This image is taken from the book "A Shorter Model Theory" of Wilfred Hodges, page 250 in the beginning of Chapter 9, structure and categoricity. It is the beginning of the motet Non vos relinquam of William Byrd.
My question is, what does Hodges mean with the paragraph below the image? In what sense does the music illustrate an indiscernible sequence?
Clearly he means the 6-note theme repeated 4 times at different pitches to correspond somehow to the 4 members of the indiscernible sequence. Hodges says "the two central properties of EM functors are known in the trade as sliding (...) and stretching (...)."
I suggest that "sliding" might be his analogy for the operation taking one repetition of the theme to another higher or lower on the scale. He says that the tune could be "stretched to $\omega$", as an ascension into heaven: presumably that would be a repetition $\omega$ times at successively higher pitches.
As I interpret it, the "spine" of indiscernibles in the notional EM model is the sequence of the first notes of the themes, which are identical except for their (ordered) pitch, and each repetition of the theme is the subset of the model generated by terms over the respective first notes.
It's a bit dubious! But it's a few levels of mathematical sophistication higher than the similar thoughts in Hofstadter's Goedel, Escher, Bach. (I always find Hodges remarkably unintelligible. The Wikipedia page on the Ehrenfeucht-Mostowski theorem is about three lines long but explains what's going on in a way Hodges doesn't manage to, even with this analogy.)