sour dough starter/mother starter?

Your starter will work.  Just use the amount he calls for in the formulas with the same hydration level and you will be just fine.

People/authors use different names for the same thing…or so I have learned, but what it all boils down to is getting a wild yeast starter that will work in your breads and a way of maintaining it's integrity so it stays healthy.

Janet

I don't know Peter Reinhart but from what I've red from your post, his method seems to be the European (maybe just German and Northern European Countries) way:

1. Keep a few grams of your Sourdough and store it in a cold place (fridge)
2. Take this stored dough as a seed starter and feed it in 1 or 3 steps to a ripe sourdough.
3. Keep a small part (step 1) and use the rest in your Bread dough as you would use your "continuously fed starter" the American way.

If you feed it in 3 steps, it has the advantage of better reproducibility in taste and timing which is needed if you want to sell the bread (look and taste) and work on a lot of breads simultaneously (timing). For home made bread that may differ a bit every time, you really can follow a much simpler approach.

Also for rye bread this approach is a good one. Traditionally rye needs the sourness to form a stable crumb. The above approach gives sourness and a rise. Today's rye flour has less enzymes so the sourness isn't that important anymore. But still: No rye without sourdough.

I use a simpler approach (ratio by weight):

My seed starter: - every few weeks or when I'm running low
I keep a seed starter in the fridge that I refresh every few weeks 1:2:2 (seed starter:rye flour:water) until it peaks in 4 hours or less.

My sourdough (starter): - the evening before I bake (10-18 hours earlier)
I use a ratio of 1:10:10 to 1:20:20. Let it ferment overnight on falling temperature. (In the cold oven with a teapot full of boiling water). The different temperature levels will give you different things: high: flavourful lactic acid; middle: yeast; low: strong acetic acid.

My bread dough: - about 1 hour before I heat my oven
Ratio 1:2:x on rye bread; On wheat or spelt I need less sourdough (starter).
There is no more "bulk fermentation" on this dough. After 10 minutes of kneading (and maybe another 5 after 10 minutes of pause) I will directly form the loafs and bake them 1 to 2 hours later.

If you want to try this, just take a teaspoon of your starter as seed starter.
If you want to experiment: Bake the bread with your starter (just take the amount of starter the recipe demands in the final dough) and a newly fed starter ("Sourdough", "Mother Starter", whatever you call it).
Or just try it with your starter. If it works, it works.
But I was really surprised about rich the flavour when I first tried the "feed a new starter from a seed" method.

lg|Adrian