# Why are there only twelve different notes on a piano?

Asked by PhiNotPi (12656) March 14th, 2011

Every piano, xylophone, clarinet, and every other musical instrument has twelve notes in the chromatic scale. Why are there 12 notes? Why not 10, or 20?

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blueiiznh (16678)

“To answer this question, we first need some background information. A note’s pitch or frequency is measured in cycles per second; for example, A’ is 440 cycles per second. The distance between two notes, measured as the ratio of their pitches, is called an interval. If the interval between two notes is a ratio of small integers, such as 2/1, 3/2, or 4/3, they sound good together — they are consonant rather than dissonant. People prefer musical scales that have many consonant intervals.

There is no absolutely definitive list of consonant intervals because the concept of consonance involves subjective aesthetic judgment. However, the following seven pure intervals, smaller than or equal to an octave (2/1) and larger than unison (1/1), are commonly considered to be consonant.

In the past, people constructed scales based on pure or natural ratios of small integers. For example, the just intonation system uses the exact ratios shown in the table below. However, this method runs into serious problems. Although some of the intervals are perfect, other combinations of notes sound very bad (“wolf intervals”). After the Middle Ages in Europe, music became more complex, with more polyphony and more key changes, and these bad intervals became more common.

The modern equal temperament system was invented (in the 1500s) to solve this problem. (Galileo’s father, a music theorist, was one early proponent of equal temperament.) The octave is divided into twelve exactly equal intervals. In this system, the smallest interval, the semitone, is not a simple integer ratio, but is the twelfth root of two (21/12) or approximately 1.059. Larger intervals are multiples of the twelfth root of two, as shown in the table below. Although no interval (except the octave) is perfect in this system, the error is “spread around” evenly so there are no very bad intervals.”

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marinelife (62177)

Some believe it’s connected to the physics of human speech.

the100thmonkey (11225)

Excellent question. To summarize @marinelife completely correct answer, each note is a set fraction of the other notes.

But interestingly, although the intervals are fixed, the tones are not. In 1955 there was an international agreement that “A” would be at 440 hertz. http://piano.about.com/od/musicaltermsa1/g/GL_concert-pitch.htm

I’m a banjo player in the style of Earl Scruggs. In a lot of Earl’s early records his G was off—he was tuned a bit higher than a regular G, so his early albums were slightly sharp.

Rarebear (25144)

@the100thmonkey: The expert in that article was Professor of Neuroscience, Dale Purves, who was fluther’s @girlofscience’s mentor and someone I knew from his days at a Philly Quaker School.

gailcalled (54507)

In Indian classical music, there are more recognized pitches. We call them quarter steps. In East Asian music, as well as many other musical traditions, they often use the pentatonic scale, which has five notes per octave. There are also microtonal scales that use as many as 43 pitches per octave. There are many different scales. The 12-tone scale is the most common one found in Western classical music. The piano—an instrument that can play many different parts at the same time and is generally considered a classical instrument uses that scale because it is most helpful for classical musicians who play Western classical music, as well as other forms such as songs and some folk music.

wundayatta (58568)

In addition to what @marinelife wrote we could ask the question why 24 notes on a piano are not common, see

http://en.wikipedia.org/wiki/Quarter_tone

“Quarter tone pianos have been built which consist essentially of two pianos stacked one above the other in a single case, one tuned a quarter tone higher than the other.”

There is the http://en.wikipedia.org/wiki/Arab_tone_system but the piano was invented in Italy and at the time Arab music was virtually unknown there.

mattbrowne (31580)

The secret to understanding this question is the layout of the piano itself. Most pianos has 88 keys. (There are some that have more and less) So you’d think to yourself, then I’d have 88 notes to play with, right? Wrong.

For ex: Notice the black keys. Concentrate on the two sets of black keys. Now count the white keys surrounding the two black keys, starting with the C note. Count all keys, including black keys until you stop at another C note. Notice a pattern?

AshlynM (9887)

@AshlynM I know that there are only twelve notes. It is in the title of this question. I never said anything about thinking that there were 88 notes.

PhiNotPi (12656)

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