Understanding Overtones

How Understanding Overtones Enhances Musicianship, Presentation for Virginia Music Teachers Association, Martha K. Smith NCTM, Richmond, October 29, 2011

I. How tonal harmony is derived. Overtones are produced by independently vibrating segments of any fundamental pitch. Low C on the piano supplies these examples, but the intervallic relationships are the same for any pitch:

1. Overtone #1, from sound wave produced by the two halves of the fundamental string vibrating independently, is an octave higher, or C.
2. Overtone #2, from the fundamental string vibrating in three parts, is a 5th higher, or G. Now we have Tonic and Dominant. The function of the dominant is to aid and abet in the establishment of C being “home base.” The special relationship the dominant enjoys with the tonic, owes to their proximity in the harmonic series.
3. Overtone #3, from the four quarters of each string vibrating independently, is again C, a fourth higher than the G.
4. Overtone #4, from five sections of the string vibrating independently, is again a new pitch, this time a major third higher, or E. When placed in scale order, we now have a major triad, the foundation of Western tonal music.
5. Overtone #5, somewhere between A and Bb, is a stranger to Western tonal culture. It can’t be found on the piano, because the piano is a tempered instrument. Construed as a B-flat above C, it makes a dominant seventh. Construed as A, it’s a sixth
6. The next new overtone (#7), D, is a 9th.

II. Overtones are basic building blocks of universal, traditional melodies.

1. The Universal Playground Chant consists of Overtones #2, #4 and #5, the ones that differ from the fundamental pitch, in that order, with the fundamental note implied. In key of C: G-E-A-G-E. Children all over the world sing these three pitches without knowing that they are responding to overtones and obeying the laws of physics.
2. The Pentatonic Scale consists of Overtones #1, #2, #4, #5 and #7, rearranged to C-D-E-G-A, the basis of folk music in many cultures.

III. Focusing on Overtones to improve musicianship

1. Singing: I help students find their singing voice so that they can sing along with a melody and eventually make the piano sing.

• Start with the Universal Playground Chant (easy, childish songs: Rain, Rain, Go Away; Ring Around the Rosy) then substitute local names, composers’ names or students’ interests to make them more appealing (Arlington Virginia, Ludwig van Beethoven)
• I teach Happy Birthday by rote, beginning the RH melody on C in the key of F. Clap the rhythm first: “Happy” is always a pair of 8^th notes on the 3^rd beat of 3-4 time

• 1^st phrase: “happy birthday” on neighbor notes, then up a 4^th
• 2^nd phrase; “happy birthday” on neighbor notes, then up a 5^th
• 3^rd phrase:  “happy” jumps up an 8ve, then takes 2 skips down and 2 steps down
• 4^th phrase: “happy” bounces on B-flat, then finds its way home to tonic
• When melody is firmly established, add I, V and IV roots in LH; later, chords.

B. Hearing: I often demonstrate the first two overtones when introducing a new piece.

• First have student identify the key from its signature. Then play that pitch low on the keyboard and listen for the dominant overtone. Identifying the key of a piece, its tonic and dominant are difficult for most students, but keep at it.
• Encourage picking out Amazing Grace and other pentatonic melodies on black keys

C. Seeing: Visually identify Tonics and Dominants in these pieces; look for “big picture”

• Aria, Notebook for Anna Magdalena Bach – 1^st part ends on V; 2^nd part returns to I
• Musette, Notebook for Anna Magdalena Bach  – includes V of V
• German Dance, Joseph Haydn

D. Feeling: Listen with imagination for

• the tension of the dominant: V-I cadence
• the relief of resolving to the tonic ii -V- I
• the suspense of dominant pedal points: Bach WTC 1 – Prelude No. 1 in C major
• the spice of non-overtones: Beethoven Ecossaise in G;  Mozart Minuet in F
• the surprise of a deceptive cadence: Mozart’s Minuet in F; Chopin Prelude in B minor

E. Composing: Let “The Ghost Next Door” by John Robert Poe inspire original Halloween songs: Press a low bass cluster silently, play treble notes staccato—loud and soft.

F. More Benefits: Pedaling – when to let strings vibrate sympathetically and when not to. Appreciating bass lines, with their more audible overtones. Coach your students to build their interpretations on these fundamentals. Ex: Chopin Waltz in A minor. Awareness of when a piano is out of tune. Accompanying – Listening for overtones helps pianists improve their sense of pitch.

IV. Conclusion Teaching an awareness of overtones strengthens listening to, reading and expressing music. It also appeals to students who appreciate order in the universe and leads to a more-informed, scientifically-based appreciation of the rich grandeur of musical sound.

References

The Unanswered Question, Six Talks at Harvard by Leonard Bernstein, 6 Disc Set of DVDs, www.kultur.com and at Amazon.

Piano Repertoire, Level Two, selected and edited by Keith Snell, Neil A. Kjos Music Company

J.S. Bach, Prelude in C (No. 1 from the Well-Tempered Clavier, Book I) FJH Music Company

Frederic Chopin, Prelude in B minor, Op. 28, No. 6; Waltz in A minor

John Robert Poe, The Ghost Next Door, Myklas Music Press, 1985

Circle of Fifths: Keyboard Fingering Guide for Major and Harmonic Minor Scales. Handy letter-size cardstock chart created by Evelyn Westwood, ewmusic@comcast.net. Available from Music Educator’s Marketplace www.musicedmarket.com. Item #EW1 $2.95 or 4/$10.00.