When a song transposes
Anchor note modification is when there is a shift in the underlying the ai collection that is so obvious that we should think about it in a new way. One example of this would improvising over a modal tune like "So What", let's have a listen and hear the pattern move up one step.
Most of the song is in 2* minor, except for when it changes to 3* minor for a while. Let's first consider our standard approach, which is not to change our anchor note.
If that's the case our anchor intervals for the 2* minor part are 0 2 3 5 7 9 10, and the 3* minor part are 1 3 4 6 8 10 11, when we think like this we can see between the two collections easier, as we know ending on a 4 would be a good choice for the 3* minor section as it can move to 3 or 5 easily from the 4.
If instead we think of them as two separate collections one where we have an interval collection of 0 2 3 5 7 9 10 anchored on 2* and then one where it's anchored on 3*, then it will be easier for us to use content that we created on the 2* on the 3* since the way it's notated will be the same.
As you can see thinking in these two different ways will have their own pros and cons. If we keep our anchor note as 2* the whole time, then we will be able to see between the chords but then in our notation if we play one line on the 2* part and the same line up one step on the 3* part, then the way it's notated would be different, on the other hand if we change our anchor note they would be notated the exact same way.
Let's say we were playing on the 2* minor part and we play the line 0, 2, 3, 9, 7, 10, 11, 0 and we're holding the 0 and then it changes to the 3* minor part, if we decide to change our anchor note than that 0 no longer becomes a 0, so what does it become?
The way we can answer that question is to think about the note that it represents. So 0 with anchor note of 2* represents the note 2*, then if we change our anchor note to be 3*, 2* now becomes 11. All at once we did (2 * + 0 - 3*) which is the same as (0 - (3* - 2*)) = 0 - I(2*, 3*), so all we have to do to modify the ai is to subtract the interval between the two anchor notes.
That is, given the original anchor note O*, and the new anchor note N*, and an anchor interval X measured against O*, then when we change anchor note to A*, X gets modified from X to X - I(O*, N*).