why was the musical scale divided into 8 or 12 equal parts?

Answer 1

Actually, it is based on what is known as the harmonic series.

Modern music doesn't follow it exactly because one (or more?) of the original notes was (were?) adjusted to sound more pleasing to the human ear.

It goes like this:

Start with a pitch (let's assume C for this example). It is vibrating at its exact frequency, no matter what source (trumpet, guitar, even wind blowing across a pipe... C is C).

Now divide that frequency in half. Repeat this process until you come back to C one octave higher.

That is the harmonic series, and that is the structure that gave us western music.

Sometime ago, it was decided to adjust at least one pitch for the sake of audience approval, and what we were left with survives today.

One other thing... music from other cultures does not always follow this. The most prominent example is music from India, where they distinctly recognize many more notes that we have no way to refer to, except by the blanket designation of "quarter-tones" which means any deviation in pitch of less than one half-step (C to C# is one half step).

Hope this helps.

Answer 2

The 12 notes of the scale in western music is based in nature. A vibrating string or column of air of a certain legnth will produce a tone, but it also produces harmonics or overtones. The vibrations produce interference at the octave above, then the fifth above, then another octave, etc. These are audible especially if you can stop a string at the mid-point when you pluck it (the first octave).

Well if you take an A, then the next octave will be an A above. The fifth will be an E above that. But then take that E. What happens when a column or string has E as the fundamental? It produces *ITS* overtones. A fifth above E is B. Then a fifth above B is F# and so on.

Well, actually it breaks down because as soon as you come back around to A, it's not really A anymore. It's a little lower in pitch from the original. This is called the Pythegorian Comma. Since the overtones get flatter and flatter, the true circle of fifths in nature are actually a spiral.

Temperament is a way to overcome the Pythagorian Comma. It makes adjustements to the tones so that the intervals between the notes are equal and that they come back around to a full circle.

A - E - B - F#/Gb - C#/Db - G#/Ab - D#/Eb - A#/Bb - E#/F - C - G - D and A. That makes 12 different notes (instead of infinity, like the Pythagorian Comma).

However 12 is NOT the only division of the octave that exists. Far from it. There are many different numbers of divisions of the octave. 12 is just the most common in the West and it's pretty much taken for granted.

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Answer 3

Well, first of all, it is the *western* musical scales that are divided in the way you describe. Other cultures have different scales. In fact, even in the west, the pentatonic (aka the "blues") scales aren't divided into 8 or 12 equal parts.

The traditional western scales are based on the mathematics of ancient Greece. They looked at how the pitch of a vibrating string changes with length. Then, they picked fractions that would divide "evenly" (i.e. without a remainder). The resulting pitches became formalized by usage into the musical scales that we recognize (in the west) today.

Answer 4

Because someone (J.S. Bach?, Newton? Barry Manilow?) figured out that there should be an equal SOUND between notes, and so somehow figured that each note should be a factor of 1.0592 higher or lower than its surrounding notes. That would be a number called the twelfth root of two, so I think Newton had something to do with it after that apple fell on his head.

Now, then, existing music before this switch was important to keep, but they couldn't match it exactly (sort of like how we can't play Atari games on the PC and still have them be exactly the same). So they kind of smushed in as much as they could and figured out that major scales should have each note '2 notes' apart from each other, except at the change from the 3rd note to the 4th note and the 7th note to the 8th note, where there is only one note's difference.

Once all that happened, it became easier to make instruments that were able to hit the various notes. Some of the already existing musical instruments had to be modified or be played in a slightly differen fashion (violin is fretless, so that was okay). But anyway, you'd think Bill Gates was alive back then, trying to standardize the music scales so he could sell thousands of instruments or something.

Answer 5

n music, a scale is a set of musical notes that provides material for part or all of a musical work. Scales are typically ordered in pitch, with their ordering providing a measure of musical distance. Scales differ from modes in that scales do not have a primary or "tonic" pitch. Thus a single scale can have many different modes, depending on which of its notes is chosen as primary.

The distance between two successive notes in a scale is called a "scale step." Composers often transform musical patterns by moving every note in the pattern by a constant number of scale steps: thus, in the C major scale, the pattern C-D-E might be shifted up a single scale step to become D-E-F. Since the steps of a scale can have various sizes, this process introduces subtle melodic and harmonic variation into the music. This variation is what gives scalar music much of its complexity.

Answer 6

no longer many human beings are attentive to this, yet once you create equivalent tempered notes spanning an octave, testing 5 steps, 6 steps, and so on. as a lot as twelve steps and previous, and then attempt making uncomplicated chords with them, plainly 12 equivalent tempered steps enables the richest type of harmonious chords, more desirable than the different. the subsequent richest variety is permitted by using a 5 step equivalent tempered octave, which occurs to be the jap scale. both structures advanced independently over centuries of experimentation, and initially the 12 note equipment became no longer equivalent tempered, generating some really harmonious chords at the same time as leaving othes no longer so harmonious. the excellent income of the equivalent tempered scale is that the harmonic high quality of chords are consistent no remember what particular scale is getting used, C, C sharp, D flat, D, and so on.

Answer 7

The math of it seems quite natural. Our remote ancestors recognized an octave for a long time without anybody knowing that it represented an exact doubling of frequency. And modern explanation of modes is ingrained in our arithmetic minds but our ancestors just divvied things up in ways that seemed to work. Who knows, maybe in the primitive brain the A note began not as multiples of 55 Hz but as multiples of 54, 3x3x3x2 with octaves x2x2x2, etc., and is even tied to the length of the day! We are, at some basic level, mathematic creatures.

Answer 8

There 8 equal parts in a scale... b c d e f g a and another b would bring you to the next octive. Every eighth note from where you started is in a new octive, so that is why it's in 8

Answer 9

The idea of the tempered fifth might be interesting to you.

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

http://www.jimloy.com/physics/scale.htm

Answer 10

Two very long, but interesting dissertations:

I doubt that I can improve on these explanations.