Sus7 Chromatic Climb

Here's a little chromatic thing I stumbled upon one day at the piano. I like it because you get the smoothness of chromaticism (obviously), but also variety via slightly different chords.

The chords here alternate between a sus-7-with-9th and a sus-7-without-9th.

That 9th or 7th in the top voice in itself creates a satisfying shape and is a nice contrast to the straightforward half-step climb in the lower voices.

Here it is with the voices separated, which makes it easier to notice some of the intervallic relationships between each voice. In this image, I described each voice's movement and made note of each voice's relationship to the bass.

"West Side Score-y" Pt. 3: Tri-tones...They're Everywhere!!

Part 3

It seemed appropriate that Part 3 of this series was about the tri-tone. Even if it weren't for this numerical match-up, a post about the tri-tone seems inevitable when writing about West Side Story. Bernstein throws them into the score like I throw chocolate chips into cookie dough (excessively, perhaps, but to great effect).

Part 1 addressed something I called the "Smush Chord," and
Part 2 explored Bernstein's rhythmic stuff.
Part 3 continues, below... (read on!)

The Tri-Tone

Literally meaning "three-tones," the tri-tone is the musical interval spanning the range of three whole steps (6 half steps). Since our octave is most typically divided into 12 half steps, the tri-tone represents the octave divided exactly in half. The sonic result is a jarring, highly dissonant sound—so dissonant that history has given it the sinister nickname "diabolus in musica" (the Devil in music).

(More about the tri-tone and other intervals here.)

Melodic Appearances

1. "Do" up to "fi." Of course, the best-known example of the tri-tone (at least, within the realm of West Side Story), is in "Maria." The interval, here appearing as an augmented 4th, is heard in the first two syllables: "Ma-ri..." 
2. "Cha-Cha"
3. "Cool" (pictured below)
4. Basically everywhere.

from "Cool" (C up to F#, an augumented 4th)

Harmonic Appearances

from "Prologue" [C major over F#] and [Eb major over A]

1. Polytonal-type chords (a la Petrushka), in which a major triad is coupled with a tone 6 half steps away from the root, appear in selections such as "Prologue" (pictured above), "The Rumble," "I Have a Love," and several scene changes. In fact, the very last musical sound heard in the show is one of these puppies, with C major up high, F# down below.
2. Major chords, with #4 (a.k.a. #11). These bright chords, which suggest the Lydian mode, can be found, among others, in "Prologue," "Jet Song," and "Gee, Officer Krupke" ("Dear...")
3. #ii°7 diminished chords (in 3rd inversion). Closely related to the previous chord, this one is just slightly crunchier in sound. It's featured most prominently in "Something's Coming."
4. Whole-tone spots: "Tonight" m. 37 (pictured below)
5. Again, basically everywhere.

Pitch inventory (F, G, A, B, C#) comprised of whole tones.
(Tri-tone appears on beat 2, between F and B.)

Conclusion

To sum up (clumsily, quickly), that there are tri-tones just about everywhere in West Side Story is perhaps "needless to say," but there, I said it.

Being such a grating interval, it certainly catches the ear, and the sound sticks with you. It's what helps make the lyrical "Maria" so beautiful ("Say it loud and there's music playing / Say it soft and it's almost like praying..."), and it's what makes the show's final chord so hauntingly dissonant.

Inverting Intervals

To invert an interval means to move one note (out of the two) up or down by an octave. For example, to invert a 3rd (C and the E above), I can move the C up an octave. This effectively puts the C above the E. So, the new order from lower to higher is E up to C. Furthermore, this creates a different interval: the 3rd became a 6th.

Here's a visual, which matches the style of a previous post on reading intervals from a staff:

When you invert an interval on the staff, its line/space category becomes reversed (same to different, or different to same). Click to enlarge.

You'll see that interval numbers of each inversion pair always add up to 9:

• A unison inverts to an octave (1+8=9)
• A 2nd inverts to a 7th (2+7=9)
• A 3rd inverts to a 6th (3+6=9)
• A 4th inverts to a 5th (4+5=9)
• And vice versa

Seeing Intervals on a Staff

When I teach beginner-level piano students, one of the first things they learn is the "step" vs. "skip" concept. This coincides with their introduction to reading music from a staff. If a "line" note goes up to the adjacent "space" note, we call it a step (like stepping up on a flight of stairs). But if that line note goes up to a note on the next line above, we call it a skip (it is skipping the space between the lines). This is often how students begin their understanding of intervals. They soon learn that the line-space example is called a 2nd, and the line-line example is a 3rd.

Beyond 2nds and 3rds, of course, the intervals become larger, and perhaps can be a little trickier to identify on a staff. Fortunately, with a little practice, this becomes easier and easier, until soon enough it is second-nature.

Here's a handwritten sheet showing what different intervals (unisons up to octaves) look like on the staff (5 lines, 4 spaces) The ability to quickly recognize an interval (and eventually, several intervals/chords at once) when reading from written music notation--especially when sight-reading--is very valuable.

I hope my handwriting is legible for you. Click to enlarge.

In quotation marks, I wrote out simple mental steps someone might go through when looking at each interval. Visually, when I see a 7th, I like to imagine climbing up the rungs of a ladder (i.e. going from one line to the line above). On each rung, I can count up by odd numbers: "1, 3, 5, 7." A four-line ladder means I'm looking at a 7th.

The basic nugget of information to take-away from this post is this:

Intervals of Odd Numbers (1, 3, 5, 7) always appear as line-line or space-space.
Intervals of Even Numbers (2, 4, 6, 8) always appear as line-space or space-line.

To help visualize these intervals in another way (pianists especially), it would be a good idea to plunk out each of the intervals depicted above on a keyboard. Begin doing this in the key of C major (all white keys), and when comfortable try out some other keys in order to incorporate black keys into your visual memory bank.

Intervals

What is an interval?

An interval is the distance between two notes.

An improper method of measuring intervals on the piano. (There is no "inches to semitones" conversion.)

The smallest interval (in Western music) is the half step, also called a minor second. As you increase the number of half steps between two notes, the interval gets larger until, eventually, you arrive at an octave (12 half steps apart).

Each interval has its own distinct sound, and this aural aspect of intervals will be the focus of this post.

The following is a list of all the intervals (within the range of one octave; not beyond) and some examples of their corresponding aural identities.

Intervals and Their Aural Identities

• Unison (0 half steps): likely the easiest interval to identify aurally. It's the interval that's created when two people sing the same pitch. It's the interval that piano tuners try to achieve between all three strings of one key.
• Musical example: the first two notes of "America the Beautiful" (Oh beau-)
  

• Minor 2nd (1 half step): a small, very dissonant interval. In solfeggio, it's the distance from ti to do.

• Musical example: the ominous bass tones from the "Jaws" theme song
  

• Major 2nd (2 half steps): appears in the first two notes of a major scale.

• Musical example: in the first line of "Happy Birthday," the interval from "-py" to "birth-" (and back down to "-day")
  

• Minor 3rd (3 half steps): often used to establish a minor tonality and express sadness or grief. In a minor scale, it appears in the leap from the first note to the third note.

• Musical example: the first two notes of the guitar riff from Deep Purple's "Smoke on the Water"
  

• Major 3rd (4 half steps): often used to establish a major tonality and express happiness or joviality. In a major scale, it appears in the leap from the first note to the third note.

• Musical example: the first interval of "When the Saints Go Marching In"
  

• Perfect 4th (5 half steps): a rather stable, consonant interval.

• Musical example: the first intervallic leap of "Here Comes the Bride"
  

• Tritone (6 half steps): this interval presents itself either as an augmented 4th or as a diminished 5th. It it is so dissonant that, dating back to Medieval times, it has been dubbed "diabolus in musica" (the Devil in music). Since the interval has historically served as a symbol of evil, people often associate its sound with danger and the unknown.

• Musical example: the first two notes sung by the choir in "The Simpsons" theme song (The Simp-)
  

• Perfect 5th (7 half steps): a very stable interval.

• Musical example: the "Winkie Chant"  from "The Wizard of Oz"
  

• Minor 6th (8 half steps): in a second inversion minor triad, the distance from 5 up to 3 (solfeggio: mi up to do).

• Musical example: the first interval in "Black Orpheus"
  

• Major 6th (9 half steps): in a second inversion major triad, the distance from 5 up to 3 (solfeggio: sol up to mi).

• Musical example: the first two notes of NBC's three-note jingle
  

• Minor 7th (10 half steps): the inversion of a major second. In a dominant (major-minor) seventh chord, it appears in the leap from the root to the seventh. In this context, the minor 7th has a strong pull toward resolution (as in the following musical example).

• Musical example: from "Somewhere" (Leonard Bernstein's "West Side Story"), the first two notes (There's... a...)
  

• Major 7th (11 half steps): the inversion of a minor second. In a major seventh chord, it appears in the leap from the root to the seventh. In this context, the major 7th wants to resolve up to the consonant octave.

• Musical example: Norah Jones' "Don't Know Why"
  

• 8th/Octave (12 half steps): the leap from a note up or down to the next occurrence of the same note name.  The frequencies of two notes an octave apart have a ratio of 2:1.

• Musical example: the first big leap in "Somewhere Over the Rainbow"

Symphony of Intervals

I'll leave you with this video (audio only) of a symphony's pre-concert tuning and warm-up. Intervallically speaking, listen for the unisons created immediately after the tuning note is sounded, then listen for all other intervals as each musician warms up individually and deviates from the initial unison. The swirl of different tones and timbres is rather enchanting.