Topic: Bug? Significant inharmonicity even with 10m piano

Hi all,

Tonight I took some measurements of the Pianoteq 7.2.0 PRO "Grand Ant Petrof" sound with the string length set to 10m. The manual says:

"Inharmonicity decreases very rapidly with string length. Experiment by changing the String length. The difference will be most evident in the bass range. You can choose up to a 10 meter long piano! At such a size, there is almost no inharmonicity. People say that piano manufacturers dreamed of producing pianos without inharmonicity..."

However, even at 10 meters there is significant inharmonicity, at least for the notes I tested. In particular, the harmonics track very well to the standard Harvey Fletcher equation for stretched partials due to string stiffness.

For instance, for "B" above A4 (so about 494 Hz), I measured the inharmonicity coefficient "B" equal to 0.000854634239097124, to which the harmonics have an extremely good fit. Given this, we can then measure the cents deviation of each harmonic from its "just" version with no inharmonicity. Those deviations are:

                         1          0.85100734626789
                         2          3.39902100548722
                         3          7.62911367488012
                         4          13.5167286476116
                         5          21.0281493252212
                         6          30.1211301330984
                         7          40.7456645903049
                         8          52.8448621854427
                         9          66.3559033372764
                        10          81.2110410865593
                        11          97.3386191477907
                        12          114.664078308312
                        13          133.110926583857
                        14          152.601652675856
                        15          173.058566779242
                        16          194.404557344766
                        17          216.563756744031
                        18          239.462112719482
                        19          263.027865893305
                        20          287.191936388401

So you can see there is still some very significant deviation from true inharmonicity. Even the 7th harmonic, for instance, is almost a quarter tone sharp, the 11th harmonic is a semitone sharp, etc.

This coefficient barely seemed to change *at all* with the string length. The only strings whose coefficients changed were the very low ones. I did check the "Note Edit" view as well and all of them supposedly changed to 10m.

How can I decrease the inharmonicity to 0? I would certainly like to request this be possible somehow. Is this a bug?

Last edited by battaglia01 (25-04-2021 21:08)

Re: Bug? Significant inharmonicity even with 10m piano

This is not a bug. It is due to how the "10 m" piano is built, see in particular
https://forum.modartt.com/viewtopic.php...366#p13366
https://forum.modartt.com/viewtopic.php...93#p928593

Re: Bug? Significant inharmonicity even with 10m piano

Thanks. So based on what I am measuring, and hearing, and what I am seeing in those other posts, the "String Length" parameter has a significant audible effect mainly in the lowest notes, which lessens rather quickly as you go up the keyboard.

I would very much like to be able to reduce the inharmonicity to 0 - either via "string length" or some other parameter - for *every* note.

FWIW, for the "B4" I had above, the measured coefficient changed a little bit from 2.72m to 10m, but not really significantly. At 10m the coefficient was 0.000854634239097124, whereas at 2.72m the coefficient was 0.000983605660911475. So slightly less, but not far from zero.

These are the measured cents deviations for both, for reference.


            #          10m        2.72m
            1      0.73947      0.85101
            2       2.9541        3.399
            3       6.6326       7.6291
            4       11.756       13.517
            5         18.3       21.028
            6       26.231       30.121
            7       35.511       40.746
            8       46.097       52.845
            9        57.94       66.356
           10       70.987       81.211
           11       85.182       97.339
           12       100.47       114.66
           13       116.78       133.11
           14       134.06        152.6
           15       152.24       173.06
           16       171.27        194.4

You can clearly see that there is slightly less inharmonicity for the B4 note at 10m. However, even at the 10m level, there is still significant inharmonicity. This inharmonicity is clearly audible and I would very much be interested in listening to what it would sound like with no inharmonicity at all.

Now, this is just for the B4 note. As you get towards, for instance, a bass C0, then the difference is much more significant; there is about a 10x change in the inharmonicity coefficient. So I suspect that the "string length" parameter is kind of following the basic shape of a grand piano body, lengthening the bass strings but not the treble ones as much. So it would be very interesting to let the treble strings be lengthened also. (Note that I did have everything lengthened to 10m in "Note Edit".)

So I guess this is a feature request:
* To either make it possible to increase the string length beyond 10m
* Or make it possible to adjust the "curve" of the piano (so the treble strings aren't so much shorter than the bass strings)
* Or just give some other way to adjust the inharmonicity directly on the treble strings (and all the strings).

Last edited by battaglia01 (25-04-2021 20:11)

Re: Bug? Significant inharmonicity even with 10m piano

battaglia01 wrote:

So I suspect that the "string length" parameter is kind of following the basic shape of a grand piano body, lengthening the bass strings but not the treble ones as much.

Yes, that's exactly what happens.

Re: Bug? Significant inharmonicity even with 10m piano

Philippe Guillaume wrote:
battaglia01 wrote:

So I suspect that the "string length" parameter is kind of following the basic shape of a grand piano body, lengthening the bass strings but not the treble ones as much.

Yes, that's exactly what happens.

Would it be possible to just let this slider go to extreme values, like 1000, or even "infinity"?

Re: Bug? Significant inharmonicity even with 10m piano

It's possible to set the string length to crazy values in the Pro version by going to the 'String Length' parameter in Note Edit, setting the yellow bar to 0.80m, setting each note to 10m, then dragging the yellow bar to 10m.

Last edited by lowendtheory (26-04-2021 06:05)

Re: Bug? Significant inharmonicity even with 10m piano

lowendtheory wrote:

It's possible to set the string length to crazy values in the Pro version by going to the 'String Length' parameter in Note Edit, setting the yellow bar to 0.80m, setting each note to 10m, then dragging the yellow bar to 10m.

Awesome!!! Thank you!! And great username!