{"id":20188,"date":"2026-11-06T10:30:00","date_gmt":"2026-11-06T09:30:00","guid":{"rendered":"https:\/\/www.lukaswojcik.com\/blog\/?p=20188"},"modified":"2026-10-26T11:53:47","modified_gmt":"2026-10-26T10:53:47","slug":"kick-and-bass-at-55-hz-a-model-comparison-of-starting-phase-tuning-high-pass-and-ducking","status":"publish","type":"post","link":"https:\/\/www.lukaswojcik.com\/blog\/en\/music-production\/kick-and-bass-at-55-hz-a-model-comparison-of-starting-phase-tuning-high-pass-and-ducking\/","title":{"rendered":"Kick and Bass at 55 Hz: A Model Comparison of Starting Phase, Tuning, High-Pass and Ducking"},"content":{"rendered":"

Kick and bass can occupy the same low-frequency range. A kick settling at 55 Hz and a bass playing A1 bring two similar oscillations together. Components can reinforce when their excursions point the same way, or weaken when the excursions oppose each other. The position within an oscillation cycle is called phase. This experiment examines the sum at different starting phases, tunings, high-pass settings and temporary bass reductions.<\/p>\n

The synthetic signals were originally measured on 23 September 2026 using NumPy and FFmpeg 7.1.5. This review reran both measurement scripts and reproduced the saved results. The numbers describe this model, not a listening test with music recordings.<\/p>\n

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Kick and bass at 55 Hz: the effects of starting phase, a continuously running bass oscillator, the synthesizer component generating the wave, and a high-pass filter. Sum values are relative to the individual signal energies calculated for each case.<\/figcaption><\/figure>\n

How the measurement works<\/h2>\n

At a 48 kHz sample rate, the synthetic kick drops from 160 to 55 Hz over 40 ms, with the fall becoming progressively slower. Its amplitude then decays with a 120 ms time constant: after another 120 ms, about 37% of the previous value remains, rather than silence. The bass is a 55 Hz sine, a pure tone without harmonics. Both signals reach a peak of about 0.5; a value of 1 represents digital full scale. <\/p>\n

The usual measurement window is the first 250 ms. Sample values are squared, meaning multiplied by themselves, then added. The metric is 10\u00b7log10(energy of sum \/ (kick energy + bass energy))<\/code>. Positive values indicate net reinforcement and negative values net weakening relative to this reference. A value of 0 dB means only that the interaction balances across the chosen window; reinforcement and weakening can still occur within it.<\/p>\n

The five experiments cover equal sine tones, twelve bass starting phases in 30-degree steps, 16 beats at 128 BPM, high-pass corner frequencies from 20 to 50 Hz, and bass reductions up to 24 dB. The high-pass and ducking calculations use the energy of the already filtered or reduced bass as their reference. Changes in this metric therefore are not directly changes in absolute summed level. Neither LUFS nor perceived loudness is measured.<\/p>\n

Two equal tones: double amplitude or ideal cancellation<\/h2>\n

For two sine tones of equal amplitude and frequency, level relative to one tone is 20\u00b7log10(|2\u00b7cos(\u03c6\/2)|)<\/code> dB. \u03c6 is the phase difference. At 0 degrees the result is +6.02 dB, at 120 degrees it is 0 dB, and at 180 degrees the ideal model cancels completely. A rise of 6.02 dB means double amplitude, not automatically double perceived loudness. Numerical calculation leaves tiny rounding residues at 180 degrees, so a general accuracy claim down to trillionths of a decibel would be misleading. Half a cycle at 55 Hz lasts 9.09 ms.<\/p>\n

At 5 kHz, half a cycle lasts only 0.1 ms. Thus the same time offset creates different phase differences at different frequencies. Moving the head does not, however, change a sum already formed digitally. Loudspeaker paths and reflections add further effects in a room; those were not examined here.<\/p>\n

Twelve starting phases: a 6.08 dB spread in this model<\/h2>\n

Cancellation with the synthetic kick is less extreme than with two continuously identical sine tones: the kick changes frequency initially and then decays. Across the twelve tested bass phases, the metric ranges from \u22124.03 to +2.05 dB, a spread of 6.08 dB. The highest of these twelve results occurs at 270 degrees. The kick’s tail has about 264.75 degrees of phase offset relative to a 55 Hz sine starting at zero. The 270-degree setting works well on this test grid; it is not a universal optimum for kicks.<\/p>\n

The pitch trajectory influences both timbre and the later phase relationship. Another kick can therefore require another suitable setting. This does not establish a fixed loss, such as 4 dB, when changing samples.<\/p>\n

Continuously running bass: sum values vary between beats<\/h2>\n

At 128 BPM, one beat lasts 468.75 ms. A 55 Hz sine completes 25.78125 cycles in that interval, so its oscillation is at a different position on the next beat. Across 16 beats, the model’s metric ranges from \u22124.03 to +2.07 dB. This is an energy difference, not a direct measurement of the perceived strength of every hit. The BPM to Delay Time Calculator<\/a> gives beat durations at other tempos.<\/p>\n

When the bass restarts on every beat at the same frequency and phase, the model gives \u22120.49 dB each time. A synthesizer may offer a fixed oscillator starting phase; retriggering an envelope, the level shape over time, alone does not necessarily reset the oscillator. A sample provides repeatable starts only with the same starting point, pitch and playback settings. Legato, shifted sample starts or changing notes can alter its relationship with the kick.<\/p>\n

Detuning: a different phase trajectory within the window<\/h2>\n

Nearby frequencies have a continuously changing relative phase. This can cause beating, a slow rise and fall in the sum. A cent is one hundredth of a semitone. For the bass tuned upward here, 10 cents gives about 0.32 Hz separation, 50 cents gives 1.61 Hz, and a semitone gives 3.27 Hz. With a fixed restart, the metric changes from \u22120.49 dB without detuning to \u22121.18 dB at 10 cents, \u22122.24 dB at 25 cents and \u22123.26 dB at 50 cents. The spread of the continuously running bass also changes: at a semitone it is about 3.14 dB, compared with 6.10 dB without detuning.<\/p>\n

Compatible pitches can make musical sense without guaranteeing a favourable phase relationship. A kick does not universally need the same note as the bass, and bass lines often change notes. The Note to Frequency and MIDI Converter<\/a> helps identify frequencies. In equal temperament with A4 = 440 Hz, A1 is 55.00 Hz, G1 about 49.00 Hz and F1 43.65 Hz. Some programs use different octave numbering.<\/p>\n

A high-pass also changes phase above its corner frequency<\/h2>\n

The test uses FFmpeg highpass<\/code> with two poles, giving 12 dB per octave far below the corner, and its dimensionless default Q = 0.707, which controls the filter transition shape. This approximates a Butterworth response without a resonant peak. With a 30 Hz corner, the 55 Hz bass falls by 0.37 dB and its phase rotates by 47.7 degrees. At 40 Hz the figures are 1.07 dB and 65.4 degrees; at 50 Hz they are 2.26 dB and 82.3 degrees. A high-pass therefore does not act only below its corner.<\/p>\n

At the previously best tested starting phase, the sum metric falls from +2.05 dB without filtering to +1.26 dB with the 30 Hz high-pass and \u22120.12 dB with the 50 Hz high-pass. Both bass phase and level change. In this test the filter runs for one second before the evaluated section, so its response to an abruptly started note is not being tested. Rechecking the combination after filter changes is useful, but a change does not necessarily make the result worse.<\/p>\n

Ducking: temporarily reducing overlap<\/h2>\n

At 90 degrees, the worst of the twelve tested starting phases, the model reduces the bass immediately. The reduction stays constant for 120 ms, then the linear gain factor rises back to 1 over 20 ms. This is a prescribed curve, not a sidechain-compressor measurement. During the first 120 ms, the metric is \u22124.37 dB without reduction, \u22123.67 dB with 6 dB reduction, \u22121.92 dB with 12 dB, and \u22120.44 dB with 24 dB. <\/p>\n

Each reference includes the already reduced bass. Less negative values therefore do not automatically mean a louder sum: with 6 dB ducking, actual summed energy in that window is about 1.83 dB below the case without ducking.<\/p>\n

From 140 ms onward, the model’s bass is back at its original level. The metric from 140 to 250 ms is consequently identical in every version: \u22123.18 dB. Ducking does not permanently remove the interaction. A shorter kick, longer ducking or a different starting phase can alter the overlap; the appropriate choice also depends on the intended groove and bass envelope.<\/p>\n

Practical checks suggested by the measurements<\/h2>\n\n\n\n\n\n\n\n
Model finding<\/th>\nMeasured value<\/th>\nUseful check<\/th>\n<\/tr>\n
Twelve starting phases<\/td>\n6.08 dB spread<\/td>\nComparison of a fixed oscillator phase at several settings<\/td>\n<\/tr>\n
Continuous bass, 128 BPM<\/td>\n\u22124.03 to +2.07 dB<\/td>\nChecks across several beats and with actual oscillator retrigger<\/td>\n<\/tr>\n
Bass 25 cents higher<\/td>\n\u22122.24 versus \u22120.49 dB with fixed restart<\/td>\nSeparate checks of pitch and phase<\/td>\n<\/tr>\n
High-pass 30 Hz, Q = 0.707<\/td>\n47.7\u00b0 at 55 Hz<\/td>\nAnother check of the sum after filter changes<\/td>\n<\/tr>\n
Ducking 24 dB, 120 ms<\/td>\n\u22120.44 dB in window; \u22123.18 dB from 140 ms<\/td>\nComparison of duration, return curve and groove; the energy reference changes<\/td>\n<\/tr>\n<\/table>\n

Polarity inversion multiplies every bass value by \u22121, swapping positive and negative excursions. Comparing the whole loop can reveal which hits or frequency regions become stronger or weaker. A louder version is neither automatically better nor a definitive indication of a fault. Different notes and the rest of the mix also belong in the listening comparison.<\/p>\n

Scope and limitations<\/h2>\n

The bass is a sine tone; the kick is a sine with changing frequency and an amplitude envelope. Real samples often contain additional noise and harmonics. Those components can also overlap and reinforce or weaken each other; automatic averaging away is not guaranteed. The metric depends on level ratio, time window, pitch trajectory and envelopes. Equal peaks do not imply equal energy. Depending on the starting level ratio, reducing the bass can initially increase cancellation before a further reduction decreases it. This model does not evaluate room acoustics, stereo behaviour or listening impressions.<\/p>\n

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Questions and answers<\/h2>\n

Why does polarity inversion not stabilise a continuously running bass?<\/h3>\n

For a sine tone, inversion is a phase change of 180 degrees. The continuously running 55 Hz bass still shifts its starting position relative to successive beats by 0.78125 cycles, or 281.25 degrees per beat. A fixed inversion does not stop that motion. For a complex waveform, polarity inversion is also not one fixed time offset for the whole signal.<\/p>\n

With identical notes and repeatable starts, the inversion comparison is easier to repeat. Several beats and the complete mix remain relevant. The model does not prescribe one universally correct switch position.<\/p>\n

Why does the 30 Hz high-pass still rotate phase substantially at 55 Hz?<\/h3>\n

For the second-order high-pass used here, phase runs from nearly 180 degrees far below the corner, through 90 degrees at the corner, towards 0 degrees far above it. The 55 Hz tone is less than an octave above 30 Hz; an octave above would be 60 Hz. A measured 47.7-degree rotation is therefore compatible with only 0.37 dB attenuation.<\/p>\n

The digital biquad coefficients in the Audio EQ Cookbook give approximately the same values, with small differences from the particular FFmpeg floating-point calculation. A 20 Hz corner still produces about 30.7 degrees at 55 Hz. This describes the filter type tested. Other designs, particularly time-aligned linear phase filters, can behave differently. Slope alone does not fully determine phase behaviour.<\/p>\n

A 55 Hz cycle lasts 18.18 ms. For this single sustained tone, 47.7 degrees corresponds to about 2.4 ms of movement within the cycle. This is not a uniform delay of the entire bass signal or a reason to move the whole track by 2.4 ms. The sum merits another check after filter parameters change.<\/p>\n

Does this apply to an 808 providing both kick and bass?<\/h3>\n

When one sample plays alone, there is no separate second kick track for the comparison examined here. Internal components, overlapping notes or other tracks can still interact. When another kick is layered, pitch, sample starting point, filtering and envelopes matter alongside the timing offset. Two notes on the same grid therefore do not guarantee an identical phase relationship.<\/p>\n<\/div>\n

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Sources<\/h2>\n