Enigmatic scale (Crescentini, Verdi)

Formula

Degrees: 1 b2 3 #4 #5 #6 7.
Steps: S 1½ T T T S S (1 3 2 2 2 1 1 semitones).
On C: C Db E F# G# A# B C.

It contains a long whole-tone segment (E F# G# A#), an initial augmented 2nd (Db – E) and two final semitones (A# – B – C) that “push” toward the tonic.

Origin

The scale was proposed by Adolfo Crescentini, a teacher at the Bologna Conservatory. On August 5, 1888 the Gazzetta musicale di Milano (publisher Ricordi) published it as a “scala-rebus” (rebus scale), challenging readers to harmonize it. Giuseppe Verdi answered with the Ave Maria “on the enigmatic scale” (1889, revised in 1898), later included in the Quattro pezzi sacri (1898). In the Ave Maria the scale appears in long note values as a cantus firmus, passing from one voice to another, and Verdi harmonizes it with a different chord each time. According to many descriptions of the piece, in the descending form the F# becomes F natural (C B A# G# F E Db C), a solution that makes harmonization easier.

Characteristic note and color

The combination of b2 with 3, #4, #5, #6, 7: the tonic has two semitones next to it (B and Db) but the central part is whole-tone. The result is an ambiguous, unreal, “centerless” color: the scale contains no perfect 4th, perfect 5th or perfect 6th. It does not generate a normal tonic triad: above C, the only triad that can be built in thirds is C E G# (augmented).

Derivable chords

The “diatonic” harmony of the scale is poor in traditional chords; it is better to reason with chords of your choice:

C+ (C E G#) and Cmaj7#5 (C E G# B): the natural “tonic”.
E (E G# B): the E major triad sits inside the scale; E/C = Cmaj7#5.
F#7b5 (F# A# C E): the whole-tone combinations (E, F#, G#, A#, C) produce dominant chords with an altered fifth.
Db E G# B: a chord with a “diminished-augmented” flavor, useful as a color.

Verdi, on the other hand, harmonizes it tonally, with chords that do not belong to the scale: the scale is the melody, the harmony is free. It is the most musical approach.

Modern use

Joe Satriani, “The Enigmatic” (Not of This Earth, 1986).
Yellowjackets, “Enigma” (The Spin, 1989).
Film and video game music: dreamlike or alien colors (Cmaj7#5 pad with a melody on the scale).

How to use it in a piece

As a melodic line: a slow theme on the scale, with tonal harmonies changed on every note (the Verdi method). It is perfect for an orchestral intro or a choir.
As a modal color: C pedal, Cmaj7#5 or E/C pad, a melody that exploits the whole-tone notes and resolves B → C.
As an arpeggio: alternate the E and C+ triads within the scale for a “sci-fi” effect.

Common mistakes

Demanding a stable tonic: the scale is, by definition, an enigma.
Using it at high speed as a “shred” scale: the color is lost; it works better slow and harmonized.
Writing the notes with arbitrary spelling: keep C Db E F# G# A# B to respect the scale degrees.

Exercise

Write the scale in whole notes in the bass (cantus firmus) and harmonize it in four voices, changing chord on every note, as Verdi did (you may use major chords, minor chords, sevenths).
E/C pad with a slow melody on the C enigmatic scale: 16 bars for a dreamlike scene.
Calculate the prime form and the interval vector of the scale (see Set theory) and count the perfect fifths.

Whole-tone scale; Lydian augmented; Set theory (2); First-species counterpoint (cantus firmus); Scales for film music.