100% Fidelity is Possible as We Approach Infinity. Are We There Yet?

A back-of-a-napkin capture of the Riemann Integral. 

The first step in ephemeralizing your LPs is to record them digitally, creating permanent archival copies. This is a step you only have to take once for each of your titles, but if you do it right, once is enough.

Recall that an information-rich map is always better than a back-of-a-napkin drawing. Create rich 24-bit/96KHz copies of your source material for archiving. Why? Read on.

Because we know we can't capture infinity digitally, the recording process is to sample the original; that is, to take a reading of the original sound wave at regular intervals Δ_i. The question is, how do we design a sampling process that will produce an optimal copy? Many people will tell you that "optimal" is a completely subjective characterization—not so (not "completely").

While virtually any scientific debate can turn subjective when opinion and evidence clash, math is uniquely impervious to opinion. "a(b + c) = ab + ac. Politicize that, bi***es." (Randall Munroe)

Without a priori knowledge about the sound being recorded, it is impossible to know if it is being captured accurately. But there is a proxy calculation that we can examine objectively.

A sound wave is a function F(t) of pressure v. time. Once a sample F(t_i) is taken at time t_i, the recorded sound value remains constant for Δ_i seconds until the next sample can be taken. Any Calculus Hero will recognize that, as we are sampling a sound wave, we are simulatneously calculating the Riemann Integral (approximate area below the curve) for it. Dude.

The width Δ_i and height F(t_i) of a rectangle in the Riemann Integral determine the accuracy of the approximation. Both dimensions are under your control. Let's concentrate here on getting the proper width via high frequency sampling. Next time we'll look at getting the proper height by taking the best possible samples.

The Riemann Integral aproaches 100% accuracy as Δ_i → 0. Thus you get progressively better approximations the more samples you can take in a closed interval. That's not my opinion, that's not even consensus opinion. That's math.

Because sound sampling is a real-time process, the total number of samples is less important than the number of samples you can take per second. This is your sampling rate, expressed in samples/sec or Hertz (Hz). Riemann says, the higher your sampling rate, the more accurate your source recording.

So what is a good practical sampling rate? Common sampling rates are:

• 44.1 KHz – CD Audio (CDDA)
• 48 KHz – DVD Audio (DVD-A)
• 88.2 KHz – 2x CDDA Rate
• 96 KHz – 2x DVD-A Rate

96KHz make sense for several reasons. First and foremost, it's higher that the other candidate rates (more is better). Second, 96 KHz is a common sampling rate supported by a wide variety of computer sound interface devices, so it's likely you can find one at a price you're willing to pay. Finally, because sampling theory says you can capture any frequency f  by sampling at twice that frequency 2f, 96KHz sampling captures frequencies up to 48KHz, well into the range inaudible to humans and above the upper range limit of even audiophile-class speakers.

Therefore my first recommendation for creating numerically accurate digital copies of your LPs is to set the sampling rate to 96 KHz. What do you think? Leave a comment.

              Vinyl-to-Digital Restoration #10              

Title: Gallery

Artist: Gallery
Contributing Artists: David Samuels; Michael DiPasqua; Paul McCandless; David Darling; Ratzo Harris
Genre: Jazz
Year: 1982

Despite the personnel involved having a pretty damn good pedigree, this album is lost to history. ECM Records never released it on CD, and even today has no entry for it on the ECM discography. Long ago I bought Gallery on vinyl for its link between the Paul Winter Consort and Orgeon. One of the best reasons for shepherding your analog past into the digital future is that your memory can be jogged. The record labels' memory can't.

© 2012 Thomas G. Dennehy. All rights reserved.

Altering Physical Boundaries to Expose the True Structure of a Piece

Boundaries help define art.

In our last installment, we discussed how buying pre-packaged music means accepting someone else's decision-making when the physical boundaries on an audio delivery medium (LP or CD) do not align with the intended artistic boundaries of the music recorded.

When you ephemeralize your own LPs, you are the master of your own destiny, introducing or removing boundaries to personalize the digital result for the most important listener: you.

Two relatively simple examples were presented last time; here we discuss two more interesting examples.



            Vinyl-to-Digital Restoration #6           

Title: Bach The Goldberg Variations
Artist: Glenn Gould (1932-1982)
Genre: Classical
Year: 1982



The Goldberg Variations, originally written for harpsichord but often performed on piano, consist of an aria and 30 "diverse variations" on it. There is a definite order and structure. The variations all use the base line and chord progression of the aria. Every third variation, starting with variation #3 is a canon following an ascending pattern. The two variations following each canon also follow a distinct pattern, forming groups of 3. The 30th variation is a unique piece called the quodlibet; the aria is repeated to close the piece.

The CBS Masterworks edition of Glenn Gould playing The GV ignores the structure completely. Side 1 is the aria and variations 1-15; Side 2 presents variations 16-30 plus the aria reprise. It's an efficient use of vinyl (50% of the total piece on each side) recognizing the listener's need to flip sides to hear the entire piece. The CD re-issue went to the opposite extreme, organized as a flat list of 32 tracks.

I took a hybrid approach. Using the CD track times as a guide (accurate because the CD and LP contain the same performance) I exported the arias, variations 1&2, and the quodlibet independently, then exported the remaining nine groups of 3 as combined tracks identified by their canon. This offers playback flexibility while accurately reflecting the structure of the piece. One may not want to shuffle The GV, but a good index is always appreciated. The track list looks like this:

01 Aria
02 Variation 1
03 Variation 2
04 Variations 3-5: Canone all'Unisono
05 Variations 6-8: Canone alla Seconda
06 Variations 9-11: Canone alla Terza
07 Variations 12-14: Canone alla Quarta
08 Variations 15-17: Canone alla Quinta. Andante
09 Variations 18-20: Canone alla Sesta
10 Variations 21-23: Canone alla Settima
11 Variations 24-26: Canone all'Ottava
12 Variations 27-29: Canone alla Nona
13 Variation 30: Quodlibet
14 Aria da capo


            Vinyl-to-Digital Restoration #7           

Title: Music for 18 Musicians
Artist: Steve Reich and Musicians
Genre: Classical
Year: 1978



Music for 18 Musicians is a so-called minimalist composition for voices, strings, reeds, piano  and mallet instruments. Like The GV, Mf18M is structured as a series of variations (11 in this case) which composer Reich calls Sections, framed by the equivalent of an aria, a section entitled Pulse to open and close the piece. Unlike The GV, played as 32 self-contained pieces, Mf18M is a single continuous composition; transitions between sections are identified only by a shift in the pulse patterns and repeated phrases being played.

There are no tracks on the ECM vinyl recording, nor any time information published for the sections. Ask yourself: how does a continuous piece of music get put on LP, a medium with a distinct side A and B?

Producer Rudolph Werner solved that problem by engineering a long fade-out at the end of Section 4, which closes side A, and enginering a long fade-in at the start of Section 5, which opens side B. He effectively cut Mf18M in two to put it on disc.

As with The GV, I went to the CD re-issue to look for a strucural approach for my digital transfer for the LP. In this case, ECM chose to structure the CD as a single track containing the entire performance. I could do the same, fusing sides A and B, but that still would leave the fade-out/fade-in between sections 4 & 5.

So in the end, I chose to remain as true as I could to the composer's intent for the piece and the producer's intent for the LP, and transferred the side A and side B tracks as is.

Sometimes you slay the dragon. Sometimes the dragon wins.


© 2012 Thomas G. Dennehy. All rights reserved.

LPs and CDs Are Fraternal Twins

An LP and his digital twin.

Raise your hand if you think there are files on a CDDA disc (an "audio CD").

OK, put them down. There is some misinformation out there.

When you put an audio CD into your computer's drive, Windows Explorer will display a CDA (CD Audio Track) file for each track. If you double-click one, Windows Media Player opens and plays the track.

But the files don't really exist. Each one is a shortcut to where the corresponding audio track starts on disc. Explorer just calls them files because files are what it understands. Without the physical CD loaded, the "files" are meaningless.

A CD is a continuous laser groove of 16-bit digital stereo audio samples, starting at the inner edge and radiating outward. The implicit sampling rate is 44.1 KHz, meaning no time information needs to be encoded with the audio.

An LP is a continuous physical groove capturing an analog stereo waveform, starting at the outer edge and radiating inward. The implicit recording and playback rate is 33 1/3 rpm.

Both are round, have a hole in the center, spin while playing, and are read by a tracking sensor.

Thus, they are fraternal twins. A CD is basically a digital LP (played in reverse, but not saying Paul is dead). That's one reason CDs and LPs share common playback inconveniences, and why dematerialized digital playback has made the CD seem just as clunky as his analog twin.

In my professional life at Harman International, I manage development of multimedia infotainment/navigation systems for the OEM automotive market. Our newest systems don't even include a CD player. An iPod/USB interface is now standard, reflecting the market preference for dematerialized play.

But that didn't stop an OEM customer's test group from flagging a Harman system because "it didn't play CDA files." They thought that dragging and dropping CDA files onto a memory stick was equivalent to making an audio copy of a CD. We quietly buried the bug report as "not reproducible" (so to speak).

Our digital transfer process for LPs will produce more accurate results.

                Vinyl-to-Digital Restoration #1              

Title: The Survivors' Suite
Artist: Keith Jarrett
Contributing Artists: Charlie Haden, Dewey Redman (1931-2006), Paul Motian (1931-2011)
Genre: Jazz
Year: 1976

My interest in jazz got its start with a college housemate's copy of Keith Jarrett's The Köln Concert. But it really took off in grad school as I started mining through the ECM catalog at dear, departed Schoolkids Records in Ann Arbor MI. My jazz holdings stand now at roughly 250 titles, and you can trace a path back from virtually any of them to one of the four members of this quartet.

The most labor-intensive task in the digital transfer pipeline is extracting and isolating individual LP tracks. Not surprisingly, the task time grows linearly with the number of tracks on the disc. You're grateful for a title like The Survivors' Suite, where side 1 is track 1 and side 2 is track 2. Quick and clean.



© 2011 Thomas G. Dennehy. All rights reserved.