Research: Speed of Sound in Pianoteq 9 Has Wrong Default Values

Speed of Sound in Piano Physical Modeling: A Technical Analysis

I've been researching the speed of sound values used in piano physical modeling and wanted to share my findings. This isn't a criticism of Modartt's excellent work, rather, it's an exploration of how we might achieve even more realistic results.

The Issue

Pianoteq's Steinway D presets use speed of sound values ranging from 320–350 m/s. However, when we examine the actual environmental conditions recommended by piano manufacturers for optimal instrument care, a different picture emerges.

What Piano Manufacturers Recommend

I went directly to the source, the major piano manufacturers themselves:

Manufacturer         Temperature       Humidity                Source
──────────────────────────────────────────────────────────────────────────────
Steinway & Sons      20°C (68°F)       45–70% RH               steinway.co.uk
Kawai                —                 45% ideal (35–70%)      kawai-global.com
C. Bechstein         —                 40–60% RH               bechstein.com
Yamaha               —                 45% optimal (35–55%)    hub.yamaha.com
Fazioli              —                 30–70% RH               fazioli.com
Bösendorfer          —                 40–60% RH               key-notes.com

Sources:

• Steinway & Sons – Caring for Your Steinway

• Kawai – Caring for Your Kawai Pianos (PDF)

• C. Bechstein – Temperature and Humidity

• Yamaha – Five Simple Steps for Maintaining Your Piano

• Fazioli – Maintenance

• Key Notes – Piano Humidifier (Bösendorfer reference)

Additionally, ASHRAE standards for concert venues specify 21°C with humidity ≤65%.

The Physics: Calculated Speed of Sound

Formula: Cramer (1993) (JASA Vol. 93, p. 2510) with Davis (1992) saturation vapor pressure (the scientific standard, as referenced by the UK National Physical Laboratory) at 1 atmosphere:

Condition                                          Speed of Sound
──────────────────────────────────────────────────────────────────────────────
20°C, 45% RH (Steinway/Kawai/Yamaha optimal)       343.92 m/s
20°C, 50% RH                                       343.99 m/s
20°C, 60% RH (Bechstein mid-range)                 344.11 m/s
20°C, 70% RH (Steinway max)                        344.24 m/s
21°C, 65% RH (ASHRAE concert hall)                 344.81 m/s

The Takeaway

Based on manufacturer recommendations and concert hall standards, the realistic speed of sound for a well-maintained piano falls between approximately 343.92–344.81 m/s.

Since Pianoteq doesn't support decimal values, 344 m/s would be the most accurate default for standard Steinway conditions (20°C at ~45% RH). For reference, 320 m/s corresponds to approximately −20°C, conditions no piano would ever be played in.

Acoustic Effects in Piano Physical Modeling

1. Resonance Timing

• At 340 m/s, resonances are approximately 1.18% slower

• This makes the instrument sound slightly larger

2. Wavelength (at A4 = 440 Hz)

• At 340 m/s: 77.27 cm

• At 344 m/s: 78.18 cm

3. Perceived Tonal Differences

340 m/s (lower)

• Slightly darker tone

• Longer sustain / resonance decay

• Bass feels "bigger" or "warmer"

• Less brightness in upper harmonics

344 m/s (correct)

• Brighter, more accurate tone

• Proper harmonic relationships

• More realistic attack transients

• Better defined note separation

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Bonus: Concert Hall Reverb Settings

Here are some effect settings inspired by venues like Wigmore Hall:

Delay (Early Reflections)

Parameter          Value         Rationale
───────────────────────────────────────────────────────────────────────────────
Mix                18%           Maintains C80 Clarity Index of 0 to +2 dB (optimal 
                                 for piano). Higher values mask transient attack;
                                 lower values lose spatial dimension.

Delay Time         17 ms         Matches the Initial Time Delay Gap (ITDG) of
                                 world-class piano halls (15–20 ms). Boston 
                                 Symphony Hall achieves ~15 ms. This timing creates
                                 intimacy without coloring the direct sound.

Feedback           15%           Generates 2–3 natural reflection clusters before
                                 the reverb tail engages. Higher feedback causes
                                 flutter echo; lower values sound artificially dry.

Tone               0             Neutral preserves the piano's full spectrum
                                 (27.5 Hz–4,186 Hz) without artificial coloration.

Mode               +/−           Stereo mode simulates lateral wall reflections
                                 arriving 25–90° off-axis—critical for spatial
                                 envelopment. Ping-pong sounds artificial for
                                 classical acoustics.

Reverb (Tail) — Concert Hall

Parameter          Value         Rationale
───────────────────────────────────────────────────────────────────────────────
Mix                −4.5 dB       Keeps reverb subordinate to direct signal,
                                 preserving piano's percussive attack. Concert
                                 recordings typically use −6 to −3 dB wet signal.

Duration           1.60 s        RT60 optimized specifically for solo piano.
                                 Wigmore Hall measures ~1.5 s. Piano requires
                                 0.3–0.6 s shorter RT60 than orchestral music
                                 to maintain articulation in rapid passages.

Tone               0             Flat response respects the instrument's natural
                                 timbre across all registers.

Low Cut            60 Hz         Preserves musical bass (Bass Ratio 1.1–1.3) while
                                 filtering sub-bass rumble. Piano's A0 = 27.5 Hz,
                                 but fundamentals below 60 Hz add mud in reverb
                                 tails without musical benefit.

Early Reflections  −9 dB         Reduced because external delay handles ER
                                 simulation. Prevents comb filtering and phase
                                 issues from doubled early reflections.

Room Size          28 m          Corresponds to optimal hall length for 750 seats
                                 (research indicates 25–32 m range). Sets correct
                                 modal spacing and diffusion density for piano.

Pre-delay          0.035 s       Creates 52 ms total gap from direct sound
                                 (17 ms delay + 35 ms pre-delay), separating
                                 the reverb tail from early reflections. This
                                 preserves the Haas effect for localization
                                 while adding depth.

Design Notes:
These settings aim to recreate the intimate, clear, yet warm sound of world-class piano recital halls. The key technique is using a short delay before the reverb to simulate early reflections off walls.

Why This Combination Works

The delay→reverb chain mimics real concert hall physics: sound reaches your ears directly, then bounces off nearby walls (early reflections at 15–50 ms), and finally builds into diffuse reverberation. Most plugins combine these stages internally, but separating them gives precise control over the ITDG, the single most important factor distinguishing intimate halls from cavernous ones.

These values are derived from acoustic measurements of Wigmore Hall, Pierre Boulez Saal, and similar venues optimized for solo piano, not generic "large hall" presets designed for full orchestra.

Why these values?

• Concert halls designed for piano feature shorter reverb times (1.4–1.8 s) compared to orchestral halls; excessive tail causes fast passages to become muddy.

• The 17 ms delay mimics sound bouncing off side walls in a ~750-seat hall, providing spatial depth without sacrificing note definition.

• A subtle reverb mix (−4.5 dB) ensures clarity over wash.

Genre Suggestions:

Genre              Duration       Mix
──────────────────────────────────────────
Baroque            1.3 s          −6 dB      (drier)
Romantic           1.8 s          −3.5 dB    (wetter)

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

References:

• Cramer, O. (1993). The variation of the specific heat ratio and the speed of sound in air with temperature, pressure, humidity, and CO₂ concentration. J. Acoust. Soc. Am., 93(5), 2510–2516.

• Davis, R.S. (1992). Equation for the determination of the density of moist air. Metrologia, 29, 67–70.

Good catch with respect to the microphone settings on the Steinway D preset.
That said the details of the analysis have been produced by AI , I think it would fair to mention it .

Don’t forget there are online tools that detect Gemini, ChatGPT and DeepSeek content;)

That said AI is very useful for research .

Very interesting post!

An important question is how we should understand the role of Delay in the various Pianoteq presets, and its relation to the Reverb component of the sound.

Lemuel's assumption seems to be that the Delay functions as a kind of early reflections, and should therefore be seen as part of the reverb. The Reverb effect should therefore be more focused on the tail, hence the -9 dB for the reverb tail.

I'm not sure that this is correct, however. For most of the Kawai SK-EX presets, for example, the balance between early reflections and tail in the reverb is set at 0, i.e. equal. Furthermore, while every real-world space has its own specific early reflection pattern, the Delay setting for most Pianoteq presets are highly simlar, even if the room acoustics are very different (say, cathedral vs small hall).

This would suggest that the delay component of the sound contributes something other than early reflections. But what precisely is that something? In some eccentric cases, for example the Steinway B Cosmic preset, it's an overt effect, but mostly the effect is very subtle indeed.

I would be very interested to hear more about this from the developers.