All of the tape recording standards now specify the recorded flux on the tape as a function of frequency. They specify that the flux is constant from low- to mid-frequencies, then falls at 6 dB/oct above a "transition" (-3 dB) corner frequency. (This response is the same as that of a single-pole low-pass filter.) This means that, for flat overall response, the reproducer must have a response that is complementary to the recorded flux (not to the recording pre-emphasis!). This complement is a HF boost at 6 dB/oct starting from this same transition frequency. The lower the transition frequency, the more HF boost there is in reproduction, making more HF headroom, and more HF noise to go with it. The formula for the flux level vs frequency, and all of the transition frequencies, are given in Sec. 1.2.3 of MRL's "Choosing and Using MRL Calibration Tapes....", and the values of flux level vs frequency are given in a table. A more-detailed explanation with examples and graphs of the frequency response of magnetic recorders is given in an AES Journal paper.
The usual reproducing head is inductive, and it therefore
differentiates the tape flux.
That simply means that, for a constant flux input to the head vs
the head output voltage will rise at 6 dB per octave. To compensate
the usual reproducing amplifier is an integrator, whose response falls
at 6 dB per octave. Thus constant flux thru a differentiating
thru a integrating amplifier gives constant output voltage vs
frequency. (The terms "differentiator" and "integrator" come from the
mathematics of the circuit analysis. For our purposes, "differentiator"
is just a short way of saying "makes the frequency response rise at 6
dB per octave", an "integrator" is a short way of saying "makes the
frequency response fall at 6 dB per octave".)
Since the standard tape flux falls 6 dB/oct above some frequency -- say 3150 Hz for 15 in/s NAB equalization -- the reproducer equalizing amplifier response must rise 6 dB/oct relative to integration above that frequency. This simply means that the integration is stopped at that frequency. So the repro pre-amp voltage response falls 6 dB/oct from some low frequency (say 16 Hz) to the standard transition frequency (3150 Hz for 15 in/s NAB), then is flat above that frequency. Again, you may want to refer to the more-detailed explanation with examples and graphs of the frequency response of magnetic recorders that is here.
ONE MORE DETAIL: Everything said above assumes that the head is
no low-frequency head bumps and droop; no gap loss; no head resonance;
perfect azimuth adjustment and head-to-tape contact; etc. In reality,
of those things have to be corrected or compensated in a practical
so it behaves as tho it were using an ideal head.
Actually, most modern professional reproducing heads are pretty close
If you want to read a modern general theoretical discussion of tape recording equalization, see:
" Pre- and Postemphasis Techniques as
Audio Recording Systems", by Louis D. Fielder
Audio Engineering Society Journal, Volume: 33, Issue: 9, Page: 649...658 (1985). Available for purchase from the AES at http://www.aes.org/journal/search.cfm
Abstract: Audio recorders benefit from pre- and postemphasis, which reshapes the noise spectrum to match human audibility thresholds. A 10-dB increase in apparent dynamic range is realized for some digital audio systems. A first-order boost based on the CCITT J.17 preemphasis standard is shown to be appropriate for dynamic range expansion. A survey of peak acoustic levels present in 36 music performances is also included.
Equalizations for 15 in/s -- NAB, IEC, AME, proposed Studio Master, ADE, NagraMasterNOTE This discussion is ONLY for 15 in/s. 7.5 in/s and 30 in/s Eq are a whole 'nother set of stories, if anyone's interested.
The present 15 in/s NAB eq was designed
by Frank Lennert, at Ampex, for the Ampex Models 300, 301, and 201, in
1948 or 1949. It was for use with the standard professional tape of the
day, 3M 111, and it was within ±1.3 dB of the equalization
then already used by Ranger, Brush, and RCA, as shown by a figure
in the Ampex 201 manual. (The Magnecord equalization was quite
different.) The Ampex
equalization was approved as an NAB Standard in 1953. It was
appropriate in its day.
Q. Is the NAB standard optimum for recording at 15 in/s on modern tapes?
A. Without a doubt, it is far from optimum. I argued for making a change in the 1970s, but others said "Don't bother, analog is almost dead". Ha!
By the mid-to-late 1960s, the wavelength response of the tape had improved so much that a high-frequency cut is necessary to get the standard flux on the tape, and thereby flat overall response. This makes the recording equalizer hard to design, inflexible (hard to get flat for different tapes), and terrible for utilization of the tape -- there's way too much HF "overhead" room, and way too much noise to go with it.
Several proposals have been made for a more appropriate 15 in/s standard eq. The easiest is to use the IEC1 Standard (also called IEC, CCIR, and DIN) eq, as the Tascam 8 track ½ inch system does. I discuss other possibilities below. The irony is that 2-track masters on ½ inch tape at 15 in/s still use the NAB eq! Ugh! But apparently many or most 2-track on ½ inch tape are at 30 in/s, which has a better if not necessarily optimum equalization.
For 15 in/s with modern tapes, five
(really the curves for recorded flux vs frequency) have been
proposed, or used commercially:
1 IEC2/NAB Standard: Recorded
HF flux droops from a transition
frequency at 3150 Hz, requiring the reproducer to boost (relative to
from this frequency. This repro boost gives about 3 dB more HF boost in
reproduction than the inherent recording losses of the tape, so an HF
is necessary in recording to match the standard flux curve -- that is,
to give flat overall response. This is a shambles, dictated by all of
machines in the field that are set up this way, and all of the
recorded this way since 1950, and still.
This Standard also use a low-frequency boost and cut -- see
"Low-Frequency Equalization", below.
2 IEC1/IEC Standard: Transition frequency 4500 Hz. Just about matches the tape losses, and is the best you can do if you want to use an internationally-standardized eq. Has been widely used in Europe for ¼ in width master recording since the 1950s. Is used always (even in the US) for the Tascam, Otari, Fostex "double track density" recorders (8 tracks on 1/2 inch, 16 tracks on 1 inch, &c). This Standard does not use a low-frequency boost and cut -- see "Low-Frequency Equalization", below.
3 MRL-SM (Studio Master): Transition frequency 6300 Hz.
For technical details, see "Proposed Equalization for 15 in/s Studio Master Recording on High-Output Low-Noise Tapes", by J. McKnight and T. Kendall.
Audio Engineering Society Preprint Nr: 920, Convention No: 45 (1973), also available for purchase from the AES . This Standard is based on the IEC/CCIR Standard, and does not use the low-frequency boost and cut of the NAB Standard -- see "Low-Frequency Equalization", below.
purchase a Calibration Tape with the MRL-SM equalization, see the Publication
101SM for catalog numbers and prices for all tape widths.
Abstract: A new equalization and reference fluxivity are proposed: no LF pre-emphasis, reproducing HF equalization +3 dB at 6300 Hz (“25 µs”) and reference fluxivity of 250 nWb/m. Measured data and a demonstration compare the NAB and proposed performances. Pre-emphasis at 4 kHz is increased from
-2 to +1 dB; at 16 kHz, from +1 to +6.5 dB (NAB was +11 dB in 1950, when developed). Noise and maximum signal at 4 kHz are thus reduced 3 dB, and at 16 kHz, 5.5 dB. Recording response with less than a total of 0.5 dB ripple up to 20 kHz is achieved with one R-C recording equalizer.
Comment: In 1973, MRL thought this was a pretty good practical compromise of noise and headroom. We offered Calibration Tapes with this equalization, but we soon withdrew this as a standard product because people who don't read carefully missed the "proposed", and would buy this calibration tape when they really wanted the old NAB tape. This eq was and is used in the Pacific Recorders (now Research) & Engineering "CAT" broadcast carts at 15 in/s.
For a handy/cheap substitute Calibration Tape: The HF eq (that is, above 250 Hz) on a wavelength basis is the same as the standard 7.5 in/s NAB HF response. So just play a 7.5 in/s NAB Calibration Tape at 15 in/s, set the repro response above 500 Hz (at 15 in/s) to "flat", and you've got the "MRL Studio Master" equalization. Note that you cannot use the frequencies below 250 Hz on this tape, since they have the low-frequency boost of the NAB equalization.
4 ADE (Ampex
Duplicator Equalization): Transition
frequency 12.5 kHz.
See "Master-Tape Equalization Revisited", by John G. McKnight; Peter F. Hille
Audio Engineering Society Preprint Nr: 856, Convention No: 42 (1972), available for purchase from the AES.
Abstract: Optimum signal minus noise level of a commercial tape or disc record requires the signal- and noise-spectra of the studio master tape to be matched to those of the commercial record. The use of the NAB 380 mm/s (15 in/s) equalization (3150 Hz transition frequency) with modern tapes results in frequency- and noise-spectra which have much higher levels at higher frequencies than the final records. Other practical equalizations are studied, and a 12,500 Hz reproducing transition frequency is suggested for further evaluation.
Comment: This eq was used by Ampex Stereo Tapes for the 15 in/s masters for duplication to 7.5 in/s copies (the "EX+" series). The "Nagra Master Eq", used at 15 in/s, is essentially the same, but with a LF boost/cut. A Calibration Tape with ADE is available from MRL at standard prices.
5 AME (Ampex Master Equalization)
for details and more links.
CBS Labs independently arrived at a very
not used outside of CBS, published in:
"A New Equalization Characteristic for Master Tape Recording ", by A.. A. Goldberg; Emil L. Torick
Audio Engineering Society Journal, Volume: 8, Issue: 1, Page: 29...33 (1960). Available for purchase from the AES.
Abstract: Although the signal-to-noise ratio of master tape recorders is good by present standards, a low level background noise still exists. This is heard as hiss, due to the characteristic of the ear. Hiss reduction is accomplished by a new equalization that increases the tape loading in the frequencies between 1000 and 15,000 cps and decreases the hiss by 6 db as compared with NAB equalization. This is achieved at the expense of increased distortion within the hiss frequencies.
The German Broadcasting research institute
at a similar equalization, and I believe used it in their radio
It was published in German, but not (that I know of) in English.
All above completely ignores the low-frequency (LF) response & equalization. LF boost & cut is used for IEC2/NAB, AME, & Nagra Master; but is not used for the others. For arguments against an LF boost and cut, see
"The Case Against Low-Frequency Pre-Emphasis in
", by John G. McKnight,
Audio Engineering Society Journal, Volume: 10, Issue: 2, Page: 106...108 (1962). Also available for purchase from the AES.
Abstract: Data on low-frequency energy distribution in music do not justify the use of low-frequency pre-emphasis, and subjective low-frequency noise does not require it. Therefore the elimination of low-frequency pre-emphasis is suggested. Practical implications are also discussed.
"Am I the only old analog guy who used your SM eq back in the mid-70s? I have so many tapes done that way, and I always preferred them to the ones I did with Dolby A.
"In fact, I used SM until 1978, when I switched to 30 ips using my own "in-house" special curve, which was approximately 3 dB hotter from about 4 kHz on up. [That curve came about because my combination of Paradyne electronics and Ralph Norton high inductance heads couldn't quite make the normal 30 ips AES playback curve. The electronics were a dB or so from going into oscillation, but the tapes sure were quiet!]
"Unfortunately, I lost my SM test tape when I left my briefcase on the roof of the Port Authority parking garage one hot afternoon in 1980. Good thing many of my SM masters have tones on them!
"Does MRL still make a SM test tape?
Yes - see "3 Studio Mastering", above.
Q: "How does all this relate to Dolby SR?"
A: I'm not really sure. The Dolby NR systems are "dynamic" equalizers, as opposed to all of the others above which are "static" equalizers. I believe that Dolby based his design on the 15 in/s NAB curve. If so, he has already modified the responses to minimize the "evil" effects of the 15 in/s NAB curve.
See:" The Spectral Recording Process", by Ray Dolby
Audio Engineering Society Journal, Volume: 35, Issue: 3, Page: 99-118 (1987). Available for purchase from the AES.
Abstract: A complementary audio signal
encoding and decoding
format, called spectral recording (SR), for use in professional
recording and similar applications is described. The processing
is highly responsive to the spectral properties of the signal. A
characteristic used by encoding de-emphasizes high-level signal
in the frequency regions usually subject to channel overload. The
results in a significant reduction of audible noise and distortion
in the channel.
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Originally "Fundamentals" and "15 in/s Equalizations" were two separate files; combined 2000-04-05.
2003-08-06 Minor text clarifications; links added to papers.
2005-02-18 link to pub101sm added.
Edited 2006-01-18 to emphasize that the MRL SM equalization does not use the low-frequency boost and cut of the NAB Standard.