Why Are There Only 12 Pitch Notes (C, C#,

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3/7/2016 Why are there only 12 pitch notes (C, C#, ..., B) in the world? - Quora

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Why are there only 12 pitch notes (C, C#, ..., B) in the

world?I learned that pitch is determined by frequency of the sound waves. I know that each note

has specific frequency Hz. For example, C3 is 130.8Hz and C#3 is 138.6. So what the

heck is between those two pitch notes? If there are so many pitches between these half-

step notes, how come it feels like a... (more)

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Why are there 12 notes in an octave, and why do we

ascribe the specific frequencies that we do to them?

Is there any reason that music has only 12 notes and

not more?

Music Theory: Is there any good reason the note 'C'

is not called 'A'?

Why is there no E# or B# black note? Why are there

only eight notes?

How does the pitch of a C-note vary on different

instruments?

Why are some common brass instruments pitched in

B flat not C?

Why do we see 3 primary colors (Red, Green, Blue)

but distinguish between 12 musical notes/pitches?

Which notes does a C#min7b5 chord contain?

What are the notes in a C7 chord?

What's the name of the song from spongebob that

starts with the notes E A D D C# B A E E A F# E D E?

More Related Questions

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12 Answers

This is a fascinating question and I went down a long rabbit hole researching and thinking

about it - including talking to Tim who also has a great answer here.

First of all - let's cover some basic stuff. What is frequency?

Here is the sound wave of a recording of me playing the low E string on my guitar.

There are multiple oscillations happening here and you can what's called a Fourier

transform to figure out how much of each frequency there is.

Lukas Biewald, founder, CrowdFlower

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You can see that there are multiple frequencies in this sound, but the strongest frequency

is at around 82 Hertz or 82 oscillations per second. We perceive this sound as a low E

note.

If I play the next higher E note on my guitar the dominant frequency is twice as high (164

Hz). If I play the next higher E the dominant frequency doubles again.

Here the x axis is the perceived pitch or note and the y-axis is the frequencies. Each A note

is an octave apart but the frequency is doubling each time.

The perceived pitch difference between two frequencies goes down as the frequencies go

up. Another way of saying this is the frequency difference between two notes gets

further apart as the notes get higher.

Here's a little illustration of that with the real frequencies of notes.

A scale is generally divided into even pitch increments (this is called "equal

temperament"). This means that the ratio of the frequency of a note and the frequency of


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the next note is always the same.

So why 12 intervals?

There's a second fact about the way we perceive sound which is that two sounds with a

simple frequency ratio sound good. There is a lot of fascinating research about when

and why this is true - I really enjoyed Music, A Mathematical Offering by Dave Benson that

goes really deep into how our ear works and why we perceive sound the way we do. But

let's take this as given.

For example two notes an octave apart have a frequency ratio of 2:1 and they sound very

resonant.

Besides an octave, the simplest possible ratio is 3:2 - halfway to the next octave. It's the

basis of all the most common chords and it's really nice to have this ratio in a scale. But if

we want to evenly space the pitch of our notes, we will never get exactly this nice ratio.

For example if we have 6 notes we don't even get close.

Starting at note "0", we have no note in our scale that is anywhere near halfway to the next

octave.

But if we use twelve notes we happen to get really close.

Note number 7 happens to be almost exactly halfway between our root note zero and the

next octave higher.

This turns out to really just be a happy coincidence. For fun I graphed all the possible


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scales between one and 24 notes.

It turns out 12 notes happens to have a note that is way closer to the halfway point than

any other number of notes. When we get to 24 notes the same note shows up.

Another way of looking at this is just plotting how close each scale gets to the halfway

note. This "halfway note" is extremely confusingly often called a "fifth" in music.

... (more)

Upvote Downvote Comments 6+206

I'm interpreting the question this way: why the heck should there be exactly *twelve*pitches (in most Western music and on many Western instruments (e.g. piano)), when the

spectrum of frequencies is continuous?

There is a genuinely non-arbitrary reason for twelve pitches, though it takes some

explaining (and, as we'll see, a worldwide conspiracy spanning hundreds of years(!) and

the collaboration of none other than J.S. Bach!).

Starting point: human perception of harmony between two tones is surprisingly

arithmetic, meaning that the closer two tones come to having a simple ratio of frequencies,

the more "harmonious" (or consonant) the two tones sound.

So let's build a scale by starting with one tone and adding more and more tones that are

"harmonious" with the ones already in the scale.

The simplest first addition is the octave - for example. play middle-C on the piano along

with the C one octave above that. In this case the higher note has a frequency exactly twice

the lower note. Two tones that are separated by an octave sound so harmonious that many

people would describe them as "the same note" even though one is higher than the other.

If octaves have a 2:1 ratio of frequency, the next simplest ratio to try is 3:2 (a perfect fifth),

and the next one (greater than one) after that is 4:3 (a perfect fourth). If we start with

middle C on the piano, then the perfect fifth corresponds (roughly) to G above middle C

and the fourth corresponds to F above middle C.

Note that fourths and fifths are kind of inverses of each other: take the 4:3 ratio of the

fourth, divide the frequency by 2, and you get 2:3. Multiply that by 3:2 and we are back to

our starting point. In other words: go up by a fourth, then go down by an octave, then go

up by a fifth and you are back to the start. (This is already most of the way towardexplaining why I-IV-V chords are so pervasive in popular music.) Also notice the frequency

difference between the fourth and fifth in terms of the start note: 3/2 - 4/3 = (9-8)/6 = 1/6,

which is twice 1/12. Hmm.

So imagine that we have a scale comprised only of start tone, fourth, fifth and octave. How

should we expand the scale to include more notes?

Tim Converse, Know-it-all wannabe

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Let's suppose that we work outwards from the three notes we already have in our scale,

and successively add notes that are "harmonious" with the notes we already have (i.e. have

a perfect-fourth or perfect-fifth relationship with them), and taking octave relationships as

equivalent.

Now, there is no point in taking a note that we reached by a fifth from a previous note in

the set and then adding the fourth of that second note, because we will have just added the

octave of that very first note. Instead, let's see how far we can get by adding fifths and

dividing by 2 when we feel like it (since that just drops us down an octave).

It turns out that if we take a note and raise its frequency by a ratio of 3:2 twelve times in arow, then this happens:

(3/2)^12 =

129.746 ~=

1.013 x 2^7

In other words, it takes 12 steps around what is called the "Circle of Fifths" until you reach

an approximate power of two of the original tone (meaning some number of octaves above

it).

If you're looking for the simplest explanation for why piano scales have the magic number

of 12 steps between octaves, this would be it.

On the piano, the Circle of Fifths looks like this: C, G, D, A, E, B, F#, C#, G#, D#, A#, F, C(treating all black keys as sharps). And there we have all the twelve tones on the piano.

Now all this doesn't *quite* add up, because the power of two is only approximate. So to

make it all add up let's, um, slightly detune the piano so that perfect fifths are *just* a little

bit less than a 3:2 ratio, so that when we go up by fifths twelve times, instead of

1.013 x 2^7, we get

1.000 x 2^7

so that after 12 steps we end up right back at our starting tone (dropping down octaves

when appropriate).

To make this all work, let's not only detune the piano and other instruments (to pretendthat 1.013 == 1.000), let's have a *worldwide* *conspiracy* to detune all instruments

*everywhere*. And let's keep it going over hundreds of years, and enlist none other than

Johann Sebastian Bach to make musical arguments on our behalf (see: The Well-

Tempered Clavier )..... I am not kidding.

To recap, the simplest explanation why there are twelve tones you hear all the time is: 3/2

to the 12th power is approximately 2 to the 7th power.

=====

Update: my answer above applies to equal-tempering (where every step up on the piano

corresponds to the same multiple of frequency of the step below it). This is not quite what

Bach was pushing for (he wanted well-tempering), and my answer makes it sound like

'well' and 'equal' are the same thing.

See Well v.s. equal temperament

Updated Mar 2, 2015 • View Upvotes

Upvote Downvote Comments 345

Various methods of dividing the octave

Malcolm Zachariah, Flutist since 2000, oboist for a few years, singer since I was

a child (at le...

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Actually, there are semitones in Western tonal music, which are between each note (e.g.

one tone halfway between C and C#).

Semitone

Then there are microtones of even smaller intervals. Many non-Western Classical music

genres use them.

Microtonal music

In fact, there are 72 tones in Byzantine music theory, dividing the octave into twelfth-

tones.

Turkish microtonal guitar

Written Mar 2, 2015 • View Upvotes

Upvote Downvote Comment 14

North Indian (Hindustani) Classical music has evolved over the years to include 12 notes

per "Saptak" (octave). This includes soft notes of rishabh, gandhar, dhaivat, and nishad;plus hard madhyam, along with the seven "pure" notes.

But south of the Vindhyas, music had already evolved beyond 12 notes per octave, and

indeed 22 shrutis (notes) per octave is the norm there. Even in Hindustani music, in some

of the raagas, there is a rule about taking the higher one of the madhyam. Or a lower one of

the Komal Rushabh, that corresponds to the shrutis.

So, 22 tones per octave seems to me the thinnest granularization so far. Not 12.

Written Dec 15, 2012 • View Upvotes

Milind Bhandarkar, parallel programmer, hadoop evangelist, distributed systems

student

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You are right in that there are infinite pitches. SImply whistle and steadily increase the

pitch, or listen to a trombone glissando and you hear all of them. However, music becomes

much simpler to write and notate if we apply some limits. Throughout the renaissance,

people developed different tuning systems for this purpose before one, known as Equal

Temperament, was almost universally adopted in the Western World. In Equal

Temperament, 12 pitches are established from the octave, each with an equal (perceived)

distance. Thus the amount of these half-steps defines the interval (two is M2, three is m3,

four is M3, and so on). Just look at a piano and you will see this. There exists a note

between the half-step known as the quarter tone. It has its own notation, and is used

sparingly in Western music. The only example I can think of is in blues, where a vocal

effect bends the pitch of the third degree of the scale down a quarter-tone. Eastern musical

scales, however, are loaded with strategically placed quarter tones, giving them a

characteristic flavor. In general, the difference between semitone and quarter-tone is not

firmly established in the ear so they are infrequent outside of avant-garde and eastern

music.


Ben Hendel

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As others have suggested, the premise of your question is incorrect. In Arabic, Turkish,

Persian, and Indian music, there are well-developed systems of more than 12 notes in an

octave.

If you want to know why there are 12 notes to the octave in Western music, the Tim

Converse's answer above is a good one as to how that became the consensus on a practical

limit.

Two caveats:

even in Western music, there are many more pitches used, it is only the equal-tempered

instruments that are restricted to 12 pitch classes.

There are many more than 12 pitch names (A#, Bb, D#, Eb, F#, Gb, Fx, Abb, etc), and for

good reasons. This hints at the fact that the 12 pitches are a convention that is arrived at

for practical reasons (it is impractical to have 40 keys or frets per octave), not for any

inherent musical reason. On an instrument with more or less continuously variable pitch,

one is not restricted to 12 pitches and may well play a Gb as a distinct pitch from an F#.

Written May 13, 2014 • View Upvotes

Kent Reed, Musician

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Upvote Downvote Comment3

The simplest answer is that there aren't! There is a lot of microtonal music in the world,

and it's very sad to me that people think music is limited to 12ET. Of course there are very

good reasons behind 12ET and it's a brilliant system, but it is not at all the only one in the

world.

24ET and 53ET are common in maqam music, and they both yield some absolutely

wonderful sounds. There's western microtonal music that can use 72ET and more. There is

non-equal-tempered music, of course, especially historically. There are instruments that

aren't equal-tempered. There is a lot outside of modern western music in this regard.

Written Mar 6, 2015

Nikhil Singh, Musician and Producer

802 Views

Upvote Downvote Comment

Although Tim Converse's answer holds an interesting story on how equal-tempered tuning

came into being, I feel that it doesn't necessarily answer the question why we identify all

pitches we hear on this 12-tone scale.

I'd say that this is purely for cultural reasons. In the Western world we are used to dividing

an octave in 12 semi-tones, but in other parts of the world, such as Iran and the Arab

world, they make a lot of use of quarter tones [1] in their music, and musicians from those

parts are also trained to hear the difference between quarter-tones.

Interestingly, such music cannot be reproduced on all instruments that are prevalent in

Western music, because some instruments are closely tied to the 12 semi-tone system

(such as a piano). Playing quarter tones requires the instrument to be able to produce

pitches on a continuous scale.

One more interesting tidbit about equal-tempered tuning: one reason it was invented, is

that by adhering to pure mathematical ratios, it becomes impossible to transpose a piece of

music to any key. This makes it hard for instance, for a singer to sing a song that - in its

original key - is too high or low to reach, because you can't just transpose it. This was

especially noticeable on organs, because they are built with these exact mathematical ratios

in mind (pipes' lengths are related to each other). When you transpose a piece of music in

this old "mathematical" tuning, it sounds increasingly "out of tune", in certain keys. Equal-

temperament solves this problem.

[1] Quarter tone

Written Mar 6, 2015

Daniel Debie, Data Engineer @ The New Motion721 Views


There aren't. However, only 12 notes are used in the modern Western tuning system, 12-

tone Equal Temperament, or 12TET. 12TET was probably first developed because of the

Benjamin Keilty , Music lover

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piano. Using more keys, while making the piano able to hit better tuned intervals, would

make the piano a daunting instrument to play, and a full piano would either have

infinitesimally small keys, multiple layers, or would be in excess of 15 feet wide. All of these

would not be feasible to play. As such, most other instruments (and virtually all with

valves, keys, or frets) were made to play in 12TET. Other instruments, though, such as the

trombone and orchestra string instruments, can play other temperaments with relative

ease, even though for most instruments, due to their design, 12TET is the only easy (or

sometimes the only possible) system to use. However, other tuning temperaments are

used, such as 17TET, where notes are divided into 3 instead of 2 and C# and Db are not

enharmonic, and 22TET, where notes are divided into four and quarter steps are used.

34TET, 55TET, 5TET, and many more are used. There are many different tuning

temperaments that are not equal temperament, such as Pythagorean tuning, in which justly tune fifths are also used. If you want to know more, Wikipedia, for once, has fairly

reliable information because this knowledge is common enough that many know about it,

but not cared about enough to be vandalized.

So, in conclusion, music is not limited to 12 tones, but they and their octaves are the only

ones you will usually hear, due to instrument design and the simplicity and widespread

usage of 12TET.

Written Mar 15, 2015


It is true that the western system has only 12 semitones in notation and they are equally

tempered (separated with an equal pitch). But if you listen closely to the violin or vocals

you’d realize that frequencies in between the semitones are present too. They were pianos

that were in production earlier with special pedals that could vary the pitch of the notes so

that you could obtain microtones (tones in between 2 semitones). But this made music

highly complex, and most ears were not accustomed to this special addition to the piano.

If you look at music around the world, you do find music in which an octave is divided into

more or less than 12 notes. In the Chinese system you have the 5, 7 and 12 note octaves

which of equal temperament. The Indian classical music system uses a moveable seven-

note scale with intervals smaller or greater than a semitone.

The tuning of musical instruments to A440, which is tuning the A note to a frequency of

440Hz came into practice only after the standardization of pitch. Earlier in time, the A

note was tuned to a wide frequency around 440Hz and a lot of instruments were tuned to

435 Hz, which was then recommended by the Austrian government.

If you have the opportunity to ever come across pianos or other instruments that are quite

old, (150 years or more) you’d realize that the A note is tuned to a slightly different pitch.

These instruments were not usually upgraded to the A440 convention as the frame of the

instrument would generally not be able to handle the additional stress.


Naveen Vijayan

1.4k Views


a great question!

there is a fascinating section on the musical scale in P. D. Ouspensky's book In Search of

the Miraculous. excerpt 1:

The seven tone scale is the formula of a cosmic law which was worked out by ancient

schools and applied to music.

it mentions ratios that are uneven (not equal temperament) thus:

1, 9/8, 5/4, 4/3, 3/2, 5/3, 15/8, 2/1, from C(n) to C(n+1).

the differences are: 1/8, 1/8, 1/12, 1/6, 1/6, 5/24, 1/8

moreover the book also mentions that each octave contains inner octaves, suggesting thatthere are 7 notes between all of these seven notes. and so on for those inner octaves ad

infinitum.

links:

Inner Octaves and Eastern Music

Fourth Way enneagram

Heerdyes Mahapatro, programmer

536 Views

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9/9


https://www quora com/Why are there only 12 pitch notes C C B in the world 9/9

music is indeed sublime!

Written Mar 8, 2015


There are other pitches of other frequencies in the World. "Eastern" music on "Esatern

instruments have notes and scales characteristic to their "songs". The pitches we are

accustomed to, evolved with a Weatern, if not European cultures and instruments wereconstructed for our "do, re, mi..." Pattern. Some 20th Century compositions forces a

Western instruments to make sounds inbetween our notes. Electric guitar rock artist slide

around in these "spaces" (frequencies). I have two sons; each have Master's of Music

Degrees; one from Boston Conservatory, the other from Peabody Inst JounsHopkins.

Teachers and composers.

Written Nov 9

Charles Rogers

1.1k Views


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