§ 01
Wave & Frequency
Universal converter between frequency, period, wavelength and samples.Universal Converter
f · T · λ · samples — all fields editable
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
Phase
°
Frequency
Hz
Result
Time offset—
↳ in samples—
Period at f—
t = (φ/360) × T · T = 1000/f
Bandwidth
Octaves between two frequencies
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
Reference
Hz
Semitones (±)
st
Result
Resulting frequency—
Interval—
f_out = f_ref × 2^(n/12)
Octave segments
Thirds, fifths, octaves
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
Reference value
Measured value
Result
dB change—
Multiplier—
% change—
dB = 20 × log₁₀(V_meas / V_ref)
dB → Linear
Convert logarithm back to factor
dB value
dB
Result
Voltage factor—
Power factor—
% Voltage—
V = 10^(dB/20) · P = 10^(dB/10)
Correlated summation
Add two correlated signals
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
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
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
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
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
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.Audience → coverage °
Derive speaker angle from audience dimensions
Audience depth
m
Audience width
m
Result
Audience FAR—
Required coverage °—
FAR = D / W · angle = 2 × arcsin(1 / FAR)
Coverage ↔ FAR & LAR
Convert speaker coverage to FAR / LAR
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
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—
Rule of thumb: delay towers needed above Δt > 40 ms (≈ 14 m at 20 °C) — below that you still localize the main system correctly.
§ 05
Sub Array
Inline gradient, spacing and center frequency for subwoofers.Inline Gradient Sub Array
Front + rear sub with XOVR & delay
−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
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
Lower sub frequency
Hz
Upper sub frequency
Hz
Result
Center frequency—
f_c = √(f_low × f_high)
§ 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.
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.
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.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.