§ 01
Wave & Frequency
Universal converter between frequency, period, wavelength and samples.Universal Converter
f · T · λ · samples — all fields editable
What: Frequency, period, wavelength and samples — all the same phenomenon in 4 units.
When: When you need 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 focus on λ (wavelength), for latency checks on samples, for comb-filter diagnosis on period.
Tip: 100 Hz ≈ 10 ms ≈ 3.43 m at 20°C — a useful anchor to memorize.
When: When you need 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 focus on λ (wavelength), for latency checks on samples, for comb-filter diagnosis on period.
Tip: 100 Hz ≈ 10 ms ≈ 3.43 m at 20°C — a useful anchor to memorize.
Frequency
Hz
Period
ms
Wavelength λ
m
Samples
smp
Derived values
½ λ—
¼ λ—
¼ λ period—
Octave up—
f = 1/T · 1000 · λ = c/f · smp = SR/f
Phase Delay
Phase shift expressed as time
What: Converts phase (°) at a given frequency into time offset (ms / samples).
When: Sub-to-top time alignment, phase tuning, or understanding why small delays cause big filter effects.
How: Type phase and frequency → time offset and samples are calculated.
Action: 180° = perfect cancellation, 0°/360° = perfect summation. Anything in between creates comb filtering.
Tip: 90° at 1 kHz = 250 µs. Memorize this — it's gold for live tuning.
When: Sub-to-top time alignment, phase tuning, or understanding why small delays cause big filter effects.
How: Type phase and frequency → time offset and samples are calculated.
Action: 180° = perfect cancellation, 0°/360° = perfect summation. Anything in between creates comb filtering.
Tip: 90° at 1 kHz = 250 µs. Memorize this — it's gold for live tuning.
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 work — how wide does the bell need to be to cover the range?
How: Type lower and upper −3 dB frequency.
Action: 1/3 octave (Q ≈ 4.3) for surgical notch, 1 octave (Q ≈ 1.4) for tonal correction, 2 octaves for gentle shelf-like effect.
Tip: Narrow Q = surgical (kill feedback, leave the rest). Wide Q = musical (change character without sounding harsh).
When: Parametric EQ work — how wide does the bell need to be to cover the range?
How: Type lower and upper −3 dB frequency.
Action: 1/3 octave (Q ≈ 4.3) for surgical notch, 1 octave (Q ≈ 1.4) for tonal correction, 2 octaves for gentle shelf-like effect.
Tip: Narrow Q = surgical (kill feedback, leave the rest). Wide Q = musical (change 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 frequency ratios (musical logic).
When: Pitch tuning, feedback hunting on musically-meaningful points, or understanding why certain EQ boosts sound harmonically pleasing.
How: Type 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 chasing feedback → 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 harmonically pleasing.
How: Type 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 chasing feedback → 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: Splits octave steps from a reference frequency into thirds, fifths and octaves.
When: RTA setup, multiband compressor splits, or fine-grained EQ tuning on musically logical points.
How: Type a reference frequency — the table shows all harmonic points.
Action: 1/3 octave = classic live RTA. 1/6 octave = medium resolution. 1/12 = very fine. 1/24 = Smaart-grade.
Tip: Human perception reliably distinguishes frequency differences down to ~1/6 octave; finer than that is mostly inaudible.
When: RTA setup, multiband compressor splits, or fine-grained EQ tuning on musically logical points.
How: Type a reference frequency — the table shows all harmonic points.
Action: 1/3 octave = classic live RTA. 1/6 octave = medium resolution. 1/12 = very fine. 1/24 = Smaart-grade.
Tip: Human perception reliably distinguishes frequency differences down to ~1/6 octave; finer than that is mostly inaudible.
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. double the voltage) into a dB change.
When: When you want voltage / level ratios (voltmeter readings, ADC levels) translated into familiar dB values.
How: Type 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 when checking voltage 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 voltage / level ratios (voltmeter readings, ADC levels) translated into familiar dB values.
How: Type 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 when checking voltage 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
Convert logarithm back to factor
What: Converts dB values back into voltage and power factors.
When: When you know "the mix is 6 dB too loud" and want to know exactly how much less power the amp needs to deliver.
How: Type the 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 ≈ "half as loud" perceived.
When: When you know "the mix is 6 dB too loud" and want to know exactly how much less power the amp needs to deliver.
How: Type the 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 ≈ "half as loud" perceived.
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 with same phase (coherent summation).
When: Sub pairing, coupled clusters, dual PA — or simply to know "if I add another box, how much louder does it get?"
How: Type two levels A and B in dB.
Action: Equal levels (A=B) → +6 dB sum. 6 dB difference → only +1 dB. 10 dB+ difference → essentially no summation.
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, dual PA — or simply to know "if I add another box, how much louder does it get?"
How: Type two levels A and B in dB.
Action: Equal levels (A=B) → +6 dB sum. 6 dB difference → only +1 dB. 10 dB+ difference → essentially no summation.
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
Total sum—
Δ above loudest—
Voltage factor—
L = 20 × log₁₀(10^(L_A/20) + 10^(L_B/20))
Passive Speaker Headroom
Amplifier headroom above speaker
What: Ratio between amp power and speaker power handling, expressed as dB headroom.
When: Choosing an amp for passive boxes — "can I drive this box safely with this amp?"
How: Type amp RMS and speaker RMS power handling.
Action: +3 dB headroom (amp 2× as strong as speaker) is industry standard for clean peaks. +6 dB is premium for live sound. At +0 dB → no headroom, clipping = damage.
Tip: Better: stronger amp + limiter than too-weak amp — clipping kills tweeters much faster than honest overload.
When: Choosing an amp for passive boxes — "can I drive this box safely with this amp?"
How: Type amp RMS and speaker RMS power handling.
Action: +3 dB headroom (amp 2× as strong as speaker) is industry standard for clean peaks. +6 dB is premium for live sound. At +0 dB → no headroom, clipping = damage.
Tip: Better: stronger amp + limiter than too-weak amp — clipping kills tweeters much 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 setups, reflection diagnosis or multi-mic recordings.
How: Type the estimated or measured time offset (ms).
Action: Dips show where the sound is "cancelled" (thin, hollow). Peaks where it gets too loud. "Summation Stop" = above this frequency comb effects become 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 setups, reflection diagnosis or multi-mic recordings.
How: Type the estimated or measured time offset (ms).
Action: Dips show where the sound is "cancelled" (thin, hollow). Peaks where it gets too loud. "Summation Stop" = above this frequency comb effects become 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 path
Two sources → C, with comb analysis
What: Compares two sound paths (sources A and B reaching the same listener position C) and shows distance diff, time diff, level diff and resulting comb frequencies.
When: When comparing two sound sources at the same location — main system vs. wall reflection, sidefill vs. main, or drum mic spill.
How: Type both arrival times in ms (from Smaart/Systune or simply distance/c).
Action: Big Δt → identify comb frequencies and consider delay. Small Δt → can be ignored.
Tip: Level difference > 10 dB → the weaker source becomes acoustically irrelevant, no comb problem.
When: When comparing two sound sources at the same location — main system vs. wall reflection, sidefill vs. main, or drum mic spill.
How: Type both arrival times in ms (from Smaart/Systune or simply distance/c).
Action: Big Δt → identify comb frequencies and consider delay. Small Δt → can be ignored.
Tip: Level difference > 10 dB → the weaker source becomes 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 each note value (half, quarter, eighth, triplets).
When: FX setup for vocals, guitar, synths — when the delay should match the beat instead of drifting.
How: Type tempo (BPM), pick a note value, read ms.
Action: Quarter = "slap" like classic tape echo. Dotted eighth = U2/Edge-style delay. Triplets = swingy. Plug values directly into your FX plugin.
Tip: At slow tempos (< 90 BPM) → eighths/16ths often work better than quarters (quarters get too slow, sound like repeats not ambience).
When: FX setup for vocals, guitar, synths — when the delay should match the beat instead of drifting.
How: Type tempo (BPM), pick a note value, read ms.
Action: Quarter = "slap" like classic tape echo. Dotted eighth = U2/Edge-style delay. Triplets = swingy. Plug values directly into your FX plugin.
Tip: At slow tempos (< 90 BPM) → eighths/16ths often work better than quarters (quarters get too slow, sound like repeats not ambience).
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: Calculates audio delay time from video frame offset (e.g. "3 frames later").
When: Lip-sync tuning for live video, broadcast, theater with projection or concert IMAG.
How: Type frame rate (24/25/30/50/60) and the desired frame offset.
Action: Plug the ms value into the audio output delay of the mixer or DSP. Positive values = audio comes later, negative = earlier.
Tip: Perception threshold: ±50 ms is usually fine, >100 ms becomes annoying. For TV: audio can be max 1–2 frames before video, but up to 3 frames after (perceptual asymmetry).
When: Lip-sync tuning for live video, broadcast, theater with projection or concert IMAG.
How: Type frame rate (24/25/30/50/60) and the desired frame offset.
Action: Plug the ms value into the audio output delay of the mixer or DSP. Positive values = audio comes later, negative = earlier.
Tip: Perception threshold: ±50 ms is usually fine, >100 ms becomes annoying. For TV: audio can be max 1–2 frames before video, but up to 3 frames after (perceptual asymmetry).
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 room dimensions → system recommendation (real cone geometry)
What: Quick selection of which PA system fits your venue.
When: In the warehouse while packing, or at the venue as a reality check before setup.
How: 1. Estimate or measure room width (W) and depth (D) — 2. Type in — 3. Read recommendation.
Action: Pick a system from the truck whose coverage falls in the recommended range:
· Long-throw / Narrow → line array or narrow 60–70° tops
· Standard / Wide Main → classic 80–110° tops
· Short-throw / Wide → short-throw point sources, wide pattern
· Multi-Box / Line Array → multiple clusters or array required — plan more gear
Tip: "Max throw" tells you the longest sound path in the room — important for headroom and speaker choice.
When: In the warehouse while packing, or at the venue as a reality check before setup.
How: 1. Estimate or measure room width (W) and depth (D) — 2. Type in — 3. Read recommendation.
Action: Pick a system from the truck whose coverage falls in the recommended range:
· Long-throw / Narrow → line array or narrow 60–70° tops
· Standard / Wide Main → classic 80–110° tops
· Short-throw / Wide → short-throw point sources, wide pattern
· Multi-Box / Line Array → multiple clusters or array required — plan more gear
Tip: "Max throw" tells you the longest sound path in the room — important for headroom and speaker choice.
Room width W
m
Room depth D
m
Recommendation
Speaker spacing (s)—
Coverage range—
Max throw—
FAR · LAR (@ rec)—
Recommended system—
s = min(W,D)/3 · θ_min = arctan((W+s)/2D) + arctan(|W−s|/2D)
Audience → coverage °
Derive speaker angle from audience dimensions
What: Calculates the required speaker coverage angle from audience depth and width.
When: When you have a specific room and want to check if your speaker coverage fits — or what angle would be ideal.
How: Type D (depth) and W (width). Optionally "Speaker actual °" for comparison.
Action: Gaps (red) → tighter speaker placement or wider pattern needed. Overshoot (purple) → reduce level or pick narrower pattern, otherwise wall reflections.
Tip: This calculation uses the chord/circle model (classic McCarthy) — gives slightly larger angles than a pure cone model. Conservative and field-proven.
When: When you have a specific room and want to check if your speaker coverage fits — or what angle would be ideal.
How: Type D (depth) and W (width). Optionally "Speaker actual °" for comparison.
Action: Gaps (red) → tighter speaker placement or wider pattern needed. Overshoot (purple) → reduce level or pick narrower pattern, otherwise wall reflections.
Tip: This calculation uses the chord/circle model (classic McCarthy) — gives slightly larger angles than a pure cone model. Conservative and field-proven.
Audience depth
m
Audience width
m
Result
Audience FAR—
Required coverage °—
Compare
Speaker actual °
°
FAR = D / W · angle = 2 × arcsin(1 / FAR)
Coverage ↔ FAR & LAR
Convert speaker coverage to FAR / LAR
What: Geometric ratios of speaker coverage. FAR = throw/half-width (how deep), LAR = inverse (how wide per throw).
When: Box selection, when you want to know "how far does my 80° top actually cover?" or "how wide at what distance?"
How: Type speaker coverage in °.
Action: FAR × half-width = max throw. LAR × throw = full coverage width at that distance. Narrow pattern (60°) → high FAR, long and thin. Wide pattern (120°) → low FAR, short and wide.
Tip: 90° has FAR=1.41 (the symmetry point). Below 90° → long-throw character. Above → short-throw character.
When: Box selection, when you want to know "how far does my 80° top actually cover?" or "how wide at what distance?"
How: Type speaker coverage in °.
Action: FAR × half-width = max throw. LAR × throw = full coverage width at that distance. Narrow pattern (60°) → high FAR, long and thin. Wide pattern (120°) → low FAR, short and wide.
Tip: 90° has FAR=1.41 (the symmetry point). Below 90° → long-throw character. Above → short-throw character.
Speaker coverage
°
Result
FAR (Forward AR)—
LAR (Lateral AR)—
FAR = 1 / sin(°/2) · LAR = 2 / FAR
Do I need delay speakers?
Front- vs. back-row distance from main system
What: Checks if delay towers are needed and where they should go — based on path-length difference between front and back row.
When: Deep rooms (>20m back row), open-air, gymnasiums, festivals or long narrow halls.
How: Type tweeter height, ear height, front- and back-row distance from speaker base.
Action: Check Δt status: green = no delays needed, orange = borderline (tower optional), red = set up towers as listed and enter delay value at the DSP.
Tip: Tower spacing is 14m (40ms threshold), temperature-dependent — the header temp value is automatically applied.
When: Deep rooms (>20m back row), open-air, gymnasiums, festivals or long narrow halls.
How: Type tweeter height, ear height, front- and back-row distance from speaker base.
Action: Check Δt status: green = no delays needed, orange = borderline (tower optional), red = set up towers as listed and enter delay value at the DSP.
Tip: Tower spacing is 14m (40ms threshold), temperature-dependent — the header temp value is automatically applied.
Tweeter height
m
Audience ear height
m
Speaker base → front row
m
Speaker base → back row
m
Analysis
Distance front—
Distance back—
Δ distance—
Δ time—
Distance ratio—
Δ level (1/r²)—
Recommendation—
Δt status—
Rule of thumb: delay towers needed above Δt > 40 ms (≈ 14 m at 20 °C) — below that you still localize the main system correctly.
Spatial Crossover
Level + time transition main → delay tower
What: Where main system and delay tower meet level-wise, plus the exact delay value for time alignment.
When: After tower placement, before sound check — the two key values for tower tuning.
How: Type distance main → tower (tape or laser) and level offset (typically 0 to −6 dB).
Action: Enter delay setting (ms) at tower DSP. Note the crossover position visually — the transition zone, where phase coherence is 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 sound check — the two key values for tower tuning.
How: Type distance main → tower (tape or laser) and level offset (typically 0 to −6 dB).
Action: Enter delay setting (ms) at tower DSP. Note the crossover position visually — the transition zone, where phase coherence is 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
Tower 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 at midpoint
Line Array Splay
Splay angles with just a laser distance meter
What: Estimates splay angles between line array boxes — using only rigging height and distances to front/back row.
When: When the rigger is still waiting, you want a rough idea of what's needed, or as a sanity check before MAPP/ArrayCalc verification.
How: Measure rig height (top of array) and ground distances to front and back row with a laser meter, type 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 a uniform splay — real arrays splay progressively (tighter at top, wider at bottom). Verify with manufacturer software before showtime.
When: When the rigger is still waiting, you want a rough idea of what's needed, or as a sanity check before MAPP/ArrayCalc verification.
How: Measure rig height (top of array) and ground distances to front and back row with a laser meter, type 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 a uniform splay — real arrays splay progressively (tighter at top, wider at bottom). Verify with manufacturer software before showtime.
Rigging height (top of array)
m
Distance → front row
m
Distance → last row
m
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)
Uniform-distribution estimate. Real-world arrays splay progressively — tighter at the bottom, wider at the top. Verify with manufacturer software (MAPP, ArrayCalc, Soundvision) before show start.
Uniform-distribution estimate. Real-world 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: Calculates offset and delay for a 2-sub inline gradient array (front + rear, polarity-inverted) — the classic cardioid configuration.
When: When building sub arrays that need stage cancellation — festivals, theatres, stages with mics directly in front of subs.
How: Type the XOVR frequency (typically 80–120 Hz).
Action: Place rear sub at "Rear Sub Offset" (m) behind front sub, set "Rear Sub Delay" at the DSP, invert polarity. Polar plot shows forward cardioid.
Tip: Works best at the maximum summation frequency (= 2/3 × XOVR). Above that the pattern breaks down progressively.
When: When building sub arrays that need stage cancellation — festivals, theatres, stages with mics directly in front of subs.
How: Type the XOVR frequency (typically 80–120 Hz).
Action: Place rear sub at "Rear Sub Offset" (m) behind front sub, set "Rear Sub Delay" at the DSP, invert polarity. Polar plot shows forward cardioid.
Tip: Works best at the maximum summation frequency (= 2/3 × XOVR). Above that the pattern breaks down 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 coverage.
When: Setting up 2+ subs — whether stereo split, distributed array or LCR sub setup.
How: Type the sub XOVR frequency (typically 80–120 Hz, system-dependent).
Action: Never place subs farther apart than d_max in the live setup. For wider stages → use more subs distributed, or array as cardioid.
Tip: Low XOVR (e.g. 60 Hz) → generous spacing (2.86m). High XOVR (120 Hz) → tight (1.43m). Rule of thumb: better too tight than too wide.
When: Setting up 2+ subs — whether stereo split, distributed array or LCR sub setup.
How: Type the sub XOVR frequency (typically 80–120 Hz, system-dependent).
Action: Never place subs farther apart than d_max in the live setup. For wider stages → use more subs distributed, or array as cardioid.
Tip: Low XOVR (e.g. 60 Hz) → generous spacing (2.86m). High XOVR (120 Hz) → tight (1.43m). Rule of thumb: better too tight than too wide.
Sub XOVR frequency
Hz
Result
Maximum 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 mass" of the sub band.
When: Parametric EQ on the sub bus, time-alignment reference, polar pattern verification or sub model evaluation.
How: Type the lower and upper sub frequency (e.g. 40–100 Hz for classic live).
Action: Use f_c as center frequency in EQ (e.g. a "sub drive" filter), as test tone for cardioid polar tests, or as level measurement reference for SPL.
Tip: 40–100 Hz → 63 Hz (NOT 70). Think geometrically because hearing is logarithmic — 100 Hz to 200 Hz "feels" the same distance as 200 Hz to 400 Hz.
When: Parametric EQ on the sub bus, time-alignment reference, polar pattern verification or sub model evaluation.
How: Type the lower and upper sub frequency (e.g. 40–100 Hz for classic live).
Action: Use f_c as center frequency in EQ (e.g. a "sub drive" filter), as test tone for cardioid polar tests, or as level measurement reference for SPL.
Tip: 40–100 Hz → 63 Hz (NOT 70). Think geometrically because hearing is logarithmic — 100 Hz to 200 Hz "feels" the same distance 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 + reverse box with polarity invert for stage cancellation
What: Calculates delay and polarity for a 2-sub cardioid arrangement (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 behind PA.
How: Type sub depth (box depth or acoustic offset) and the desired pattern frequency.
Action: Place rear sub at distance d behind front sub (or reverse-stack on top), set delay (= d/c) and polarity (inverted) at DSP. Polar plot shows the cardioid.
Tip: Works best at f_opt = c/(4d) — there you get +6 dB forward gain. At lower frequencies less gain, but cancellation persists.
When: When you need stage cancellation — vocal mics directly in front of subs, drum riser protection, conferences with lavalier behind PA.
How: Type sub depth (box depth or acoustic offset) and the desired pattern frequency.
Action: Place rear sub at distance d behind front sub (or reverse-stack on top), set delay (= d/c) and polarity (inverted) at DSP. Polar plot shows the cardioid.
Tip: Works best at f_opt = c/(4d) — there you get +6 dB forward gain. At lower frequencies less gain, but cancellation persists.
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-facing narrow cardioid pattern with rear rejection.
When: When you want sub energy focused in one direction (festival front clusters, IPS sub distribution, long indoor halls).
How: Type number of subs (n), spacing (typically 0.6–1.2m) and pattern frequency.
Action: Per sub, enter the calculated delay value at the DSP — rear sub at 0 ms, each one in front +d/c later. Forward gain = 20·log(n) dB boost.
Tip: 4 subs in line yields ~+12 dB forward and ~−14 dB rear rejection at 60 Hz (with d=0.6m). Top setup for modern festival designs.
When: When you want sub energy focused in one direction (festival front clusters, IPS sub distribution, long indoor halls).
How: Type number of subs (n), spacing (typically 0.6–1.2m) and pattern frequency.
Action: Per sub, enter the calculated delay value at the DSP — rear sub at 0 ms, each one in front +d/c later. Forward gain = 20·log(n) dB boost.
Tip: 4 subs in line yields ~+12 dB forward and ~−14 dB rear rejection at 60 Hz (with d=0.6m). Top 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
Number + crossover + stage width → configuration suggestion
What: Recommends the optimal sub configuration (Single, Coupled, Stereo, Cardioid, End-Fire, Distributed) based on number of subs, XOVR frequency and stage width.
When: When planning a new setup, or as a sanity check whether your planned setup makes sense for the venue dimensions.
How: Type number of subs, planned XOVR frequency and stage width.
Action: Follow the recommendation, then consult the corresponding specific card (Cardioid Stack, End-Fire, Inline Gradient) for exact delay values.
Tip: "Power alley" warning (red comb stripes) means: subs too far apart for the XOVR. Either tighten spacing, lower XOVR, or pick mono center.
When: When planning a new setup, or as a sanity check whether your planned setup makes sense for the venue dimensions.
How: Type number of subs, planned XOVR frequency and stage width.
Action: Follow the recommendation, then consult the corresponding specific card (Cardioid Stack, End-Fire, Inline Gradient) for exact delay values.
Tip: "Power alley" warning (red comb stripes) means: subs too far apart for the XOVR. Either tighten spacing, lower XOVR, or pick mono center.
Total subs
pcs
Crossover frequency
Hz
Stage width
m
Recommendation
Configuration—
Reasoning—
Rule of thumb: max sub spacing = λ/2 at XOVR · beyond that comes power alley · cardioid trades output for directionality
§ 06
Reference
Quick-look without typing — 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 vs. 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 in 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 the app.Basics & Waves
Frequency · wavelength · time
fFrequency
Number of oscillations per second, in hertz (Hz). Determines perceived pitch — 440 Hz = concert pitch A.
TPeriod
Time for one complete oscillation.
T = 1 / f. At 100 Hz, T = 10 ms.λLambda · Wavelength
Spatial length of one oscillation 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. Rises with temperature (~0.6 m/s per °C).
HzHertz
Unit of frequency: 1 Hz = one oscillation 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 samples. Samples per unit of time depend on the 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 in the oscillation 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 perceptually.dBVdB relative to 1 V
Level reference: 0 dBV = 1 volt RMS. Common on consumer gear (−10 dBV).
dBudB relative to 0.7746 V
Level reference: 0 dBu = 0.7746 V RMS (historic 600 Ω reference). 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 (threshold of hearing). Live concert ca. 100 – 110 dB SPL.
RMSRoot Mean Square
Root mean square — describes continuous power handling / output, more relevant than peak values.
1/r²Inverse-square law
Sound pressure halves with each doubling of distance — i.e.
−6 dB per doubling in the free field.HeadroomDynamic reserve
Reserve between nominal and maximum level. Critical so peaks don't clip.
CorrelatedIn-phase
Two signals with identical content and identical phase. Add linearly (voltage sum) — two equal signals produce +6 dB.
WWatt
Unit of electrical power. Amplifier and loudspeaker handling typically stated in W RMS.
Filter & EQ
Bandwidth · Q · comb
QQuality Factor
Filter selectivity. Higher Q = narrower bandwidth of a bell-type EQ filter. Q 1 ≈ 1.4 octaves, Q 10 ≈ 0.14 octaves.
BWBandwidth
Frequency range, often stated in octaves.
BW = log₂(f_high / f_low).EQEqualizer
Frequency-response adjustment. 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 a time offset between two correlated signals (e.g. two mics or two speakers).
DipCancellation
Frequency at which two signals interfere destructively — level drop in the frequency response.
PeakBoost
Frequency at which two signals sum constructively — level peak in the frequency response.
f_cCenter frequency
Center frequency of a filter or band. For bell EQ, the point of max boost/cut. For a sub range = geometric mean:
f_c = √(f_low × f_high).NotchNarrow-band cut
Very narrow EQ cut (Q ≥ 4) for surgical removal of a resonance or feedback frequency, without affecting the rest of the sound.
XOVRCrossover frequency
Transition frequency between two bands (sub↔top, LF↔HF). For a sub array, it determines the maximum spacing (λ/2 rule).
Phase & Time
Delay · BPM · frame sync
PhaseOscillation position
Current position in the cycle, in degrees (0 – 360°). 180° equals polarity inversion.
Phase delayPhase as time
Phase angle expressed as a time delay. Frequency-dependent: the same angle corresponds to different times at different frequencies.
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 image in a video sequence. At 25 fps, one frame lasts 40 ms.
Note Values
Rhythmic subdivisions
𝅗𝅥Half note
2-beat 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 regular ones. ⅛ triplet = 3 in one beat. At 120 BPM an ⅛ triplet ≈ 167 ms.
Musical Intervals
In semitones, equal temperament
UnisonPerfect prime · 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 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 keys.
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 sense of consonance. Note name repeats.
Ninth / Tenth / …Compound intervals
Compound of an octave + a smaller interval: 9th = octave + 2nd, 10th = octave + 3rd, 11th = octave + 4th, 12th = octave + 5th, etc.
PA & Live Sound
Speaker geometry · system terms
PAPublic Address
Public-address system for live sound reinforcement — mixer, amplifiers, loudspeakers.
FOHFront of House
Main mix position in the room — where the engineer stands to mix for the audience.
FARForward Aspect Ratio
Throw distance vs. half the coverage width.
FAR = 1 / sin(°/2). 90° → FAR 1.41, 60° → FAR 2.LARLateral Aspect Ratio
Lateral ratio:
LAR = 2 / FAR. Tells how far apart speakers can be placed for a given throw distance.Coverage °Dispersion angle
Dispersion angle of a loudspeaker, usually measured between the −6 dB points.
ThrowReach distance
Distance over which a speaker stays usably loud.
SplaySplay angle
Angle between two adjacent boxes in a coupled line / line array.
TweeterHigh-frequency driver
Driver for high frequencies (typically > 2 kHz). Mounted at the top of the enclosure.
SubSubwoofer
Low-frequency driver for the lowest band (typically < 100 Hz). Usually floor-placed.
LF / MF / HFLow / Mid / High Frequency
Low / mid / high frequency range. Typical boundaries: LF < 250 Hz, MF 250–4 k, HF > 4 k.
XOVRCrossover
Filter splitting the signal into bands — typically between sub and top, or between LF/HF in multi-way boxes.
Delay towerDelay speaker
Additional speaker position farther back in the audience, electrically delayed to time-align with the main system. Rule of thumb: needed above Δt > 40 ms.
Time alignmentTime alignment
Time-aligning multiple sound sources so all signals arrive simultaneously at the listener. Prevents comb filters at the transition (e.g. sub↔top, main↔delay tower).
Spatial CrossoverSpatial transition
Position in the audience where two sound sources reach equal level — e.g. the takeover point between main and delay tower. Phase coherence is most critical here.
CoupledCoupled cluster
Multiple boxes tightly together (spacing < λ/2) — radiating coherently as one acoustic unit. +6 dB summation per doubling of box count.
DistributedDistributed array
Boxes spread along the stage front (max λ/2 spacing) for gap-free horizontal coverage — typical for wide rooms with shallow seating.
Stereo SplitL/R configuration
Classic L/R speaker arrangement. Above spacing > λ/2, comb filters (power alley) develop in the center field at that frequency.
Long-throwNarrow coverage
Speakers with narrow dispersion (≤ 70°) for long, narrow rooms. High FAR, long throw, precisely aimed.
Short-throwWide coverage
Speakers with wide dispersion (> 110°) for shallow, wide rooms. Low FAR, short throw, energy widely distributed.
Multi-BoxMulti-cluster / Line array
Multiple boxes per position as cluster or line array — when a single point-source speaker can't deliver the required coverage or SPL.
RakeAudience rake
Rising seating toward the back row (theater, stadium, raked seating). 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 topmost point above ground.
Front RowFront-most row
First audience row. Distance from speaker determines the front slant for the delay tool and line array geometry.
Back RowBack-most row
Last audience row. Determines whether delay towers are needed (Δt > 40 ms vs. front row) and what throw the main system must deliver.
Sub Array
Subwoofer configurations
Inline gradientFront + rear sub
Two subs in line — the rear one electrically delayed. Creates cancellation behind the stack, protecting the stage from sub energy.
End-fireDirectional sub array
Multiple subs in line with progressive forward delay — focuses energy in the throw direction.
Cardioid subCardioid pattern
Sub configuration with a cardioid radiation pattern — loud forward, quiet rearward.
Power alleyCenterline build-up
Narrow, very loud zone along the centerline between two subs placed too far apart. Caused by constructive summation — with 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 boost
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 via destructive interference. Cardioid and end-fire reduce sub energy behind the stage — protects mics and backstage.
Polarity InvertPolarity reversal
180° phase inversion of a signal (DSP button). Applied to the rear sub in cardioid setups — combined with delay it creates the cardioid 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=0.6m → f_opt ≈ 143 Hz.PatternPolar pattern
Spatial distribution of sound energy around the speaker. Cardioid = kidney-shaped, 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 = direction of radiation.
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 low level: −60 to −40 dBV (1 – 10 mV RMS). Requires pre-amplification.
Line Pro+4 dBu
Pro-audio line level: +4 dBu = 1.228 V RMS. Balanced, typically via XLR or TRS.
Line Cons.−10 dBV
Consumer line level: −10 dBV = 316 mV RMS. Common on HiFi gear via RCA, unbalanced.
SpeakerAmplifier output
+20 to +40 dBV (10 – 100 V RMS) from a very low source impedance (< 100 mΩ). Speaker input: 4 – 16 Ω.