Bob, I don't think there is such a bible, but measurements are very important in all of this. Vinyl is all about precision and proper set up for best sound. Precision requires measurements, computer or otherwise.
What do you understand Marc Gomez to mean when he writes that the 9" arm is more "accurate"? Lower distortion? Sounds more like real music? Is more transparent to the information cut in the grooves? I preferred the sound of the 12" version of my tonearm. Others may prefer the 9" version. I described how the two sounded different to me. How does "accuracy" fit in to those preferences? What does it mean, how is it measured?
At some point with future advancements in tonearm design, the effects of rigidity and moment of inertia may be less and less audible and other considerations like tracking distortion may become more primary to people's preferences. Right now, Mr. Gomez has his opinion on his designs. And as ddk wrote, I commend Mr. Gomez for his candor in sharing that opinion. However, I do not we should extrapolate from those opinions and assume they are applicable to all other designs.
I would like to read how Mr. Gomez, or anyone else, describes the difference in sound between his two arm lengths.
Thanks Peter for your time and candid interest in the art of analog vinyl music reproduction to the highest level possible today June 2018.
Earlier Henry posted a very interesting perspective, and Brock brought some excellent points. Yourself are a top TT explorer, with everything related...cartridges, tonearms, suspension, all that groovy jazz.
David is the master TT expert of this forum and high up in the art of horn music reproduction from vinyls.
Michael Fremer needs no introduction; when he speaks people step in their tracks like a needle in the grooves.
And Marc Gomez wrote a professional paper that I've read twice to fully absorb with correctness.
All of you together strike a chord. ...A music note from a piano key @ higher velocity, in the higher frequencies of the audio spectrum. It is that chord, that note, that key, that strike of that string I want to hear in balance with my surroundings.
Here's an excerpt from Marc's paper:
"... the groove reading and the sound quality will suffer. We are talking about deformations in the order down to nanometers (1/1.000.000 of a millimetre).
It is then obvious that any engineer would want to design this groove-reading devices as rigid as possible in order to reduce the detrimental deformations. That wouldn’t be any problem if the arm didn’t need to allow the cartridge to follow the warps and eccentricities - we could then use a very big, massive structure and have deformation levels orders of magnitud* lower than with current designs.
Unfortunately, we need to deal with record imperfections and the limitations that the cartridge suspension imposes on how massive an arm can be. This is why designing and building a truly high performance pickup arm is such a demanding task - two main opposing requirements must be met: very high rigidity and very low resistance to free movement in the vertical and horizontal planes.
The moment of inertia of an arm, which is related to what is usually called effective mass, represents a measure of how much resistance to initiate a rotating movement the arm has. An arm with low moment of inertia will react quickly to wraps and eccentricities, while a high moment of inertia will make the arm more sluggish and deflect the cartridge suspension more.
The laws of physics dictate that, due to the loads an arm is subjected to, a shorter length has a higher potential for rigidity and lower moment of inertia. Given an arm tube with a certain length, diameter, cross-section and material, when the length is doubled the bending and torsional stiffness will decrease to half. In the same example, the moment of inertia will increase to 4 times the original one.
To bring the stiffness of the 12 inch arm tube to the same levels as the 9 inch version, one must add material which will substantially increase the moment of inertia. Given a certain maximum moment of inertia allowed as design specification, I can always design a 9 inch version with much higher stiffness - every single time - no matter what kind of design the arm tube has.
Vibration and resonance
Arm design is a technical subject and require the use of accurate technical terms in order to reduce the risk for misinterpretations. Many are mixing the terms vibrations and resonances to refer to two different phenomena, though they are related. All bodies vibrate at their own natural frequencies and modes when excited, as well as their harmonics (multiples of the fundamental frequency). A longer and less stiff body will start vibrating from a lower frequency while a shorter and stiffer body will start vibrating at higher frequencies.
An arm tube vibration is mainly caused by the loads generated on a cartridge suspension. As this cannot be avoided, what matters is at what frequencies and, most importantly, with what amplitude the vibrations occur. The higher the amplitude the more detrimental the effect will be for reproduction accuracy."
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* magnitude
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Let's forget for a moment reference versus preference, or accuracy versus euphony, or small classical chamber versus symphony.
The music that is being tracked and played back and reproduced and heard in our ears, are those the same notes that were first recorded and mastered on those vinyls, are they the same chords the same keys the same strings hit by the musicians and recorded by the master recording engineers?
I mean in the most accurate way possible and without personal identification of preference.
...On an engineering level.