There's been a few music theory videos going around -- some better than the others. I understand there are 13 notes or 12 "half"-steps from C to (shining?) C. So why an "octave", then? Why not a "sextave" or "hextave" with six "notes" and an accidental in between each?
Edit: ok, wow. What a broad range of answers, and thanks for the "Cannibal the Musical" reference--a classic! I didn't understand why some half-steps were considered accidentals and got little black keys on the piano and funny symbols next to them (#/b), meanwhile, some other half-steps just get regular old letters. Why is it usually a whole step between notes, but sometimes a half-step? Well, thanks to the internets, I think my curiosity has been sated.
Basically, what you all are saying, is that when early people started making instruments, they played what sounded good. Because of math, and phi, and Pythagoras, what sounded good turned out to be 8 consecutive notes with the first and last having the same ...quality? pitch? Jai ne se qua? Anyway, they made a flute (or something)with just enough holes to play those 8 notes and they labeled them ABCDEFGA. And this was music for a while. It became what we now call the A Minor scale. But, people started playing around, adding octaves and trying to start the scale at different notes, with varying success. It turns out, you can divide the range from A to A by twelve (semitones, eh?) and you end up with all the original notes, plus some new ones that need to get squeezed in somehow (they become sharps and flats). Going back to Pythagoras (et alia), the ear doesn't enjoy direct advancement up the scale--we like a little drama. So major and minor scales follow patterns--wwhWwwh for major, whwWhww for minor. So, when they made that first scale, ABCDEFGA, they were inadvertently labeling half steps and whole steps the same way: AwBhCwDWEhFwGwA (note the half-step between B/C and E/F.
Anyway, ok, thanks. I get it now. You guys were wonderful.
This is a very difficult question and it comes with a long story…
The reason is that we inherit our scale system from the ancient scholastic christians, who inherit it from the Greeks via the Romans.
Greeks had a seventh note system, very similar to ours. They used to invert the scale, that means to play the scale starting from each one of those notes, so they had 7 scales, or modes. The scale was not regular, it was not a whole tone succession, nor a half tone succession.
Greeks had a very interesting approach to this situation: Once you have irregularities, every mode is different. Each greek mode had a certain color, so they related each scale to different gods, emotions and ethic values. They named their modes after the Greek provinces (dorian, frigian, lydian, etc.) Imagine that you wanted to make a song about courage. Then you will use the mode related to Apollo. So, at the end they associated moral values, gods and aesthetic in a system were everything was related to a particular mode.
The only way that you can have different modes by inverting an scale is that your scale is irregular, otherwise every mode would be a transposition of the original scale. So irregularity is essential to modal and tonal systems.
First christians loved that idea, but they muddle the names and the modes. They tried to reconstruct the system but they lost most of the information about it, so they ended up with the same modes and the same names, but mixed. Their dorian scale was not the greek dorian scale.
As Christianity evolved, their aesthetic values evolved too. Many indo-european tribes had taken fragments of the greek system to make their own music. For christians, those types of music sounded too heathen, too pagan. So the hegemonic christian system imposed and we forgot about the modes for a while in the scholastic christian music. In that moment two scales where privileged: our major scale (jonian scholastic mode) and aeolian scale. Aeolian was still too pagan, so they made some updates to the scale, and they altered the 6th and 7th degrees, to make it more similar to the jonian mode but keeping a minor third from the root.
They kept the idea of relating the scales to emotions and values, but as long as they just had one god, everything was made to adore him. Major scale related to joy and glory; minor scale related to introspection, sadness, loneliness.
All this process lasted many centuries (from IVth to XIIth century).
They also knew that the scale can be transposed and not just inverted. With the transposition of the scale we got the different tonal centers. So we can play in C major or G major or D major. But they still had the idea that all those key centers where transpositions of a 7 note scale.
When the first chromatic keyboards where created, they kept this idea. Our modern keyboards inherit this principle: our keyboard shows a C major scale, but with the addition of black keys, so that we can transpose the scale.
This is a very general and fast explanation of somethings that happened during long periods of time. Please forgive the simplification and the omissions.
Who told you there is no E# or B#? They both exist, and in certain keys some notes are double sharped, or raised twice. Rare but it happens.
The seven notes of a standard scale or key came about due to the natural harmonics and overtones that occur, and the need to make a system which allows for different instruments to play together. You can start to see natural sound as harmonics on a guitar or other string instrument.
If you touch the string at the half way point it produces an octave, but if you touch it at the 1/3 or 2/3 it produces a fifth. For more about this look up "Guitar Harmonics” on Wikipedia.
A bugle is basically a trumpet with no valves. The notes it produces are done by aiming the air differently and increasing or decreasing pressure with the lips. The pitches are harmonics similar to the guitar. The spacings are almost identical, and our ears tend to push them into identical frameworks.
Piano tuners have to choose a method of tuning which makes the most musical sense, and there is some disagreement about what that should be. Some guitar players tune off of the harmonic at the 7th fret, but that will push the string sharp. Some pianos are tuned to a “stretch” tuning. It is not possible to tune off the fifth and resolve at exactly an octave over so many strings. Physics will not allow it.
It gets complicated, but this is called the “harmonic series”. And here we start the problem. Some instruments are in C, others in Bb and others in Eb etc. How do we get them all to play together?
When you begin to define some common ground, then it becomes necessary to allow for the possibility that any and all possible notes within the harmonic sequence may be played. So while the bugle may only be able to hit five notes, the other two pitches must be allowed, at least we think this is how we got to seven notes.
My apologies for the rambling.