The formula for a radial scratch/break is simply
Time between pops = 60/RPM
The time between pops will not vary between outer and inner grooves
if the scratch or crack is “radial” (i.e. perpendicular to the
In your example, 1 second between pops means 60 RPM. And 1 second
between pops at the outer groove will still be 1 second between pops
at the inner grooves.
If the scratch/break is not orthogonal (not perpendicular to the
grooves), then the time between pops will vary depending upon the
angle of the scratch/break.
Of course, the formula has additional terms if the scratch/break
crosses a groove at an angle. But you’ll see that the effect of
angle and pitch are fairly small.
The formula would look something like:
Time between pops =
60*pi*D / (RPM * (pi*D + 1/(pitch/tangent(angle))))
pi = 3.141596
D = groove diameter (inch)
angle = measured in degrees from orthogonal
pitch = grooves per inch
RPM = rotations per minute
Plugging this into a spreadsheet for 4.5-inch from the center
(D = 9 inches) and 120 pitch at 60 RPM (1 sec between pops)
and the angle of the scratch at 20 degrees…
Time between pops = 0.99989 (D = 9 inches, angle = 20 deg)
Time between pops = 0.99981 (D = 5 inches, angle = 20 deg)
Difference = 0.00008 sec
Clearly, the variation in periodicity due to pitch, groove
diameter, and scratch angle is quite small (0.01 milliseconds)
and a second-order effect.
As the scratch gets closer to being tangent to the groove:
Time between pops = 0.99890 (D = 9 inches, angle = 75 deg)
Time between pops = 0.99802 (D = 5 inches, angle = 75 deg)
Difference = 0.00088 sec
In theory, being able to identify the periodicity in noise and
using that to automate impulse noise reduction, seems helpful.
But it also assumes that the scratch is uniform in the way it
damages each groove (uniform depth and width). And the analysis
needed to distinguish impulse noise from percussion impulses
may not be practical. Asking someone to input scratch location
and angle is also not particularly practical either.
So, for all intents and purposes:
Time between pops = 60/RPM
This, of course, assumes a CRV (Constant Rotational Velocity =
constant RPM) disc, which is the majority of analog recordings
on disc media. However, to make things exciting, there are CLV
(Constant Linear Velocity) recordings that were used by Gray
Audograph dictation discs. In that case, these formulas won’t
work because the RPM varies with the groove diameter. Gray
Audograph is one of our specialties for transfer work.
On 11/27/15, 12:56 PM, "Association for Recorded Sound Discussion List on
behalf of Malcolm" <[log in to unmask] on behalf of
[log in to unmask]> wrote:
>Hi Eric -
>Nice info, thanks. Good to know. Now, how about a mathematical formula
>that will tell one, if there is a linear scratch or a break that goes
>straight from record edge to center hole, exactly when the pop will
>sound from revolution to revolution along the groove.
>For instance (and I am just picking numbers out of the air by way of
>supposition) if it takes 1 second between two pops at the outer edge of
>the record, say 4.5" from the center, how long will it take between pops
>at 2.5" from the center? And how much less time will elapse per
>revolution at, say, a 120 groove pitch? It will obviously be a
>decreasing number the closer to the center of the disc one goes. There's
>got to be a (simple) formula!
>I have long thought that using an algorithm to determine where the pops
>will fall would be of great help in digitally removing most of a scratch
>or crack in a 78 (or any other speed record for that matter). Maybe as a
>plug in for existing audio editors.
>On 11/27/2015 9:48 AM, Eric Jacobs wrote:
>> For those who don¹t mind a physics/mathematical representation of
>> what¹s going onŠ
>> The torque of the turntable motor is constant.
>> When cutting...
>> The torque due to stylus friction while cutting a groove varies with
>> Stylus Torque = Radius X Stylus Cutting Force
>> Radius outer groove > Radius inner groove
>> Stylus Torque (outer grooves) > Stylus Torque (inner grooves)
>> When playing...
>> Stylus Cutting Force > Stylus Playback Force
>> When cutting...
>> Net Torque = Turntable Motor Torque - Stylus Torque
>> Net Torque (outer grooves) < Net Torque (inner grooves)
>> RPM (outer grooves) < RPM (inner grooves)
>> Because there is more net torque when cutting the inner grooves, the
>> turntable spins a bit faster when cutting the inner grooves. Or you
>> can think of it the other way - that the turntable spins slower when
>> cutting the outer grooves because there is less net torque.
>> When playing...
>> Net Torque is more constant because the Stylus Torque during
>> playback is so much smaller than during cutting.
>> Net Torque = Turntable Motor Torque - Stylus Torque (very small)
>> Net Torque (outer grooves) ~= Net Torque (inner grooves)
>> RPM (outer grooves) ~= RPM (inner grooves)
>> Pitch variation is a function of playback speed variation
>> IMPORTANT: When playback speed is faster than the recording speed,
>> the pitch is higher, and vice versa. This is the essence of why
>> there is pitch variation.
>> Recall from above:
>> When cutting: RPM (outer grooves) < RPM (inner grooves)
>> When playing: RPM (outer grooves) ~= RPM (inner grooves)
>> and therefore
>> RPM cutting (outer grooves) < RPM playback (outer grooves)
>> The playback RPM on the outer grooves is faster than the original
>> cutting speed. Therefore the outer groove pitch is higher than the
>> pitch on the inner grooves (or vice versa, the pitch on the inner
>> grooves is lower than the outer grooves).
>> To account for this variation in speed during recording, the
>> recording engineer would cut the first disc in a series starting
>> with the outer groove. The second disc in a series would start
>> on the inner groove, so that the speeds would more closely match
>> between the first and second discs. Inner and outer groove start
>> would continue to alternate during the recording session.
>> Hopefully this somewhat long-winded mathematical explanation is
>> ~ Eric
>> Eric Jacobs, Principal
>> The Audio Archive
>> 1325 Howard Ave, #906, Burlingame, CA 94010
>> Tel: 408-221-2128 | [log in to unmask]
>> On 11/27/15, 9:09 AM, "Association for Recorded Sound Discussion List on
>> behalf of DAVID BURNHAM" <[log in to unmask] on behalf of
>> [log in to unmask]> wrote:
>>> I think the obvious answer to your second question is insufficient
>>> on the recording turntable. This happened on many recorded sides, one
>>> example that comes to mind is the Weingartner "Les Preludes" by Liszt.
>>> The cutting stylus puts considerable drag on the turntable and that
>>> increases towards the centre of the disc, dragging the speed down. If
>>> the recording turntable motor is not VERY strong and is unable to
>>> maintain the corrrect speed throughout the cut, the resulting slower
>>> speed towards the end of the side gradually raises the pitch on
>>> With modern digital workstations, this error is easy to fix, but back
>>> the days of reel to reel tape, trying to rejoin the sides on the
>>> aforementioned "Les Preludes" was a nightmare.
>>> On Friday, November 27, 2015 11:48 AM, Andrew Hallifax
>>> <[log in to unmask]> wrote:
>>> Thanks for your contribution Jolyon. I am in fact following all such
>>> and practices as you describe. We're working on the presumption that
>>> standard pitch seems to have been adopted in Argentina sometime during
>>> late 30s. Regardless of how true that is, our presumption is supported
>>> most other discs in the series produced during the 1950's which render
>>> or less reliably A442ish at nominal 78rpm.
>>> However, my question to the list was aimed not so much at resolving the
>>> pitching/speed conundrum per se, but in the hope of discovering whether
>>> anyone might offer an insight into why speeds were inconsistent across
>>> two sides of discs recorded on the same day and bearing adjacent
>>> and also, why or how certain recordings of this period change pitch
>>> the side.