# What are ways to use the palindromic property of a palindromic scale?

A palindromic scale, as I've seen it described on a number of music theory websites, is defined as one whose sequence of intervals is the same when ascending and descending.

For instance: D Dorian (D E F G A B C D) is palindromic because it consists of the interval pattern WHWWWHW, which is a palindrome.

Why should we care? Is there anything that can be done with D dorian that can't be done with C Ionian because it's a palindromic scale?

• As a fan of Olivier Messiaen, who used similar ideas (palindromic rhythms, modes of limited transposition), I'd say it may be useful for generating ideas in the composition process, but ultimately it's unimportant to the listener. Commented Feb 15, 2019 at 2:36

One possible use is that inversion around a particular pitch axis will create the same scale collection.

Let's use D Dorian, since that was in your example. If we invert `D F G A C B E D` around tonic (or G♯), the result is still a D-Dorian collection: `D B A G E F C D`. This is important because if we inverted those same scale degrees in a different collection—let's say D major (`D F♯ G A C♯ B E D`)—around tonic we'd be left with yet another collection: D Phrygian (`D B♭ A G E♭ F C D`).

In other words, palindromic collections allow for inversion around tonic while staying within the same collection, which is not true for non-palindromic collections.

• Interesting - +1, but mainly academic? Would most of us have a clue something was written with this phenomenon in mind? Not knocking, just curious!
– Tim
Commented Feb 15, 2019 at 13:14
• I really appreciate the final summary sentence. Would it be correct say that "staying within the same set" is synonymous with "staying in the same tonality?" I think "yes", but maybe I'm overlooking something. Commented Feb 15, 2019 at 13:42
• @Tim, I agree many probably wouldn't hear this, but then again it takes a lot of education to recognize all the different fugue devices, but most anyone will appreciate the overall effect even if they aren't aware of what's happening technically. Commented Feb 15, 2019 at 13:44
• So is this basically saying that an inverted melody or tone sequence will have the same tonality/modality? Commented Dec 22, 2019 at 5:09
• @awelotta If the given melody or tone sequence is a part of a palindromic scale collection, yes. Commented Dec 22, 2019 at 5:11