Atammayatā is a fairly simple word. Even though it’s used rarely, the etymology and contexts make the meaning clear.
It’s found either in the abstract or plain form (atammaya) in AN 3.40, AN 6.104, MN 113, and MN 137.
- a- = negative
- -tam- = that
- -maya- = made
- -tā = (abstract suffix)
So literally it is “not-made-of-that-ness”. More sensibly, “non-identification”. It is one of the many terms used in the texts to refer to “not-self”.
To understand this, consider the two main dimensions of not-self. A stream-enterer has let go of sakkāyadiṭṭhi, “identity view”. This is where we identify ourselves with something, and have an idea or view that that is us. It may be something physical, our body, for example.
A stream-enterer has seen through this and they no longer believe that they have a self that can be identified with anything. But they still have a residual sense of self in a general way. This is called māna, or conceit. Only an arahant has let go of conceit completely. So even though a stream-enterer knows that nothing is their self, they still sometimes unreflectively act or think as if they did have a self.
This can be compared to a phantom limb. Even though you know you have lost an arm, sometimes you forget, and speak or think or act as if it was still there.
One of the ways that the Suttas express this difference is by distinguishing between identifying (ahamasmi = “I am”), and identifying with something in particular (eso hamasmi = “I am that”).
Note that Pali tends to express this notion of specificity in this way. Rather than saying “I identify with a specific thing” they say “I identify with that”, where “that” is understood to be any specific thing.
The term atammayatā is simply another way of expressing this distinction. It refers to the more basic attachment to self, equivalent or similar to sakkāyadiṭṭhi or eso hamasmi, the identification with a specific thing (tan). In other words, the self is “not made of that” specific thing.
Thus in the few contexts where we find it, it is explicitly identified with not-self (especially AN 6.104), and is treated as the non-identification with specific things, most often with stages of meditation (MN 113 and MN 137).
I hope that’s helpful!