Awaiting specimen. Upload an audio file to begin spectral interrogation, or activate a take from the library.
What you see
A short-time Fourier transform (STFT) of the signal, rendered as a surface whose height is the magnitude of each frequency bin at each moment in time. The signal is sliced into overlapping Hann-windowed frames; each frame is FFT-transformed, yielding a time × frequency grid. For a struck cymbal this reveals the broadband attack at t≈0, the rich crown of inharmonic modes that follows, and the characteristic order in which high partials die before low ones. Rotate, zoom, and tilt the surface to inspect individual modal ridges.
Interactive STFT magnitude surface
What you see
Two complementary views of brightness — how high in the spectrum energy sits and what fraction lies above key cutoff frequencies. Both measures descend over time as high partials decay faster than low ones. Brighter cymbals (crashes, splashes) stay elevated longer; darker instruments (heavy rides, low-pitch bells) start low and drop quickly.
Spectral rolloff — 65 / 75 / 85 %
Energy accumulation threshold
The frequency below which a given percentage of the total spectral energy is contained. Lower thresholds (65%) track where the bulk of energy sits; higher ones (85%) capture the tail of the brightest components. Watching all three together reveals how uniformly or sparsely the energy spreads across the spectrum.
High-band energy ratio — 500 Hz / 1 kHz / 2 kHz
Above-cutoff energy fraction
Fraction of total spectral energy above each cutoff frequency (0 = none, 1 = all). The 500 Hz cutoff separates sub-bass from mid energy; 1 kHz splits mid from upper-mid; 2 kHz isolates the air band. Comparing the three curves shows how the cymbal's energy distribution shifts with decay.
What you see
Four descriptors that quantify noisiness — how broadband, disordered, or peaky the spectrum is. Cymbals are inherently noisy (inharmonic dense partials); these curves let you see how that noisiness evolves — usually peaking at the attack and decaying as tonal modes emerge.
Spectral flatness & entropy
Disorder measures
Spectral flatness (Wiener entropy) — geometric mean divided by arithmetic mean. 1 = perfectly flat (white noise); 0 = pure tone. Spectral entropy — Shannon entropy of the normalised power spectrum, rescaled to 0–1. High values = energy spread uniformly across many bins; low values = concentrated at a few peaks.
ZCR & spectral crest
Temporal & spectral peakiness
Zero-crossing rate — time-domain proxy for the dominant frequency content and noisiness of the waveform. Spectral crest — ratio of peak magnitude to mean magnitude. Pure tones have very high crest; broadband noise has crest ≈ few.
What you see
Four descriptors that quantify harmonicity — how tone-like the spectrum is and how closely its peaks align with an integer-harmonic template. Cymbals are strongly inharmonic (their modes do not sit on integer multiples of a fundamental), so these descriptors reveal how much "pitch" survives through the decay.
Harmonicity & tonal-to-noise
Pitchedness measures
Harmonicity index — for each STFT frame, every tracked partial in the 50–2000 Hz range is tried as a candidate fundamental; each candidate is scored as the fraction of total partial amplitude that falls within 3 % of one of its integer multiples; the best single-template score is the frame value (0 = no harmonic series accounts for significant energy, 1 = nearly all energy sits on one harmonic template). Tonal-to-noise ratio (TNR) — dB ratio of peak energy to residual (broadband) energy. High TNR = pitched; low TNR = wash.
Peak count & peak-to-average
Modal density
Peak count — number of prominent local maxima in the spectrum (modal density). Peak-to-average (PAR) — mean dB height of the top-5 peaks above the frame mean. Taken together these show whether the sound is many thin modes (high count, high PAR) or a dense smear (low count, low PAR).
What you see
Spectral centroid and spectral slope — two complementary descriptors of the overall shape of the spectrum over time. The centroid is the magnitude-weighted mean frequency; the slope measures how steeply the spectrum tilts from low to high frequencies. Together they reveal whether a cymbal is bright and spectrally flat, or dark and steeply falling.
Spectral centroid
Brightness locator
The magnitude-weighted mean frequency — the spectral "centre of gravity". High centroid = the energy sits in the upper registers; low centroid = dominated by lower modes. Centroid typically descends over time as high partials decay faster than low ones.
Spectral slope
Spectral tilt
Least-squares regression of log-power vs. log-frequency, in dB per octave. Near-zero slope = spectrally flat, rich with high-frequency content; steep negative slope = low-pass character, energy concentrated at low frequencies. Crash cymbals stay close to zero; heavy rides and bells fall steeply.
What you see
Two spectral analyses of the excitation event — the brief window in which the implement transfers energy into the cymbal. The excitation spectrum shows how broadband the initial energy injection is; the temporal envelope shows how long that injection lasts before the cymbal rings freely at its own modes. Single-value impact descriptors are collected in the Assay tab (§07).
Excitation vs. modal spectrum
Bandwidth of excitation
Two spectra computed from the raw signal and normalised to the attack peak, plus their difference. Excitation (purple, dashed): single FFT of the onset window — reflects the broadband energy imparted by the implement; harder sticks produce flatter, wider-band excitation. Ringing (blue, dashed): spectrum at the onset-termination time — shows only the resonant modes that survive once the stick has left. Difference (lime): excitation minus ringing in dB — peaks where energy is driven by the impact alone and does not persist as free vibration.
Attack-energy envelope
Duration of excitation per band
Band-limited RMS envelopes (1 ms hop) over the first 500 ms from the start of the recording, each normalised to its own peak. A dashed white line marks the detected onset. Crossover frequencies divide the spectrum into low (purple), mid (blue) and high (lime) bands. Dotted vertical markers show when each band crosses −3, −10 and −20 dB after its peak — stacked at band-specific heights so they stay legible. Larger window sizes smooth the envelopes and shift the crossings later; high bands generally decay faster than low ones on a freely-vibrating cymbal.
What you see
Spectral flatness computed with a variable-length analysis window sweeping through the first 300 ms from the onset. Spectral flatness (Wiener entropy) peaks during the broadband attack, when the spectrum looks like white noise, and falls as distinct resonant modes emerge. The highlighted region is the transient window — the half-maximum width of the flatness peak — which objectively delimits the excitation event. Within that window the spectral centroid, spectral spread, and spectral slope are shown in detail to characterise how the impulse energy is distributed and how quickly the spectral balance shifts during the strike.
Spectral flatness — onset region
Transient detection · Flatness Viewer
Left: Spectral flatness over the onset region. Each point is Wiener entropy computed from a short FFT using the window length set by the slider. Flatness peaks when the spectrum is broadband and noisy (impact); it falls as discrete tonal partials dominate. The shaded lime region and dashed markers show the half-maximum width of the flatness peak — the operational transient window. Right (Flatness Viewer): Mean values of all four descriptors averaged over the transient window — flatness, centroid, spread, and slope — for a single-glance summary of the attack character. Centroid and spread are normalised to a 0–1 scale relative to the Nyquist frequency.
Spectral shape within the transient window
Excitation spectral trajectory
Time series of three spectral descriptors, restricted to the transient window. Centroid (lime) — magnitude-weighted mean frequency in Hz; its trajectory during the attack shows how the excitation energy migrates across the spectrum. Spread (blue) — standard deviation of the spectral distribution in Hz; wide spread = spectrally diffuse impulse, narrow spread = energy confined to a band. Spectral slope (red, right axis) — dB per octave regression of log-power vs. log-frequency; near-zero = flat broadband excitation (hard stick), steep negative = soft low-frequency bias (mallet). Both frequency quantities share the left log axis.
What you see
After the initial transient, a struck cymbal gradually opens up — high-frequency modes accumulate energy, the spectral centroid climbs, and the spectral slope becomes less negative. This tab tracks that ascent from the onset to the centroid peak, defining it as the opening phase. Duration and intensity of the opening reflect the physical properties of the instrument: larger, heavier cymbals tend to bloom slowly; lighter cymbals open almost instantly.
Opening phase — spectral centroid & slope ascent
Spectral ascent trajectory
Spectral centroid (lime, left log axis) — magnitude-weighted mean frequency per STFT frame; raw (faint) and smoothed (solid, window set by the slider). The centroid rises as high-frequency partials gain energy during the opening and plateaus once they begin to decay. The opening end (dotted vertical, labelled) marks the smoothed centroid peak; the shaded lime region is the opening phase. Spectral slope (red, right axis) — dB per octave; a rising slope (becoming less negative) confirms that energy is spreading toward high frequencies.
1/3 Octave band energy gain · Opening phase summary
Band gains · Summary
Left — 1/3-octave energy gain: dB change in each 1/3-octave band between the onset frame and the opening-end frame. Positive bars indicate bands that gained energy during the opening. The highlighted bar (lime) is the most prominent band — the spectral region that built most strongly. Bands that were already loud at the onset and then decayed show negative gain. Right — Opening phase summary: three normalised values — opening duration (ms, ceiling 1.2 s), opening intensity (centroid rise in octaves, ceiling 2 oct), and the peak band log-position (100 Hz–20 kHz). Text labels carry the physical values; bar heights support cross-take comparison.
What you see
A peak-continuation tracker in the style of McAulay & Quatieri (1986): in each STFT frame, local magnitude peaks are detected and refined to sub-bin resolution via parabolic interpolation, then matched frame-to-frame into trajectories. Each line is one such partial. Colour and line thickness both encode peak amplitude — bright lime for the loudest modes, dark blue-grey for the quietest. The amplitude colour scale is shown in the strip to the right of the plot.
Partial frequency trajectories
Detected partials
| # | Freq (Hz) | Amp (dB) | Duration (s) | Drift (Hz) |
|---|
Octave-band decay curves
Schroeder integrated
One curve per octave band showing normalised backward-integrated energy in dB computed via the Schroeder backward integration method. A straight downward line is a pure exponential decay; curvature indicates a two-stage decay — common in cymbals, where a fast early component is followed by a slower residual from long-lived modes.
What you see
Two complementary views of modal activity over time. Modal density counts how many tracked partial tracks are simultaneously alive at each moment — high density signals a rich, complex sound; a rapid drop marks modes dying out. Frequency entropy measures how evenly the active modes are spread across the log-frequency axis: maximum entropy means modes are uniformly distributed across octaves; low entropy means they are clustered in a narrow band. Both metrics are derived from the partial tracker, not from the raw spectrum, so they describe structural modal behaviour rather than spectral energy.
Modal density
Simultaneous modes
Number of partial tracks alive at each STFT frame. Each track is counted from its onset to the last frame it was matched, regardless of amplitude. A high plateau early on reflects the initial excitation of many modes; the subsequent fall-off speed is a proxy for overall decay complexity.
Frequency entropy
Log-frequency spread of active modes
Shannon entropy of the amplitude-weighted modal distribution across log-spaced frequency bins. Computed on an exponential (log) frequency scale so each octave contributes equally. High entropy means modes span the spectrum broadly; drops indicate the sound is narrowing to a few dominant partials as higher modes decay.
What you see
Spectral fractal dimension (SFD) — Higuchi's fractal dimension applied to the dB power spectrum of each STFT frame. The spectrum is treated as a 1D curve; SFD measures how self-similar its roughness is across scales. A value near 2 indicates a broadband, noise-like spectrum with detail at every scale (high complexity); a value near 1 indicates a smooth, tonal spectrum dominated by a few discrete peaks (low complexity). At the strike the spectrum is maximally complex; as tonal modes take over, SFD falls and stabilises at a level characteristic of the instrument's modal density.
Spectral fractal dimension — full spectrum
Whole-spectrum complexity over time
Higuchi FD computed on the full dB magnitude spectrum (DC excluded) at every STFT frame. The initial drop from the attack plateau to the sustain floor captures the transition from broadband excitation to modal ringing. A slow, shallow fall indicates a spectrally dense cymbal whose complexity persists well into the sustain; a rapid drop signals a quick simplification to a few dominant modes.
Spectral fractal dimension — by frequency band
Band-resolved complexity
Three simultaneous FD curves computed on frequency-band slices of the dB spectrum: low (<1 kHz, purple), mid (1–5 kHz, blue), high (>5 kHz, lime). High-frequency bands typically collapse fastest as the overtone wash decays; the low band is last to simplify as bell modes linger. A high-band FD that stays elevated long after the attack is a marker of a dense, complex overtone structure.
What you see
Three complementary views of spectral irregularity over time — how jagged, spiky, or unevenly concentrated the spectrum is at each STFT frame. All three descend from a complex broadband attack towards a simpler sustain, but they emphasise different structural properties: Jensen irregularity captures local bin-to-bin deviation from the neighbourhood average (peak sharpness); log roughness captures the first-derivative jaggedness (how rapidly adjacent bins differ); and the Gini coefficient captures global energy concentration (whether a few bins hoard most of the power). Together they profile the texture of the spectrum independently of overall level, brightness, or decay.
Spectral irregularity — three measures
Three complementary irregularity descriptors overlaid
Jensen irregularity (RMS dB deviation of each bin from its 3-bin local mean) and log roughness (RMS of successive dB first-differences) share the left axis. Gini coefficient of the power spectrum — 0 = flat noise, ~1 = all energy in one bin — is on the right axis. Jensen and roughness differ in character: Jensen is elevated when isolated peaks stand above their neighbours; roughness is elevated whenever adjacent bins alternate rapidly. Gini is the global view: it rises as a few long-lived partials concentrate all remaining energy. All three descend over the decay but at different rates and to different floors, making their divergence a fingerprint of the cymbal's modal structure.
What you see
Three derivations of quadratic phase coupling (QPC) over the interaction frequency f1+f2.
For every pair of spectral components (f1, f2), nonlinear mode coupling generates
energy at their sum frequency whose phase and amplitude carry a fingerprint of the interaction.
Each curve asks a different question of the same biphase triplet φ(f1)+φ(f2)−φ(fsum):
bicoherence uses both phase and amplitude;
phase locking value ignores amplitude entirely;
amplitude modulation coupling ignores phase entirely.
Their agreement or divergence distinguishes purely phase-coherent coupling from
amplitude-driven energy transfer and from coincident modulations with no locked phase relation.
Quadratic phase coupling — three derivations
Three views of the same nonlinear interaction
Bicoherence (b, lime) is the Kim-Powers normalised bispectral magnitude: b = |E[X(f1)X(f2)X*(fsum)]| / √(E[|X(f1)X(f2)|²]·E[|X(fsum)|²]).
It measures coherent nonlinear energy transfer — a strong peak means both phase alignment and amplitude are co-contributing.
Phase locking value (PLV, blue) is the circular concentration of ψ(t) = φ(f1,t)+φ(f2,t)−φ(fsum,t) across STFT frames — amplitude blind; a peak here means the triplet phases lock regardless of level fluctuations.
Amplitude modulation coupling (AMC, orange) is the Pearson correlation of A(f1,t)·A(f2,t) with A(fsum,t) — phase blind; a peak here means the sum-frequency amplitude tracks the product amplitude in time.
All three are weighted by mean triple amplitude and averaged across all (f1, f2) pairs that sum to each plotted frequency.
Peaks shared by all three indicate robust parametric coupling; a PLV peak without AMC indicates a stable phase relation without correlated amplitude envelopes (a common signature of near-harmonic inharmonic spacing); an AMC peak without PLV indicates amplitude modulation from a common excitation without phase coherence.
T60 by octave band
Band-wise reverb
Per-band T60 alongside EDT × 6 (EDT extrapolated to a 60 dB drop). When EDT differs substantially from T60 the decay is non-exponential — one of the most audible cues that distinguishes lively instruments from quickly-damped ones.
What you see
A mode-by-mode inventory of decay: each tracked partial's amplitude envelope is fit in log-domain to recover its individual T60. A classic cymbal footprint shows longer decays at lower frequencies, with high-frequency partials (>5 kHz) dying within hundreds of milliseconds while sub-kHz modes can ring for several seconds. The trend line is a regression of log-T60 vs. log-frequency.
Per-partial decay constants
Mode-by-mode
Each point is one tracked partial, plotted as its mean frequency versus the T60 obtained by linear regression of its log-amplitude trajectory. Point size encodes peak amplitude; the dashed line is the power-law trend. Outliers above the trend line are unusually long-ringing modes — often the fundamental bell modes in crash/ride cymbals.
Q per Partial
What you see
Bars are sorted left-to-right by descending peak energy — index 1 is the loudest partial. Bar height = Q factor, measured directly from the STFT: the magnitude spectrum is averaged over the partial's tracked duration and the half-power (−3 dB) bandwidth is read at the partial's centre frequency — Q = f / BW. This is the same definition used for bandpass filters, so the values are directly comparable: a cymbal mode and a resonant filter at the same Q have the same relative bandwidth. Colour fades from lime (most energetic) to dim blue-grey. Hover for frequency, Q, bandwidth, and relative amplitude.
Drift per Partial
What you see
Bars are sorted left-to-right by descending peak energy. Bar height = frequency drift normalised to centre frequency — the net start-to-end frequency change of the partial's tracked trajectory divided by its mean frequency, expressed as a percentage. Positive values indicate upward drift; negative values indicate downward drift. Near-zero bars are stable, pure resonances; large values indicate modes whose pitch shifts significantly as the cymbal decays — a signature of nonlinear coupling or modal interaction. Colour fades from lime (most energetic) to dim blue-grey. Hover for frequency, absolute drift, and relative amplitude.
AM per Partial
What you see
Bars are sorted left-to-right by descending peak energy. Bar height = AM depth (dB RMS) — the root-mean-square deviation of each partial's amplitude track from a best-fit exponential decay, expressed in decibels. The fit removes the expected gradual decay so that only genuine amplitude fluctuations remain. Near-zero bars decay smoothly; tall bars indicate amplitude modulation — beating between closely-spaced modes, nonlinear energy exchange, or periodic support loss. Colour fades from lime (most energetic) to dim blue-grey. Hover for frequency, AM depth, and relative amplitude.
Mode Jumping
What you see
Partials are arranged left-to-right by ascending frequency on a log scale. Circle size = peak amplitude; circle colour: lime = stable partial, purple = monotonic frequency drift, blue = oscillatory frequency drift. Arcs connect anti-correlated pairs — partials whose amplitude envelopes move in opposite directions after removing the expected exponential decay trend, the signature of energy being exchanged between modes. Arc thickness = energy cascaded, scaled as |r| × √(overlap energy); the thickest arc carries the most transferred energy. The arc curves upward proportionally to the log-frequency separation of the pair, so widely-spaced couplings arch high and closely-spaced ones hug the baseline. Use the Min |r| slider to suppress weaker couplings and reveal the strongest transfer paths. Hover arcs for frequencies, amplitudes, and correlation coefficient; hover circles for frequency and relative level.
MFCC mean ± 1σ by coefficient
Timbral centroid
Bars show the time-averaged MFCC, with error bars indicating one standard deviation of temporal variation. C0 ≈ overall loudness. C1 captures spectral tilt (positive = dark, negative = bright). C2–C4 capture broad formant structure. Higher coefficients describe fine spectral ripple. Tall bars = that coefficient carries strong signal; long whiskers = the timbre evolves along that axis.
Higher-order statistics
Shape of the distribution
Per-coefficient skewness and excess kurtosis of the MFCC time-series. Skewness ≠ 0 means the coefficient drifts more in one direction (useful for distinguishing attack-dominated from sustain-dominated timbres). High kurtosis indicates spiky/bursty temporal behaviour (transient events); near-zero indicates a smoothly evolving cepstrum.
Velocity & acceleration envelope
Cepstral dynamics
For each frame we compute the root-mean-square MFCC velocity (first difference Δ across coefficients) and MFCC acceleration (second difference ΔΔ). Large velocity = the timbre is changing quickly (attack, mode-hopping); large acceleration = the rate of change is itself changing. Both peak at the onset and decay toward a steady-state plateau.
MFCC matrix (raw heatmap)
The source
The raw MFCC matrix from which all statistics are computed. Vertical axis = coefficient index, horizontal axis = time. Darker = lower cepstral value, brighter = higher.
Impact fingerprint
Excitation signature
Attack time (ms): 10%→90% amplitude rise time — hard sticks <1 ms, soft mallets >5 ms. Peak/steady (dB): transient peak relative to the 50–100 ms RMS — quantifies impulsive vs. sustained character. Attack centroid (kHz): mean frequency of the onset window. Attack slope (dB/oct): spectral regression of the onset window — near-zero = hard bright implement, steep negative = soft dark implement.
Sustain by octave band
Frequency-resolved decay
RT60 extrapolated from the late-decay slope in each octave band. High-frequency bands typically decay fastest; low-frequency bands ring longest. A flat profile indicates even decay; a steep drop from low to high indicates a darker, fundamental-mode-dominated sustain character.
What you see
Five whole-take physical and psychoacoustic descriptors, each on a 0–1 scale.
Stick rates the hardness of the implement contact, after Freed (1990); ping the tonal definition of the tip-strike above the wash; wash the broadband density of the sustain; hum the slow modulation in the 100–500 Hz region (low-mode beating, the "ride hum"); buzz the rapid AM in the 1–8 kHz band (auditory roughness, after Aures / Daniel & Weber). When the active take is assigned to a cymbal, all other already-analysed takes of the same cymbal are drawn alongside as a parallel comparison so a single strike can be judged against a full take history. See
docs/DSP_CRITIQUE.md §3 for the formulas.
Excitation & sustain quantifiers
Reading the chart
The active take is rendered with full-opacity bars; other takes of the same cymbal are overlaid as faint outline bars in matching positions. A cymbal that consistently scores high on ping and low on wash is a defined, articulate ride; one that scores high on both wash and buzz with low ping is a dense crash. Hum spikes when low partials beat against each other; buzz spikes when mid-band partials are densely intermodulating. Stick reflects the strike, not the cymbal — it should rise with harder implements across takes of the same cymbal.
Spectral character
Time-averaged spectral descriptors
Each bar is the mean of a time-varying descriptor collapsed to a single number. Brightness: fraction of spectral energy above 2 kHz. Harmonicity: how closely tracked partials align to a harmonic template. Flatness: Wiener entropy (geometric/arithmetic mean ratio) — high = noise-like. Entropy: normalised Shannon entropy of the power spectrum — high = energy spread evenly across bins.
Modal inventory
Partial structure at a glance
Tracked partials: number of stable sinusoidal modes above the noise floor lasting at least ~50 ms — a proxy for modal density. Cascade events: inter-modal energy exchanges detected via frequency drift or anti-correlated amplitude envelopes. Mean partial T60: average decay time across all partials with a valid fit — how long individual modes ring.
What you see
Nine scalar chaos-theoretic invariants derived from the delay-embedded mono waveform (Touzé & Chaigne 1999 lineage). All bars are normalised to [0, 1]; hover for raw values. RQA group (blue): recurrence rate (RR), determinism (DET), diagonal entropy (ENT), mean diagonal length (L), and laminarity (LAM) characterise how often the system revisits prior states and whether those recurrences form structured patterns. Lyapunov (red): positive λmax confirms sensitive dependence on initial conditions — the defining signature of chaos; zero or negative means regular or damped dynamics. Complexity (purple): correlation dimension D₂ estimates attractor geometry; sample entropy and permutation entropy measure irregularity from two complementary angles. Higher values on all three indicate more complex, less predictable dynamics.
Chaos quantifiers
Interpreting the bars
A cymbal driven into a nonlinear regime shows high λmax, low DET (trajectories rarely form long deterministic diagonals), high SampEn and PE (unpredictable, high-complexity signal), and D₂ in the range 1–4 (low-dimensional strange attractor). A lightly struck cymbal in the linear regime shows low λmax, high DET and LAM (quasi-periodic, laminar structure), low SampEn and PE, and D₂ approaching 1–2. Consistent cross-take comparisons of the same cymbal isolate how strike intensity shifts the dynamical regime.
Specimen qualifiers
Physical and contextual descriptors for this cymbal. Click a chip to tag the specimen — selections are saved with the take and persist across sessions. Use these categories to enable controlled comparisons across the library.