Much of the good stuff already said.
One aspect unmentioned - the french-press is a b*tch to clean up compared to pour-over. Those spirals on most FP pots tangle w/ the coffee granules and require a brush and TOO MUCH TIME to get free, then a de-oiling wash. I sincerely appreciate my several FPs, but it's a few tweaks short of a love affair.
Gotta disagree with the venerable BW on a few MINOR points.
IMO the FP will release more oils than the pour-over+swiss-gold. This is pretty apparent in the body/mouthfeel.
Yes swiss-gold type metal filters are a LOT better than paper, but they still create a filter-bed effect in the grounds that retains a lot of oils. So as much as hate the clean-up, something pretty wonderful happens when the granules "go commando" in hot free FP water.
If someone-else is doing the clean-up and doing a really good job - then definitely FP over pour-over. I never put these in the dish-washer, but ... maybe someone else can comment on that. Somewhere closer to Realityville (where we must face our own messes in the morning light by the kitchen sink) - FPs are a dirty greasy mess-about-to-happen, but can produce a really good cup w/ a modest effort. You get more, you pay more.
I'd need to crack out my coffee-sci lit, but I seriously doubt coffee has much true tannins - that is polyphenolic matte able to cross-link proteins. Simple phenolic compounds produce an amazing array of colors and flavors, some good & important, many awful. These tend to polymerize under oxidative conditions (like roasting or even aging), and the smaller poly-phenolic compounds *tend* to be perceived as bitter (in a bad, coarse way, unlike the good/sharp-bitter goodness of caffeine). As the size of the phenolics (molecular DP, degree of polymerization) increases to "tannoids" these lose any characteristic flavor, but fall into the modestly bad-bitter realm and begin to produce a tongue-drying effect usually called "astringent". Coffee seldom get to the astringent range, much less the tannin range, tho' I recall one monster-bean Mexican that was offensively "woody" (like adding a pinch of toasted hardwood sawdust to a pot) and was astringent, but that was exceptional. The solubility of these phenolic compounds drops dramatically w/ DP, but since we swirl up clouds of insolubles, particularly in a FP .... We probably get more from a FP. The solubility of polyphenolics is highly dependent on pH, which leads to the next topic.
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The "water hardness" issue needs to be seriously addressed .. somewhere. The nostrums (like 80ppm hardness) are a crude start, but fail to address the basic issues. This is no thread for a treatise on water chemistry, but in broad strokes ....
Harness is defined as the concentration of multivalent metal ions in solution - *mostly* Calcium(Ca) & Magnesium(Mg).
In "natural" water sources there is commonly a prevalence of Ca(calcium) over Mg ions (maybe 3:1 or 4:1)
These metal ions can be associated with Carbonates (called temporary hardness) and also (most commonly Sulfates called) permanent hardness. There are other forms of permanent hardness, like chlorides or other metal salts, for example
Generally speaking, well water has high level of hardness, primarily temporary (carbonate) hardness. Surface water (lakes, rivers) have similar or lower levels, and rain-water is relatively free of ions. Local conditions can of course vary. Municipal water facilities "treat'" water for two issues - temporary hardness and sanitation.
The sanitation measures include addition of sodium hypochlorite (bleach) at ~2-3ppm Cl- ions which is expected to produce ~0.2 - 0.3ppm Cl- at the tap. *OR* (increasingly popular) the addition of "chloramines". These are chlorine/amino acid compounds that dissociate slowly and are intended to retain 0.2-0.4ppm of Cl- in solution. The chloramines are more effective at sanitation b/c they persist longer throughout the pipes, BUT they also generally persist at higher levels in tap water. Tap filter methods do not remove chloramines.
Since chloro-phenolic compounds have horrific flavor profiles, de-chlorinating water is a very good measure. The commercial methods of chlorinating water include the addition of sodium or potassium meta-bisulfite (available at any home-brew or wine-making shop) , OR the addition of ascorbic acid, OR the addition of peroxide (hydrogen peroxide available at any drugstore). Any anti-oxidant can do the job, but meta-bisulfites & peroxide are particularly quick-acting. Typical additions rates are 600mg of sodium metabisulfite / 1000 l (a hot-tub full) of water, but ~2.5 tsp (10ml) of the 3% hydrogen peroxide per 1000l works as well. I use UNchlorinated, too-hard well water at home, but I did and would suggest using hydrogen peroxide (3% HP in diluted by 1:100 (to 0.03%), store in fridge, added at 1ml[1/4 tsp] per liter or quart. Add to water and mix well. Don't be afraid to add 2tsp/57fl.oz of the very dilute peroxide. Any peroxide excess is likely to oxidize something else (perhaps coffee oils) - but would be overwhelmed by the relatively huge qty of oils. Metabisulfite excess will reduce rather than oxidize, but will increase the available SO2 level to noticeable levels only in massive excess.
The other FUNK wrt hardness is that not all hardness is alike, and it dramatically impacts acidity (which in turn impacts polyphenolic solubility). Temporary hardness is entirely due to carbonates, and these have a major impact on acidity & pH (two distinct concepts). Muni water supplies prefer to get TEMPORARY hardness <80ppm so they don't produce a scum-ring when the water is boiled. Folks operating commercial boilers have a similar problem with this carbonate scum & accretion.
Carbonates in solutions have 3 forms; carbonates (high pH, limited solubility), bi-carbonates (intermediate pH, very soluble), carbonic-acid (low pH=CO2-carbonation). Muni-water suppliers reduce *TEMPORARY* hardness by two methods, MOST add slaked lime, this increases the pH, and causes a lot of the carbonates to drop out of solution as chalk and these have limited solubility and so drop out of solution. Another method that is common in homes and rarer (but still used) in muni-supplies is a permutit filter. There is a resinous material that traps the Ca & Mg ions and replaces these with Na or K (sodium or potassium mono-ionic ions) and these also replace carbonics with (primarily) chloride (very soluble, NOT temporary).
So (again in broad strokes) the carbonate & bi-carb (TEMPORARY hardness) in your water (typically 80+% of hardness) acts as an acidic buffer, It prevents the natural acids in coffee beans from pushing the water toward lower pH, more acidity. The PERMANENT hardness in softened water or de-carbonated water does NOT do this. So its sorta-stupid to talk about hardness w/o taking about the TYPE of hardness.
Not dumping on BW at all. Normally most hardness is temporary (even in Muni supplies) so his <80ppm is at least reasonable but not IMO a correct or reasoned position.
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For many years I have believed the UK penchant for adding citrus or lemon to tea was all about adding acid, reducing phenolic solubility (tea flavor is primarily abt phenolics, and tea can form a phenolic "scum"ring that is clearly defined) by reducing the pH of their typically temporary hard water. My suggestion is that reducing the water pH (adding acid to water) and removing the TEMP hardness by CO2 evolution before making tea.
I *suspect* the coffee suggestions to use modestly hard water is all about avoiding the problems of very hard, heavily buffered water (which overwhelm the coffee acids), and perhaps adding the benefit of the flavor active sodium ions (from permutit filtration) to the water which tends to accentuate sweetness [note all the early comments about adding salt(NaCl) to coffee].
