Parallel Capacitors-Theoretical Question

I want to replace the capacitors in my speaker's crossover networks. My Large Advent's came stock with 13uf NPE's which I would like to replace with PIO caps. Unfortunately, PIO caps are unavailable in that value. What's the best way to get to 13uf, (12uf + 1uf) or (6uf + 7uf)?
This is a purely theoretical question and I realize either method would probably sound the same, but I'm wondering if there is a reason why one method would be preferred over the other. Are there phase, impedance or other issues associated with either method. I realize of course that I could simply use 12uf or 15uf and probably never notice anything given that the original 13uf NPE had a 20% tolerance, but in theory, what's the best way and why?
If you decide to go with single cap different from 13uf, you'll simply change the crossover frequency slope.
In case of parallel caps you'll simply have larger tolerance.
The best way is to get a number of caps and choose one(s) that would match the crossover slope closest to the speaker specs or not to replace at all.
I believe it's better to go with 6uF + 7uF.
Some cap makers have 6.2uF & 6.8uF values, e.g., ClarityCap MR (630V).
The other safe way is to measure the actual capacitance of the original one and than choose out of many to match exactly.
Please remember this is a theoretical question. The original 13uf value may have been chosen because of availability and price at the time. The nominal value is probably something else. What I want to do is replace the capacitor with a value as close to the original without creating another problem.
Given that the paralleled caps would presumably be similar in design, I'm not sure that using dissimilar values would make any difference compared to using values that are close to each other. But my instinct would be to use values that are as close as possible, because doing that keeps the higher of the two values as low as possible. Everything else being equal, a cap having higher capacitance can be expected to have higher stray inductance, which would be undesirable if the difference were significant in degree.
In case of parallel caps you'll simply have larger tolerance.
I respectfully disagree. For example, 6uf +/-10% in parallel with 7uf +/-10% = 13uf +/-10%.

-- Al
Theoretical answer to the theoretical qustion is 2 + 2 = 3 + 1 = 3.5 + 0.5 = 4.

But in physical situation 12 uf + 1 uf will give an added benefit of a small value capacitor added in parallel to the larger value capacitor because small value capacitors are better for filtering higher frequencies. The rolloff of the filter will be the same but you will also filter out high order harmonics that will pass through higher value capacitors.
"The rolloff of the filter will be the same but you will also filter out high order harmonics that will pass through higher value capacitors."

What? They are in parallel...

As usual, Almarg is the voice of reason. The only real reason I can see using say a 12uf and a 1 uf is if already had the part on hand or if I wanted to "bypass" the larger one with one of a different type. Bypassing is a mixed bag IMO, but some people like it...
"The rolloff of the filter will be the same but you will also filter out high order harmonics that will pass through higher value capacitors."

What? They are in parallel...

Sorry, I meant to say - high order harmonics that will NOT pass through higher value capacitors, but will pass through the parallel lower value capacitor.
Since the engineers at Advent used a single 13uF cap, my guess is that they didn't want the high order harmonics. Using 6.2uF & 6.8uF would alter the harmonic structure somewhat; and using 12uF & 1uF would alter it more. I guess the choice would depend on what kind of tweeter is in the Advent, e.g., silk dome or metal.
Jburidan-very good insight. I think the Original and New Large Advent tweeters were more silk than metal and were described as the "fried egg" tweeters. They had their own unique sound which I think defined the character of the speaker. The crossover was a simple 6db first order type. Advent later changed the tweeter to a black poly unit and used a different crossover (3rd order), which in my opinion ruined everything.
Can anyone explain how adding a bypass capacitor would affect the sound? Is that what the old "Vitamin Q" was about? Why was it described as a mixed bag earlier in this thread?
That 13uf electrolytic cap is 20% tolerance, a 12uf would probably be fine.
I gather that the results of adding bypass caps are unpredictable. Some reviewers (Auw Jimmy, Jon L. & Tony Gee) make the analogy of usng spices in cooking. They experiment until they hit upon a sound flavor they like.
I was really trying to get away from experimentation, it gets too costly. I realized that after rolling op-amps into my phono preamp recently. Before I knew it, I had spent nearly $300.
Capacitors are a bit more complex I think. There are more issues than their face value that can affect them. For example, Mundorf interleaves their capacitor's windings to cancel inductance. After I read that, I wasn't sure what might happen with 2 caps in parallel. Would they induce each other and do strange things at a particular frequency? There's also ESR to consider.
Although I realize many designers make their component choices from an economic standpoint, I still respect those choices as being the best available at the time to get the job done. After all, isn't engineering the art of compromise? That's why I wanted to keep the 13uf value, or get as close to it without causing other problems. It would therefore seem that a good 12 uf capacitor would be the place to start, maybe add 1uf to see how it changes things, and maybe add a bypass 0.1mf after that.
Thanks for your help guys. If anybody's interested in the final result, contact my email and leave me a message.
Capacitors in parallel are the same as resistors in series.
Al shouldn't the tolerances for cap add in quadrature? (0.1^2 + 0.1^2)^0.5 = 0.14 or 14%?

kind of ticky tack, sorry. I'm more curious and electronics are not my field.
03-22-11: Paulsax
Shouldn't the tolerances for cap add in quadrature? (0.1^2 + 0.1^2)^0.5 = 0.14 or 14%?
Hi Paul,

You ask a good question, as usual.

If the two tolerances are the same in percentage terms, then as I stated the tolerance of the parallel combination will be that same percentage. That can be seen by calculating the worst case values. For example, if a 10uF 10% capacitor is paralleled with a 5uF 10% capacitor, the minimum possible value of the combination is 9uF + 4.5uF = 13.5uF. The maximum possible value of the combination is 11uF + 5.5uF = 16.5uF. In both cases the deviation from the nominal value of the combination (15uF), is 1.5uF, or 10%.

My statistics courses are now a (very) distant memory, but I believe that combining inaccuracies on an rss (root sum square) basis such as you described would be applicable to standard deviation and related calculations, that involve the PROBABILITY that a combined inaccuracy will fall within limits that are NARROWER than the worst-case limits.

That in turn would typically involve situations where tolerances are being combined that act on the same nominal value, not on nominal values that sum together.

Best regards,
-- Al
Speaking theoretically, the most predictable performance will be from two capacitors of the same manufacturer and series, and close in value - that is, the 6uF and the 7uF together. This is because their residual inductance and ESR will also be close as well . . . which will give improved characteristics (over a single 13uF capacitor) without the possibility of a secondary HF resonances as can happen when an electrolytic is bypassed with a high-Q film cap.

As far as tolerance goes, Al is correct for the worst-case scenario - two 10% tolerance components in parallel have a maximum deviation of 10%. But in reality the tolerance does indeed get better the more components are placed in parallel, the extent of how much is dependent on their probability density function:

The "normal" or Gaussian function can be used to derive an approximate tolerance, but some manufacturers will actually have documentation that specifies this. Frequently the required testing and documentation for these sorts of things is what comprises the difference between mil-spec and standard components, and is what drives up the cost of the former.
Kirkus, please elaborate on the statement that 6uF & 7uF caps together will be better than one 13uF. Isn't there a benefit to having two less solder joints in the filter?
Hi Jay . . . the most basic model of a real-world capacitor is an ideal capacitor in series with both an inductor and a resistor. For a high-quality film cap, the inductance comes from the leads and the fact that it's impossible to acheive a perfect "non-inductive" wind to the film/foil itself. Series resistance comes from the leads and the (usually crimped) connection from the leads to the foil. Virtally all of these non-ideal properties increase with the physical size of the capacitor, especially inductance. Larger caps also tend to be more suceptible to crosstalk from nearby inductors.

For electrolytics there are additional losses and parasitic properties from the electrolytes, which can be signal-modulated and heat-modulated. And while these properties do get better with physically larger capacitors, doubling the number tends to make much larger improvements than merely increasing the physical size, and it does so without incrasing inductance. And if there is significant ripple current (causing heat), two caps will disipate the heat much better than one, given the greater surface area.

Compared to all of this, any solder-joint of reasonable workmanship is but a tiny grain of sand on the beach. The biggest vulnerability would be for i.e. a production wave-soldered PC board, which frequently has "thermal" pads of significant resistance . . . but even in this case, paralleling two smaller caps would mean less weight (hence less vibration stress) on each connection, and the resistance of the board traces and thermal pads would be in parallel. So, still an improvement.
Thanks, Kirkus :)

the most basic model of a real-world capacitor is an ideal capacitor in series with both an inductor and a resistor
Excellent point. If caps are in parallel than total parasite resistance and inductive impedance would be halved if used two caps of the same value and same manufacturer.