Theoretical Record Frequency Response

[Craig Maier]

A disc record exhibits a variable frequency response. Since its tangential velocity varies, it has the largest range of response at the outer edge of the recording and it decreases towards the center.

The size of a phono stylus must be small enough so as to contain no more than one half of a cycle of a signal within the width as it passes by. In other words, the stylus dimension must be at least one half the wavelength of the signal of interest. Using general intuition, you can imagine that if the stylus only needed to be the width of one cycle of the highest frequency signal of interest, then the positive and negative portions of that signal would cancel out as it passed through that portion of the groove. Elliptical styli produce higher frequency response compared to their conical counterparts because a smaller dimension is occupied tangential to the groove with that smaller dimension in actual contact with the groove wall.

The following equations pertain:

W = V / F x 2

wherein -

W = Smallest dimension of the styli (in inches)

V = Tangential Velocity of the record at the point of interest (in inches per second)

F = Maximum reproducible frequency (in Hz or cycles per second)

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Considering a constant angular velocity rotating disc (like a Vinyl LP record), the following formula describes its tangential velocity:

V = Pi x D x RPM / 60

wherein

D = Usable Diameter of the Record at various locations (in inches)

RPM = Constant Angular Velocity of the Record in Revolutions per Minute

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combining & simplifying the above equations and solving for Frequency (F in Hz)

F = (Pi x D x RPM) / (W x 120)

wherein

D = Usable Diameter of the Record at various locations (in inches)

RPM = Revolutions Per Minute of the Record in Question

W = Smallest dimension of the styli (in inches)

Pi ~ 3.1416

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Now, lets calculate the maximum theoretical frequency response of some common records played with some common styli types using the above equation for each:

1. 33 1/3rd RPM, 12 Inch Record

This type of record has 11.5 inches on its outer most edge and 6 inches on its inner most edge (by inspection).

Using an elliptical 0.7 x 0.3 mil phono stylus, the frequency response will be as follows:

Theoretical Starting Frequency Response: 33.33 KHz
Theoretical Ending Frequency Response: 17.5 KHz
Response Variance: 15.83 KHz
Average Response: 25.42 KHz

2. 45 RPM, 7 Inch Record

This type of record has 6.5 inches on its outer most edge and 4.5 inches on its inner most edge (by inspection).

Using an elliptical 0.7 x 0.3 mil phono stylus, the frequency response will be as follows:

Theoretical Starting Frequency Response: 25.5 KHz
Theoretical Ending Frequency Response: 17.6 KHz
Response Variance: 7.9 KHz
Average Response: 21.55 KHz

3. 78 RPM, 10 Inch Record

This type of record has 9.5 inches on its outer most edge and 4.5 inches on its inner most edge (by inspection).

Using an elliptical 2.7 x 1.2 mil phono stylus, the frequency response will be as follows:

Theoretical Starting Frequency Response: 16.25 KHz
Theoretical Ending Frequency Response: 7.7 KHz
Response Variance: 8.55 KHz
Average Response: 11.97 KHz

4. 78 RPM, 12 Inch Record

This type of record has 11.5 inches on its outer most edge and 4.5 inches on its inner most edge (by inspection).

Using an elliptical 2.7 x 1.2 mil phono stylus, the frequency response will be as follows:

Theoretical Starting Frequency Response: 19.57 KHz
Theoretical Ending Frequency Response: 7.7 KHz
Response Variance: 11.87 KHz
Average Response: 13.64 KHz

5. 33 RPM, 16 Inch Acetate Transcription Record

This type of record has 15.5 inches on its outer most edge and 8.5 inches on its inner most edge (by inspection).

Using an elliptical 2.7 x 1.2 mil phono stylus, the frequency response will be as follows:

Theoretical Starting Frequency Response: 11.27 KHz
Theoretical Ending Frequency Response: 6.18 KHz
Response Variance: 5.09 KHz
Average Response: 8.73 KHz

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Note: Interestingly, the 45 RPM Record seems to be the most optimal design if the requirement for audio reproduction is limited to 20 KHz.

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[DougMac]

45's

More interesting information. Thanks, Craig. From what I've read, the engineers at RCA put a lot of research and thought into developing the replacement for the 78. Nothing was arbitrary. The 45 format, including speed and size, was determined to be the optimum. Everything else is a comprimise and came about for reasons other than the best possible reproduction.

I have several "albums" of 45's, such as Perry Como and movie soundtracks such as "Showboat". Sadly, the hi fi's of the time couldn't adequately demonstrate the superiority of 45's over 33's, so the convenience of the LP won out.

Doug

[Craig Maier]

It is also worth noting that 45 RPM records do not play (track) properly on 33.33 RPM turntables designed for 12 inch vinyl LP records. They really want to be played on those small, cheap machines.

ps - As you can see, I had too much extra time on my hands tonight.

[Doug]

78 RPM, 10 Inch Record
Theoretical Starting Frequency Response: 16.25 KHz
Theoretical Ending Frequency Response: 7.7 KHz

I've noticed that alot of 78s are limited to ~80Hz-8kHz when using the spectrograph - and I wonder if this is why...maybe they intentionally limited the initial frequency response to ~8kHz so that it matched the final theoretical response of the record?

A good reason to run a 6-8kHz low pass filter when restoring then!

[Craig Maier]

Doug,

I am not sure, but that would make some sense. That way the recording would sound more "even" with much less variation in sound quality from the beginning to the end of play.

[Dan McDonald]

Sadly, the hi fi's of the time couldn't adequately demonstrate the superiority of 45's over 33's, so the convenience of the LP won out."

Doug

I think convenience almost always wins out over quality in terms of mass market. It's kind of sad, but that's what happens.

mp3s over wav (in terms of popularity - and mainly for storage convenience), cassettes over open-reels, now portable video starting to make inroads over dvd.

I think that what happens is that first an innovation is very poor quality, and only a few people use it, then it is improved until it is "acceptable" to most people, at which time the majority of people switch to it.


Doug - for the 78s, you mean the later 78s are limited to 8 kHz? I only work with acoustic 78s and cylinders, so I don't have much experience with later 78s. I always assumed the poor frequency response was because of the recording horn on the ones I work with.

Dan

[Craig Maier]

Dan,

I wonder if, in the future, we might see the mass market go back to the 44.1 KHz, 16 bit non-lossy PCM audio format (like Red Book CD audio). Imagine, sometime in the future, when a Terabyte of storage costs 50 cents and fits on the head of a pin. What reason would there be not to go back to a high quality audio system rather than sticking to that of lossy compression (mp3, etc).

[Dan McDonald]

that's true... but then you can always do the math and think.. well, I can have 2 gazillion mp3s instead of half a gazillion wav files in the same space...

But you may be right. Sort of like cassettes kept increasing in quality of tape and in recorders over the years. I think that's a way to get people to upgrade. SO I guess I'm really saying that people opt for convenience over quality, then, over time, they pay for increases in quality of the more convenient technology.

I'd bet that the storage space will continue to increase and the players will get better, and the standard mp3 compression schemes will eventually pretty well match wav quality, but won't save any space over wavs. You can already run mp3s at near cd quality, but people don't because of the space issues. As space gets cheaper, the player/recorders will generally standardize around wav quality, but mp3 format. Then something better will come along (maybe satellite-based music libraries or something) so that everything will be accessible with a wireless device instead of mp3 player, and that will be more convenient.

[Craig Maier]

Quoting Dan:

"Then something better will come along (maybe satellite-based music libraries or something) so that everything will be accessible with a wireless device instead of mp3 player, and that will be more convenient."

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Sort of like a gigantic jukebox in the sky.

[Dan McDonald]

Sort of like a gigantic jukebox in the sky.

Yes.. and I might add much better to use satellites for music than for missiles.

To quote Barry Manilow (and this is the first time I've ever quoted Barry Manilow - possibly the first time anyone's ever quoted Barry Manilow?)

"I'd like to teach the world to sing in perfect harmony..."

Dan

[Craig Maier]

That is undeniably a noble goal, indeed. It is hard to believe that there are people on the planet that would argue with that, but there are.

[DougMac]

I Need Your Help Barry Maniloww

"I'd like to teach the world to sing in perfect harmony..."

Dan

Heck, I'd settle for teaching Barry Manilow to sing in tune! (Just kidding)

We need a statistician to plot the MP3 compression trends plotted against the age trend of all us geezers. Why save all those notes if you can't hear them. Hey? What did you say? SPEAK LOUDER!

Maybe that's why I like 78's so much. Their bandwidth matches my hearing capabilities!

Speaking of the great Juke Box in the Sky, I went to Rhapsody and did a "Select All". It's taking a while... ;-)

On a more serious note, a terabyte or two of RAID 5 storage is not that outrageous. I've seriously considered setting up a file server and ripping all my CDs to it. I already have a wireless network and have tested playing songs stored on one computer with another member of the network. The file played fine. You could either build or pick up a used computer and throw in a decent sound card for a couple of hundred bucks. I've got some lefover speakers and and amps, including a Dynaco 120 I bought at a garage sale for $6.00.

One last musing. Have any of you been a victim of "CD Rot"? I've got a couple of hundred CD's that are stored properly. It's not much of a problem, but I've had a second CD develop this affliction. The first is pristine, no physical damage, but there's a perfectly round pinhead sized hole in the aluminum substrate.

Doug

[Craig Maier]

Quoting Doug: "Have any of you been a victim of "CD Rot"?"

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I have heard of it but have not experienced it; I dread the thought of it, as do most of us!! My first CD still plays just fine. Maybe this CD Rot is the byproduct of production mishandling. A little acid on the substrate for a long time would produce aluminum etching which would fit your description. Let's hope that is all that it is and not a "media time bomb".

[cromag]

Have any of you been a victim of "CD Rot"?

No, at least not yet. I first heard of the possibility back in '85. There was a news report that implicated some inks that were used for the on-disc artwork. Bummer!

I've also, fortunately, have not (yet) had any CD-Rs go toes-up -- even though my first ones were burned to cheaper makes.

[Doug]

Craig,
Now that you've pointed out the absolute best theoretical frequency response on a 78rpm recording...is there a way to flaunt this fact in the INF and other filter? obviously anything above ~8kHz is artefact.