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Why is major "happy" and minor "sad"?

“All art constantly aspires towards the condition of music” - Walter Pater

Music as Abstract Art

The “condition” that Walter Pater, one of the most influential essayist and art critics of his time, is referring to is the abstraction of music. While music is often paired with poetry, dance, and film, it also exists independently. It does not need a storyline; the subject of a piece of music is the music itself. A listener can be moved to tears or joy through his or her own interpretation. These emotions occur without the guide of words, images, or physical gestures. Two readily perceptible examples are major and minor scales.

Major vs Minor

People often associate minor with sad and major with happy feelings, even if they do not realize it. Listen to this example of the same Beatles' song, "Hey Jude," once in a minor key and once in a major key.

"Hey Jude" in the original minor key:

"Hey Jude" in the released major key:

Basic Physics of Pitched Instruments

A quick way to hear both harmonies side-by-side is to listen to the beginning of Also Sprach Zarathustra by Richard Strauss. The piece starts with a quiet, slow build that grows until the orchestra plays a quick C major chord and then changes to hangs on a sustained C minor chord. It then repeats only inverting the progression, from C minor to C major. Do you hear this opening as the uneasy and mysterious Objectively, this stability vs instability can be explained by the physics of music.

I am going to use the guitar in my discussion, but the same physics can be applied to any other pitched instrument. Sound is generated by a guitar when the strings are plucked. For example, when the A string of a guitar is plucked it moves the soundboard creating pressure waves that travel through air. Eventually these waves vibrate our eardrums and we hear a note. The main frequency that our ears perceive is 110 hz, which we call an A2 in music, but that is not the only frequency produced.

The sound wave produced by the vibration of the A string is a complex wave. Figure 1 shows an example of a complex wave and its component simple waves. In the case of the vibrating A string’s complex wave, the component simple waves are produced by the string vibrating simultaneously at full length, at ½ length, at ⅓ length, and so on. This series of ratios is called the Harmonic Series or the Overtone Series and is more clearly seen in Figure 2. The frequencies and notes produced by the different vibrations of the A string are 110 hz (A2), 220 hz (A3), 330 hz (E3), etc., called harmonics or overtones and their values can be obtained by multiplying the fundamental frequency (110 hz for our A string) by the inverse ratio of the desired harmonic. For example, if we want to find the first harmonic, which is produced by the string vibrating at 1/2 its length, we multiply the fundamental frequency of 110 by 2/1 and get a value of 220. 220 hz is the note A3 one octave above the fundamental.

Using the same formula we can determine the harmonic series for any fundamental frequency. Figure 3 shows the harmonic series over four octaves starting on the note C1. All of these tones are heard when C1 is played, though the relative volume decreases dramatically as the harmonics increase. This series of overtones is what causes major harmony to elicit the feeling of happiness and minor sadness.

Stability vs Instability

The first five notes in this series are C1, C2, G2, C3, and E3, which can be combined to form the three most consonant intervals in music; the octave (C1-C2), the fifth (C2-G2), and the major third (C3-E3).* We hear the harmony of a major third as consonant because of its early presence in the overtones.

This explains what happens when we play two notes together. When we play C and E at the same time, there is stability. This stability comes from the reinforcement of the note E by the overtone E. In contrast, Figure 3 would have to extended to 19 overtones before it included an Eb, the minor third of C. If we play C and Eb, the resulting sound is unstable for two reasons: 1) there is no reinforcement from the C’s overtone series and 2) the Eb clashes with the overtone E.

The intense presence of the major third harmony in the overtone series of any note means that we hear major thirds every single time we play a note. This causes major harmony to be reinforced and stable while minor is weak and unstable. This is why we perceive the stable major as happy and the unstable minor as sad. Our emotional reactions and interpretations of music can be traced to the physical properties of sound production itself.

“Music is the pleasure the human soul experiences from counting without being aware that it is counting.” - Gottfried Wilhelm von Leibniz

*The interval produced by G3-C3 is not mentioned to prevent confusion. Trained musicians will note that the interval is a perfect fourth but, in the context of C, G is the perfect fifth. Since this discussion concerns the overtones heard when the note C1 is struck, the resulting G will be heard as the fifth.

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