This might make a good lesson on applying this design guideline, something that a busy pro might use to explain it to people in general. A diagram might be helpful if you have one.

thanks Rosie,
right now I don't have a diagram in file format. I only have older revisions. I can post those to get the layout idea of which cabinets I'm talking about, but you'll have to ignore some of the dimensions because they adjusted. Let me see if I can correct the relevant dimensions on the older revision then post. I know it's hard to follow a typed description.

Also, maybe I'm misunderstanding a "15 inch cabinet" to mean a solo/single cabinet. I'm wondering if he's talking about the door sizes.

I'll get my diagram up asap.

I'm guessing 15" single cabinet. I had three 12" cabinets in my old kitchen, and they were a pain - as deep as they were wide, things got pretty well crammed in. It's surprising what a difference that extra 3" can make in functionality. Your 27" cabinets sound great!

here are the older diagrams, I had to use paint to make the corrections, sorry for the poor way to accomplish this. The whole kitchen got shortened by 4" between the last revision and now so I have a paper copy of the current revision but no email copy yet.

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i trust that when you click on these you can zoom in. please let me know if not.

Those are fine.
It is avoid "cabinets under 15" -single cabinets, not door size, not opening size. Perhaps a better way to put it is avoid 9 and 12" cabinets. Pushing down to say a 14" in a pinch, depending on function is even ok. No rules remember.
The point of it is often some choices are made elesewhere in a layout that force the use of narrow cabinets. Sometimes there is no choice, sometimes it is the right choice. But if that is happening take a real hard look to see what other way it can be layed out to avoid the skinny cabinet(s). Often thaat alternative actually offers more storage, better function, looks better AND reduces cost.
It is simply a red flag to challenge what you are doing. I rarely end up with 9's or 12's.
Remember- no rules.

illinigirl, I love how you have so many of your spaces labeled as to what will go where! I did the same thing, and it is a very useful exercise.

One thing I'm glad I did in my kitchen was order extra shelves for some of the cabinets - like those designated for glasses and cups, canned goods, and large items like roasting pans and large mixing bowls. I see a few places in your layout where an extra shelf could be useful.

I have two twelve inch cabinets (lowers) and, honestly, I don't have a problem with them, either in form or function. I keep cookie sheets in one and cutting boards in the other. One is to the left of the sink so that the sink could be centered under the window. The other 12-inch is next to my stove and was the only size that would work ... the cabinet above my range hood is hiding an A/C duct in addition to the hood duct, and the stove had to go in that one spot. Sometimes you just have to work with what you have and a smaller cabinet cannot be avoided. I can see not wanting an entire kitchen full of them, but you can likely find a use for just one or two, and they don't look bad at all. As jakuvall says, sometimes using a narrow cabinet turns out to be the right choice.

Ok thank you! I am relieved.

I have one 13" upper and it works out pretty good for glasses.

For future searchers, my thoughts on my 12 in cabs:

My 12 in pantry pull out is great, but it is frameless so that helps. It is placed to allow the fridge to open.

My 12 in tray pull out is ok, I think different dividers would make it better (I cheated this weekend and removed a cross brace and it's much better).

The 12 in upper pull out, at standard 12 in depth, isn't so great. It's very short front to back, and a little fussy about closing correctly with the 36 in tall door. But where it is located a regular cabinet wouldn't be much, if any, better.

Those last two are between the range and wall. I wanted to get as much space between the range and sink as possible (without moving the plumbing), this allowed us to have 27 inches. Still not optimal, but a huge improvement over 18 inches!

These were used for very specific reasons, and I try to talk people out if them if possible. They are just not very useful in most cases, especially in framed cabinets, and especially the uppers! I'm glad I only have the few that made the design function.