Notes that are one octave apart are so closely related to each other that musicians give them the same name. A note that is an octave higher or lower than a note named "C natural" will also be named "C natural". A note that is one or more octaves higher or lower than an "F sharp" will also be an "F sharp".
The notes in different octaves are so closely related that when musicians talk about a note, a "G" for example, it often doesn't matter which G they are talking about. We can talk about the "F sharp" in a G major scale without mentioning which octave the scale or the F sharp are in, because the scale is the same in every octave.
Because of this, many discussions of music theory don't bother naming octaves. Informally, musicians often speak of "the B on the staff" or the "A above the staff", if it's clear which staff they're talking about. But there are also two formal systems for naming the notes in a particular octave.
Many musicians use Helmholtz notation. Others prefer scientific pitch notation , which simply labels the octaves with numbers, starting with C1 for the lowest C on a full-sized keyboard. Figure 3 shows the names of the octaves most commonly used in music. The octave below contra can be labelled CCC or Co; higher octaves can be labelled with higher numbers or more lines.
Octaves are named from one C to the next higher C. For example, all the notes between "great C" and "small C" are "great". One-line c is also often called "middle C". No other notes are called "middle", only the C. Exercise 4. Go to Solution. The word "octave" comes from a Latin root meaning "eight". It seems an odd name for a frequency that is two times, not eight times, higher.
The octave was named by musicians who were more interested in how octaves are divided into scales, than in how their frequencies are related. Octaves aren't the only notes that sound good together. The people in different musical traditions have different ideas about what notes they think sound best together. In the Western musical tradition - which includes most familiar music from Europe and the Americas - the octave is divided up into twelve equally spaced notes.
If you play all twelve of these notes within one octave you are playing a chromatic scale. Other musical traditions - traditional Chinese music for example - have divided the octave differently and so they use different scales. You may be thinking "OK, that's twelve notes; that still has nothing to do with the number eight", but out of those twelve notes, only seven are used in any particular major or minor scale.
Add the first note of the next octave, so that you have that a "complete"-sounding scale "do-re-mi-fa-so-la-ti" and then "do" again , and you have the eight notes of the octave. These are the diatonic scales, and they are the basis of most Western music. Now take a look at the piano keyboard. The eighth note would, of course, be the next A, beginning the next octave. Throwing in reciprocals for each of these intervals yields all the intervals that made up western music until the rise of chromaticism.
The tritone such as C to F is also omitted from this list, an interval that did not affect the evolution of the western scale as it was not used in western music until twelve note chromaticism had become firmly established. The idea behind twelve is to build up a collection of notes using just one ratio. The advantage to doing so is that it allows a uniformity that makes modulating between keys possible. Without a compromise most keys would be unusable as most of the basic intervals would not be captured in the different keys see the table at the end of this essay.
Unfortunately, no one ratio will do the trick exactly. However the most important constraint- namely that we get a repeating pattern going up in octaves, is almost satisfied by this scheme. The chromatic scale reflects this fact. See the essay I wrote on this. One can also use a major 3rd i. This is discussed towards the end of this essay. Also scores. And playing in public. Nobody comes anyway.
If we start it on C and divide it into 3 which is a nice brain-friendly proportion we will get a lovely 3 note scale:. Both of these scales just seem to go on forever and ever, I can't tell what's what. I know! Why don't you mix and match the proportions so they are slightly more uneven? Then I can figure out the bass note. All right! But its 70, years ago and there's loads of poor bastards buggerin' round the the scenery getting crunched and munched by sabre tooth tigers and suchlike.
Lotta funerals. Mucho sadness. Like Trump nowadays, you should know! Need variety. It's awesome. Now there's chieftains, mud huts, jewelry".
I know, like this: move the seventh up, the sixth down, the fourth up, and the second down! For western music the greeks were the first to figure out the math that occurs naturally in the harmonics overtones generated by horns and other wind instruments. The Greeks applied the same mathematical ratios golden ratio to strings. Pythagoras invented the pythagorean tuning of perfect fifths and Octaves to match naturally occurring harmonic overtones.
Later the greeks invented 7 modal scales based on pythagorean tuning. Seven Modes with eight notes in a scale. We still use Ionian Major and Aeolian Minor.
The flaw with natural harmonics is that the octaves between each mode were slightly off from each other. Aristoxenus in the 4th century BC invented the 12 tones between octaves in an attempt to use the same ratio between each note. Later Keys were invented to use these 12 tones as a home base for each scale.
The problem was that by nature these keys are slightly off from each other. To solve this J. Bach in the early 's promoted the use of the Tempered Scale. He equalized the natural occurring gap between each of the twelve semitones.
Brass instruments in the baroque period had a bag of different sized crooks to adjust for each key that they performed in. String instruments also had to retune for each key change. By using the tempered scale a performer could switch between all of the different keys without re-tuning. No other division by a fair number of notes, 10 to 19, can even slightly approach this. This is mathematically remarquable and the reason why we use 12 notes and not 13, 11, or etc.
Great answer by john Baldwin above. Jut wanted to add that these minimum divisions are also the most practical to use. And then if we start dividing it further it slowly starts getting very fine sub harmonies for the human hearing to discern.
And these 12 divisions then also repeat in the higher and lower octaves and so on. The easiest to identify is 4 divisions which is a divisor of 12, which makes up a pentatonic scale with the higher note, and is why is easily enjoyable. Based on your wording of the question I would say that it is by design. It is not a coincidence that 12 half steps fit into an octave rather than 11 or Though the details may change if one assumed just tuning I will explain assuming equal tempered tuning.
First you should know that there is a continuum of frequencies and therefore pitches between any two notes. We have converged on a particular choice of pitch combinations for the western diatonic scale through centuries of experimentation. The notes in a scale reflect what is pleasing to the ear s for a particular culture.
Over time Westerners standardized the half step by splitting the octave into 12 steps using the relation. IMO a few posts here are putting the cart before the horse.
You cannot demonstrate that the octave has only 12 semitones using the above definition of a semitone. Rather you ask what does the ratio have to be in order to ensure there are 12 in an octave. To that end there are all sorts of alternate chromaticisms that attempt to place N equal steps in an octave. These result in the tuning equation,. There is a 24 TET containing 24 equal quarter steps in an octave. And you absolutely could build a scale with.
Now the issue of how we got there is a longer story. Before 12TET tuning the Just major scale with 8 notes including octave have more than 5 accidentals. You can google this and find Wiki articles on the topic but there were, I believe, just scales with as many as 17 independent notes in the octave. Though all consecutive notes are probably slightly different ratio. Sign up to join this community. The best answers are voted up and rise to the top.
Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Why are there twelve notes in an octave? Ask Question. Asked 10 years, 6 months ago. Active 1 year ago. Viewed 67k times. Improve this question. Agares Agares 1, 2 2 gold badges 10 10 silver badges 8 8 bronze badges. Do you mean "given the interval we call the 'half step,' why do 12 of them make an octave" or "given the interval we call the 'octave,' why do we split it into 12 half steps"?
Presumably the latter, but I could be wrong. In addition to some good answers here - this book provides a fairly good explanation amazon. Another in-depth answer can be found here. A nice demonstration of other tunings is here. Add a comment.
Active Oldest Votes. This requires an excursion into musical history.
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