Staff Symmetry and the Location of Half Steps
For this course, you will need to instantly recognize the notes on three different musical staves: those using treble clef, bass clef and alto clef. Also, the treble and bass clefs, when grouped together, form the grand staff, used for keyboard writing, and you must have fluency in moving upwards and downwards within the grand staff.
To help in this endeavor, some observations of symmetry are in order:
Bass Clef
Even though we usually are taught the treble clef first in primary school, the bass clef is actually a more ancient clef symbol, with roots going back to the earliest period of Gregorian chant notation. It is very useful to perceive that the bass clef, even though alternatively named the F Clef (because of the two dots above and below the pitch F), actually centers itself around the pitch D at the midpoint of the staff.
If you look at the boxes, you'll notice that they move tone-semitone-tone-tone-tone-semitone in opposite directions from the center point.
As we will learn in our early classes, this "centeredness around D" has some interesting and important historical connections. One continuing manifestation of the centeredness of D is how stringed instruments are tuned. The violin family (violin, viola, cello and mandolin) are tuned in fifths, centered around D (GDAE for violin and mandolin, CGDA for cello and viola). This comes from the historical “Dness” of much early modal music. Similarly, all you guitar and bass players know that your bottom four strings are tuned around the D pitch, only in fourths instead of fifths (EADG). Thus the “Dness” of the bass clef is not accidental.
Anyway, if you look at these series of ascending and descending pitches, centered around D, you will notice that the half step from E to F and the half step from C to B are symmetrical to the center line of D. As we expand out to the single ledger line, you will notice the continuation of the symmetry: the B on top of the staff is a half step to the C on the first ledger line, and the F at the bottom of the staff is a half step to the E on the lower ledger line.
Treble Clef
In the Treble clef, the symmetry is not quite so neat, and you just need to remember that the half steps lie from E natural to F natural, and from B natural to C natural. (The why of this will be part of our explorations in the early part of the semester). Nevertheless, even here there is an inverse symmetry between the E and F at the bottom of the staff (low E moves up a half step to F) and between the E and F at the top of the staff (the high F moves down a half step to the E.) As to the half step between B and C in the middle of the staff, well there it is, slightly assymmetrical: you just need to learn it!
Grand Staff
When the two staves are brought together into the grand staff, another beautiful symmetry emerges, this time centered around C. (As keyboard instruments came into vogue and finally formed a central compositional and performance tool for European music, a shift to C-centeredness (“Cness”) came into being.) Here, we find middle C floating beautifully on its own line, and the C an octave above and below resting on the second space from the top or bottom, and finally the higher and lower Cs finding their location two ledger lines above or below the staff. Study this symmetry well until this image is clearly in your mind’s eye.
Alto Clef (Viola clef)
Finally, and speaking of symmetry, there is one more clef that you will need to learn this semester, in addition to the familiar bass and treble clef, which is the alto clef. This clef is used exclusively by viola players today (it used to also be the clef that altos sang in choirs, but no longer). You will need it when we begin to look at Beethoven’s 5th Symphony. It is not a hard clef to learn, in fact it is the easiest clef, were it not for the fact that few of you have ever had to read it. It is completely symmetrical, with “middle C” on the piano resting dead center in the middle of the staff. The other notes follow in reverse symmetry from the center.
