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Pitches and Tuning systems

Posted by Vicster 
Pitches and Tuning systems
March 20, 2017 09:46PM
Hello everyone! Recently got an interesting assignment to accomplish.
Sooo...here is:
Usually there are 4 to 12 pitches around the world.
Why tuning system tend to range between 4 and 12 pitches? Whats the reason?
Thanks in advance
Re: Pitches and Tuning systems
March 27, 2017 09:16PM
I can't help you with 4 but the 12 relates to the strength of the perfect fifth. If you start with a frequency and double it, you get an octave, which as you know kind "sounds the same but higher", right? If you triple it, though, you get a totally new note. To get that note back into the same octave as the first note, you divide this new frequency in half, and bang! you've create the magical interval we call the perfect fifth. This interval is extremely consonant, after the octave, the most natural sounding interval there is to your ear. The basic reason for this is that when two notes are played a fifth apart, for every three cycles of the upper note, you get two cycles of the lower note. This results in a very fast beat frequency, where the pitches go in and out of phase really fast, and that just drives your brain crazy with good energy (okay so maybe nobody really knows exactly why, but it sounds really good!)

So once you have another note, you can start there and find another note that is fifth away from that one (multiply frequency by 3 and divide by 2. You can do this 12 times, and you'll get a totally new note every time, and these twelve notes, in this order we call the cycle of fifths. In ascending pitch order, it's the chromatic scale. Why do we stop at twelve? Well the thirteen time you try it, you get a pitch that is almost exactly an octave up from the note you started with. It's not perfectly the same, but it's so close that it doesn't make any sense (and wouldn't sound very good) to call it a new note. That tiny little difference is called the Pythagorean comma, and dealing with it the reason there are a handful of different tuning systems in existence. I could go ON and ON about that but I won't... unless you want more details.
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