Cognitive Cow

What is music? My definition, in a most general sense, is a subset of all noise. The specific that we’re interested in is the subset of noise that is pleasing to listen to and evokes some kind of memory or feeling. All noise is derived from waves: vibrations in the air we breathe. If those vibrations are within 20hz to 20khz, we perceive this as sound. Consider the most pure sound: a simple wave defined by its frequency. As the frequency increases, the pitch gets higher and as the frequency decreases, the pitch lowers. The ‘ideal’ wave will look like a sine curve and only sound exactly one pitch. Imagine a tuning fork hitting the soul of a shoe or a ringing in one’s ears. A pure tone like this is very rarely experienced.

Observe that by doubling or halving a given frequency, the quality of the pitch does not change. This is called an octave. It’s a very interesting quality about the way we perceive sound. If one were to describe two notes of the same frequency, they’d easily be able to say that they are the exact same note. If one were asked to describe two notes that are an octave apart, the sensation would be something like, “They’re the same sound but one is higher.” Each octave of a frequency holds the same basic musical properties of the other octaves. This gives a way to derive subsets of sound. For example, 440hz, 880hz, and 1760hz are in the same class of frequencies.

It’s important to note the logarithmic nature of human pitch perception. The fact that the interval from 130hz to 260hz is perceived by the brain as one octave the same way that the interval from 1040hz to 2080hz is perceived should raise an eyebrow. The two intervals ‘feel’ the same but are very different in terms of actual frequency changes. To understand this visually, Imagine the neck of a guitar. Ever notice how as you climb up the fretboard, the frets get closer and closer together? The relationship between the frets’ distance is logarithmic to account for the way we perceive sound.

An octave is an interesting interval but what about other intervals? Someone had to ask the question, “What other pitch intervals sound good?” Pythagoras did this very experiment and found that a frequency ratio of 3 to 2 produced what we now know as a perfect fifth and a ratio of 4 to 5 produced what we call a perfect fourth. At the time, these were just recognized as very pleasing intervals (sometimes called God’s interval) and later became the basis for western music as we know it. Using the fundamental interval of an octave as we’ve defined and keeping in mind the 3:2 and 4:5 pitch ratios, one can then derive a series of pitches that are equally spaced between an octave and give abstract names to these pitches. The first abstraction is called the cent. It was defined some time ago that 1200 cents are in an octave. So whether going from 220hz to 440hz or 880hz to 1760hz, there are always 1200 cents in that range of frequencies.

From there, we have the basis of equal temperament. Divide the 1200 cents into 12 equal parts of 100 cents and that interval is called a semitone. Two semitones is called a tone. Musicians today use the semitone as the smallest level of abstraction. All musical notation today is only capable of expressing in terms of semitone resolution.

It is useful to give names to these abstractions. There are 12 notes that need to be named. Seven of those notes are A, B, C, D, E, F, G. A is defined as 440hz and all multiples thereof. A tone above A is called a B. A semitone above A is called an A♯ or B♭. B♯ is the same sound as C and E♯ is the same sound as F. The twelve notes can be expressed in either sharps or flats with adjacent notes being exactly one semitone apart:

A A♯ B C C♯ D D♯ E F F♯ G G♯

-or-

A A♭ G G♭ F E E♭ D D♭ C B B♭

Notice a couple interesting things about this: The layout of semitones is exactly the way a piano keyboard and guitar are laid out. Each adjacent key on a piano is exactly one semitone apart. Each successive fret on a guitar fretboard is exactly one semitone apart.

You may have noticed that an A played on a paino, guitar, and trumpet make distinctly different sounds so how can they all still be the same A at the same frequency? The answer is that they all have a different timbre (t-AM-ber). Timbre is the color of sound, the mood of a specific sound. The timbre of a single oboe steadily playing a B♭ varies greatly from a trumpet whaling on the same B♭. Whenever any note is produced, there’s a fundamental frequency which we perceive as the pitch and there are overtones. Overtones are other frequencies that are produced on top of the fundamental frequency. Each and every instrument from vocals to saxophone to piano to drums produce different overtone patterns. Think of a fundamental frequency as a color in the basic rainbow (red, orange, yellow, green, blue, violet) and timbre is the characteristics of the color. Instead of just red (fundamental frequency) you might have magenta, fuchsia, carmine, or maroon which are all different colors that evoke different feelings but still fundamentally red. In a way, instrumentation is simply choosing overtone qualities that have a certain quality to evoke the emotion that is desired from the music. The same way that universities choose maroon instead of red as their color because while the fundamentals are the same, maroon screams ‘academic.’ This is one reason why a MIDI version of a song doesn’t quite compare to an orchestral version: lack of meaningful timbre.

Using the new ‘note’ abstraction, the definition of a perfect fifth and perfect fourth can now be redefined. Before we defined them as a pitch ratio of 3:2 and 4:5 respectively. Using the new abstraction, a perfect fourth is 5 semitones above the root note and a perfect fifth is 7 semitones above the root note. Notice that if A is the root note, the perfect fourth is D and the perfect fifth is E. All intervals have a name:

We cannot make music by just haphazardly combining these twelve notes. The concept of a scale is used to reduce the set of 12 notes to a manageable set picked to get a certain mood out of a piece of music. The major and minor scales are the most common and they’re defined as the following intervals (T = Tone, S = Semitone):

Major: T T S T T T S
C Major: C D E F G A B C

Minor: T S T T S T T
C Minor: C D E♭ F G A♭ B♭

Major scales have the quality of sounding happy, triumphant and positive. Minor scales have the quality of sounding sad and introspective. The words used to describe the sound of a song in a minor key vs a major key differ from person to person and song to song. A scale provides the song with a key signature which in a way is a framework from where the song stems. This is not a rigid guideline, however. One can include notes not in the specified key for added effect though in general songs adhere pretty closely to a specific key (or multiple keys in some cases).

Take this abstraction further to define chords. A chord is any two or more notes sounding simultaneously. Ten minutes at a piano will tell you that not every combination of multiple notes sounded at the same time make a pleasing sound. Try playing C, C♯, and A together at the same time. It sounds terrible. Now play C, E, and G and realize how much better that chord sounds. A, C♯, E has a very similar ‘feel’ to C, E, and G. We can use this information to develop classes of chords. C, E, G and A, C♯ E both follow the exact same pattern of a root note, a major third, and a perfect fifth. This pattern of three notes is always called a major chord. The name of the chord depends on the lowest (root) note. In the case of C, E, G this chord would be called a C major chord. Interestingly, if you just drop the third down a semitone to E♭, the chord takes on a completely new feeling. Just one note changed one semitone evokes a new emotion. That’s powerful.

A chord can be voiced. Voicing describes how the notes in a chord are ordered and expressed. a C major chord has the notes C, E, and G. However, there are tons of different ways to play those three notes. One can play C, E, G, G in which the second G is an octave higher. One can invert the chord and put the third on the bottom: E, C, G. In multi-part arrangements, voicing is done across instruments as well. Tuba will play the root, saxophones play the third, trumpets play the fifth. Chords in combination with voicing offer a seemingly endless array of chord choices, each offering a different feel and mood.

A chord sounds nice alone, but what really creates music is chord changes. Using the abstraction of a chord, we can now experiment with what chords sound nice together. a C major chord followed by an F# major chord will sound pretty terrible and rightfully so. the C major scale contains none of the notes in the F# major chord. However, a C major chord followed by a G7 chord (G, B, D, F) followed by a C chord has resolve. A collection of chords in order is a chord progression. A chord progression is the basis of most music as we know it. Most people cannot pick out individual chords and name them but every one of certainly knows the transition from a IV chord to a I chord feels like.

Chords can be generalized to be key-independent. A C major chord and a D major chord are really the same thing when speaking in the key of C and D respectively. To generalize this, we call both of those chords I (one) chords in their respective keys. the V (five) chord in the key of D would be A major and the vii (minor six) chord would be Bm. A very common chord progression is I, IV, V. Listen to a song like Brown Eyed Girl by Van Morrison or Crane Wife 3 by The Decemberists to get a feel for a song with only three chords.

Music isn’t all just notes and chords. Rhythm plays just as important a role as the notes them self in producing music. All songs have a tempo. A tempo measures the beats per minute. Those beats are grouped together into what’s called measures. Measures are put together together to form phrases. Phrases usually contain some multiple of 4 measures. The 12 bar blues, for example, describes a 12 measure phrase of chords which usually goes something like I, I, I, I, IV, IV, I, I, V, IV, I, I. In a jazz group, a bass player might repeat this phrase while a soloist improvises in the given key.

The most wonderful thing about music is that all I have described so far just scratches the surface. Abstraction is such a key aspect to understanding and interpreting music that my hope is that anyone who is interested in music will eventually discover how to make conscious sense out of what we unconsciously enjoy.