1999 First Web Reports 
On Serendip 
Neurobiology of Harmony
David BennerHow sound waves produced by instruments become sensible representations in the brain, and how the perceptions become meaningful are interesting questions for neurobiology to ask, as well as necessary ones if knowledge of the brain is to account for all behavior. The brain is able to discern harmony because the inner ear is capable of differentiating between different frequencies. The brain's differentiation between pitches and chords corresponds to the physical, "real," differences between notes and chords, although our sense of music built from perception of harmonies through time, is more subjective and variable.
Our faculty of hearing derives from the anatomy of the inner ear and the brain, as well as from the existence of external stimuli in the outside world. Sound is both the mechanical energy of waves and the sensation produced by receptors in the brain (1) . Each wave has an amplitude and a frequency. The amplitude of a vibration corresponds to its volume and is measured by decibels on a logarithmic scale. Frequency is logarithmic, as well, but corresponds to differences in pitch. Greater frequency results in a higher pitch. Mathematically, pitch is represented as the number of vibrations per second (1)  (2)  .
Vertebrates hear sound through their neurobiological makeup. The ear's tympanic membrane, or eardrum, vibrates as a result of being subjected to sound waves. The waves then travel to the inner ear or cochlea which is the site of sound's transduction into chemical energy. Within the cochlea, sound waves travel through fluid which stimulates the stereocilia, small hair-like projections of hair cells along the basilar membrane. The actions of the stereocilia cause the release of K+, potentially depolarizing the cell (1) . The flexibility of the basilar membrane allows stereocilia to move back and forth in response to the waves in the Cochlear fluid. Each stereocilium is linked to another through structures called "tip links" (1)  , (3)  As the stereocilia move towards the tallest ones, the tip links cause ion channels to open, depolarizing the cell and allowing free K+ to move into the cell (1) . Importantly, the stereocilia move in direct response to the sound waves and are cumulative rather than spiking. Neurotransmitter release corresponds to the frequency and amplitude (pitch and volume) of a sound input. Sounds must be sufficiently loud and within a given range in order to cause action potentials. Different sounds will produce different outputs, allowing for discrimination of harmony on a neural level (1) .
Another way in which vertebrate neurobiological makeup allows for the discrimination of pitch, and therefore the assembly of harmony is the property of "tuning" of stereocilia. Sound waves affect different parts of the basilar membrane differently. Low frequencies cause the high end of the membrane to vibrate more than other regions; the converse is also true. Additionally, short, stiff stereocilia vibrate more at higher frequencies meaning that for each hair cell, there exists a "best excitatory frequency" or characteristic frequency. A hair cell will respond to its best excitatory frequency at the lowest stimulus intensity (1)  , (3) .
Additionally, each hair cell has what is called an "electrical tuning frequency." The electrical tuning frequency is the frequency of oscillation of the membrane potential in a depolarized hair cell. One should note that not all cells have identical oscillation of the membrane potential When the stimulation frequency is similar to the electrical tuning frequency, the amplitude of the oscillation will increase, adding to the depolarization of the cell. What this means is that each hair cell best hears a single pitch, and if the stimulation frequency of a given pitch is equal to the pitch the hair cell is most adept at "hearing," the effect will be greater (1) . Moreover, since each hair cell is tuned to hear a given frequency, more than one frequency can be transducted into an action potential at the same time, but through different hair cells.
While the behavior of stereocilia and hair cells in response to sound inputs suggests that the faculty of hearing enables the brain to convert sounds into chemical energy through mechanoreceptors that correspond directly with how the sounds exist mathematically, there is still room to be deceived by the senses. The inner ear engages in "two tone suppression." Two tones which are similar in pitch will cause mechanical interference and the tones close to the characteristic frequency of a neuron will reduce to one tone (1) . An additional effect of two-tone suppression is the ability to create quantified scales. While the ear can discern pitches between degrees on a scale, the ability to create discrete distinctions in pitch is necessary for harmony. Two-tone suppression does not apply to two notes divergent enough in pitch that they act on different neuron's best excitatory frequencies and therefore create two independent transduction events.
Once frequency and amplitude are converted into action potentials, the biochemical pathway leads sounds from the inner ear along the auditory nerve which is part of cranial nerve VIII through parts of the medulla, pons, midbrain, thalamus, and finally to the auditory cortex of the temporal lobe (1)  , (3) The parts of the brain involved in the perception of sound locate its origin and involve the limbic system in the recognition of a given input. The brain can find meaning in aural inputs, making music possible as a form of expression.
What distinguishes harmonic inputs from other sounds?i Music is composed of pure elements of sound, pitch and meter, and has an internal order, as well as external significance for the listener. Harmony is the relationship of different pitches to each other and can therefore be described by ratios of various frequencies. The relationship of frequencies in a scale is logarithmic. A pitch an octave above another will have a frequency double that of the lower note. For example, middle A has a frequency of roughly 440 Hz meaning that a note an octave above it will produce vibrations of 880 HZ. An octave ratio is therefore 2:1. However, the next frequency at which there is an integer relationship is the interval of an octave and a fifth. The ratio of a fifth (dominant) note to the root is generally 3:2 (E 660: A 440). The ratio of the note an octave and a fifth to the root is 3:1 because the fifth an octave higher is twice the frequency of the original fifth, and 3/2 (the fifth) x 2 (the octave) is 3. (2) .
The series of intervals that has whole-number ratios is called the harmonic series. The intervals are an octave, a fifth, a fourth, a major third, a minor third, a minor third, a major second, ad infinitum. In musical terms, if C is the root, the notes of the harmonic series are C, C, G, C, E, G, B-flat, C, ad infinitum. When the base of a harmonic series is played, and every note has its own series, the other notes in the series, the "overtones" will also resonate due to the principle of aural harmonics, if very faintly (4) . Harmony derives from levels of consonance between two or more pitches. For example, in the key of C, G is the most consonant note other than C because it is the note which appears most in the harmonic series other than the root. Since C to G is an interval of a fifth, and the fifth is the second interval in the harmonic series, the fifth of all chords must be the most consonant pitch after the root, followed by intervals of the fourth and major third, minor third, major second, etc. In terms of the ratios between the notes, a major chord which is constructed by a fifth and a major third is more consonant than a minor triad which contains a fifth and a minor third (4) . Because of the greater level of consonance between major triads than minor triads, they appear more "wholesome" to our sensibility.
On the other hand, while the transduction of major frequencies is different from that of minor chords due to the specialization of pitch receiving in the hair cells of the basilar membrane, neither the chords themselves, nor their transduction, give humans the common judgment that major chords are "happy" and that minor chords are "sad." Social and environmental factors affect our response to pieces of music. The limbic system is involved in recognition and remembrance of harmony, and, very often, composers attempt to mimic elements in nature likely to draw an emotional response, such as Rimsky-Korsakov's "Flight of the Bumblebee." Expectations about tonal resolution can be taught (5) . in the Baroque period, pieces in minor key were expected to end on a major chord, as opposed to now when we expect minor to resolve to minor.
Although there is a strong correlation between sound waves produced and the inputs to the Central Nervous System, pure harmony does not necessarily cause the emotional response to a piece of music. Rather, there is a "symphony" in play involving memory, recognition, and social constructs, as well as real differences in consonance.
Works Cited:1) "Delcomyn, Fred. Foundations in Neurobiology. New York: W.H. Freeman, 1998."
2) physics of music 
4) Physics of Sound 
1. Research Project on Cognitive Musicology , information on work intended to look at behavior, including music perception through continental philosophy and neurobiology.
2. Music Mind and Machine , a look at computer models of behavior to understand music perception.
3. Juslin, Patrik. "Emotional Communication in Music Performance." Music Perception. Vol. 14, no. 4, pp.383-418.
4. Pechmann, Thomas. "Memory for Chords:Tthe Retention of Pitch and Mode." Music Perception. Vol.16, no.1. pp.43-54
5. Music Perception Abstracts 
Basic definitions of musical terms such as scales and intervals are available at musica theoria-main . Different chords, scales, and harmonic progressions can be heard at piano on the net '97 .Special thanks to my piano teacher, Joan Campbell.
Comments made prior to 2007