The Mono Button
Most systems play the bass in mono, and a bass widened for headphones pays for it there. A 10 ms delay on one side reads as out of phase and takes 16 dB off a 55 Hz bass in the sum. A detuned pair pumps in mono every 1.6 s, 54 dB deep. Sum and difference combs are as wide as either and lose nothing at all, measured.
What it is
A bass, four ways of making it wide, and a button that plays it the way the club will.
The bass is 55 Hz with eight harmonics falling at 1/h, a plain saw. Dry puts the same signal on both sides. Haas puts the right side 10 ms late, which is the widening trick everyone learns first. Detuned puts the whole bass 10 cents down on the left and 10 cents up on the right. Complementary puts the bass plus a 10 ms copy on the left and the bass minus it on the right, which is how pseudo stereo was done before any of us were born.
Every one of them is wide on headphones. The mono button sums the two sides, which is what a club system does to the low end, what a phone does to everything, and what a lot of bluetooth speakers do without telling you. The page measures what each trick turns into once that happens.
The circle is a goniometer, left against right, turned so a mono signal is a vertical line. The strip is the mono sum over four seconds with the dry bass behind it. The bars are the eight harmonics, dry in amber and what is left of each in mono next to it.
How it works
Width is the correlation between the two sides: 1 is mono, 0 is as wide as it gets, and below zero the sides are pulling against each other. Mono loss is the level of the sum at each harmonic against the dry bass, read with a Goertzel filter over a whole number of cycles once the delay lines have filled. For the detuned pair the sum isn’t steady, so the page watches the level at 55 Hz over time and reports how fast it pumps and how deep.
The arithmetic for a delay is a comb. Summing a signal with a copy d seconds late multiplies each frequency by the cosine of pi f d, so the nulls sit at odd multiples of 1 over 2d. At 10 ms that’s 50, 150, 250, 350 and 450 Hz, and a 55 Hz bass has its fundamental 5 Hz from the first one. Measured off the sum it loses 16.1 dB there, 6.9 dB at 165 Hz and 10.2 dB at 440, and every one of the eight harmonics matches the cosine to a tenth of a dB.
The real graph is the same recipe in Web Audio nodes: a periodic wave for the bass, a DelayNode for the late side, detune in cents on a second oscillator, a gain of minus one for the difference side, and the mono button is a GainNode with one channel, which down-mixes to half the sum. Rendered offline in two channels, it agrees with the sines in every cell: a width of -0.527 and losses of 16.1, 0.4, 6.9, 1.8, 3.0, 4.6, 1.0 and 10.2 dB for the 10 ms delay, a pump of 0.635 Hz and 54.1 dB for the detuned pair, and 0.0 dB at all eight harmonics for the complementary pair.
What surprised me
The Haas bass reads as out of phase. Its correlation is -0.53, which is the number a phase meter would go red for, and it’s the most common widening trick going. The sides aren’t inverted, one is just late, but at a 55 Hz fundamental 10 ms is a third of a cycle and the correlation doesn’t know the difference.
Whether a delay is safe depends on the note, not the delay. At 10 ms the fundamental drops 16 dB in mono and the octave above it loses 0.4, so the sum isn’t quieter, it’s a different note. At 20 ms the fundamental loses 0.4 dB and the fifth harmonic at 275 Hz is gone, -166 dB measured against -180 predicted, which is the floor of the window. At 9.1 ms the fundamental itself goes, 52.8 dB. Any rule of thumb about Haas delays and bass is a rule about one key.
The detuned pair doesn’t lose level in mono, it loses it and gets it back, 0.635 times a second. The two sides drift through each other and the 55 Hz sum swings 54 dB, which is silence, every 1.6 seconds. Each harmonic pumps at its own rate, the fourth at 2.54 Hz, so what the club hears isn’t a bass fading in and out but a bass whose tone churns. Either side alone is steady to half a dB. My per-harmonic table read nothing at all for the upper harmonics of this one, -42 dB and below, because averaging a level that cancels every cycle gives you the average, and that’s a number about the instrument rather than the sound. The page swaps the rows out for this mode and reports the pump instead.
The complementary pair is the answer, and it’s old. Correlation 0.000, as wide as the meter goes, and the mono sum is the dry bass to a hundredth of a dB at every harmonic, because the delayed copy is added on one side and subtracted on the other and the sum removes it exactly. Each side alone is comb filtered, so it colours the sound in stereo, but nothing you do to it in mono can hurt it. Width doesn’t have to cost anything. The two tricks that do cost are just the two people reach for.
What I would do next
A real bass patch rather than a saw, with an amp envelope and a filter, and a sweep of the delay from 1 to 30 ms reporting the loss at the fundamental for each key of the octave. That’s the chart a producer would actually pin up, and it would show the safe delays for a key as a set of windows rather than a number.
Then the same measurement on a wide unison lead, where the detuned pair is seven voices and the pumping is smeared into something that’s supposed to sound like width. I want to know how much of a supersaw survives the mono button.