My method of gaining understanding of various principles and ideas of the Work is to simplify them to a picture I can keep in my mind while I contemplate the idea.
Regarding intervals, it was helpful to me that I had studied the piano years ago. All those scales wow. The fingering for a scale for the right hand is thumb, index finger, middle finger (do, re, mi) and then comes an interval where the poor thumb has to make an `extra effort' to bend under the index finger to start the next sequence and play the note fa---thumb, forefinger (sol), middle finger (la) (they have now had to `work' a second time, then 4th finger (si) and pinky (plink) (do).
The mi-fa interval is a toughie, and the same fingers have to play the fa-sol-la sequence after already doing the do-re-mi. (They should get higher pay.) (And sometimes mi-fa of an interval is bridged with more money --- maybe a new loan!)
Now at this point, one can see the first interval is of a certain magnitude, and the next interval (si-do) doesn't seem quite as complex. The 4th finger is kind of a weak sister, but all the same one can usually get from si to do without too much trouble---unless another octave is immediately to follow (which usually is the case with trying to `do' something).
It's now been too long a distance from my piano lessons to remember just how that dang si-do interval is handled on the piano if there is more than one octave of scales being played. Nevertheless, the fingering will demonstrate intervals in that they are not simply the `next finger' to come along. For emotional types (such as me), this is a helpful way to `see' something in a new way to help make it more understandable.
When we look closely to whatever it is we want to accomplish, most of the time we see do-re-mi, do-re-mi, do-re-mi, and a lot of unfinished business. One of the reasons for this is that we don't have the energy to bridge intervals because we got so excited and talked too much about our plans with friends. yakityyakityyak --- there goes the energy we could have used to get through an interval if we hadn't pooped it out over coffee with friends!
Look in closets and old storage sheds. Full of do-re-mi stuff! Little piles and boxes and shelves with do-re-mi stuff all over the place! (G)
Try it sometime --- and it will be apparent quickly. Make a small aim (has to be really something you want to accomplish or peform), and shut up. (G) Chances are it will go well---unless it's not very important to you and you get the `so what' sense about mi-1/2. (G)
Maybe even try it on a piano. As high as one goes, to the very last (plink), there are only two intervals to an octave, the big one at mi-fa and the smaller one at si-do. Intevals don't increase in frequency of appearance --- they might increase in frequency of vibrations, though! (G)
There. Are we all confused now? (G)