L7 Natural [Jan 4 2026] FXP. Tuning (+/- cents) research

Yes, stretch exists in a piano whether we measure it or not, it's a physical reality caused by string stiffness (inharmonicity). The "stretch curve" is just how we visualize and measure this phenomenon. So the stretch is there in the actual instrument; the curve is our way of documenting it.

BTW, I'm familiar with that from the Pianoteq 9 manual, section 6.5 on Octave Stretching: "When the octave stretching parameter is set to 1, the stretching follows the natural inharmonicity of the strings (depending on string length), so there's still slight stretching. If you want no stretching at all, use the flat temperament."

But here's the issue, their default settings don't match reality. Take the Steinway D: Pianoteq defaults to a maximum string length of 2.70m, when the actual Steinway D measures 2.01m. That's nearly 70cm shorter in real life!

The problem is that Pianoteq aims for mathematical perfection rather than physical realism. It produces near-perfect calculated sound, but it's not grounded in real-world physics or the latest research through December 2025/January 2026. It's ironic, really, you'd need to tune and measure an actual piano, then manually reconstruct those settings in Pianoteq to get realistic sound. That 70cm difference alone affects everything, and there are plenty of other parameters that need adjustment too.

NOTE: in my research check Part 8: Why This Matters for Virtual Instruments

"If you are working with physical modeling plugins like Pianoteq, or building your own instruments, you might notice that the default tuning is often perfect 12-TET equal temperament at 0 cents across all keys. That is mathematically correct but not physically or musically accurate.

Real pianos tuned by professionals always have this stretch curve baked in. Sampled instruments like those from VSL or Spitfire already include it because the original piano was tuned before recording. Physical modeling instruments often need manual adjustment to sound realistic.

The Steinway Model D is the most documented concert grand in existence, with measurements going back to Railsback in 1938 and continuing through modern studies like Jaatinen and Patynen's 2022 JASA research. The physics predicts what tuners have known intuitively for centuries."

I tested Pianoteq output as well, and the results need to be examined more carefully. First, the tuner you used matters significantly. Standard chromatic tuners do not have the precision required for this type of measurement. You need a strobe tuner to get accurate readings at the cent and sub-cent level.

Free option: LockOn by SubMission Audio (VST3, requires iLok account): https://www.submissionaudio.com/products/lockon

Paid options: StroboSoft 2.0 by Peterson Tuners (https://www.petersontuners.com/products/strobosoft/) or Polytune by TC Electronic (https://www.tcelectronic.com/product.ht...e=0815-AAG)

Now let us examine the numbers. You measured -20 to +30 cents, totaling 50 cents of stretch. Here is the documented data for actual Steinway Model D pianos:

Piano Stretch Tuning Comparison

Your Pianoteq measurement
Bass (A0): -20 cents | Treble (C8): +30 cents | Total Stretch: 50 cents

Railsback empirical (1938)
Bass (A0): -17 cents | Treble (C8): +40 cents | Total Stretch: 57 cents

Precision Strobe measured Steinway D
Bass (A0): -17 cents | Treble (C8): +40 cents | Total Stretch: 57 cents

Physics-based (Fletcher + 2022 JASA)
Bass (A0): -19 cents | Treble (C8): +45 cents | Total Stretch: 64 cents

Railsback curve data for Steinway D goes from -17 cents at A0 to +40 cents at C8. Not -20 to +30. The Precision Strobe database confirms this with actual measured Steinway D data: http://www.precisionstrobe.com/apps/str...teind.html

Your measurement shows +30 cents at the treble extreme. The documented research consistently shows +40 to +45 cents in that register. That is a 10 to 15 cent discrepancy in the upper octaves.

Regarding the string length parameter: the problem is evident if you use the default stock preset "NY Steinway Model D" in Pianoteq 9.1, which Modartt describes as their most accurate model of the acoustic piano. If you have the Stage or Standard version, you cannot see the individual string parameters. But in the Pro version, you can verify this directly: by default, every string comes with a value of 2.70 m. All 88 keys. Same value.

On a real Steinway Model D, the longest bass string (A0) is approximately 201 cm (79.25 inches). The shortest treble string (C8) is approximately 5 cm. The inharmonicity coefficient B is inversely proportional to the square of string length. If all strings share the same length value in the model, the inharmonicity curve cannot accurately represent a real Steinway D.

From the Pianoteq 9.1.0 Manual, Section 8.1.2 String Length:

"Each piano note produces a complex sound, mainly composed of overtones with approximate frequencies f, 2f, 3f... where f denotes the fundamental frequency. A parameter which greatly affects the timbre (and the tuning) is the so-called inharmonicity: the more inharmonic the strings, the more the overtone frequencies of each string are driven away from their theoretical values f, 2f, 3f... and the more the piano sound will resemble a bell. 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..."

Modartt clearly understands the theory. The manual states it directly. The question is whether the default preset implements that theory with correct per-string values. The evidence suggests it does not.

If you want to verify, open the Pro version, load the default "NY Steinway Model D" preset, and check the string length values across all 88 keys. Then compare what you see to the physics formula:

B = (π³ × E × d⁴) / (64 × T × L²)

Where L is the string length. If L is constant across all keys in the model, B cannot follow the correct curve, and neither can the resulting stretch tuning.

I will continue researching this and provide more precise results with exact calculations. In the meantime, get a strobe tuner and measure again. The data will speak for itself.

Lemuel, Yves is correct in pointing out that the String Length control actually changes the overall length of the piano. Under the hood, all strings do have their proper length and inharmonicity, and these are carefully taken into account when Pianoteq computes the tuning.

You may be interested in the options under "Advanced Tuning > Stretch > Edit stretch points" and "Advanced Tuning > Stretch > Transfer the stretching into Detune note-edit". This will let you see how Pianoteq selects the appropriate tuning depending on the inharmonicity.

To add to the research: Pianoteq’s user interface uses an impractical string-length range. The editor only allows string lengths between 0.80 m and 10.00 m, so any real piano strings shorter than 0.80 m cannot be entered, even for extreme treble notes. That’s a problem for modeling instruments like a Steinway Model D, where many treble strings are far shorter than 0.80 m.

I extracted real Steinway D measurements from the INRIA technical report by Juliette Chabassier and Marc Duruflé (Physical parameters for piano modeling, RT-0425, INRIA, 2012; ⟨hal-00688679v2⟩). I truncated each value to two decimal places (I removed the third decimal digit rather than rounding). The resulting string-length array (A0 → C8) is:

String Length = [2.01, 2.00, 2.00, 2.00, 1.99, 1.98, 1.96, 1.93, 1.91, 1.87, 1.84, 1.80, 1.76, 1.70, 1.65, 1.60, 1.54, 1.49, 1.44, 1.37, 1.83, 1.75, 1.66, 1.59, 1.48, 1.40, 1.32, 1.25, 1.19, 1.12, 1.07, 1.01, 0.96, 0.90, 0.86, 0.81, 0.77, 0.73, 0.69, 0.65, 0.62, 0.59, 0.55, 0.52, 0.50, 0.47, 0.45, 0.42, 0.40, 0.38, 0.36, 0.34, 0.32, 0.30, 0.29, 0.27, 0.26, 0.24, 0.23, 0.22, 0.21, 0.20, 0.19, 0.18, 0.17, 0.16, 0.15, 0.14, 0.13, 0.13, 0.12, 0.11, 0.11, 0.10, 0.10, 0.09, 0.09, 0.08, 0.08, 0.07, 0.07, 0.06, 0.06, 0.06, 0.05, 0.05, 0.05, 0.04]

Out of these 88 values, 84 (95.5%) are taken directly from the INRIA document. The remaining 4 values were extrapolated using documented patterns and Steinway’s official specifications (for example, C8 ≈ 0.049 m).

Note: you can access per-note editing only in Pianoteq Pro, but even then the software’s allowed string-length range (0.80–10.00 m) prevents you from entering the true Steinway treble lengths. In short, Pianoteq’s UI is not designed to accept the realistic, very-short string lengths found on concert grands like the Steinway D.

Reference: Juliette Chabassier & Marc Duruflé, Physical parameters for piano modeling, INRIA Technical Report RT-0425 (2012). ⟨hal-00688679v2⟩ https://inria.hal.science/hal-00688679v2

No AI will simply tell you "You are absolutely right!" just because Alexis suggested using Advanced Tuning > Stretch > Transfer the stretching into Detune note-edit. While this option allows you to see how Pianoteq selects the appropriate tuning based on inharmonicity, his explanation is only partially correct.

Yes, A0 = -15 cents and C8 = +42 cents are reasonable values for the User Interface when applying that option as Alexis suggested. However, compared with real-world measurements, these values are still inaccurate.

To illustrate: when measured using Reaper 7.58 (DAW) with the VST3 plugin LockOn 1.0.4, the results are A0 = +5 to +7 cents and C8 = +48 to +50 cents. This discrepancy reveals that the formula is still incorrect. The value displayed in Pianoteq's interface (A0 = -15 cents) differs significantly from real-world measurements (A0 = +5 to +7 cents in LockOn). This is the core problem.

If you check each key from A0 (2.01 m string length) to Ab3 (0.816 m) using the string length data I shared previously in this post, you can verify that any measurement hardware or software will yield more accurate real-world values, in a real Steinway D.

Regardless, for those interested in reference data, I recommend consulting the Railsback Curve (1938) and Precision Strobe measurements:
http://www.precisionstrobe.com/apps/str...teind.html

Data for Future Calculations in Pianoteq

Octave Matching Formula (A4 = 440 Hz):

• 10:5 - A0 to Ab1

• 8:4 - A1 to E2

• 6:3 - F2 to C3

• 4:2 - Db3 to C4

• 2:1 - Db4 to D7

• 4:2 - Eb7 to C8

String Lengths (in meters, A0 to C8):

[2.010, 2.009, 2.008, 2.007, 1.997, 1.981, 1.965, 1.938, 1.911, 1.879,
 1.842, 1.805, 1.762, 1.709, 1.655, 1.602, 1.548, 1.495, 1.442, 1.378,
 1.837, 1.757, 1.660, 1.591, 1.482, 1.403, 1.329, 1.259, 1.192, 1.129,
 1.070, 1.013, 0.960, 0.909, 0.861, 0.816, 0.773, 0.732, 0.694, 0.657,
 0.622, 0.590, 0.559, 0.529, 0.501, 0.475, 0.450, 0.426, 0.404, 0.383,
 0.363, 0.344, 0.326, 0.308, 0.292, 0.277, 0.262, 0.249, 0.236, 0.223,
 0.211, 0.200, 0.190, 0.180, 0.171, 0.162, 0.153, 0.145, 0.138, 0.130,
 0.124, 0.117, 0.111, 0.105, 0.100, 0.095, 0.090, 0.085, 0.081, 0.076,
 0.072, 0.069, 0.065, 0.062, 0.058, 0.055, 0.052, 0.049]

Cents Deviation from 12-TET Equal Temperament: (Whole numbers)

Anyway, if you want more information consult my post: https://forum.modartt.com/viewtopic.php?id=12942

Good luck, man.

Look, I did the math, and honestly, I’m done with this topic. For those octave-matching variables you’ll need an extra formula to get accurate measurements; otherwise use dedicated tools like TuneLab 5.3, Verituner 4.1, PianoMeter, etc. . There’s just too much calculation involved to chasing a marginally “more realistic” sound.

Thank you Lemuel for your contribution!

Regarding this length question, I agree it is a bit tricky/confusing, but do not worry, the string lengths are set correctly in all pianos, please read this following old post: https://forum.modartt.com/viewtopic.php...93#p928593

That confirms BTW what YvesTh wrote above. Sorry for the confusion.