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Piano Suite

Professional piano tuning, inharmonicity analysis, and string scale design — all in one place.

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Piano Tuner

Live pitch detection, inharmonicity profiling, stretch tuning, and tuning fork generator.

YIN pitch · ETD · Railsback

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Partial Analyzer

FFT-based partial structure analysis with PFD B-coefficient solver and SNR diagnostics.

65536-pt FFT · TF Reassignment

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Scale Designer

String scaling, tension modelling, Tholey analysis, Röslau gauge snapping, and inharmonicity-guided layout.

Tholey · Engelbrecht · Mägi · Stulov

Estonia Parlour · Röslau Blue Label wire standard

Inharmonicity Measurement

Record notes to build a full inharmonicity profile. The app auto-advances through selected notes using onset detection.

Recording mode

Note coverage Reference pitch A4 (Hz)

440.0 Hz

Controls

Select a mode and press Record to begin.

↑ Load profile

Multi-Partial Fusion (sub-cent accuracy)

B estimation re-record to apply

0 notes measured

Note selection — click to jump

FFT spectrum — selected note

Select a note and record to see spectrum.

B coefficient — log scale

f₁ deviation from ET (cents)

Inharmonicity Analysis Dashboard

B coefficient — all samples (log)

ETD stretch — P2 cents above ET per note

f₁ cent deviation from equal temperament

Max partial deviation from inharmonic model (cents)

Detected partial count per note

B-fit RMS residual (¢) — lower = better

Regional summary

Region	Avg B	Quality
Bass A0–C3	—	no data
Tenor C3–C5	—	no data
Treble C5–C8	—	no data

Tuning

Live pitch detection with stretch tuning. Pitch detection is always active on this tab.

Method

Reference A4

440.0 Hz

Detection mode Pitch method

Adaptive Threshold: On

Multi-Partial Listening: On (MPF live refinement)

Refines EPT curve via Monte Carlo

Live — current note

—

— Hz

— ¢

—

Pitch detection active.

listening

Tuning schedule — all 88 notes

#	Note	ET (Hz)	Target (Hz)	Offset ¢

Tuning Fork

Reference tone generator with waveform selection and fine-tuning.

440.00Hz

Octave 4 · key 49

Waveform

Controls

Volume

50%

Fine tune

0 ¢

Waveform preview

Partial Analyzer

Strike a key to record and analyze its harmonic series. The PARSHL+TFR engine estimates the inharmonicity coefficient B using time-frequency reassignment.

Key selection

Multi-Partial Fusion (MPF) (sub-cent accuracy)

B method

Display mode

Import Scale Designer reference

Select a key and press Record. Strike the key after the prompt.

Partial spectrum with amplitude markers

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Partial amplitude bars

Partial cent deviation — Δ cents: measured vs ideal harmonic nf₁

Inharmonicity summary

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B coefficient

—

Fundamental f₁

—

Partials found

Run a recording to see PFD solver output.

Scale comparison

No scale-designer reference imported.

Import Main scale, B-mode, or Smooth-σ data to compare theoretical B and partial placements against the recorded note.

Partial table — inharmonic series

#	Measured (Hz)	Δ model (¢)	Δ scale (¢)	Amplitude	SNR

Piano Setup

Define speaking lengths, string counts, and striking point ratios — or import an existing scale as CSV/JSON.

Instrument profile

Piano name Total keys Reference pitch A4 (Hz) String density ρ_s (kg/m³)

Import scale data

Drop CSV or JSON

or click to browse

Fields: key, L_mm, l_mm, N

String layout — choir counts & speaking lengths

Load demo data or import a file, then edit individual cells.

Fill L: from to mm

Key	Note	Freq Hz	L (mm)	l (mm)	L/l	N strings

Tension Model

Define ideal string tensions using the Engelbrecht-Mägi method: linear regions with continuity conditions at choir-count transitions.

Bass anchor (key 1)

T₁ — first string (N)

1320 N

T₁₀ — last single-string (N)

1188 N

Transition tensions

T₁₁ — first 2-string note (N)

840 N

T₂₆ — first 3-string (N)

620 N

Transition analysis

Distribution law

Bass (keys 1–10)

Mid-bass (11–25)

Treble (26–88)

Ideal tension distribution

String Scaling

Compute core diameters from ideal tensions, snap to Röslau gauge steps, then solve for winding wire diameters.

Constraints

Min relative stress σ_min

0.00

Max relative stress σ_max

0.50

Wound string threshold — max plain d₁ (mm)

1.150 mm

Min winding d₂ (mm) Max winding (mm)

Wire standard

Röslau Blue Label: core snapped to 0.025 mm steps (≤1.2 mm) or 0.05 mm steps (>1.2 mm). Winding rounded to 0.05 mm.

Steel density ρ_s (kg/m³) Copper density ρ_c (kg/m³)

Core & outer diameter progression

Scale & Analysis — Unified View

Editable scale table with inline Tholey analysis. Click any row to select. Edit L / l / N directly in table cells. All Tholey-derived parameters update live after "Apply changes".

↑ Import Optimized Scale

#	Note	Hz	L mm	l mm	L/l	N	T N	σ	d₁	d₂	d₃	Type	B×10⁻⁵	RTF	Harm%	HarmL%	Elong	Atk	Imp

Click row to select · Edit L/l/N inline · Run scaling first to populate d₁/d₂/d₃/T/σ · Tholey columns (RTF, Harm%, HarmL%, Elong, Atk, Imp) auto-compute

String Editor

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— Hz

Speaking L (mm)

Striking l (mm)

Choir N

Core d₁ (mm)

Winding d₂

Winding d₃

T — σ — μ g/m — B ×10⁻⁵— Loudness f— Elongation— Atk time— Impedance—

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Analysis Charts — Tholey Formulas & Physical Parameters

String tension — per string (blue), per choir (teal), target (amber dashed)

Relative tensile force (Tholey) — balance across scale

Harmonicity % — tonal transparency vs reference (Tholey)

Harmonicity of length % — geometric inharmonicity ratio

String elongation (mm, log) — tuning stability indicator

Attack time (relative) — l / (T / loudness factor)

Mechanical impedance (mcΩ) — LN(f / elongation)

Relative stress σ — target ≤ 0.50

Inharmonicity B (log scale)

Core diameter d₁ (mm) — Röslau gauge steps

Linear mass density µ (g/m)

Speaking length L (mm)

Inharmonicity stretch ¢ — ideal harmonic vs inharmonic model (B-derived)

Inharmonicity-guided Scaling

Builds the scale by targeting a smooth B curve across all 88 keys — minimising jumps at section breaks — then back-solves tensions and wire gauges.

1 · Target B curve

2 · Run solver

3 · Compare

4 · B-mode table

B-curve shape & anchors

B = π³Ed₁⁴ / (64TL²). Typical: bass ≈ 1–4×10⁻³, treble ≈ 2–8×10⁻⁵. The solver fits a smooth power-law spine then chooses gauges to track it.

B at key 1 (×10⁻⁴)

B at key 88 (×10⁻⁶)

Curve shape exponent

2.20

Section-break tolerance (×B)

1.25×

Diameter monotonicity

Tension bounds (N)

—

Target B spine (log scale)

Section break continuity targets

Smooth-σ Scaling

Based on Quality Strings / Paulello methodology. Targets a user-defined stress-rate curve σ(k) and selects gauges to match — producing a homogeneous tonal progression.

Background: σ = T / (π/4·d₁²·UTS). For a plain string, σ ≈ (2fL)²·ρ/UTS — nearly independent of diameter. A smooth σ curve primarily comes from the tension model. This solver optimises gauge selection for each note to track the target curve as closely as possible within available Röslau gauges.

Target σ curve — Bézier (bass → mid → treble)

σ at key 1 (bass)

0.42

σ at key 44 (mid)

0.48

σ at key 88 (treble)

0.55

Max stress sigma max

0.62

Plain-to-wound crossover

1.150 mm

Diameter monotonicity

Tension bounds (N)

Winding d2 bounds (mm)

Winding d3 bounds (mm)

Adjacent core d1 step max (mm)

Adjacent outer d0 step max (mm)

Adjacent winding step max (mm)

σ achieved (teal) vs target (dashed blue)

Core d₁ — Smooth-σ (teal) vs Tension-first (amber)

Smooth-σ scale table

n	Note	f Hz	L mm	N	T N	σ actual	σ target	μ g/m	d₁ mm	d₂ mm	d₃ mm	Type