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.

Italian composer Giuseppe Verdi, who supposedly invented the scale actually returned to composition with this, "arbitrary scale," in his "Ave Maria (sulla scala enigmatica)" (1889, revised 1898), in response to a challenge printed in the Milan Gazzetta musicale to employ a musical conundrum. The "Ave Maria", compiled as part of the Quattro Pezzi Sacri (1898) [4 sacred pieces], has been described as, "that still almost incomprehensible into-one-another-gliding of harmonies over the entirely 'unnatural' scala enigmatica". The piece features the scale both in its harmonies and as a cantus firmus throughout the short piece in half-note values in the bass and then each successively higher voice accompanying, "queer counterpoint which...is far-fetched and difficult of intonation; [and] the total effect is almost, if not quite, as musical as it is curious".

The scale, is as follows:

And has a formula of: 1 - ♭2 - 3 - ♯4 - ♯5 - ♯6 - 7.

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

The scale lacks a perfect fourth and a perfect fifth above the starting note. Both the fourth and fifth degrees of a scale form the basis of standard chord progressions, which help establish the tonic.

...
Wikipedia