9", 10" or 12" tonearm?

Can anyone explain why many analog aficionados like or dislike 12" tonearms? What is the main sonic difference between a 9 or 10" tonearm and a 12" one? Is the 12" dogma outdated? I must say that in the past there were more 12" designs (SME 3012, SAEC, Audiocraft) than nowardays. Is 12" for "audiophools" with strong nostalgic feelings (like me)? (Especially when combined with those old Denon 103 or Ortofon SPU).
The chief advantage to the longer tonearm is that it has a "shallower" tangential (i.e., tracking) arc than a shorter arm. The ideal way for a tonearm/cartridge combo to play an LP is linear tracking -- a straight line from the edge of the LP to the center hole (this replicates the path of the cutting head used for making the "mother" copy of the LP). Cartridges mounted on a shorter tonearm will have a sharper arc in the path they trace than a longer tonearm.

From a geometry perspective, an infinitely long tonearm would have almost no tangential tracing distortion, but since there are obvious practical limitations to length, most audiophile arms have been 12" or less. If your turntable plinth is large enough to allow use of the 12" tonearm, the longer arm may provide less tracing distortion, and therefore better sound, than the shorter arm. I don't know that "nostalgia" plays much role in some audiophiles preferring longer tonearms, and the prevalence of shorter tonearms today may be due mainly to the smaller "footprint" of today's turntable designs.
Why don't people just buy those tangential arms? Cost? I'm curious as tangential arm seem to mimic what the vinyl cutting machines do.

Cost is one factor...but Tangenital arms or linear tracking arms have their own set of problems. It is very difficult and expensive to get a linear tracking arm to be completely "friction" free which is one of the prinicple advantages of these arms as well as the tracing geometry that is more suited to the cutting lathe. Linear arms use either a type of air bearing or electric servo to help them track the groove of the record. The old Rabco arm was a popular arm in its day..but had enough internal resonance to be a factor on the better tables. Walkers air bearing linear arm is state of the art today..but the arm alone costs more than some complete analog set ups..So, it mainly comes down to being able to design a linear arm thats up to snuff and yet compete with the more popular pivoted designs out there today, which are quite good in themselves!

As SdCampbell mentioned..the longer 12" arms provide less tracking error due to their shallower offset..but many tables with compact plinths and armboards cannot acccept that size. If you can though, it may be worthwhile to go with the 12"
Dear Sdcampbell: I agree with you, but:

+++++ " the longer arm may provide less tracing distortion, and therefore better sound, than the shorter arm. " +++++

The theory told us that that statement is true. In three of my tonearms where you can interchange arm wands ( pipes ) : Audiocraft AC4400/3300, Micro Seiki MAX 282/237 and Moerch DP-6, I own and used long and short arm wands trying to " see " if there are any improvements on the long ones: till today I never find that the longest had less distorted sound, there are very slightly differences in the sound that I think is for a diferent resonance point due to the diferent effective mass of the arm wands. I can't tell of those diferences like a " better sound ".

All these tonearms and the today top tonearms are very well made and it is very dificult by " ear " to tell if the theory be fullfiled on practice.

Other points are that a longer tonearm has its own problems about: torsion forces and slightly high self resonances due to its " long " and bearing " forces " diferences against a short one .

I think that if exist a good tonearm design and a good execution design both type of tonearms: short and long, perform always almost the same.

Regards and enjoy the music.
Linear is on best stuff out there like most expensive tables out there (Walker etc) but as mentioned to make it work reliablkity is diffeerent issue the ET arms are still comanding a high price but who wants top deal with pumps and surge tanks?The there was B&O and Revox.I always wondered about those designs (maybe I should look them up in OLD archives) but since the audio world didn't beat a path to same designs it probaly didn't work out to well.Keep my Technics SL5 in my Bebroom system and play lesser Lp's I trust to this technolgy (though I use newer carts with clean styli) to have otion to crash to some tune other than CD and FM.Hope the denizens have pointed you to a solution but if your like my freind you might invest in a different arm.
So in general it is not true that 9" arms are more agile and dynamic sounding than 12" arms and that 12" arms are slower and more colored sounding (with emphasis towards midbass and bass)? I've seen that some audiophiles are using the SME 3012 + SPU strictly for classical music. Does this mean that the combo is not suitable for pop, rock and disco/techno?

But. Lets say the Avid Volvere SP. I dont think you have a choise. I guess its only take a long or short arm dilemma. 
Maybe i`m wrong. But i guess a TT is made for either 9" or 12" 

Geoffrey Owens of Helius Designs makes a 9", 10", and 12" version of his excellent Omega arm. It is his opinion that the 10" provides the best balance between the advantages and disadvantages of all lengths. 12" arms, while providing significantly smaller tangency error than do 9", have far greater moment-of-inertia mass, generally not a good thing. Geoffrey feels the 10" arm’s tangency error advantage over the 9" is worth the only-slightly greater m-o-i of the arm, a justifiable trade-off. But the m-o-i penalty of the 12" in relation to the 10" is greater than it’s lower tangency error advantage over the 10", an inadvisable compromise.

The introduction of the Trans-Fi Terminator air-bearing linear-tracking arm has changed the landscape of that design. Go to the T-F website for details. Perhaps the greatest tonearm value right now---just over $1000!

I'll just throw in that my two Jelco 750 12" arms sound better with anti-skating off. (Think they look nicer over 9" too)

@dazzdax i also use "9, "10 and "12 tonearms and all of them are great, but for some turntables like Technics SP-10mk2, SP-20 the "10 and "12 tonearms are much easy to use and to mount. Aesthetically "10 and "12 are better (imo). So you can't be wrong with "10 inch tonearms like Technics EPA-100mk2 for example. My reference is Reed 3p "12, it's had to find anything like that, because with Reed anyone could adjust absolutely everything (including azimuth) on the fly (the best engineering).  
Another advantage of a 12" arm is that once you set the correct VTA/SRA, it changes less with different weight records than does a shorter arm.
Another advantage of the 12" arm that has not yet been mentioned is that VTA changes less with different record thicknesses.  Also, because the offset angle is lower on a 12" arm, skating forces should be reduced.  

As others have mentioned, the tradeoff on long arms is that, for any given effective mass, the arm will be less rigid and more prone to problems with resonance.  Not only are the arms themselves slightly heavier, having the heavy cartridge well out on the end of what is a cantilever means that the effective mass (inertial mass) of the cartridge is much higher.  If one were to try to reduce effective mass by reducing the mass of the arm itself, that means less material in the arm and less rigidity or damping capability.

Linear tracking arms come in a WIDE variety of designs.  Those that rely on very low friction to allow the arm to be pulled along by the forces on the stylus (like the air bearing arms), put more stress on the cartridge's cantilever than do pivoting arms (because of no mechanical advantage of a pivot and lever).  Some say that the requirement of such designs to yank the cantilever sideways enough to move the arm actually means the cantilever is almost always further out of tangent than on a conventional arm. 

Whatever the theory, I cannot say that I've heard differences in performance that are consistently attributable to one type of arm or to particular lengths of arms.  
VPI's HW is working on a 14" arm that's nicknamed the Longboy. I got the feeling it ain't goin' to be cheap :-(