if the hooch forms while in the fridge, is that ok?
That's fine. Hooch is a natural side effect of sourdough (yeast plus grain plus moisture plus time = some sort of alcohol). Remember, the fridge does not halt your sourdough, it just slows it down
a lot. The fridge hooch will be (almost) the same as any hooch that forms while your starter is sitting on the countertop.
And if I were to feed it 1 cup of flour and a half cup of water every week to 10 days would that help improve it?
Short answer, that's probably too much flour for the water. It's usually very close to 1:1 when measuring by volume (as opposed to by weight). Also, probably a lot more flour than you need.
Long answer, There are literally hundreds of different ways to go about feeding your starter. On top of that you have different kinds of flours have different moisture content which vary from year to year, so the amount of water will change depending on the flour... and so on.
The best way I've found to keep a starter going is to use it every two weeks (more often is better). This is because it removes a good chunk of the starter and then you feed the starter new food. Because your yeast is going to be dormant from the temperature of the fridge, using a sponge will really liven it up.
Removing some of the starter when feeding is actually benificial because it gets rid of... over simplified: starter eats, starter poops, too much poop make starter sick, so need to get rid of some of the old stuff. Starter poop includes dead yeast and alcohol and other things that are good for you but generally, not so good for the starter.
If you aren't able to use the starter, then feeding it every week or two is a good idea. But how much to feed it? Most people judge this on the size of the starter. A lot of people say you absolutely need to double the size of the starter; however, for home baking it's not necessary. Doubling it is really good for large batches at a bakery or for getting a very specific texture, but is in no way required for keeping your starter alive and viable.
Generally, if I'm just keeping the starter viable, then I'll give it a couple of tablespoons (aka, a fist full, because I put my hand in the flour and grab a fist full of flour) of flour and some water until it's the texture I want. The other thing that governs how much I feed my starter is the size of the container it's in.
As an example: when I'm travelling I'll keep a starter of 2 or 3 teaspoons in size, because I can always use the sponge to increase the amount of yeast to what I need for a recipe. When I feed my travel starter (It travels with me at room temperature so I have to feed it at least once every 24 hours, unless I forget, then it's every 48 hours), I feed it literally one pinch of flour and a few drops of water. If I use it, then I'll replace the volume that I used. If I fed it more than that, it would climb out of it's travel-size container (or if tightly sealed, will explode the container).
Set measurements like cups and teaspoons, &c. are a really new thing to baking and a normal person's kitchen. Though they started showing up in the late 19th Century cookbooks, but only really took off 100 years ago (in the early 1920s). Sourdough has been around long before that, and people didn't worry about getting the amounts just so. We don't need to worry about it either. Your sourdough will forgive you if you don't get out your measuring cups.
The goal should be to get the desired texture and effect, not hold yourself firm to set amounts.
Just to clarify: Feeding your starter means giving it flour and water then leaving at room temperature for a few hours to start 'eating' it before going into hibernation (fridge) again.
Also, the recipe I had for the starter said to add a pinch of sugar every time I used and fed it. Do you know why that is and if it makes a difference in my starter?
A pinch of sugar!?!
No! Don't do that. Please don't. Pretty please! Not only is it unnecessary, it will encourage other things to grow in your starter that either make it taste bad or will kill it.
All it needs is flour (I like rye or wheat, or better still alternate between the two) and water. The bacteria in your starter digests the starches in the flour, magically transforming them into a sugar that your yeast feeds on. The bacteria is what's making things sour, the yeast is what's making things rise.
The only time you need sugar in your bread, well two times... is if you want it to taste sweet or if you are using fast acting commercial yeast which is designed to feed of fast sugars.
See if your local library has Nigella Lawson's book, How to be a Domestic Goddess. Her sourdough recipes are the simplest and most clear cut for just starting out. She does give specific amounts, but in a way that act as a comfort for those who are trained to use cups and measures, but not so strict as to be insulting to the history of sourdough.
Doing my best to be the change I want to see in the world, one meal at a time.
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Currently Culturing
Kombucha, perry, cider, wine (red and white), mead(s), miso, sourdough, & seasonal veg my garden gives me