1kHz Test Tone: Does increasing the number of PCM values really matter? And Stereophile's "still listening" to the community (so they say).

Hey there audiophiles, lots happening in life to keep me busy these days as we enter summer 2025, so let's do another little follow-up of a topic based on reader comments.

In the previous post, there was a comment by Mister MB about the 1kHz test tone and the idea that it would be good to use tones that employ more PCM values as quoted from Ken Pohlmann's book Principles of Digital Audio (currently 6th Edition, 2011, from page 81, emphasis mine):

"Digitally generated test tones are often used to measure D/A converters; it is important to choose test frequencies that are not correlated with the sampling frequency. Otherwise, a small sequence of codes might be reproduced over and over, without fully exercising the converter. Depending on the converter’s linearity at those particular codes, the output distortion might measure better, or worse, than typical performance. For example, when replaying a 1-second, 1-kHz, 0-dBFS sine wave sampled at 44.1 kHz, only 441 different codes would be used over the 44,100 points. A 0-dBFS sine wave at 997 Hz would use 20,542 codes, giving a much better representation of converter performance. Standard test tones have been selected to avoid this anomaly. For example, some standard test frequencies are: 17, 31, 61, 127, 251, 499, 997, 1999, 4001, 7993, 10,007, 12,503, 16,001, 17,989, and 19,997 Hz."

Certainly a good point to think about. However, if we look at actual hi-res DACs these days, and the way we're running 1kHz tests to show routinely >100dB SINAD, would we actually see significantly different results depending on how we create these test tones, specifically whether more or less PCM codes are being used in the signal sent to the DAC?

Well, while I still have the Topping DX9 on my testbench, let's have a look at the analog output from the device with a few ~1kHz test tone variants.

First of all, I think it's useful to note the release year for Pohlmann's 6th Edition was 2011, that's around 15 years ago now, an eternity when it comes to technological developments even if we argue (IMO correctly) that audiophilia progresses much slower than the bleeding edge! The first edition of this book I believe came out in the 1980's. In all that time, obviously many things about digital audio have evolved. Back in 2011 with the 6th Edition, we were just getting started with having albums be released as hi-res downloads and just beginning to see asynchronous USB DACs with very low jitter (devices like my first low-jitter USB TEAC UD-501 by 2013).

As such, does it still stand that we need to construct test signals with more PCM codes to "fully exercise" the converter?

[By the way, this concept can also be found in an article in B&O tonmeister Geoff Martin's blog titled "997 Hz?" (2017) where he discusses the use of 997Hz (a prime number, often used as a standard in testing) in place of a round number like 1000Hz.]

So, let's explore by creating a "perfect" 1,000Hz sine wave at 48kHz which is a perfect multiple (as opposed to 44.1kHz CD standard). Here's a display of the waveform in Audacity showing the points zoomed in:

Notice that there are only a few levels repeated over and over again, we can easily count how many quantized number make up that signal. To be more precise, let's analyze these levels in the form of a histogram:

So, converting the 24-bit integer number to a level from +1 to -1, we can see the quantization levels of all the data over 48,000 samples (1 second) into the "bins" above. There are only 25 numbers needed to define an exact 1kHz signal at 48kHz.

As an undithered 24-bit signal with just 25 PCM repeated values, what does this look like when played through the hi-res Topping DX9 DAC?

Using the current set-up on my table (not using the E1DA Cosmos APU), I see about -119dB THD+N playing the 1kHz tone with the lowest number of PCM codes.

Now once we go off from 1kHz (ie. 48kHz no longer an integer multiple), we'll start seeing that many more levels are used to represent the waveform. For example, let's look at the tonmeister's 997Hz:

We no longer see the same levels on either side of the symmetrical sine wave, and over time, the levels shift. The crossover points no longer have 0-value samples. Many more PCM levels are being employed to encode the waveform and here's what it looks like on the histogram for 1 second (48,000 samples) of the sine wave:

Many more levels are being used - numbering over 24,000 across the 48,000 samples. This means that 50% of all the samples have a unique 24-bit number. For a 24-bit number, there are a potential 16.8M integers, so even 24,000 is just a tiny 0.14% of all the possibilities!

So, does playing a 997Hz tone, using all those extra numbers in the 24-bit signal change the output from the Topping DX9?

No it doesn't. With a result of -118.7dB THD+N, that's really no different from playing exactly 1,000Hz despite the fact that we're now using way more PCM levels than just 25!

Okay, how about trying again, if we play the next prime number frequency beyond 1000Hz which is 1009Hz at 24/48?

Like with 997Hz, this frequency will utilize many more values than the 25 at 1000Hz. And again, we're not seeing any significant change in the THD+N measured nor significant change in the detailed FFT harmonic distortion pattern from the DAC.

So, what does this all mean? Quite simply that with modern hi-res DACs of excellent  performance, there's no reason to worry about whether an otherwise well-constructed 24-bit 1kHz tone uses only a few PCM levels or thousands.

The reasons are pretty clear if we think about how modern DACs work:

1. Modern hi-res DACs (except when specifically set to Non-Oversample mode) will oversample the input many times, and interpolate the PCM values to intermediate numbers that are not seen in the original quantized file. For example, the Topping DX9's AKM AK4499EQ chip uses an 8X 32-bit oversampler internally and will use those 7 extra numbers internally calculated for the conversion process.

2. Internally, most modern DACs use multibit sigma-delta modulation anyways. So even though the PCM numbers for each sample may be 16-bits or 24-bits, this will end up getting transformed by a multibit SDM modulator (I think 7-bits for the AK4499 series, similar to DSD's 1-bit PDM). It's not the exact PCM numbers themselves that are being converted in the digital-to-analog process. What is important is whether the DAC is capable of linear performance throughout a wide output level. In the case of the Topping DX9, we can see that it's basically flat down to below -120dB (as measured here). 

A corollary is that for those running R-2R DACs, make sure the manufacturer has done a good job with maintaining linearity across the output levels in the resistor network! I know some audiophiles really like their R-2R designs, but this is an older principle and there might be more irregularities due to resistor/switching imprecisions; make sure to check with measurements. (Recent measurements of the Topping Centaurus R2R DAC look pretty decent.)

For the results shown here, note that I'm testing in 24-bits. If measuring at lower-performance 16-bits, I would certainly use dithering to clean up truncation artifacts which will show up in the measurements. To be honest, truncation distortions are probably low enough in level such that in actual recorded music they will not affect musical enjoyment.

There's the interesting discussion on ASR mentioned by danadam last time about "self-dithering" where the tiny variations playing 16-bit 999.91Hz @ -0.01dBFS between samples function like random noise to prevent truncation distortion. Clearly, we don't need to do this in 24/32-bit audio which is why the usual recommendation is that we dither when going down from 24-bits to 16-bits, but generally is not needed in the studio with native 24/32-bit work.

As per the concept of "perceptibly perfect" DACs, performance these days is very high without selling a kidney to achieve state-of-the-art quality. 🤣  The implication being that high-fidelity digital conversion is very much a "solved problem" that audiophile needs not worry about.

The concern that "a small sequence of codes might be reproduced over and over, without fully exercising the converter" explored in today's post is not really relevant any more except in perhaps esoteric cases (like R-2R DACs maybe). Thankfully, I don't think this idea is entrenched among audiophiles like the myths some audiophiles/reviewers keep mentioning like high levels of noise in digital (so they can sell you ethernet switches and expensive streamers/computers?), or audible jitter, or even magical sounds from analogue gear (as if something more mystical is happening beyond the objective limitations of older technologies).

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Stereophile: "We're Still Listening"

So that didn't take long! In less than a week since my last post, it looks like Stereophile has totally scrubbed all the comments added by readers over the years (decades!) to their articles online. Apparently in a previous post that I see has disappeared (it has subsequently been moved here), Stereophile claims that they're "still listening" to public feedback. To be honest, have they even listened to the community in the last few years?

The comment was reposted here:

We're Still Listening: Email Us Your Thoughts
Fri Jun 6 03:35:07 GMT 2025

Dear readers,

Thank you for being an engaged part of the Stereophile community. While we've retired the in-page commenting feature on our website, your voice remains essential to us.

Share your thoughts, questions, and system notes:

STletters@stereophile.com

Selected letters will continue to appear in the magazine and online. Your feedback shapes our reporting and reviews. We appreciate every note you send.

—The Stereophile team

Do we think Stereophile is going to be publishing many critical letters, even if highly thoughtful commentary about product reviews or feedback on their editorials using this E-mail mechanism?

As you can see, Stereophile is going pre-Y2K when it comes to community engagement! This is simply unhealthy and the publication must be going through some kind of soul-searching in the background. I doubt it's purely operational dollars unless things are very desperate since keeping comments open on a website is a basic function these days that probably doesn't add much to the cost. Furthermore, why do it in two steps such that comments were still available to read for more than a week before erasing everything by around June 18th? Did they have a change of heart and decide to just go completely commentless?! Given that the magazine must be funded mainly by ad revenue (given the low cost of each subscription), I'm guessing this decision must have been guided with consideration of Industry-funded forces.

Let's talk about the comments that we audiophiles post. Over the years, I think civility on audiophile forums have very substantially improved. Have a peek at the Steve Hoffman Hardware Forum for example. Even with very contentious threads like this one, it doesn't look too bad does it? Nobody's threatened, we acknowledge that people hear things differently, rationales are given, not much ad hominem attacks, nobody's swearing, and as adults we can filter out and ignore noise from certain individuals.

While I believe there are trolls and individuals with mal-intent lurking on the Internet (including snake oil shills and maybe paid agents to promote products), the audiophile world is quite small - maybe at most tens of thousands of us would be interested enough to dig deep into the kinds of gear Stereophile reviews or the measurements they publish. Furthermore, based on my survey back in 2023 (consistent with the folks I run into at audio shows), we are quite demographically homogenous - almost uniformly males, mostly between 40-70, in the middle if not upper-middle class and higher tiers. As a group of hobbyists, we're not disinhibited teenagers or typically dramatic influencers so I believe maturity is highly prevalent among us!

The comments on the Stereophile website criticizing subjective reviewers' claims, and those pointing out the discrepancies between subjective opinions and measurements appear to be born out of the frustration of middle-aged, probably upper middle-class guys!

This is not a reflection of the audiophile community having many "trolls" or immature people who have nothing better to do than cause trouble online. Rather, I believe the issue is that audiophiles have had enough of nonsensical reviewers who don't really know what they're talking about when it comes to audio technology, making all kinds of unsubstantiated, even magical claims, causing many normal, reasonable hobbyists to vent their frustrations in disgust. I believe many of us see that the "journalistic" project that presumably at one time was the goal of the magazines has gone by the wayside (not just Stereophile of course); they've lost the ability and desire to educate and advance understanding.

As one who has watched this industry for years, it looks like John Atkinson shifted the magazine in favor of Industry interests gradually after he took over back in 1986. At least Atkinson had the common sense to keep the objective measurements in the reviews and was knowledgeable enough to explore such topics even if he was unable to rightly criticize the media and Industry as J. Gordon Holt his predecessor. However, we saw his tendency to favor the Industry with articles like this and his inability to shift viewpoints subsequently. By the last decade of Atkinson's tenure, gone are the extended technical articles (like this and this and this) that helped audiophiles understand concepts and ground us in reality beyond mere opinion pieces and product reviews in the pages of the magazine.

An Editor sets the leadership, tone and quality for the publication. The magazine these days under Jim Austin since 2019 obviously can no longer "handle the truth" of an open dialogue. Sadly, I think Austin is out of his depth when it comes to adequate knowledge about audiophilia; it's easy to see clear lapses with his opinion articles like this, this, and this.

Over the years, I've seen the reversion from open engagement with the community into a form of isolationism as a harbinger of decline suggesting that the publication has already lost the support of much of its audience members so it's just doing what it can to retain ad revenue by refusing to show the conflict. Furthermore, I bet the comments added a lot of traffic for the website as readers return to the articles to look for new ideas and debates. These return visits add to the popularity of the articles on search engines. Without engagement, obscurity and irrelevance awaits.

No fear though. As audiophiles, we have plenty of online places to interact with fellow hobbyists and discuss all kinds of things regardless of Stereophile's future. I hope you're all enjoying some great music reproduced in high-fidelity!

Interesting discussion about Brian Wilson's "God Only Knows" - RIP Brian.