To understand Leonard Bernstein’s West Side Story it is important to understand diminished theory. The diminished scales and chords are some of the most interesting and amazing tools in music. Verdi, Stravinsky, Bartók and especially Leonard Bernstein made excellent use of them, as well as virtually all of the great jazz improvisers.
Diminished chords and scales are built on the interval of 3 half steps (minor 3rd or augmented 2nd).
The fully diminished chord is a series of minor 3rd (or augmented 2nd) intervals:
One of the interesting factors is that there are only 3 fully diminished chords. After that they become inversions of themselves:
As you can see, C, Eb, F#, and A fully diminished are constructed of the same notes. This also goes for F, Ab, B, D and Bb, Db, E, and G.
Note: Fully diminished chords are often notated with a circle (o), as compared to half-diminished chords with a circle and a slash (ø).
The diminished scales are symmetrical and have 8 notes. They are sometimes referred to as the octatonic scales. There are only 3 because like the chords, they become inversions of themselves. However, there are 2 ways to think of each diminished scale. They are built by alternating 1⁄2 steps and whole steps. If the scale begins with a 1⁄2 step followed by a whole step, it is referred to as “half-whole.” Accordingly, if the scale begins with a whole step followed by a 1⁄2 step, it is called “whole-half.” Below is the half-whole diminished scale starting on C. Notice that the C, Eb, F#, and A scales are made up of the same notes.
This also applies to the diminished grouping of F, Ab, B, D.
Of course, the same applies to the grouping of Bb, Db, E, G.
As you can see, with diminished we actually play in 4 keys at once.
Below is the analysis of the half-whole diminished scale in the key of C.
Notice that the scale outlines C, E, G and Bb, the notes of a C dominant 7 chord. Between these chord tones are the colorful extensions of the b9, #9, #11 and 13th.
Being a symmetrical scale, it analyzes exactly the same in Eb, F#, and A.
Important: In jazz terminology when a chord symbol has only a 7, 9, or 13, it is a dominant chord. For example, Eb7 means Eb dominant 7.
This works exactly the same for the other 2 groupings of F, Ab, B, D and Bb, Db, E, G. Since there are only 3 diminished scales before they become inversions of themselves, mathematics tells us that each must analyze identically in 4 different keys.
Notice that the #9 is the same as the b3 and the #11 is the same note as the b5. The b3 and b5 are commonly used in jazz and blues melodies and solos. If we look at the first vibraphone entrance in Symphonic Dances we see the following:
The tonality is clearly centered around A and every note is a part of the A half-whole diminished scale (written out above).
Fully diminished chords also analyze identically in 4 keys. Each fully diminished chord functions as 4 different dominant 7b9 chords:
Notice that each 7b9 chord is exactly the same: major 3rd, Perfect 5th, b7, and b9. Naturally, the other 2 groups work in the same manner. The minor 3rd is the essential interval in the diminished system.
Another important chord in this system is a diminished triad with a perfect 4th on top, or 2 minor 3rd’s and a perfect 4th. It can also be thought of as a diminished triad with a major 7th. This chord is utilized extensively in West Side Story.
It can be analyzed several different ways, however, it can be seen clearly as a dominant 13b9 chord. Below is the same chord analyzed as a G13b9.
Bernstein realized that this chord, as part of the diminished system, can move up and down in minor thirds just as the fully diminished chord does and maintain its quality as a dominant 7 chord in the key.
In the opening of the Mambo, the top line is simply this chord in parallel motion.
Later, in one of the most recognizable sections, Bernstein reverts back to this technique. The entire top staff is made up of parallel diminished triads with major 7th’s. The bottom line fills in the roots.
In the following section, Bernstein mixes in a series of half diminished chords (ø). Half diminished chords are made of a diminished triad with a major 3rd on top, or 2 minor 3rd’s and a major 3rd. This chord occurs naturally on the 7th step of the major scale. It also occurs naturally in the diminished scale.
When the bass line is added some of the half-diminished chords become upper extensions of dominant chords or minor 6 chords. Some of the notes have been spelled enharmonically to facilitate easier analysis.
Look at the notes in this portion of the vibraphone part of Cool.
All of the notes come from the following diminished scale:
In the next few measures, Bernstein uses the C13b9, moves it up a minor 3rd and back down again. In the vibes part he leaves 1 note out of each voicing. All of the notes in this passage are derived from the same C diminished scale.
He could easily have voiced the chords like this:
Bernstein then moves to the key of F and repeats the melody. This time he moves the chord down a minor 3rd and back up again.
All of the notes in this passage are derived from the F half-whole diminished scale.
The chords could have been voiced like this:
Later in the piece when the full orchestration kicks in, he does add the additional voice to complete the chord.
Now look at the first few notes of the vibraphone part in the fugue. All of the notes are from the F half-whole diminished scale.
Bernstein repeats the fugue subject starting on D# in the guitar and piano, then F# in the woodwinds, keys related by the interval of a minor 3rd.
Of course, Bernstein uses other tools as well. One of the more interesting structures is in America. In the Tempo di Huapango, the tune modulates through three keys: C, Ab, and E, the notes of an augmented triad. This structure was first used in the famous bridge section of Have You Met Miss Jones by Richard Rogers. It was then utilized by John Coltrane in his masterpiece Giant Steps.
Leonard Bernstein’s brilliance gave an original and vibrant voice to 20th Century American music. Bernstein and his music are truly American treasures.