Why does tap length matter, and why a million taps?

What a tap is

In his explanations a tap is one multiply-and-add in an FIR filter: a delayed sample is multiplied by a coefficient and summed with the others, and the name comes from tapping into a delay line Head-Fi, May 2014Head-Fi, Mar 2019Part-Time Audiophile 28:54. In 2014 he said Hugo's 26,368 taps meant "26,368 multiplications and additions" for every sample of CD data Head-Fi, May 2014.

Why tap length matters, in his account

Since 2014 he has argued from sampling theory: an infinite-tap FIR filter with a sinc impulse response perfectly reconstructs a bandwidth-limited signal, and as taps are reduced "the precision of the timing of the transient in the middle falls off" Head-Fi, Apr 2014Head-Fi, Mar 2015Head-Fi, Aug 2017. He describes the error as non-linear: with a limited filter, transients come out slightly early or slightly late, shifting with the music before and after them, which he says confuses the brain's perception of placement, timbre, pitch and the starting and stopping of notes Head-Fi, Jul 2018Head-Fi, Jun 2019ConvinceMeAudio 6:51. He has said fixed, linear timing differences (phase, frequency response) are not the issue; constantly varying ones are Head-Fi, Oct 2016Head-Fi, Aug 2017Head-Fi, Jun 2019.

He ties the rate of improvement to the decay of the sinc function: its values halve each time the time span doubles, so with the WTA algorithm doubling the tap length doubles accuracy against ideal sinc, which he states as one extra bit per doubling Head-Fi, Mar 2019Head-Fi, Aug 2017Head-Fi, Sep 2019Hifistatement 24. He attaches a condition in 2019: the gain needs the right algorithm, and "it's pointless to increase the tap length using existing algorithms" Head-Fi, Mar 2019.

As illustration he gives the extremes: a one-tap (NOS) filter "giving worst case 100uS or so timing error", and an infinite-tap filter with none Head-Fi, Jan 2017Head-Fi, Oct 2016. He has described conventional filters as having "a hundred or so" taps (2014), tens of taps for half-band designs (2016), and about 128 (2022 and 2023, the latter for the ESS9038 Pro) Head-Fi, Jul 2014Head-Fi, Oct 2016Audio Force 10:44Head-Fi, Sep 2023.

What he says he heard as tap length rose

He has repeatedly said every increase improved the sound, listing DAC64 (about 1,000 taps, 1999), QBD76 (18,000), Hugo (26,000; 26,368 in his 2014 posts), DAVE (164,000) and the M Scaler (1 million) Hifistatement 0c w 15:36Audiophile Junkie 13:35Head-Fi, May 2014. The gains he names are bass definition and pitch, timbre variation, left-to-right soundstage precision, instrument separation and the starting and stopping of notes Hifistatement 0Audiophile Junkie 14:19. His first test in the late 1990s, half-band Kaiser filters from 256 to 2048 taps, "gave an enormous sound quality improvement" Head-Fi, Jun 2015.

Not every step was large in his telling. In 2015 he said he could still hear DAVE's prototype going from 100,000 to 164,000 taps, "albeit I can now start to hear the law of diminishing returns" Head-Fi, Sep 2015. In 2017 he said DAVE's move from 26,000 to 164,000 taps sounded better but disappointed him, and that reworking the WTA algorithm and moving from 8FS to 16FS mattered more than the tap length at that stage Head-Fi, Jan 2017Head-Fi, Oct 2017. In 2021 he said the step from 164,000 to 1 million was a larger subjective change than 26,000 to 164,000 Head-Fi, Jan 2021.

Why a million: the 16-bit calculation

He says the figure comes from a calculation he made in the early 1980s as a student: to reconstruct 16-bit CD to 16-bit accuracy, keep the sinc function until its coefficients fall below the 16-bit level, and that came out at getting on for a million taps Head-Fi, Jan 2017MajorHiFi 14:33c w 17:04. He says he concluded then that a million taps would never be possible, that digital was fundamentally flawed, and that he should stick with vinyl Head-Fi, Jan 2017Hifistatement 1:28. In 2023 he stressed that the target "wasn't based upon listening tests" but on the idea that 16-bit data should be reconstructed to 16-bit accuracy Eric's Hi-Fi 2:11; in 2024 he called 16 bits "an arbitrary number" chosen because the signal is 16-bit ConvinceMeAudio 8:31.

The threshold he quotes varies between talks: about 700,000 (2017), about three quarters of a million (2018, 2019), more than half a million (two 2023 talks; in the March 2023 CanJam Singapore one the same passage goes on to "you're looking at a million taps"), well over half a million (a podcast recorded October 2025 and published March 2026), and getting on for a million in many forum posts miceblue425 27:06Pursuit Perfect System 13:16Passion for Sound 10:57Dusty Audio 39:52Eric's Hi-Fi 2:11ecoustics 10:35Head-Fi, Jan 2017. In 2014 he attached the roughly 1M figure to an 8 times oversampling filter; from 2016 on he attached it to a 16FS filter Head-Fi, Apr 2014Head-Fi, Jul 2014Head-Fi, Oct 2016Head-Fi, Jan 2017.

He separates the 16 bits from the recording's bit depth: it describes how closely the filter's coefficients match ideal sinc, so the timing error is the same with a 16-bit or a 24-bit source Head-Fi, Jan 2017Head-Fi, Oct 2017. He calls it a worst-case guarantee for transients: a steady sine wave is reconstructed far more accurately, and it does not mean the DAC is a 16.7-bit DAC Head-Fi, Sep 2018Head-Fi, Sep 2019Passion for Sound 20:18.

Where the products sit, by his figures

He has given accuracy against ideal sinc as: Hugo about 12 bits and DAVE about 14 bits (2015) Head-Fi, Jun 2015; Hugo 2 about 13 bits (2017) Head-Fi, Aug 2017, then 12.2 bits as "the exact number (assuming my spreadsheet is right)", with DAVE 13.9 bits and M Scaler 16.6 bits (March 2018) Head-Fi, Mar 2018Head-Fi, Mar 2018; Qutest, 48,000 taps, about 12 bits, and M Scaler 16.7 bits (2019) Passion for Sound 19:15Passion for Sound 19:56Head-Fi, Sep 2019. In a 2017 Hifistatement clip he put DAVE at around 13 and at thirteen and a half bits, Hugo at 12, a typical high-performance DAC at six or seven, and NOS at one Hifistatement 24Hifistatement 1:12. In 2025 he said the best DACs available reconstruct to "only two or 3 bits" Audiophile Junkie 15:08. These figures differ by source and some are transcribed speech.

How the M Scaler reached a million

He said the new FPGA came out at just over a million taps; he first built 512,000 taps because it would safely meet timing, expected an incremental gain, found "It was massive", and delayed the Blu Mk2 launch to push to 1 million miceblue425 24:38Head-Fi, Jan 2017Hifistatement 3:36Head-Fi, Jan 2017. He gave the exact count as 1,015,808 taps in 2017, when the filter was in the Blu Mk2 Head-Fi, Aug 2017; for the Hugo M Scaler he says "the full 1 million taps" and that it uses the identical filter core, and the archive has no item giving 1,015,808 for the Hugo M Scaler by name Pursuit Perfect System 13:16c w 23:19.

He said the full million also brought something earlier tap increases had not, an opening-up of soundstage depth, and that the 2/3 million tap video mode collapses it Head-Fi, May 2017Head-Fi, Jun 2017Hifistatement 2:57. He has said he does not fully understand why; his hypothesis is that the filter's span of roughly 1.25 to 1.37 seconds matches reverb times, "but I don't know" Hifistatement 4:30Head-Fi, May 2017Head-Fi, Jun 2017Head-Fi, Mar 2018. In 2022 he linked depth partly to amplitude-dependent phase shift, and in 2023 he said depth perception still increases with longer WTA tap lengths Darko.Audio 24:34Head-Fi, Jan 2023.

How his position has changed

2014 to 2016: the million was a guess. In 2014 he wrote "this is entirely a guess" and that the limit "could be 100K, it might be 10M" Head-Fi, Apr 2014; in 2016 he said of longer taps "Frankly I do not know, and its possible its not much" Head-Fi, Mar 2016.

2017 to 2019: after hearing 1M he wrote "I doubt that this is the end of the process" and said he would keep going until doubling the tap length no longer changed the sound; in 2019 he wrote "I am sure that even at 1M taps on the M scaler we are not there yet" Head-Fi, Apr 2017Head-Fi, Feb 2017Head-Fi, Jan 2018Head-Fi, Jun 2019. He planned decimate-and-reinterpolate tests with the Davina ADC to measure how far 1M is from ideal Head-Fi, Jan 2017Head-Fi, Feb 2017.

2014 to 2026: the algorithm takes priority. The idea runs back to the early WTA work: in 2014 he said the WTA gave roughly the sound of a conventional half-band filter with ten times the tap length, and in 2015 that his first 256-tap WTA "sounded much better than 2048 tap half band Kaiser" Head-Fi, Apr 2014Head-Fi, Jun 2015. In 2017 he said the algorithm "becomes even more important as the tap length increases" Head-Fi, Oct 2017. In 2020 he built 1M-tap rectangular-sinc and Kaiser filters to compare with the 1M WTA; he said "the 1M Kaiser sounds similar to what I expect a 20k tap WTA filter would sound like", that he was "more convinced that algorithm is vastly more important than tap length", and also "certain that more musical benefits are to be had by further increasing the tap length" Head-Fi, Nov 2020. In 2026 he said "the algorithm is fundamentally more important than the number of taps", while doubling the taps with a given algorithm still halves the timing error Audio Force 8:16Audio Force 9:10, and that with the wrong algorithm "a thousand taps would sound better" than a billion Part-Time Audiophile 30:14. In the Soundnews interview (published October 2026) he said "The algorithm itself is much, much more important than the number of taps, as the Blackbird illustrates and as the WTA illustrates" article, Oct 2026.

2017 to 2026: 16 bits is not enough. Doubts appear early: in January 2017 he wrote that the 16-bit guarantee "does not mean that if one uses a 16 bit source, it is good enough", and in September 2018 that "my current assumption is that any transient timing error that is constantly varying is likely to be audible, no matter how small that error is" Head-Fi, Jan 2017Head-Fi, Sep 2018. In 2021 he wrote "we need much better accuracy than 16.7 bits" Head-Fi, Jul 2021; in an interview published in August 2022 (recording date not stated), "16 bit accuracy is not good enough" AVstore 6:55; in July 2024, discussing what he learned with Quartet, "16 bit is not good enough" and it needs to be "much, much better than 16 bits" HIFICLUB 20:23; and in a July 2024 post, "any transient timing error, no matter how small, is perceptually significant", adding that his stated intent had always been to continue until he could no longer hear a change Head-Fi, Jul 2024. In a podcast recorded in October 2025 and published in March 2026 he said he had been wrong to think 16-bit reconstruction would be perfection ecoustics 3:13ecoustics 3:42.

How many taps would be needed: in 2017 he said 24-bit sinc accuracy would need 256 million taps and doubted it would be audible; in 2018 he said an 11 million tap WTA filter would match ideal sinc to 20 bits, and about 16 million would be needed for better than 20 bits miceblue425 40:07Head-Fi, Jan 2017Head-Fi, Aug 2018. In 2023 a transcript has him saying his research put the answer at "ten to the power of seventeen" Eric's Hi-Fi 4:45. In the Soundnews interview (published October 2026) he said the count needed for "reasonably good sound" was "four times 10 to the 28", a filter delay of 900 trillion years, and said "This is getting to a good reproduction ability" rather than the best article, Oct 2026article, Oct 2026article, Oct 2026; an August 2026 recording also has 28 zeros after the four, while an October 2026 podcast transcript renders it as four with twenty-six zeros The Source AV 7:27Distorsiuni Interioare 19:19. He said this led him to separate the two effects that degrade transient timing into the Blackbird WTA structure in Quartet (4 million taps), and that "the 4 million taps isn't the story" article, Oct 2026article, Oct 2026article, Oct 2026Hifi Pig TV 1:28. Asked whether he needs more than 4 million, he answered "Yes, still", saying the limit is now tens of seconds article, Oct 2026article, Oct 2026.

What he has not said: this archive has no published measurement of timing error against tap length (in 2017 and 2018 he said he had no such numbers), no published results from the planned decimate-and-reinterpolate listening files, no worked derivation of the 10 to the 17 or 4 times 10 to the 28 figures, and no tap count at which he says improvement stops Head-Fi, Feb 2017Head-Fi, Sep 2018article, Oct 2026.

Quotes

“Having all those taps means the interpolation filter does a more accurate job of reconstructing the original timing of the recording.”2014-05-16 Head-Fi, May 2014

“…to absolutely guarantee reconstruction to 16 bit accuracy you need the ideal sinc function coefficients to be smaller than 16 bit…”2017-01-07 Head-Fi, Jan 2017

“So with 1M taps are we getting close to subjective convergence? Absolutely not. Indeed, I ended up being more convinced that algorithm is vastly more important than tap length.”2020-11-11 Head-Fi, Nov 2020

“I now know that any transient timing error, no matter how small, is perceptually significant - at least to me and other listeners I use.”2024-07-18 Head-Fi, Jul 2024

Dated positions

Caveats and open points

• Spoken figures (taps needed for 16 bits, product bit accuracies, the 10 to the 17 and 4 times 10 to the 28 counts) come partly and disagree between sources; check the recordings.
• The 2014 posts tie the ~1M figure to an 8x oversampling filter; later statements tie it to a 16FS filter.
• Bit-accuracy figures for DAVE and Hugo vary between 2015, 2017 and 2018 statements.
• The Hifistatement German article paragraphs on the million-tap story are the author's paraphrase and are not quoted as Watts's words.
• Quartet and Blackbird WTA material is included only for how it changes his view of tap length; the details of Blackbird belong to a separate question.
• The exact count 1,015,808 is stated for the Blu Mk2; no item gives it for the Hugo M Scaler, which he calls 1 million taps with the identical filter core Head-Fi, Aug 2017Pursuit Perfect System 13:16c w 23:19.
• The ecoustics podcast was recorded 2025-10-28 per the publisher's page and published 2026-03-17.

Topics: Tap length and diminishing returns, Transient timing error from reconstruction, Sampling theory and ideal reconstruction