§ 01
Wave & Frequency
Universal converter between frequency, period, wavelength and samples.Universal Converter
f · T · λ · samples — every field editable
What: Frequency, period, wavelength and samples — the same phenomenon in 4 units.
When: When you want to know "how big is 100 Hz physically?" or "how many samples is 5 ms?"
How: Edit any field — the other three update automatically.
Action: For sub spacing watch λ (wavelength), for latency checks watch samples, for comb-filter diagnosis watch period.
Tip: 100 Hz ≈ 10 ms ≈ 3.43 m at 20°C — a great anchor to memorise.
When: When you want to know "how big is 100 Hz physically?" or "how many samples is 5 ms?"
How: Edit any field — the other three update automatically.
Action: For sub spacing watch λ (wavelength), for latency checks watch samples, for comb-filter diagnosis watch period.
Tip: 100 Hz ≈ 10 ms ≈ 3.43 m at 20°C — a great anchor to memorise.
Frequency
Hz
Period
ms
Wavelength λ
m
Samples
smp
Derived values
½ λ—
¼ λ—
¼ λ Periode—
One octave up—
f = 1/T · 1000 · λ = c/f · smp = SR/f
Phase Delay
Phase shift in time
What: Converts phase (°) at a given frequency into time offset (ms / samples).
When: Time-aligning Sub↔Top, phase tuning, or understanding why small delays cause big filtering effects.
How: Enter phase and frequency → time offset and samples are computed.
Action: 180° = perfect cancellation, 0°/360° = perfect summation. Values in between create comb filters.
Tip: 90° at 1 kHz = 250 µs. Memorising this is gold when tuning live.
When: Time-aligning Sub↔Top, phase tuning, or understanding why small delays cause big filtering effects.
How: Enter phase and frequency → time offset and samples are computed.
Action: 180° = perfect cancellation, 0°/360° = perfect summation. Values in between create comb filters.
Tip: 90° at 1 kHz = 250 µs. Memorising this is gold when tuning live.
Phase
°
Frequency
Hz
Result
Time offset—
↳ in samples—
Period at f—
t = (φ/360) × T · T = 1000/f
Bandwidth
Octaves between two frequencies
What: Bandwidth in octaves between two frequencies, plus center frequency and Q factor.
When: Parametric EQ — how wide does the bell need to be to cover the range?
How: Enter lower and upper −3 dB frequencies.
Action: 1/3 octave (Q ≈ 4.3) for surgical notches, 1 octave (Q ≈ 1.4) for tonal corrections, 2 octaves for gentle shelf-like behavior.
Tip: Narrow Q = surgical (kill feedback, leave rest untouched). Wide Q = musical (shape character without sounding harsh).
When: Parametric EQ — how wide does the bell need to be to cover the range?
How: Enter lower and upper −3 dB frequencies.
Action: 1/3 octave (Q ≈ 4.3) for surgical notches, 1 octave (Q ≈ 1.4) for tonal corrections, 2 octaves for gentle shelf-like behavior.
Tip: Narrow Q = surgical (kill feedback, leave rest untouched). Wide Q = musical (shape character without sounding harsh).
Lower frequency
Hz
Upper frequency
Hz
Result
Bandwidth—
Center frequency—
Q (rounded)—
BW = log₂(f_h / f_l) · f_c = √(f_l × f_h)
Frequency Interval
Semitones up/down
What: Translates semitone steps into a frequency ratio (musical logic).
When: Pitch tuning, feedback hunting on musically meaningful points, or understanding why certain EQ boosts sound harmonic.
How: Enter a reference frequency and semitone steps (±).
Action: 12 semitones = octave (×2), 7 = fifth (×1.5), 4 = major third, 0 = root. These ratios sound "natural" together.
Tip: When feedback-hunting, search in semitone steps instead of random frequencies. Resonances often follow musical patterns.
When: Pitch tuning, feedback hunting on musically meaningful points, or understanding why certain EQ boosts sound harmonic.
How: Enter a reference frequency and semitone steps (±).
Action: 12 semitones = octave (×2), 7 = fifth (×1.5), 4 = major third, 0 = root. These ratios sound "natural" together.
Tip: When feedback-hunting, search in semitone steps instead of random frequencies. Resonances often follow musical patterns.
Reference
Hz
Semitones (±)
st
Result
Resulting frequency—
Interval—
f_out = f_ref × 2^(n/12)
Octave Segments
Thirds, fifths, octaves
What: Breaks octave steps from a reference frequency into thirds, fifths and octaves.
When: RTA setup, multi-band compressor crossovers, or fine EQ tuning on musically logical points.
How: Enter a reference frequency — the table shows all harmonic points.
Action: 1/3 octave = classic live RTA. 1/6 = medium resolution. 1/12 = very fine. 1/24 = Smaart-grade.
Tip: Human perception reliably resolves frequency differences down to ~1/6 octave; below that it becomes increasingly irrelevant.
When: RTA setup, multi-band compressor crossovers, or fine EQ tuning on musically logical points.
How: Enter a reference frequency — the table shows all harmonic points.
Action: 1/3 octave = classic live RTA. 1/6 = medium resolution. 1/12 = very fine. 1/24 = Smaart-grade.
Tip: Human perception reliably resolves frequency differences down to ~1/6 octave; below that it becomes increasingly irrelevant.
Reference
Hz
above reference
⅓ octave Major third—
½ octave Tritone—
⅔ octave Minor sixth—
1 octave Octave—
below reference
⅓ octave Major third—
½ octave Tritone—
⅔ octave Minor sixth—
1 octave Octave—
§ 02
Level & dB
Linear ↔ logarithmic conversion, summation, headroom.Linear → dB
Voltage / sound-pressure change
What: Converts a linear factor (e.g. doubled voltage) into a dB change.
When: When you want to translate voltage/level ratios (voltmeter readings, ADC levels) into familiar dB.
How: Enter a reference value (e.g. 1 V nominal) and the measured value.
Action: Factor 2 = +6 dB, factor 0.5 = −6 dB, factor 10 = +20 dB. Use this logic for voltage measurements at the mixer output.
Tip: For power (W) instead of voltage, use 10·log instead of 20·log — double the power = +3 dB.
When: When you want to translate voltage/level ratios (voltmeter readings, ADC levels) into familiar dB.
How: Enter a reference value (e.g. 1 V nominal) and the measured value.
Action: Factor 2 = +6 dB, factor 0.5 = −6 dB, factor 10 = +20 dB. Use this logic for voltage measurements at the mixer output.
Tip: For power (W) instead of voltage, use 10·log instead of 20·log — double the power = +3 dB.
Reference value
Measured value
Result
dB change—
Multiplier—
% change—
dB = 20 × log₁₀(V_meas / V_ref)
dB → Linear
Logarithm back to factor
What: Converts a dB value back into voltage and power factors.
When: If you know e.g. "the mix is 6 dB too loud" and want to compute concretely how much less power the amp must deliver.
How: Enter a dB value → voltage and power factor + percentage.
Action: +6 dB = ×2 voltage = ×4 power. −10 dB = ×0.32 voltage = ×0.1 power. Useful for amp sizing.
Tip: Rule of thumb: −3 dB ≈ half the power, −6 dB ≈ half the voltage, −10 dB ≈ perceived "half as loud".
When: If you know e.g. "the mix is 6 dB too loud" and want to compute concretely how much less power the amp must deliver.
How: Enter a dB value → voltage and power factor + percentage.
Action: +6 dB = ×2 voltage = ×4 power. −10 dB = ×0.32 voltage = ×0.1 power. Useful for amp sizing.
Tip: Rule of thumb: −3 dB ≈ half the power, −6 dB ≈ half the voltage, −10 dB ≈ perceived "half as loud".
dB value
dB
Result
Voltage factor—
Power factor—
% Voltage—
V = 10^(dB/20) · P = 10^(dB/10)
Correlated Summation
Add two correlated signals
What: Adds two dB levels of the same phase (coherent summation).
When: Sub pairing, coupled clusters, double PA, or simply knowing "if I add one more box, how much louder will it get?"
How: Enter two levels A and B in dB.
Action: Equal levels (A=B) → +6 dB sum. 6 dB difference → only +1 dB. 10 dB+ difference → practically no summation left.
Tip: Two identical subs side by side = +6 dB on-axis (not +3, that would be incoherent summation like noise).
When: Sub pairing, coupled clusters, double PA, or simply knowing "if I add one more box, how much louder will it get?"
How: Enter two levels A and B in dB.
Action: Equal levels (A=B) → +6 dB sum. 6 dB difference → only +1 dB. 10 dB+ difference → practically no summation left.
Tip: Two identical subs side by side = +6 dB on-axis (not +3, that would be incoherent summation like noise).
Signal A
dB
Signal B
dB
Result
Sum (total)—
Δ above loudest—
Voltage factor—
L = 20 × log₁₀(10^(L_A/20) + 10^(L_B/20))
Passive Speaker Headroom
Amplifier reserve over speaker
What: Ratio between amplifier power and speaker handling, expressed as dB reserve.
When: Choosing an amp for passive boxes — "can I run this box safely with this amp?"
How: Enter amplifier RMS and speaker RMS handling.
Action: +3 dB reserve (amp twice as strong as speaker) is industry standard for clean peaks. +6 dB is premium for live sound. At +0 dB → no headroom, clipping causes damage.
Tip: Prefer a stronger amp with a limiter to an underpowered amp — clipping kills tweeters far faster than honest overload.
When: Choosing an amp for passive boxes — "can I run this box safely with this amp?"
How: Enter amplifier RMS and speaker RMS handling.
Action: +3 dB reserve (amp twice as strong as speaker) is industry standard for clean peaks. +6 dB is premium for live sound. At +0 dB → no headroom, clipping causes damage.
Tip: Prefer a stronger amp with a limiter to an underpowered amp — clipping kills tweeters far faster than honest overload.
Amplifier RMS
W
Speaker RMS
W
Result
Headroom—
Power Ratio—
Headroom [dB] = 10 × log₁₀(P_amp / P_spk)
§ 03
Comb & Delay
Time-offset analysis, acoustic paths, BPM and frame sync.Comb Filter Calculator
Time offset → cancellations & peaks
What: Shows at which frequencies a time offset (between two sound sources) creates comb-filter dips and peaks.
When: Tuning Sub↔Top alignment, stereo setup, reflection diagnosis or multi-mic recording.
How: Enter the estimated or measured time offset (ms).
Action: Dips show where the sound is "cancelled" (thin, hollow). Peaks where it gets too loud. At "Summation Stop" the comb effect ends — below that, summation is essentially inaudible.
Tip: Even 0.5 ms offset creates audible combs above 1 kHz. That's why time-alignment matters so much.
When: Tuning Sub↔Top alignment, stereo setup, reflection diagnosis or multi-mic recording.
How: Enter the estimated or measured time offset (ms).
Action: Dips show where the sound is "cancelled" (thin, hollow). Peaks where it gets too loud. At "Summation Stop" the comb effect ends — below that, summation is essentially inaudible.
Tip: Even 0.5 ms offset creates audible combs above 1 kHz. That's why time-alignment matters so much.
Time offset
ms
↳ in samples—
Cancellations (Dips)
Dip 1—
Dip 2—
Dip 3—
Peaks
Peak 1—
Peak 2—
Peak 3—
Transition
Single Period—
Summation Stop—
Dip_n = (2n−1) / (2·Δt) · Peak_n = n / Δt · SumStop ≈ 1 / (3·Δt)
Acoustic Transmission Path
Two sources → C, with comb analysis
What: Compares two acoustic paths (sources A and B to the same listening point C) and shows distance Δ, time Δ, level Δ and resulting comb frequencies.
When: When you compare two sound sources at the same point — e.g. main system vs. wall reflection, sidefill vs. main, or drum-mic spill.
How: Enter both travel times in ms (from Smaart, Systune, or simply distance/c).
Action: For large Δt → identify comb frequencies and apply delay. For small Δt → can be ignored.
Tip: Level difference > 10 dB → the weaker source is acoustically irrelevant, no comb problem.
When: When you compare two sound sources at the same point — e.g. main system vs. wall reflection, sidefill vs. main, or drum-mic spill.
How: Enter both travel times in ms (from Smaart, Systune, or simply distance/c).
Action: For large Δt → identify comb frequencies and apply delay. For small Δt → can be ignored.
Tip: Level difference > 10 dB → the weaker source is acoustically irrelevant, no comb problem.
Source A → C
ms
Source B → C
ms
Distances & Δ
Distance A—
Distance B—
Δ Distance—
Δ Time—
↳ Δ in samples—
Level offset (1/r²)—
Comb analysis from Δ time
Frequency @ full λ—
Comb Dip 1—
⅓ λ—
Summation Stop—
d = t × c · Level = 20·log₁₀(d_shorter / d_longer) · λ = Δd
BPM → Delay
Musically synced delay times
What: Translates song tempo into delay times for every note value (halves, quarters, eighths, triplets).
When: FX setup for vocals, guitar, synths — when the delay should lock to the beat instead of drifting.
How: Enter tempo (BPM), pick a note value, read ms.
Action: Quarter = "slap" like classic tape echo. Dotted eighth = U2 Edge delay. Triplets = swingy. Enter values directly into your FX plugin.
Tip: At slow tempos < 90 BPM → eighths/16ths often sound better than quarters (quarters get too slow, feel like repetition instead of reverb).
When: FX setup for vocals, guitar, synths — when the delay should lock to the beat instead of drifting.
How: Enter tempo (BPM), pick a note value, read ms.
Action: Quarter = "slap" like classic tape echo. Dotted eighth = U2 Edge delay. Triplets = swingy. Enter values directly into your FX plugin.
Tip: At slow tempos < 90 BPM → eighths/16ths often sound better than quarters (quarters get too slow, feel like repetition instead of reverb).
Tempo
BPM
Note values
Half
——
Quarter
——
Eighth
——
Dotted Eighth
——
Quarter Triplet
——
Eighth Triplet
——
¼ Note [ms] = 60000 / BPM
Video Frame Sync
Audio delay for frame offset
What: Computes audio delay time from a video frame offset (e.g. "3 frames later").
When: Lip-sync tuning for live video, broadcast, theatre with projection, or concert IMAG.
How: Enter frame rate (24/25/30/50/60) and desired frame offset.
Action: Apply the ms value to the mixer or DSP audio output delay. Positive = audio later, negative = audio earlier.
Tip: Perception threshold: ±50 ms usually OK, >100 ms becomes audibly off. For TV: audio may lead video by max 1–2 frames, but trail by up to 3 frames (asymmetry of perception).
When: Lip-sync tuning for live video, broadcast, theatre with projection, or concert IMAG.
How: Enter frame rate (24/25/30/50/60) and desired frame offset.
Action: Apply the ms value to the mixer or DSP audio output delay. Positive = audio later, negative = audio earlier.
Tip: Perception threshold: ±50 ms usually OK, >100 ms becomes audibly off. For TV: audio may lead video by max 1–2 frames, but trail by up to 3 frames (asymmetry of perception).
Frame Rate
fps
Frame offset
frm
Result
Audio delay—
↳ in samples—
Frame duration—
Delay [ms] = (Frames / fps) × 1000
§ 04
PA System
Coverage angles, FAR/LAR and speaker geometry.Stereo PA Quick-Eval
Enter venue dimensions → system recommendation (true cone geometry)
What: Quick selection of which PA system fits your venue.
When: While packing the truck, or on-site as a reality check before setup.
How: 1. Estimate or measure venue width (W) and depth (D) — 2. Type them in — 3. Read the recommendation.
Action: Pick a system from your truck that falls into the shown coverage range:
· Long-throw / Narrow → line array or narrow 60–70° tops
· Standard / Wide Main → classic 80–110° tops
· Short-throw / Wide → short point sources with wide pattern
· Multi-Box / Line Array → multiple clusters or array needed — plan extra gear
Tip: "Max Throw" tells you the longest acoustic distance in the venue — critical for level reserve and box choice.
When: While packing the truck, or on-site as a reality check before setup.
How: 1. Estimate or measure venue width (W) and depth (D) — 2. Type them in — 3. Read the recommendation.
Action: Pick a system from your truck that falls into the shown coverage range:
· Long-throw / Narrow → line array or narrow 60–70° tops
· Standard / Wide Main → classic 80–110° tops
· Short-throw / Wide → short point sources with wide pattern
· Multi-Box / Line Array → multiple clusters or array needed — plan extra gear
Tip: "Max Throw" tells you the longest acoustic distance in the venue — critical for level reserve and box choice.
Venue width W
m
Venue depth D
m
Speaker spacing s (empty = auto)
m
Recommendation
Speaker spacing (s)—
Coverage range—
Max Throw—
FAR · LAR (@ rec)—
Recommended system—
Fills
Outfills—
Nearfills—
s = min(W,D)/3 (auto) · θ_min = arctan((W+s)/2D) + arctan(|W−s|/2D) · Outfills when θ > 100° · Nearfills when s/D > 0.5
Audience → Coverage °
Speaker angle from audience dimensions
What: Computes the required speaker coverage angle from audience depth and width.
When: When you have a concrete venue and want to check whether your speaker coverage fits — or what angle would be "ideal".
How: Enter D (depth) and W (width). Optional "Speaker actual °" for comparison.
Action: Gaps (red) → tighter speaker placement or wider pattern. Overshoot (purple) → reduce level or pick a narrower pattern, otherwise wall reflections.
Tip: Uses the chord/circle model (classic McCarthy) — gives slightly wider angles than a pure cone model. Conservative and proven in practice.
When: When you have a concrete venue and want to check whether your speaker coverage fits — or what angle would be "ideal".
How: Enter D (depth) and W (width). Optional "Speaker actual °" for comparison.
Action: Gaps (red) → tighter speaker placement or wider pattern. Overshoot (purple) → reduce level or pick a narrower pattern, otherwise wall reflections.
Tip: Uses the chord/circle model (classic McCarthy) — gives slightly wider angles than a pure cone model. Conservative and proven in practice.
Audience depth
m
Audience width
m
Result
Audience FAR—
Required coverage °—
Comparison
Speaker actual °
°
FAR = D / W · Angle = 2 × arcsin(1 / FAR)
Coverage ↔ FAR & LAR
Convert speaker coverage to FAR/LAR
What: Geometric ratios of a speaker's coverage. FAR = throw / half-width (how deep), LAR = inverse (how wide per throw).
When: When picking a box: "how far does my 80° top actually reach?" or "how wide at what distance?"
How: Enter speaker coverage in °.
Action: FAR × half-width = max throw. LAR × throw = full coverage width at that distance. Narrow patterns (60°) → high FAR, long and thin. Wide patterns (120°) → low FAR, short and wide.
Tip: 90° has FAR=1.41 (symmetry point). Narrower than 90° → long-throw character. Wider → short-throw character.
When: When picking a box: "how far does my 80° top actually reach?" or "how wide at what distance?"
How: Enter speaker coverage in °.
Action: FAR × half-width = max throw. LAR × throw = full coverage width at that distance. Narrow patterns (60°) → high FAR, long and thin. Wide patterns (120°) → low FAR, short and wide.
Tip: 90° has FAR=1.41 (symmetry point). Narrower than 90° → long-throw character. Wider → short-throw character.
Speaker coverage
°
Result
FAR (Forward AR)—
LAR (Lateral AR)—
FAR = 1 / sin(°/2) · LAR = 2 / FAR
Do I Need Delay Speakers?
Distance comparison front/back row from main system
What: Checks whether delay towers are needed and where to place them — based on path-length difference front vs. back row.
When: Deep venues (>20 m back row), open-air, sports halls, festivals or long narrow venues.
How: Enter tweeter height, ear height, and front/back row distances from the speaker.
Action: Check Δt status: green = no delays needed, orange = borderline (tower optional), red = place towers per the list, enter delay value at the DSP.
Tip: Tower spacing 14 m (40 ms threshold) is temperature-dependent — the header Temp value is factored in automatically.
When: Deep venues (>20 m back row), open-air, sports halls, festivals or long narrow venues.
How: Enter tweeter height, ear height, and front/back row distances from the speaker.
Action: Check Δt status: green = no delays needed, orange = borderline (tower optional), red = place towers per the list, enter delay value at the DSP.
Tip: Tower spacing 14 m (40 ms threshold) is temperature-dependent — the header Temp value is factored in automatically.
Tweeter height
m
Audience ear height
m
Speaker base → front row
m
Speaker base → back row
m
Analysis
Front distance—
Back distance—
Δ Distance—
Δ Time—
Distance ratio—
Δ Level (1/r²)—
Recommendation—
Δt status—
Rule of thumb: delay towers needed when Δt > 40 ms (≈ 14 m at 20 °C) — otherwise the main system localises correctly in front.
Spatial Crossover
Level & time transition main → delay tower
What: Where main system and delay tower meet in level, plus the exact delay value for time-alignment.
When: After tower placement, before soundcheck — the two most important numbers for tower tuning.
How: Enter distance main → tower (tape measure or laser) and level offset (typically 0 to −6 dB).
Action: Apply delay setting (ms) to the tower DSP. Note the crossover position visually — that's the transition zone where phase coherence becomes most critical.
Tip: Tower at 0 dB → image often collapses to the tower. At −3 to −6 dB → image stays clearly at the main, tower only adds reach/level.
When: After tower placement, before soundcheck — the two most important numbers for tower tuning.
How: Enter distance main → tower (tape measure or laser) and level offset (typically 0 to −6 dB).
Action: Apply delay setting (ms) to the tower DSP. Note the crossover position visually — that's the transition zone where phase coherence becomes most critical.
Tip: Tower at 0 dB → image often collapses to the tower. At −3 to −6 dB → image stays clearly at the main, tower only adds reach/level.
Distance main → tower
m
Delay level rel. main
dB
Level transition
Crossover position—
↳ from main—
↳ from tower—
Time alignment
Delay setting (tower)—
↳ in samples—
x_c = D / (1 + 10^(ΔdB/20)) · t = D / c · Default Δ=0 dB → crossover in the middle
Line Array Splay
Splay angles using a laser distance meter
What: Estimate of splay angles between line-array boxes — using only rig height and distances to front/back row.
When: While the rigger is still waiting, when you want a rough idea, or as a sanity check before MAPP/ArrayCalc verification.
How: Sight rig height (top of array) and floor distances to front and back row with a laser distance meter, enter number of boxes + audience rake.
Action: Use avg splay (rounded to 0.5°) as a starting point for rigging configuration. The side elevation shows visually how the array should tilt.
Tip: This estimate gives uniform splay — real arrays splay progressively (tighter at the top, wider at the bottom). Verify with manufacturer software before show start.
When: While the rigger is still waiting, when you want a rough idea, or as a sanity check before MAPP/ArrayCalc verification.
How: Sight rig height (top of array) and floor distances to front and back row with a laser distance meter, enter number of boxes + audience rake.
Action: Use avg splay (rounded to 0.5°) as a starting point for rigging configuration. The side elevation shows visually how the array should tilt.
Tip: This estimate gives uniform splay — real arrays splay progressively (tighter at the top, wider at the bottom). Verify with manufacturer software before show start.
Rig height (top of array)
m
Distance → front row
m
Distance → last row
m
Number of boxes in array
box
Audience rake (last row higher)
m
Result
Down-angle bottom box (front)—
Down-angle top box (back)—
Total Coverage—
Splay joints (n − 1)—
Avg splay (uniform)—
Avg splay (rounded to 0.5°)—
αfront = arctan(rig / dfront) ·
αback = arctan((rig − rake) / dback) ·
Coverage = αfront − αback ·
Splay = Coverage / (n − 1)
Estimate with uniform distribution. Real arrays splay progressively — tighter at the bottom, wider at the top. Verify with manufacturer software (MAPP, ArrayCalc, Soundvision) before show start.
Estimate with uniform distribution. Real arrays splay progressively — tighter at the bottom, wider at the top. Verify with manufacturer software (MAPP, ArrayCalc, Soundvision) before show start.
§ 05
Sub Array
Inline gradient, spacing and center frequency for subwoofers.Inline Gradient Sub Array
Front + rear sub with XOVR & delay
What: Computes offset and delay for a 2-sub inline-gradient array (front + rear, polarity inverted) — classic cardioid arrangement.
When: Building sub arrays that need stage cancellation — festivals, theatres, stages with mics directly in front of subs.
How: Enter XOVR frequency (typically 80–120 Hz).
Action: Place the rear sub at "Rear Sub Offset" (m) behind the front sub, set "Rear Sub Delay" at the DSP, invert polarity. Polar plot shows forward cardioid.
Tip: Works best at the max-summation frequency (= 2/3 × XOVR). Above that the pattern degrades progressively.
When: Building sub arrays that need stage cancellation — festivals, theatres, stages with mics directly in front of subs.
How: Enter XOVR frequency (typically 80–120 Hz).
Action: Place the rear sub at "Rear Sub Offset" (m) behind the front sub, set "Rear Sub Delay" at the DSP, invert polarity. Polar plot shows forward cardioid.
Tip: Works best at the max-summation frequency (= 2/3 × XOVR). Above that the pattern degrades progressively.
−3 dB XOVR frequency
Hz
Result
Max summation frequency—
Rear sub offset—
Rear sub delay—
↳ delay in samples—
Offset = c / (4 × ⅔·XOVR) · Delay = Offset / c · 1000
Max Sub Spacing
Max distance without power alley
What: Maximum distance between two subs (= λ/2 at the XOVR frequency) — beyond that, comb filters appear in the coverage.
When: Setting up 2+ subs — whether stereo split, distributed array or LCR sub setup.
How: Enter sub XOVR frequency (typically 80–120 Hz, depending on system).
Action: Never space subs farther apart than d_max in live setup. For larger stage widths → distribute more subs or use cardioid arrays.
Tip: Low XOVR (e.g. 60 Hz) → generous (2.86 m). High XOVR (120 Hz) → tight (1.43 m). Rule of thumb: better too tight than too wide.
When: Setting up 2+ subs — whether stereo split, distributed array or LCR sub setup.
How: Enter sub XOVR frequency (typically 80–120 Hz, depending on system).
Action: Never space subs farther apart than d_max in live setup. For larger stage widths → distribute more subs or use cardioid arrays.
Tip: Low XOVR (e.g. 60 Hz) → generous (2.86 m). High XOVR (120 Hz) → tight (1.43 m). Rule of thumb: better too tight than too wide.
Sub XOVR frequency
Hz
Result
Max distance—
Wavelength at XOVR—
d_max = c / (2 × XOVR) = λ / 2
Sub Center Frequency
Geometric mean of the sub range
What: Logarithmic center (geometric mean) of a frequency range — the "center of gravity" of the sub band.
When: Parametric EQ on the sub bus, time-alignment reference, polar-pattern verification or sub-model evaluation.
How: Enter lower and upper sub frequencies (e.g. 40–100 Hz for classic live).
Action: Use f_c as the EQ center frequency (e.g. a "Sub Drive" filter), as a test tone for cardioid polar tests, or as the SPL measurement point.
Tip: 40–100 Hz → 63 Hz (NOT 70). Think geometrically because hearing is logarithmic — 100 Hz to 200 Hz "feels" the same width as 200 Hz to 400 Hz.
When: Parametric EQ on the sub bus, time-alignment reference, polar-pattern verification or sub-model evaluation.
How: Enter lower and upper sub frequencies (e.g. 40–100 Hz for classic live).
Action: Use f_c as the EQ center frequency (e.g. a "Sub Drive" filter), as a test tone for cardioid polar tests, or as the SPL measurement point.
Tip: 40–100 Hz → 63 Hz (NOT 70). Think geometrically because hearing is logarithmic — 100 Hz to 200 Hz "feels" the same width as 200 Hz to 400 Hz.
Lower sub frequency
Hz
Upper sub frequency
Hz
Result
Center frequency—
f_c = √(f_low × f_high)
Cardioid Sub Stack
Front + rear box with polarity invert for stage cancellation
What: Computes delay and polarity for a 2-sub cardioid setup (front + reverse box) — apple-shaped pattern with forward output and rear null.
When: When you need "stage cancellation" — vocal mics directly in front of subs, drum riser protection, conferences with lavalier mics behind the PA.
How: Enter sub depth (box depth or acoustic offset) and desired pattern frequency.
Action: Place the rear sub d behind the front sub (or reverse-stack on top), set delay (= d/c) and polarity (inverted) at the DSP. Polar plot shows the cardioid.
Tip: Works best at f_opt = c/(4d) — that's where you gain +6 dB forward gain. At lower frequencies you get less gain, but cancellation remains.
When: When you need "stage cancellation" — vocal mics directly in front of subs, drum riser protection, conferences with lavalier mics behind the PA.
How: Enter sub depth (box depth or acoustic offset) and desired pattern frequency.
Action: Place the rear sub d behind the front sub (or reverse-stack on top), set delay (= d/c) and polarity (inverted) at the DSP. Polar plot shows the cardioid.
Tip: Works best at f_opt = c/(4d) — that's where you gain +6 dB forward gain. At lower frequencies you get less gain, but cancellation remains.
Sub depth / offset (d)
m
Pattern @ frequency
Hz
Result
Rear delay—
↳ in samples—
Rear polarity—
Optimal frequency—
Forward Gain—
Rear Rejection—
PATTERN (POLAR)
LAYOUT (TOP-DOWN)
τ = d/c · |F(θ)| = 2·sin(kd(1+cos θ)/2) · f_opt = c/(4d)
End-Fire Array
n subs in line with progressive delay → forward cardioid
What: n subs lined up, each with progressive delay — creates a forward-pointing narrow cardioid pattern with rear rejection.
When: When you want to focus sub energy in a specific direction (festival front cluster, IPS sub distribution, long narrow indoor venues).
How: Enter number of subs (n), spacing (typically 0.6–1.2 m) and pattern frequency.
Action: Enter each sub's computed delay at the DSP — rear sub at 0 ms, each one ahead +d/c later. Forward gain = 20·log(n) dB boost.
Tip: 4 subs in line yield ~+12 dB forward and ~−14 dB rear rejection at 60 Hz (with d=0.6 m). Top-tier setup for modern festival designs.
When: When you want to focus sub energy in a specific direction (festival front cluster, IPS sub distribution, long narrow indoor venues).
How: Enter number of subs (n), spacing (typically 0.6–1.2 m) and pattern frequency.
Action: Enter each sub's computed delay at the DSP — rear sub at 0 ms, each one ahead +d/c later. Forward gain = 20·log(n) dB boost.
Tip: 4 subs in line yield ~+12 dB forward and ~−14 dB rear rejection at 60 Hz (with d=0.6 m). Top-tier setup for modern festival designs.
Number of subs (n)
pcs
Sub spacing (d)
m
Pattern @ frequency
Hz
Result
Forward Gain—
Rear Rejection—
Delay range—
Delays per sub—
PATTERN (POLAR)
LAYOUT (TOP-DOWN)
τ_i = (i−1)·d/c · |S(θ)|² = sin²(nα/2)/sin²(α/2), α = kd(cos θ−1)
Sub Setup Recommendation
Count + crossover + stage width → configuration suggestion
What: Recommends the optimal sub configuration (Single, Coupled, Stereo, Cardioid, End-Fire, Distributed) based on sub count, XOVR frequency and stage width.
When: When planning a new setup or as a sanity check that the planned setup makes sense for the venue dimensions.
How: Enter number of subs, planned XOVR frequency and stage width.
Action: Follow the recommendation and consult the more specific card (Cardioid Stack, End-Fire, Inline Gradient) for the exact delay values.
Tip: "Power Alley" warning (red comb stripes) means: subs too far apart for the XOVR. Either move them closer, lower the XOVR, or pick mono center.
When: When planning a new setup or as a sanity check that the planned setup makes sense for the venue dimensions.
How: Enter number of subs, planned XOVR frequency and stage width.
Action: Follow the recommendation and consult the more specific card (Cardioid Stack, End-Fire, Inline Gradient) for the exact delay values.
Tip: "Power Alley" warning (red comb stripes) means: subs too far apart for the XOVR. Either move them closer, lower the XOVR, or pick mono center.
Configuration
Total subs
pcs
Crossover frequency
Hz
Stage width
m
Recommendation
Configuration—
Reasoning—
Rule of thumb: max sub spacing = λ/2 at XOVR · above that → power alley · cardioid costs output, gains directivity
§ 06
Reference
Quick lookup — no typing needed: distance/level, BW/Q, voltage/impedance.Distance Attenuation
Level loss with distance (1/r²)
| dB | Distance (m) | Distance (ft) |
|---|---|---|
| 0 | 1 | 3.3 |
| −3 | 1.4 | 4.6 |
| −6 | 2 | 6.5 |
| −9 | 2.8 | 9.3 |
| −12 | 4 | 13 |
| −15 | 5.7 | 19 |
| −18 | 8 | 26 |
| −21 | 11 | 37 |
| −24 | 16 | 52 |
| −27 | 23 | 74 |
| −30 | 32 | 105 |
| −36 | 64 | 209 |
| −42 | 128 | 418 |
Bandwidth ↔ Q
EQ Q values to octave bandwidths
| BW (Octaves) | Q (rounded) |
|---|---|
| 2 | 0.7 |
| 1.4 | 1 |
| 1 | 1.4 |
| 0.7 | 2 |
| 0.5 | 3 |
| 0.35 | 4 |
| 0.25 | 6 |
| 0.167 | 9 |
| 0.125 | 12 |
| 0.08 | 16 |
Multiplier ↔ dB
Voltage factors to dB
| Factor | dB |
|---|---|
| 1.1× | 0.83 |
| 1.25× | 1.94 |
| 1.5× | 3.50 |
| 1.75× | 4.90 |
| 2× | 6.00 |
| 4× | 12.00 |
| 10× | 20.00 |
| 31.6× | 30.00 |
| ~1000× | 60.00 |
Voltage & Impedance Reference
Pro-audio signal levels and impedances
| Type | Impedance | Level |
|---|---|---|
| Mic Out | 50–600 Ω | −60…−40 dBV |
| Mic In | 1.5–15 kΩ | −60…−40 dBV |
| Inst Out | 10–100 kΩ | −20 dBu |
| Inst In | 47 k–10 MΩ | −20 dBu |
| Line Out Pro | 75–600 Ω | +4 dBu |
| Line In Pro | 10–50 kΩ | +4 dBu |
| Line Out Cons | 75–600 Ω | −10 dBV |
| Line In Cons | 10–50 kΩ | −10 dBV |
| Speaker Out | < 100 mΩ | +20…+40 dBV |
| Speaker In | 4–16 Ω | +20…+40 dBV |
| Aux Out | 75–150 Ω | −10 dBV |
| Aux In | > 10 kΩ | −10 dBV |
| Phones Out | 0.1–24 Ω | — |
| Phones Amp | 0.5–120 Ω | — |
| Phones In | 8–600 Ω | — |
§ 07
Index
Glossary of all abbreviations, symbols and technical terms used in this app.Basics & Waves
Frequency · Wavelength · Time
fFrequency
Number of cycles per second, in Hertz (Hz). Determines perceived pitch — 440 Hz = concert A.
TPeriod
Time for one complete cycle.
T = 1 / f. At 100 Hz, T = 10 ms.λLambda · Wavelength
Spatial length of one cycle in air.
λ = c / f. At 100 Hz and 20 °C, λ ≈ 3.43 m.cSpeed of sound
Speed of sound in air, ≈ 343 m/s at 20 °C. Increases with temperature (~0.6 m/s per °C).
HzHertz
Unit of frequency: 1 Hz = one cycle per second. kHz = 1000 Hz.
msMillisecond
1/1000 of a second. Standard unit for audio delays. Sound travels about 34 cm in 1 ms.
smpSamples
Digital sample values. Number of samples per unit of time depends on sample rate: 1 ms at 48 kHz = 48 samples.
SRSample Rate
Sampling rate in Hz. 48 000 Hz means 48 000 samples per second. Standard pro-audio rates: 44.1k / 48k / 88.2k / 96k / 176.4k / 192k.
ΔDelta
Difference between two values. Δt = time difference, Δd = distance difference, Δ dB = level difference.
φPhi · Phase
Angular position within the cycle, 0 – 360°. 180° = inverted, 360° = one full cycle.
Level & dB
Logarithmic units · Power
dBDecibel
Logarithmic ratio unit.
+6 dB = 2× voltage, +10 dB ≈ twice as loud perceived.dBVdB relative to 1 V
Level reference: 0 dBV = 1 Volt RMS. Common for consumer gear (−10 dBV).
dBudB relative to 0.7746 V
Level reference: 0 dBu = 0.7746 V RMS (historically 600 Ω). Pro-audio standard: +4 dBu = 1.228 V RMS.
0 dBu ≈ −2.2 dBV.SPLSound Pressure Level
Sound pressure level in dB, referenced to 20 µPa (hearing threshold). Live concert ~100–110 dB SPL.
RMSRoot Mean Square
Quadratic mean. Describes continuous handling / power — more relevant than peak values.
1/r²Inverse Square Law
Sound pressure halves per doubling of distance — equals
−6 dB per doubling in the free field.HeadroomLevel reserve
Reserve between nominal and maximum level. Important so peaks don't clip.
CorrelatedIn phase
Two signals with identical content & phase. Add linearly (voltage sum); two identical signals yield +6 dB.
WWatt
Unit of electrical power. Amplifier and loudspeaker handling, typically rated in W RMS.
Filter & EQ
Bandwidth · Q · Comb
QQuality Factor
Filter quality. Higher Q = narrower bandwidth of a bell-EQ filter. Q 1 ≈ 1.4 octaves, Q 10 ≈ 0.14 octaves.
BWBandwidth
Frequency range, often expressed in octaves.
BW = log₂(f_high / f_low).EQEqualizer
Frequency-response shaping. Boost or cut in a defined band.
OctaveFrequency doubling
One octave up = double the frequency; one octave down = half the frequency.
Comb FilterComb filter
Alternating cancellations and peaks in the frequency response, caused by time offsets between two correlated signals (e.g. two mics or two speakers).
DipCancellation
Frequency where two signals interfere destructively — a level dip in the frequency response.
PeakOvershoot
Frequency where two signals sum constructively — a level peak in the frequency response.
f_cCenter Frequency
Center frequency of a filter or band. For a bell EQ, the point of max boost/cut. For a sub band = geometric mean:
f_c = √(f_low × f_high).NotchNarrow-band cut
Very narrow EQ cut (Q ≥ 4) to surgically remove a resonance or feedback frequency without affecting the rest of the sound.
XOVRCrossover frequency
Transition frequency between two bands (Sub↔Top, LF↔HF). For sub arrays, sets max spacing (λ/2 rule).
Phase & Time
Delay · BPM · Frame sync
PhaseCycle position
Current position within the cycle, in degrees (0 – 360°). 180° equals a polarity flip.
Phase delayPhase as time
Phase angle converted into a time delay. Frequency-dependent: the same angle = different time depending on frequency.
BPMBeats per Minute
Tempo in beats per minute.
¼ note [ms] = 60 000 / BPM.fpsFrames per Second
Video frame rate. Standards: 24 (cinema), 25 (PAL), 29.97/30 (NTSC), 50/60 (sports/HFR).
FrameSingle image
One frame from a video sequence. At 25 fps, one frame lasts 40 ms.
Note Values
Rhythmic subdivisions
𝅗𝅥Half note
2 beats duration. At 120 BPM = 1 000 ms.
♩Quarter note
1 beat — reference note for BPM. At 120 BPM = 500 ms.
♪Eighth note
½ beat. At 120 BPM = 250 ms.
♪.Dotted eighth
1.5× the normal duration (eighth + sixteenth). At 120 BPM = 375 ms. Popular for dub delays.
Triplet3 in the time of 2
3 equal notes in the time of 2 normal ones. Eighth triplet = 3 in one beat. At 120 BPM, an eighth triplet ≈ 167 ms.
Musical Intervals
In semitones of equal temperament
UnisonSame pitch · 0 ST
Same frequency, no interval.
Second2nd degree · 1–2 ST
Minor = 1 semitone (tension), major = 2 semitones (diatonic).
Third3rd degree · 3–4 ST
Minor = 3 ST (minor character), major = 4 ST (major character). ⅓ octave = exactly a major third.
Fourth4th degree · 5 ST
Frequency ratio ≈ 1.335. Consonant, often used as a resolution interval.
Tritone6 ST · ½ octave
Exactly half an octave. Historically «diabolus in musica» — very dissonant.
Fifth5th degree · 7 ST
Frequency ratio ≈ 1.498 (≈ 3:2). Most important harmonic interval, defines key.
Sixth6th degree · 8–9 ST
Minor = 8 ST, major = 9 ST. ⅔ octave = exactly a minor sixth.
Seventh7th degree · 10–11 ST
Minor = 10 ST (dominant seventh), major = 11 ST (leading-tone tension).
Octave12 ST
Frequency doubling. Strongest consonance. Note name repeats.
Ninth / 10th / …Compound intervals
Built from octave + smaller interval: ninth = octave + second, tenth = oct + third, eleventh = oct + fourth, twelfth = oct + fifth, etc.
PA & Live Sound
Speaker geometry · System terms
PAPublic Address
Sound-reinforcement system for public playback. Includes mixer, amps, speakers.
FOHFront of House
Main mixing position in the venue — where the engineer mixes for the audience.
FARForward Aspect Ratio
Ratio of throw to half-coverage-width.
FAR = 1 / sin(°/2). 90° → FAR 1.41, 60° → FAR 2.LARLateral Aspect Ratio
Lateral ratio:
LAR = 2 / FAR. Tells you how far apart you can place speakers for a given throw.Coverage °Dispersion angle
Speaker dispersion angle, typically measured between the −6 dB points.
ThrowReach distance
Distance over which a speaker remains usefully loud.
SplayHinge angle
Angle between two adjacent boxes in a coupled line / line array.
TweeterHigh-frequency driver
Driver for high frequencies (typically > 2 kHz). Located at the top of the box.
SubSubwoofer
Driver for the lowest frequencies (typically < 100 Hz). Usually placed on the floor.
LF / MF / HFLow / Mid / High Frequency
Low / mid / high frequency range. Typical limits: LF < 250 Hz, MF 250 – 4 k, HF > 4 k.
XOVRCrossover
Filter that splits the signal into bands — typically between sub and top or between LF/HF in multi-way boxes.
Delay TowerDelay loudspeaker
Additional speaker position further back in the audience, electrically delayed to align with the main system. Rule of thumb: needed when Δt > 40 ms.
Time AlignmentTime alignment
Aligning multiple sound sources in time so all signals arrive simultaneously at the listening position. Prevents comb filters in the transition zone (e.g. sub↔top, main↔delay tower).
Spatial CrossoverSpatial transition
Position in the audience where two sound sources have equal level — e.g. the point between main and delay tower where the handover happens. Phase coherence is most critical here.
CoupledCoupled cluster
Multiple boxes close together (spacing < λ/2) — radiate coherently as one acoustic unit. +6 dB summation per doubling of box count.
DistributedDistributed array
Boxes distributed across the stage front (max λ/2 spacing) for seamless horizontal coverage — typical for wide venues and flat seating.
Stereo SplitL/R arrangement
Classic L/R arrangement of tops or subs. Above spacing > λ/2, comb filters (power alley) appear in the center field at that frequency.
Long-throwNarrow coverage
Speakers with narrow dispersion (≤ 70°) for deep, narrow venues. High FAR, long throw, precisely directed.
Short-throwWide coverage
Speakers with wide dispersion (> 110°) for flat, wide venues. Low FAR, short throw, broadly distributed energy.
Multi-BoxMulti-cluster / Line Array
Multiple boxes per position as cluster or line array — when a single point source can't deliver the needed coverage or SPL.
RakeAudience rake
Rising seating toward the back row (theater, stadium, grandstand). Affects line-array splay and tower positions — back row sits higher than front.
RigRigging height
Hang height of a line array or cluster setup. "Top of array" = height of the highest point above the floor.
Front RowFront row
First audience row. Distance from speaker determines front slant for the delay tool and line-array geometry.
Back RowBack row
Last audience row. Determines whether delay towers are needed (Δt > 40 ms vs. front row) and what throw the main system must achieve.
Sub Array
Subwoofer configurations
Inline GradientFront + Rear Sub
Two subs in line, the rear one delayed in time. Creates rear cancellation — protects the stage from sub energy.
End-FireDirected sub line
Multiple subs in line with progressive delay forward — focuses energy in the throw direction.
Cardioid SubHeart-shape pattern
Sub arrangement with cardioid (heart-shape) directivity — loud forward, quiet rearward.
Power AlleyCenter-axis amplification
Narrow, very loud zone on the center axis between two subs spaced too far apart. Caused by summation — cancellations on the sides.
Max SpacingMaximum sub spacing
d_max = c / (2 × XOVR) = ½ wavelength at the crossover frequency. Prevents power alleys.Forward GainForward level gain
Level gain in the forward direction from coherent summation. End-fire with n subs → 20·log(n) dB. With 4 subs: +12 dB on-axis.
Rear RejectionRear attenuation
Level reduction toward the rear from destructive interference. Cardioid and end-fire reduce sub energy behind the stage — protects mics and backstage.
Polarity InvertPolarity inversion
180° phase flip of a signal (button on the DSP). Applied to the rear sub in cardioid setups — combined with delay it creates the heart-shape pattern.
f_optOptimal frequency
Frequency for maximum forward summation in cardioid setups:
f_opt = c / (4·d). At this frequency, +6 dB forward boost. With d=0.6 m → f_opt ≈ 143 Hz.PatternPolar pattern
Spatial distribution of sound energy around the speaker. Cardioid = heart-shape, end-fire = forward beam, omni = spherical (subs < 100 Hz).
Polar PlotPolar diagram
2D representation of the polar pattern as a curve around the speaker. Concentric rings = level steps (typically −6 / −12 / −24 dB), angle = radiation direction.
Connectors & Impedance
Signal levels · Resistances
ΩOhm
Unit of electrical resistance / impedance. kΩ = 1 000 Ω, MΩ = 1 000 000 Ω, mΩ = 1/1000 Ω.
Hi-ZHigh Impedance
High-impedance. Typical for instrument inputs (≥ 1 MΩ) — e.g. electric guitar, bass pickups.
Lo-ZLow Impedance
Low-impedance. Standard for microphones (200 – 600 Ω) and line signals.
Mic LevelMicrophone level
Very small level: −60 to −40 dBV (1 – 10 mV RMS). Requires preamplification.
Line Pro+4 dBu
Pro-audio line level: +4 dBu = 1.228 V RMS. Balanced via XLR or TRS.
Line Cons.−10 dBV
Consumer line level: −10 dBV = 316 mV RMS. Common on hi-fi gear via RCA, unbalanced.
SpeakerAmplifier output
+20 to +40 dBV (10 – 100 V RMS) with very low source impedance (< 100 mΩ). Speaker input: 4 – 16 Ω.