Lowest A
A 440
Highest C
There are four fundamental properties of sound. Each of these properties will be discussed in terms of physics and music.
Physics |
Music |
| Frequency | Pitch |
| Amplitude | Dynamics (Loud/Soft) |
| Duration | Tempo/Rhythm |
| Timbre | Tone Color |
Frequency refers to the number of cycles per second of the sound wave. Frequency is measured in Hertz (Hz), 1 Hz equals one cycle per second. Human hearing is approximately within the range of 20Hz - 20,000Hz. As we get older the upper range of hearing diminishes. Human speech generally falls in the range from 85 Hz - 1100 Hz.
The fundamental frequencies for the notes on a piano range from 27.5 Hz to 4186 Hz.
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Lowest A
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A 440
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Highest C
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The modern standard for tuning defines the frequency of the note A above middle C to be 440 Hz. Musicians refer to this as "A-440." It's the reference frequency used for piano, guitar, and all band and orchestra instruments.
The musical term for frequency is pitch. The higher the frequency, the higher the pitch. The lower the frequency, the lower the pitch.
Low frequency = low pitch |
High frequency = high pitch |
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The amplitude of a sound wave determines its relative loudness. Looking at a graph of a sound wave, the amplitude is the height of the wave. In the following two graphs the two sound waves have the same frequency but differ in amplitude. The one with the higher amplitude has the louder sound. Studies in hearing show that we perceive sounds at very low and very high frequencies as being softer than sounds in the middle frequencies, even though they have the same amplitude.
Low amplitude = soft sound |
High amplitude = loud sound |
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Amplitude is measured in decibels. The following table shows some relative decibel levels.
Decibels |
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160 |
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150 |
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140 |
Jet takeoff |
130 |
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120 |
Threshold of pain |
110 |
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100 |
Loudest symphonic music |
90 |
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80 |
Vacuum Cleaner |
70 |
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60 |
Conversation |
50 |
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40 |
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30 |
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20 |
Whispering |
10 |
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0 |
Threshold of hearing |
Decibels are a logarithmic (base 10) ratio of the relative amplitude levels
between two sounds. For each decibel change by 10 units, the sound intensity
increases by powers of 10. For example intensity difference between the softest
symphonic music (20 dB) and loudest symphonic music (100 db) differs by a
factor of 100,000,000 (10 to the 8th power).
The musical term for amplitude is dynamics. There are eight levels of loudness commonly used in music notation. They are indicated by the following symbols.
Symbol |
Name |
Performed |
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fortississimo |
as loud as possible |
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fortissimo |
very loud |
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forte |
loud |
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mezzo forte |
medium loud |
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mezzo piano |
medium soft |
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piano |
soft |
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pianissimo |
very soft |
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pianississimo |
as soft as possible |
A musical note can be thought of in two ways: as a specific type of musical symbol appearing in a piece of written music, or as the sound you hear when the note on the page is played. A note is both a written symbol and a single sound with a distinct pitch, duration, dynamic, and timbre.
The pianoforte, the ancestor of the modern piano, was invented in Italy around 1710 by Bartolomeo Cristofori. It was the first keyboard instrument that could play loud (forte) or soft (piano) depending on the force applied to the keys. He named it the "piano forte," Italian for soft-loud. It is also sometimes called the fortepiano.
The duration of a note can be measured in absolute time or relative time. In absolute time we say the note lasted for 500 milliseconds. In relative time we say that one note was twice as long as another note, or that four of these notes last as long as one of those note.
Rhythm refers to relative time or proportional time. The duration a note is referenced to a steady beat, tick, or pulse. Most note proportions are powers of two. This note lasts for one beat, this note lasts for two beats, this note lasts for half a beat, etc.
During a musical performance one note value is chosen as the beat unit. It coincides with the underlying foundation or grid of steady beats. Sometimes a note will be played on the beat, sometimes notes will occur between beats, sometimes several notes will occur before the next beat, and sometimes several beats will pass by before the next note is played.
The relationship of notes to one another with respect to a steady beat is called rhythm. The speed of the steady beats is called the tempo.
Tempo refers to absolute time and is referenced to an external time source that marks off equal units of time. For example, your heartbeat, the sound of your footsteps on a steady walk, a clock ticking, or a metronome all provide a series of steady beats. The speed of these beats is called tempo. These steady beats (ticks, pulses, clicks) serve as the underlying foundation upon which musical rhythm and performance is built.
Tempo in music is expressed as the number of beats per minute. If you see M.M. <note value> = <number> at the beginning of a piece of music, the number indicates the number of beats per second, and the note value indicates what type of note equals one beat. M.M. is the abbreviation for Maelzel's Metronome. Johann Nepenuk Maelzel invented the metronome in 1816. In this example the tempo is 60 quarter notes per minute, or one quarter note per second. This example would last for four seconds.
Timbre (pronounced tam-burr) refers to the tone color of a sound. It's what makes a piano sound different from a flute or violin. Sounds with different timbres have different wave shapes. Here's the sound and wave shapes of different instruments playing the pitch A-440.
Piano |
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Violin |
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Flute |
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Oboe |
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Trumpet |
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Electric Guitar |
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Bell |
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Snare Drum |
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Sound frequency (pitch) is measured in Hertz. 1 Hz is one cycle per second. The modern orchestra tunes to the note A-440, or the note whose frequency is 440 Hz.
Let's calculate the distance between crests of a sound wave for the note A-
440. Here's what we know. The speed of sound equals 791 mph or 1116 feet/second
(sea level, 59 degrees F). In one second the note A-440 goes through 440 cycles
and travels 1116 feet. Therefore the distance between crests from one cycle
to the next is 2.53 feet (1116 ft/sec ÷ 440 cycles/sec). Similarly,
the distance between crests for the lowest note on the piano (27.5 Hz) is 40
feet and the highest note (4186 Hz) is .26 feet, a little over 3 inches.
When two notes are slightly out of tune, they produce beats. In the example below, the first sound is a sine wave at 440 Hz, the second is at 441 Hz, and the third sound is the combination of the two sounds. When the two sounds are combined, their waveforms create interference patterns that can be heard. These audible interference patterns are called beats. It's very difficult to hear the difference between the 440 Hz and 441 Hz sounds when played alone, but when they're combined it's easy to hear the beats.
The rate of beating is equal to the difference in frequencies. In this example the beating rate is 1 Hz. or one cycle per second.
Sine wave at 440 Hz |
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Sine wave at 441 Hz |
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440 Hz and 441 Hz combined |
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Two notes are "perfectly in tune" when they are sounding simultaneously and there are no discernible beats between them. The definition of being "in tune" is the absence of beats. As the two notes get more out of tune, the beats become faster. As the two notes get closer to being in tune, the the beats become slower. When there are no perceptible beats, the two notes are in tune.
The strings of this piano note are slightly out of tune. Listen for beats as the sound decays.