Refresher: Inductance increases as the conductor spacing is increased, while capacitance increases as the spacing is decreased (and/or, of course as the dielectric constant e is increased)
(Conductor spacing is a common trade-off in overhead high voltage transmission lines)
I'm not certain about there being a true optimum. In any event, the ratio you suggest would be rather surprising, as it results in a pair of closely-spaced (0.7%)resonances at only 5x the lowest room resonance. The traditional Fibonacci (= Golden Cuboid) ratios give resonance that are separated by at least 3% up to the 7th harmonic - and (for the same room volume) the maximum dimension can be increased by a factor of 1.57.
For large concert halls, naturally, the combination of low fundamental resonance frequency and diffraction due to hall features such as balconies makes numerical ratios pretty=much irrelevant. In this situation the harmonics in the critical frequency regions are closely spaced, and (paradoxically?) early arrival time time of first reflections becomes important. This can be achieved in many different ways, as you will see if you compare the dimensions of the "great" antique concert halls (from Grosser Musikvereinssall through Gewandhaus and Concertgebouw to Boston Symphony) with modern (or adapted) halls such as Royce the Bridgewater.
And don't forget that loud sounds are perceived differently due to direct stimulation of the stiff, less-frequency-selective inner hair cells by the basilar membrane, as opposed to softer sounds which are only detected by the softer, more selective outer hair cells~
What about stickers to improve CD sound? But these "obvious" ones don't generally catch too many people.
Contrast this with "oxygen-free", "single-crystal" and "linear-dielectric" speaker cables, that continue to be highly-rated by some "hi-fi" magazines. Unless the cable has some serious flaw (break-down, mechanical weakness), adequately low resistance, inductance, and (for marginally-designed amplifiers) capacitance are all that matter.
All the literature I've read recently about room acoustics simply ignores the overriding effect of the fundamental room dimensions: length, width and height. The usual thing that's mentioned about dimensions is that the longest dimension determines the lowest frequency that can be effectively reproduced.
We know that each dimension will resonate frequencies and their multiples related to the half wavelength of that dimension. How can we make sure that the resonant frequencies of all three dimensions are evenly distributed up the octaves? The magic ratio is the cube root of two 1.25992! KISS
In our house we built two rooms that follow the formula. One is our living room, full of the usual sound absorbing furniture, curtains etc. The other is a sun room with hard glass on three sides and a hardwood floor. Recordings I've made in both rooms sound great. In fact the live sun room with it's long reverb sounds fantastic - like some large concert hall.
Some of the best sounding concert halls in the world are rectangular boxes with varying reverb times. I'm willing to bet that their fundamental dimensions follow the ratio of the cube root of two.
In my opinion the main purpose of the complex and expensive sound absorbers and reflectors is to damp down resonances caused by off the cuff room dimensions.
Of course you want the vibration of the strings to be modified. That's just the electronic equivalent of the body of an acoustic guitar, or the horn of a saxophone; both of these filter and non-linearly distort the waveform.
Hopefully, however, you know how you want the performance to sound. The legitimate job of the recording engineer is to produce a faithful representation of the sound the artist wishes his audience to hear; if anyone is to modify the sound as heard in the venue it should be fully under the control of the artists (composer, conductor, performer.
Which reminds me of a recording sequence ca. 1963. The recording venue did not provide the acoustic desired by the composer. So the music was double-recorder using loudspeakers placed in different environments, and the composer and the engineers worked together until the composer was satisfied with the dynamics, resonance, and balance. The CD reissue (which closely recreates the original LP) remains a classic.
(I still have reservations about nearly all stereo sound produced via multi-miking, but that's yet another can of worms)
Vinyl is a deeply flawed medium indeed, and I am enjoying a large collection I inherited nonetheless. Some of it (including things I've had for years) is still remarkably good and well-worth the fuss and bother. If you keep the records clean from the outset, the actual amount of wear from playing is quite small.
Some insist that the appeal of vinyl is one of antiquarian nostalgia, that somehow the clicks and pops key in the listener to bygone days. That may apply to someone, but for the most part I think it is deeply misguided. It is IN SPITE of the artifacts, not because of them, that it is still an enjoyable medium. And of course, much current pop music, as is noted, has vagaries of equalization and compression that are at best fashionable, at worst disgraceful. And the kids listen too loud!
The idea that people prefer inaccurate systems got a new lease on life not long ago when some professor insisted that his students liked lossy formats above lossless. This prompted Sean Olive to do controlled listening tests with trained listeners in the same age group. The results were contradictory as far as the notion advanced by Guttenberg and others: kids like accuracy too! see http://seanolive.blogspot.com/.
For information on loudspeakers and rooms, Floyd Toole's book Sound Reproduction is rapidly becoming the standard in the field. I recommend it highly.
There's a renascence in vinyl recordings these days because many people say they sound so much better than CDs. What is it that is better - more noise, clicks, rumble, more distortion and poorer frequency response from this technically decrepit mechanical system?
Most studio recordings, because of their wild and piercing "equalization" settings have to tame things back down when cutting a disk so the stylus doesn't get launched out of the overlapping grooves. So yes, vinyl does sound more mellow, not because of the vinyl but because of the half deaf sound engineers "equalization".
A good demonstration of how bad the studios are is the sound of a "boom car". It goes BOOM tch tch BOOM tch tch. The tch tch is the energy in the 2Kz to 6Khz to give the recording punch and presence. I find in my home system I often have to turn off my sub-woofer because I don't appreciate chest compressions when listening to some sound sources.
So yes, the observant customer is always right even if she doesn't know the first thing about technology. It also goes to prove that most technologies can be turned into assault weapons.