the indicator scale settings or simply by pinching inside the scale. If an overpull of more than 50 cents is required when pitch raising, the scale automatically switches to ±100 Cents.

Hello Frank. Thank you very much for the awesome app, thanks for the quick updates. I have something to compare with, I choose Pianoscope.
I would like to suggest an addition. It would be possible to disable the banner about the need to measure inharmonicity in the settings at will, and automatically start the measurement with a new tuning. And in the settings you can offer a choice of which mode will be the default - Fine Tuning or Coarse Tuning

Quick question:

My household is completely free from any Apple product so far - and I have no intention whatsoever to change this. However, I am interested in this tuning app and wonder a) what are the minimum requirements in terms of hardware (iPhone version/iOS version) and b) is it possible at all to use an iPhone without becoming part of the Apple eco system in terms of requiring an account to load software or getting OS updates.

Otherwise I'll just wait and see whether there will be an Android version at one point.

Alex, thanks for your feedback. I think about turning this into one or two options.