One of the issues with phonograph records is that the edge of the record necessarily moves faster than the middle, if the turntable speed is constant. This inevitably means that sound quality differs between the first (outermost) and last (innermost) parts of the recording. Fortunately, a moment's thought and a couple of well-aimed G&Ts have provided the answer.

Suppose the outermost part of the groove is a conventional circle (technically one turn of a spiral, but you understand). And suppose also that the innermost part of the groove is not a circle, but a sine wave wrapped into a circle - a sort of cogwheel shape but smoothly sinuous. There will be, say, ten sine-wave oscillations for one revolution of the record (so, a sinuous ten-pointed cogwheel). If the amplitude of the sine wave is chosen correctly, the total length of the innermost track will be the same as that of the outermost (circular) track.

Between these two extremes (that is, in the middle tracks), the track will gradually become more and more sinusoidal, so that *all* parts of the track will move past the stylus at the same speed. If you watched the tone arm as it played a complete record, it would start out as usual by just travelling slowly inwards as the record played. As you approached the later parts of the record, the tone arm would start to swing back and forth, superimposed on a gradual inward motion.

A tiny fraction of extra space will be needed between the tracks, to accommodate the gradual increase in sinusoidality, but this will be quite small and will be largely offset by the greater overall length of each of the inner tracks.
-- MaxwellBuchanan, Sep 26 2019

YouTube: Techmoan: Tefifon player and Tefi cartridges https://www.youtube...watch?v=nBNTAmLRmUg
Mentioned in my anno [notexactly, Sep 28 2019]

Wikipedia: Tefifon § History § 1930s https://en.wikipedi.../wiki/Tefifon#1930s
Mentioned in my anno. Says: "Both [the Tefiphon and Teficord] use loose tape, unlike the cartridge-loaded tape of the Tefifon." [notexactly, Sep 28 2019]

Wikipedia: Helical scan https://en.wikipedi...g/wiki/Helical_scan
Mentioned in my anno [notexactly, Sep 29 2019]

Why not just move all the tracks further away from the hub ?
-- 8th of 7, Sep 26 2019


Because that would be pointless.

This is way to accommodate the same total amount of track, but ensure that the linear velocity is the same throughout the playback, whilst using a constant turntable speed.
-- MaxwellBuchanan, Sep 26 2019


Then why not make the recording truly linear, and avoid the problem of fixed angular velocity/variable linear velocity ?

A cylindrical form is not without possibilities ... oh, wait ...
-- 8th of 7, Sep 26 2019


This will cause the azimuth angle between the track and the needle to vary several times over the course of a turn, more severely toward the center of the disc, which will cause cross-mixing between the left and right channels if it's a stereo record.

It should be possible to unmix the channels with analog electronics, I think, maybe, but it would require knowledge of the current angle, which will vary several times over the course of a turn. Maybe the turntable and discs should have an index mark that you align when you start a record, and the player just compensates for the mixing based on its knowledge of the current azimuth of the platter.

Another solution could be to mount the needle in the tone arm in such a way that it can rotate about its vertical axis, with the tip not quite on the axis of rotation, so that it can find its own direction like a swivel caster.

[Ian], like a Tefi cartridge [link] but not continuous-loop? The Wikipedia article [link] says the Tefi company first developed tape machines using grooved tape that was loose rather than in a cartridge, but it doesn't say whether that was reel-to-reel or not (probably).
-- notexactly, Sep 28 2019


Just use long, stiff, rectangular .2cm wide records and play them linearly.
-- Voice, Sep 29 2019


Sorry, [Max], you've got a violation of Kepler's second law going on here.
-- lurch, Sep 29 2019


//a violation of Kepler's second law// How so?

//cause the azimuth angle between the track and the needle to vary// But if the record is cut using the same geometry...?
-- MaxwellBuchanan, Sep 29 2019


Well, all record players violate the "equal areas in equal times" thing, just because the radius of the point-of-play changes throughout the course of the recording. But, the diagram you'd draw to demo this looks almost exactly like the Kepler's 2nd Law picture.

You're thinking along lines of "if an inner track has the same length as an outer track, and the table speed is constant, the groove speed will remain the same." Yes, it will, however...

If you look at discrete points along the curves, you'll note that the groove speed is equal to the rotational velocity multiplied by the radius. A point on an outer groove has a longer radius than that on an inner groove. That means a groove cut tangentially to the radius of play will always have a groove speed directly related to the length of the radius.

Your gimmick here is to add grove length radially to force the needle to cover more distance during the period of rotation. However, being a sine wave, there will be an inner point that's tangent to rotation, perpendicular to the radius, and a similar outer point. It is trivial to show that the groove speed will be higher at the outer radius than at the inner one; you won't get a constant groove speed. The speed at the curve's innermost point will definitely be an absolute minima; at the outermost point will likely be an inflection point, but not necessarily a maxima. Depending on the amount of radial distance added, the outer point could well be a local minima. However, given the theorem of the mean, your groove speed will be a curve which runs through at least those two points, all points in between, and possibly points above (actually, *necessarily* points above if you're going to get the *average* of the curve to be equal to the value of the speed in the outermost groove).

Try an epicyclic needle mount next. It'll still fail, but will have really interesting failure modes.
-- lurch, Sep 29 2019


Hmmm. I have a horrible feeling that you may be right. Damn.
-- MaxwellBuchanan, Sep 29 2019


What's needed is a square record with the track laid out in a back-and-forth pattern, using a fixed stylus and a supporting table with the ability to rotate. Then there's no need for a central hole so that gives a higher density because the record is held at the edges.
-- 8th of 7, Sep 29 2019


Why not just do what CDs do, and vary the rotational speed as a function of playing-radius? It would need to be precisely controlled at both recording and playing (and the 2 need to match...) but it would be reasonably easy to do.
-- neutrinos_shadow, Sep 29 2019


// It wouldn’t surprise me to discover that there was once a stylus or magnetic based transduction system which involved keeping the tape still, laid out in a strip, and the head races along it. //

Helical scan [link] (as used in VHS and other formats) is kinda like that. The tape and the head both move, but the head moves much faster.

// But if the record is cut using the same geometry...? //

Then I feel that you might lose range or resolution in frequency, amplitude, or both, but cannot say exactly why at the moment.

// you won't get a constant groove speed //

Yes; I realized that when I read the idea yesterday. But if the record is cut using the same geometry…?
-- notexactly, Sep 29 2019


It's probably easier just to download the MP3
-- MaxwellBuchanan, Sep 29 2019


Could the record be made as a series of annular rings, with internal gearing mechanisms, so that each ring rotated with the same linear velocity as the next? Adjacent rings could have their gearing synchronised so that the groove can pass from one ring to the next when they are lined up with the needle.
-- pocmloc, Sep 30 2019


It would be a system of tiny nested epicyclic gear rings ... cool !

Nail down the details and post it.
-- 8th of 7, Sep 30 2019


Nested annular rings could be challenging to keep the entry and exit point of each track aligned at the proper time. And the artwork overlayed would take on the form of vizualized whirrled peas.

Alternatively, everyone could just adjust their singing pitch and speed to compensate. Imagine the challenge to the percussionist. I'll see if Ross Bagdasarian is available.
-- RayfordSteele, Sep 30 2019



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