Enigmatic scale

The enigmatic scale ("scala enigmatica") is an unusual musical scale, with elements of both major and minor scales, as well as the whole-tone scale. It was originally published in a Milan journal as a musical challenge, with an invitation to harmonize it in some way.

Verdi used it in his Ave Maria, part of the Quattro Pezzi Sacri (4 sacred pieces) in 1889.

The scale, (written out beginning on G) is as follows:

G, A$flat$, B, C$sharp$, D$sharp$, E$sharp$, F$sharp$, G

And has a formula of: T - m2 - M3 - #4 - #5 - #6 - M7 - 8ve.

With the musical steps as following: Semitone, Tone and a half, Tone, Tone, Tone, Semitone, Semitone, Semitone.

The scale lacks a perfect fourth and a perfect fifth.