solve the speed irregularity problems we saw in rigidly couple turntables; they merely shift the problems to a new domain.
     Belt drive turntables differ from one other in belt compliance and platter moment of inertia, so their oscillation wow patterns differ. That explains in part why belt drive turntables sound so different from one another in pace and rhythm, in steadiness of pitch, and in solidity of bass (bass notes last longer, so they require a longer sustain of turntable pitch accuracy to sound straight and massively impactive, rather than warbly, wobbly, and weak).
     Can the belt drive designer reduce or damp the unwanted oscillations between platter and belt? In principle yes, but in practice it's tricky to execute. In principle, what's required is simply the addition of some resistive damping. This would damp the reactive LC tank circuit of belt and platter so it would no longer oscillate.
     A common form of resistive damping is friction. Thus, if a knowledgeable turntable designer wants better speed constancy, he might well consider intentionally adding some friction to his rotating platter. It's worth noting that some Swiss and German engineers are so justifiably proud of their ability to produce nearly frictionless bearings that they cannot bring themselves to make turntables with high friction. As a result, the Thorens turntables exhibit some of the most spectacularly low friction bearings on the planet, and will spin seemingly forever (with the belt removed); but, at the same time they also exhibit some of the worst audible wow, in part because there is, as a matter of engineering pride, almost no resistive damping for the oscillating reactive tank circuit.
     What might be useful ways to introduce friction? The fit and/or finish between platter spindle and well could be made poor, instead of smooth and polished. But this would be causing friction via crude irregularities, like two meshing mountain ranges, rubbing each other. The crude irregularities of these two mountain ranges rubbing together would cause unwanted speed irregularities (snags and letting gos), as well as unwanted vibrational rumble (the earthquake rumble of each letting go after each snag). So that tactic is out.
     One useable tactic is to introduce a viscous fluid in the bearing, which provides friction in a liquid hence smooth form. This can be especially effective if the spindle is made in a larger than normal diameter, so that the viscous fluid has a larger moment arm (more leverage) with which to work its resistive magic (as in the Linn Sondek). The use of viscous fluid for resistively damping platter rotation can also be enhanced by various helical screw kinds of arrangements, which force the fluid to do extra work in opposing the rotation of the platter (as in the turntables from Max Townshend). It's no accident that these two brands have the best reputation among belt drive turntables for pace and rhythm, solid bass, and master-tape-like clarity. It's because both these designs recognize that belt drive, far from being a simple Hail Mary solution, brings with it new problems that must be addressed, and that overcoming the problem of speed constancy requires at least the addition of a fourth element, resistive damping, to the three usual elements of a belt drive turntable.
     Does this mean that the belt drive concept could work perfectly, if only designers would wake up and add some resistive damping? Alas and alack, no. There are still further problems with the belt drive concept, problems still related to our fundamental theme of speed accuracy and constancy.
     The belt can isolate the platter from all vibrations of the motor, including simple rumble vibrations (perhaps once per revolution) as well as kick jerk vibrations from each pole (perhaps 24 per revolution). It seemingly makes sense, then, to mount the motor on some rubber bushings, so that its vibrations don't get transmitted directly to the platter via the spindle bearing. In other words, it seemingly makes no sense to mount the motor solidly to the same substructure as also holds the spindle bearing, since vibrational rumble would be transmitted directly via this path to the platter and thence to your record groove and cartridge. The belt isolates the motor vibrations from the platter via the drive path (unlike a direct drive or rigidly coupled drive), so why not also isolate the motor vibrations via the motor mounting path?
     This idea is good in theory, as far as it goes. But it doesn't go far enough, because in practice this tactic introduces yet another penalty, yet another speed constancy problem into the belt drive can of worms. If the motor is mounted on a flexible, vibration absorbing mounting (such as rubber bushings), then its pulley can move with respect to the platter rim. This means that the belt length will change every time that the motor vibrates within its flexible mounting. As we saw above, every belt length change produces a speed irregularity for the platter (perhaps delayed in time, if the platter is very heavy). Thus, what might seem like a clever tactic for reducing rumble turns out to be a very bad thing for achieving speed regularity in a belt drive turntable.
     A nasty feature of mounting the motor flexibly is that there are so many agents which might contribute to wobbling the motor in its flexible mounting, hence might contribute to speed irregularity. The music coming from your speakers could make the motor wobble, hence cause the belt length to change at musical frequencies, thus causing a new kind of automodulation distortion, tempered only by the heavy platter (but the average speed energy input to the platter by the belt would still be skewed over time in the long run as the music changes, thus causing wavering speed irregularities governed by the music's average content over time). Footfalls would have a similar effect; since they have a very low frequency content, the reactive belt-platter filter would be only partially successful in reducing their adverse influence upon platter speed constancy. Additionally, the vibrations of the motor itself, such as once per revolution eccentricity, which would normally contribute to rumble, now directly contribute to speed irregularity; their energy content is quite low in frequency, and thus also would be only partially filtered by many belt-platter combinations.
     Perhaps the worst can of worms for the belt drive concept is introduced when not only the motor is flexibly mounted, but also the platter. The designers at Acoustic Research probably deserve the credit (or infamy) for inventing the concept of the floating subchassis, which suspends the heavy platter, spindle, and spindle bearing on a flexible mounting (usually via a separate subchassis). This design idea was then adopted by Linn and other makers of belt drive turntables. The primary intent of this design tactic is to isolate the platter (hence disc and cartridge) from external vibrations, such as footfalls and the music from your speakers. A further intent is to reduce rumble from the motor, since once again the motor and platter spindle are not directly coupled via any rigid mounting (except that this time it is the turn of the platter spindle rather than the motor to be flexibly mounted). This design tactic succeeds admirably at meeting its intended goals. However, it can have horrendously adverse impacts upon speed regularity in belt drive turntables.
     The nature of the chief problem is essentially the same: the belt changes length, and this causes speed irregularities. But this time the problem is far worse in degree. Why? The suspended subchassis, including the heavy platter (made very heavy in the Hail Mary design move above), weighs much more than the motor. And, with a goal of reducing feedback from music and footfalls to the record groove, not just reducing once per revolution rumble, the subchassis suspension has to be effective at filtering down to lower frequencies than a motor suspension. Combine these two factors, and you typically wind up with a suspended subchassis that will move much farther than a suspended motor, and will move (indeed, will continue oscillating back and forth in its suspension) at much lower frequencies than a suspended motor. This in turn means that the speed irregularities will be much worse from a suspended subchassis (since the belt length changes are much greater), and that the irregularities will occur (and even continue oscillating) at a much lower frequency. Since the speed irregularities occur at a much lower frequency, the saving grace filter of the platter's rotating inertia is much less effective in reducing the speed irregularities.
     Thus, the typical suspended subchassis in a belt drive turntable hits us with a double whammy of speed irregularity: larger amplitude irregularities, and lower frequency irregularities (which the platter inertia is less effective at reducing).
     The speed irregularities caused by a suspended subchassis can be much greater than those caused by the multipole motor's kick and coast problem. In both cases there are forces stretching the belt and then allowing it to shrink back, thus causing speed irregularities. But a suspended subchassis is so much heavier than the small internal rotor of a motor, and can move so much farther, that it is capable of imposing far higher energy to stretch a belt than the kick and coast jerks of a motor, thus causing far greater speed irregularities (though usually at a lower frequency).
     Thus, the ultimate irony of the belt drive concept, as usually implemented, is that the cure may be worse than the disease. The first turntable design concept discussed above, where the motor is rigidly coupled to the platter, inherently requires that there be no distance play between platter and motor, so the speed irregularity problem we're discussing here does not occur. Of course, the directly coupled turntable design concept has the problem that the multipole motor's kick jerks are transmitted directly to the platter. The belt drive concept solves this problem, but introduces new problems. This latest problem relates to the suspended subchassis often included with a belt drive turntable, and it can cause the worst speed irregularities of all.
     To make matters worse, there's usually a third problem (hinted at above), to constitute a triple whammy of speed irregularity for belt drive turntables with suspended subchassis. The mass of the suspended subchassis and the springs of its suspension form a reactive tank circuit, which tends to keep oscillating after any transient vibrational disturbance, often long after the transient vibrational disturbance has disappeared. Thus, such a suspended subchassis would continue to produce speed irregularities on its own, long after the  external disturbance causing the initial movement of the subchassis (and hence the original fleeting moment of speed irregularity) had ceased. Speed irregularity that drones on and on is naturally much more noticeable and objectionable than a fleeting moment of speed irregularity, so this oscillating subchassis problem would naturally make a belt drive turntable sound much worse.
     This oscillating subchassis problem itself has the worst influence on speed constancy in those turntables where the oscillations contain or allow horizontal movement (also called yaw) of the subchassis. That's because side-to-side movement of the subchassis obviously affects belt length (hence speed constancy) the most, while vertical movement of the subchassis affects belt length the least. Also, the vertical movement should be perfectly straight up and down, in order to have the least effect upon belt length. Unless the suspension is perfectly tuned to the subchassis (which is difficult to do, since the subchassis cum platter always has an asymmetrical shape and mass distribution, both static and dynamic), the vertical movement will include a rocking component (like a rocking horse), and then there will be more horizontal movement and worse speed irregularities. This explains why certain turntables (e.g. the Linn Sondek) are so sonically sensitive to the slightest changes in suspension tuning, including even lead dress of the tonearm wiring, in order to get the most perfectly vertical movement (anything short of this goal produces worse speed irregularities and also worse frequency modulation distortion of your music).
     This also explains why some carefully engineered subchassis suspension turntables (e.g. Oracle) can sound better than others, because their suspensions quickly convert external jarring (even horizontal) into purely vertical motion; thus they exhibit merely a temporary blip of speed irregularity (corresponding to the original external disturbance), and any ongoing oscillation produces merely minimal ongoing speed irregularity. Indeed, in such turntables the temporary blip of external disturbance might even result in minimal speed irregularity (even temporary), thanks to the saving grace filtering of the heavy platter working with the compliant belt.
     On the other hand, some belt drive turntables (e.g. the SOTA) allow considerable horizontal movement of their suspended subchassis, which also continues to oscillate long after the initial disturbance. These belt turntables have some of the worst audible speed regularity, out in the real world where music and footfalls disturb a suspended subchassis.
     It's worth noting that the two reactive tank circuits discussed above can compound each other, creating huge peaks and valleys of speed irregularities. A belt drive turntable with a very heavy platter (e.g. the SOTA again) creates an energy tank circuit which is very reactive, very poorly damped, and capable of cycling and recycling (oscillating) very large amounts of energy, all at a very low frequency. If the mass of this suspended subchassis is very large (which it necessarily will be, since the platter constituent thereof is so heavy), and if significant ongoing, oscillating horizontal movement of that suspended subchassis is allowed (as it is in the SOTA), then this energy tank circuit will likewise cycle and recycle very large amounts of energy at a very low frequency. Both tank circuits recycle large amounts of reactive energy that produces speed irregularities, both continue their ongoing oscillations for a long time, and both oscillate very slowly. Thus, they will add and subtract to giant speed errors as they slowly wander into phase and out of phase with each other.
     To make matters yet worse, there's also usually a fourth problem of speed irregularity with belt drive turntables having a suspended subchassis. Again, the problem is worst with those subchassis suspensions that allow horizontal movement, especially ongoing oscillations of horizontal movement, in response to external disturbances. What is the nature of this fourth problem? It's a kind of Doppler speed irregularity. If the subchassis moves horizontally, then a component vector of that motion is almost surely to be in the direction of linear groove travel under the stylus. You'll recall that this direction constitutes the time axis of your music signal. So a motion of the subchassis along the time axis would naturally add to or subtract from the speed of the turntable at that moment. If the subchassis not only moves horizontally but also oscillates horizontally, then there would be a cyclical addition to and subtraction from the nominally correct speed, i.e. a cyclical speed irregularity.
     What about the platter's large moment of inertia? Wouldn't this help to keep the platter speed constant in spite of the subchassis' cyclical horizontal movements? No. You see, the platter's inertia is based upon the frame of reference of the surrounding universe, not of the subchassis. The heavy platter tends to keep rotating at the same speed relative to the universe, not relative to the subchassis with its oscillating horizontal motions. And so that tangential vector component of the platter's inertia that lies along the time axis tends to keep the linear groove velocity constant with respect to the outside universe, not with respect to the subchassis with its oscillating horizontal motions.
     The platter's well intentioned inertia, which would tend to keep the platter rotating a constant speed, is keyed to a different reference frame than the platter itself, and the subchasiss cum platter keeps cyclically moving with respect to that reference frame. The platter, subchassis, and pickup arm keep cyclically moving within the reference frame of the universe, so they keep cyclically modulating the well intentioned effect of the platter's inertia. Thus, the oscillating horizontal motions of the subchassis are superimposed upon the platter's inertial velocity with respect to the universe, and tend to cause speed irregularities. And therefore the platter's inertia is of less help than it should be, in counteracting the various speed irregularities associated with belt stretch and shrinkage.
     Indeed, these two unwanted effects can also compound each other. With a suspended subchassis turntable, the belt is forced to stretch and shrink if the subchassis allows horizontal movement, directly causing speed irregularities. These speed irregularities are ameliorated somewhat by the platter's inertia, except that the benefits of these amelioration attempts are compromised by the platter being horizontally moved back and forth within the reference frame for its inertia. Since both bad effects are due to the suspended subchassis moving (perhaps even oscillating) back and forth, they both occur at the same rate, and so they compound each other.

     It's almost like Doppler speed irregularity. In a classic Doppler shift, the frequency of a cyclical phenomenon (say a train whistle sound) is superimposed upon a fixed velocity (like the speed of the train), and the cyclical phenomenon (whistle pitch) is shifted as the train changes position (goes by). Likewise, in this turntable example, the horizontal cyclical motion of the subchassis is superimposed upon the relatively fixed inertial velocity of the platter with respect to the universe, and shifts the effective speed up and down by shifting the subchassis' position, so that its speed (like the pitch of the train whistle) tends to go up or down each time the subchassis goes one way or the other in its cyclical horizontal motion along the vector of the linear grove direction that is the time axis. In effect, the oscillating swaying of the subchassis modulates the time axis of your music.
     It's worth noting that there's a cute technical, Einsteinian difference between the classic train example and this turntable example. In the train example, we think of the observer as being fixed and the train as going by. On the other hand, in the case of a turntable, the heavy platter tends to keep a constant fixed velocity with respect to the universe, while it is the observer, in the form of the cartridge mounted to the tonearm mounted to the subchassis, who is oscillating back and forth. From a relativistic standpoint, it is irrelevant which, of the observer or the observed object, is fixed, and which is moving. In both cases, the observer will perceive the speed, pitch, or frequency of both the train whistle and the music as changing rather than staying constant.
     Incidentally, this Doppler speed irregularity problem pertains to all turntables with suspended subchassis that allow horizontal movement. It is not restricted to belt drive turntables per se, and is not related to changes in belt length (as are the previous problems discussed above). Indeed, you could observe this problem even if you were to disconnect the belt in a belt drive turntable, give the platter a manual spin, and then start the subchassis into an oscillating horizontal motion. But we bring up this problem in the belt drive section because 99% of all turntables with suspended subchassis use belt drive.

     To be continued

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