Which cable is most important to spend money on...

I think of it like a tree with trunk, branches, and leaves. All the energy passes thru the trunk, the power cord, as Robert points out. Next most energy is thru the amp/speaker interface, and next most the preamp/amp connection, and last (the "leaves") between source/pre-amp.

The speaker cables are sort an equivalent "branch" in the hierarchy, to the amp/preamp connection (granted they carry more energy.) So one could theoretically make a case for upgrading the speaker cables right after the PCs. However, I'd argue that even decent gauge but inexpensive zipcord would allow accurate comparisons of cabling on the "input" side of the amp, and because they're not part of that "chain" of components/interconnects, that leaving them for last, after improving everything else, would allow for better hearing comparisons of different speaker cables. Just a thought ;--)
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Agree completely with Robert from Ridge Street Audio, and Nsgarch. My ears tell me that there are quite a few reasonably priced interconnects and speaker cables that get passed over because they don't offset the effects of colored power cords and AC products. Also, I don't think you can ever recover dynamics that are lost due to less than optimum AC products.

Well, Robert Ridgestreet's answer is theoretically correct. They day he can implement it (that is, marketing) for the average audiophile he'll become a millionaire! In the real world budget where I live, working on power delivery/noise control using 220V/110V isolation transformers/filters allows me to use much cheaper but still well designed power cords. I *am* waiting to save some money to purchase power cords from a friend who upgraded to Ridge Street throughout his system. He says they're the best--and this is coming from a guy who'll spend $2K on a digital IC. I'll settle for second best...and consider myself fortunate.

What a life!

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it depends on a few different issues.

where are you now?

if you are at an entry level point and don't already have some fairly good cables then i would start with more quality on power cords (and even power conditioning) as those areas are the areas of biggest shortfall with modestly priced gear and inexpensive interconnects and speaker cables can sound pretty good and not be a severe limitation.

if you already have some quality cables then it gets more complicated. what is your priority (or sonic shortfall)? as your system and room climbs the stairway of higher resolution and coherence it becomes a case of fine tuning instead of fixing problems.

what level of bass performance (how deep will it go and how does your room support it)? if your system does plumb the depths then the priority might be speaker cables. i have found that unfortunately the very best speaker cables handle bass considerably better that the 'very good' speaker cables.....and when your system can 'go there' that last bit of control and articulation in the bass will yield amazing performance gains overall.

at the top level of system performance power cables generally come next as they can significantly influence overall system energy and the 'toe-tapping' factor.

interconnects are generally last at the higher levels of system performance as they sound much more alike as you go to higher levels of performance and price (not that they sound the same just less different than speaker cables or power cords).

i have done maybe 30 whole system cable comparisons and as my system improved the above heirarchy was quite consistent.

get the bass right with the best speaker cables you can afford, get the system energy right with power cords and power conditioning, and then fine tune with interconnects.

i can live with imperfect interconnects; but the speaker cables gotta be right.

note added; i agree with Thomas above about the significance of the tonearm/phono cable. since that cable is dealing with such a tiny signal it will have more significance than any other interconnect and is really a part of your phono stage.

regarding the order of significance of interconnects; there is not one answer. it will depend on a number of factors.

in my case my preamp (the darTZeel NHB-18NS) uses a propriatary BNC 50ohm cable (Zeel) that outperforms any conventional cable when used with the darTZeel amp. i need an 8 meter set of cables between my pre and amps so optimizing that particular interconnect is most significant in my system.

some sources have 'funny' output impedence or need long lengths. digital cables can be very sensitive to lengths. my digital uses 3 ST Optical cables which can be as long as you like with no difference in performance.

the answer here is that in a very general sense i would say that the order of interconnect significance would be;

1. tt to phono stage
2. source to pre
3. pre to amp

but at the highest levels of performance generalizing is not recommended.