Mike's Music Mystery 2

I do intend to get back to Fundamentals of Music, but I can't resist trying to respond to some of Mike's questions. If, as Oliver Sacks says, we are born with an attraction to music, maybe we also resonate with the physical law of sound which involves the overtone series.

Since the idea of the overtone series can induce near-coma in anyone but a scientist, I'll try to give a simple example. Richard Strauss' Also Sprach Zarathustra (or the theme to 2001 Space Odyssey, if that's more familiar) begins with the first notes of the overtone series.

A musical tone contains more than its fundamental sound. You can prove this by silently depressing, for instance, a C on your acoustic piano so that the damper remains up and the string can vibrate. Then strike the next C up, and it will cause the original C string to vibrate. If you strike the next G, the string again will vibrate. This is because of sympathetic sound and the overtone series.

I had a kind of mad organ teacher when I was a teenager. Those of you in Piano Club have probably heard how I wasn't allowed to breathe until my hands came off the keys, and how Mr. Lee's organ playing was punctuated by audible gasps as he followed his own rule. He would always ask me "Do you hear the overtones?" And actually I never did, but I tried to look as if I believed they were there, since he said they were.

I wrote Mike:

When I tried to take a nap this afternoon, all I could think about was whether the cuckoo sound is part of a major chord or a minor chord. Then I thought of the overtone series and decided that if we're as much a part of the natural world as I think we are, it must be a the top of a major chord. I have never completely understood the overtone series, but from what I understand it would go (1) Fundamental (2) Up a fifth (3) Up a fourth (4) Up a major third, etc. Without taking it any further, you would have, for example, C, up to G, up to C, up to E, which of course would describe a major chord. I think the next note in the series is an E-flat up nearly an octave and thus a minor chord. So the children are probably taking the chord root for granted when they sing nyah nyah-nyah nyah nyah on a minor third. I picture a string vibrating its full length (the fundamental), then from center to end (octave), but I'm not very clear on where it goes from there (where the nodes are). Maybe you know, since you play guitar. Now the part in your note about God I'm going to have to read several more times before I can begin to understand it, but even without fully getting it, I think it is just wonderful.

Mike's Music Mystery

(Mike Eppley wrote this fascinating response to the Cuckoo post and gave me permission to put it on Organic Piano 101. Besides playing the Big Literature on piano, Mike plays with a well-known blues group and has twelve YouTube videos under the name MrMikeyboards.)

What an interesting lesson; that cuckoo keeps popping in and out of my mind now! So, the riddle of the cuckoo clock (your current one) that perhaps you sometimes pose to your students, may be:

"Am I singing the bottom of a minor chord, or the top of a major chord?"

Among the many things I found myself wondering:Do children latch on to that minor 3rd interval partially because of its tension, the need to resolve to a root note if the minor 3rd is really used as the top (steps 5 & 3) of a major chord? Think of "Ring Around the Rosie," when you sing "ashes, ashes (we all fall down)." Ashes, ashes equals cuckoo, cuckoo, but instead of a minor-ish context, it's really used as the top of a major chord that wants to resolve to its root. Whereas, normally when we think of a minor 3rd interval, we think of it as the 1st & 3rd steps of a minor chord, with a sad or suspenseful sound.

(I always notice this interval in movies, the moment they want you to feel suspense. If you pay attention, you'll hear it all the time! Then, of course, you can curse me for drawing it to your attention, after which you'll never be able to ignore it again while watching many movies.)

I guess it all comes down to which note in between the notes of a minor 3rd interval are being implied. There are exactly 2 notes (in Western music, anyway) in between the defining notes of a minor 3rd. If you "hear" the lower of those 2 notes as part of a scale/sequence that also includes the cuckoo notes, then it implies steps 3, 4, & 5 of a major scale/chord. But if you "hear" the higher of the 2 notes situated between the cuckoo notes, then you've constructed the first 3 notes of a minor scale.

Perhaps this duality is what's so intriguing about the minor 3rd interval? It's the Jekyl & Hyde interval of our diatonic system. (Yes, other intervals have dual contexts as well, but with this interval, the 2 contexts seem so opposite, so different, to me.)

An interesting way to think of notes, intervals, chords (that's all been occurring to me as a result of thinking about Mikie's cuckoo posting), is that a single note by itself has no context (at least a theoretical note, if you ignore timbre, etc.). It's like a "point" in mathematics (or in "flatland"); it has only one dimension. It has no context, nor relationship to anything else.

But when you add another note, you now have 2 dimensions, context, a relationship... meaning! Perhaps you could even say that you already have 3 dimensions, with only those 2 notes, because the 3rd dimension (a chord) is now implied. Maybe even parallel 3rd dimensions, since there's more than one interpretation, different types of chords/universes in which those 2 notes can live. Okay... I've gone into outer space here (I've gone cuckoo); my apologies! I'm just passing on the thoughts I've been having on the subject over the last couple of days. (I blame Mikie ;-) )

Composers can and do use these concepts all the time. They may start a piece with a single note, the future/context of which cannot be predicted by the listener until more notes are added. Then more meaning is divulged, new relationships abound, and a landscape is opened up to us. If I really wanted to go out there on a limb, I might say that we are all like notes in a musical composition. As we move through time, we build relationships to other notes. (Some might say the composer is God.)

If you've made it this far in this unrequested followup to Mikie's lesson, then I wish you a Happy New Year, as we move on in the master compositions of our lives!

(Note: Anjaline and I are currently on vacation in Arizona. Maybe the southwest is what's bringing out all this mysticism in me!)

Mike E.

The Musical Cuckoo

The cuckoo, which is said to lay its eggs in the nests of other birds, can hardly be considered a noble bird, but its call has been much used by composers for hundreds of years. The cuckoo clock near my piano has proved to be an instrument which not only helps keep time, but assists in teaching intervals, figured bass, and music history.

At first, I used the cuckoo clock to remind me when lessons were finished, since I would often forget the time once a lesson began. Then I noticed that my students were beginning to be more prompt, to arrive before the cuckoo chimed the hour.

When students began playing with the tick-tock of the clock, I wrote out a little exercise in three-four time, and the clock became a metronome. More advanced students would look pained and cast accusing glances at the clock until I stopped it, but younger students were only too happy to play at 60 or 120 beats per minute, matching the tick and the tock.

One early ear training exercise was to find the exact pitches of the cuckoo on the piano. They were B to G, a major third, until an unfortunate accident with the vacuum cleaner necessitated a new cuckoo, which chimes C to A, a minor third.

Zoltán Kodály (1882-1967) considered the minor third the first interval that children could sing in tune, which might account for the almost universal traditional Teasing Song which Béla Bartók (1881-1945) documented in his children’s pieces. American children probably know this tune as “Nyah, nyah-nyah nyah nyah.” Cuckoo pieces in music literature use both intervals.

Many students are unfamiliar with Roman numerals, and the numbers on the cuckoo clock are helpful when we begin talking about I, IV and V chords. Of course, the students will quickly point out that we do not have VIII, IX, X, XI, or XII chords.

The numbers on the clock may even encourage the students to learn the twelve major and twelve minor key signatures, since I to VI o’clock indicate the number of sharps in the major keys, going clockwise around the circle of fifths.

Many method books have cuckoo pieces, many of them in ¾ time. There is a Cuckoo in the Six Children’s Pieces (for piano, four hands) of Anton Arensky (1861-1906), and Camille Saint-Saëns’ Carnival of the Animals features a Cuckoo in the Depths of the Woods (Le Coucou au Fond des Bois). Beethoven’s Sixth Symphony has a cuckoo, as well.

There is a Baroque cuckoo, Louis Daquin’s Le Coucou for organ or harpsichord.

Haydn’s Toy Symphony has a cuckoo (and there is an instrument , a short pipe with a single fingerhole, used for just this sound). Ottorino Respighi’s suite “Gli Ucelli” (The Birds) features the cuckoo in the last movement.

My favorite cuckoo in music, however, is found in the first movement of Beethoven’s Sonata in G, Op. 79. The cuckoo first appears when the left hand crosses over the right, but Beethoven’s cuckoo is not limited to two fixed notes. He sings all over the piano, in various keys, in bass clef, and finally in octaves.