# Ch. 7 – Clues to Cracking Music Notation

Black & White Key Patterns The 88 keys on a piano can be intimidating. An adult faced with the prospect of tackling the instrument must grasp that in the beginning they will not need to engage the whole instrument. In fact from the seven (plus a bit) octaves available you can get away with learning about the two octaves near middle C.

It might be encouraging to know that J.S. Bach wrote all of his keyboard works with only a five octave range. “So what about the Black Keys? When do we learn them?” The arrangement of octaves has a mathematical phenomenon that gives us one of the few purely mathematical experiences that we encounter on a regular basis. The music we hear has a very real and complex system that is mathematically derived.

I’ve used a word without explaining it’s meaning. The “octave” is a group of eight notes that starts and finishes on what’s called an interval of an octave which is 8 scale notes apart.

Let’s consider the names of the notes. Because of the mathematical phenomenon of a frequency blending and sounding uniform when the frequency is doubled or halved the note names borrowed from the alphabet the first seven letters. So it should not be a surprise to learn that an 88 key piano starts with the letter “A” which is the farthest note left. We all know what to expect when we touch a piano down there. The sound is deep, unintelligible and often unpleasant but it begins the mathematical pattern and when you select the consecutive white notes in a series moving to the right they are names”A”, “B”, “C”, “D”,”E”,”F” and “G” then “A” starts again.

There are eight “A’s”‘, eight “B’s”‘, eight “C’s”, seven “D’s”, seven “E’s”, seven “F’s” and seven “G’s. in total”  (Please Note that several other non-english western countries use Do-Re-Mi-Fa-So-La-Ti-Do to represent the note names-which confuses us English because we have a movable “do” ) So when “A” reaches “A” again after the “G” it is called the “octave” above. You need to get used to thinking “above” or “up” or “high” is a left to right orientation and “below” or “down” or “low” is a right to left orientation.

I needed all of this preamble to explain that there is a mathematical logic and the white notes are tuned very specifically to make up the natural “A” minor or “C” major scale.  If you count the first few white notes and the only black note (four notes total) in the far left side we notice that the pattern repeats 8 times and that all remaining notes (black and white – 8 notes total) repeat seven times. That is 4×8=32 and 8×7=56 which makes 88.

“Where’s the pattern?” Two scales can be found using just the white notes (major scale, minor scale – both seven note scales) and a third scale can be found using just the black notes (pentatonic scale- a five note scale). You may know Steven Colbert who makes a joke about not seeing colour. So if the piano was all white notes it would need to be wider. You will notice that the black notes take up less width.  All three scales (natural minor, major and pentatonic) we are familiar with from some classical, popular and traditional songs.  Entire melodies can be created using just white notes and the same for just black notes.

The 36 Black Notes on a piano have a pattern of two-note and three-note groupings and they sound familiar when played in sequence. In fact our ears are more familiar than we realize and performance artist Bobby McFerrin does a nice demonstration of this on youtube

So far I’ve mentioned three scales: Natural Minor, Major and Pentatonic. Here’s a scary thought but important to try and grasp there’s twelve Natural Minor Scales and Twelve Major Scales and Twelve Pentatonic Scales. Now why is that true? A scale can start from any note. Hmmm. There’s a distance relationship between each consecutive note that changes but remains consistent each time you reach the octave. Let’s look at the Pentatonic first. Just five notes.

Pentatonic Since a scale can start on any note let’s look at what happens if we want a pentatonic scale starting on middle “C” that follows the same pattern as the Black notes. True the black notes are skinnier and shorter but the pattern is still there and the secret to understanding the pattern is to break the distance into units.

Our unit is called a semi-tone. That is the smallest distance between each note so for example all the semi-tones on the piano would be step by step all 88 keys black and white included. In fact when you look inside the piano like Colbert says you don’t see Black or White you just see strings all evenly spaced. That spacing is a semitone. If we grab a section of black notes for an example let’s look at a pattern of three on the left and two on the right. They follow the following pattern:

The name of these five black keys are Gb Ab Bb Db Eb (the small “b” is for now a “flat”)
Gb-Ab is 2 semitones
Ab-Bb is 2 semitones
Bb-Db is 3 semitones
Db-Eb is 2 semitones
Eb-Gb is 3 semitonesor to say it another way   Tone – Tone –  3 semitones -Tone – 3 semitonesMiddle “C” up a tone to “D” another tone to “E” three semitones to “G” and aother tone to “A”

C – D – E – G – A – C
is the Pentatonic Scale of C

Heptatonic That means seven note scale. These scales are the ones that most pop music uses and they are easy to discover using the white notes.

Let’s reverse engineer. Starting on “C” let’s play and name the white notes going “up”

`C - D - E - F - G - A - B - C`
`1   2   3   4   5   6   7   8`

When total beginner adults are told this is the C Major Scale what’s generally missing is the distance relationship we observed in finding the pentatonic scale. But now we know that we need to count semi-tones let’s do it.
“C” to “D” is a tone
“D” to “E” is a tone
“E” to “F” is a semitone
“F” to “G” is a tone
“G” to “A” is a tone
“A” to “B” is a tone
“B” to “C” is a semitone
So all major scales no matter what note to start on has this distance relationship between the notes
tone-tone-semitone-tone-tone-tone-semitone