Friday, January 19, 2007
Understanding the Western Tempered Scale, Tuning, Hertz and All That--Part 4 of 15

Last week we talked about the lack of standard scales in Europe in the Middle Ages and that some ingenious person figured out a solution to this problem at the end of the 16th century.

So what did they figure out? They figured out a consistent way to tune the 12-tone scale.

You know "Do-Re-Mi-Fa-So-La-Ti-Do", right? Well, that is an 8-note scale. Oops, it's not 8--we counted Do twice! Well, alright then, it has 7 unique tones. But how do we get 12 from that scale?

If you've ever played piano, you know two facts: you don't play every note when you play a scale, you skip some notes, and the distance between some notes is larger than others. When you skip a note, such as when you go from Do to Re, this is called a whole step. From Mi to Fa, where there is no skipped note, that is called a half step.

I will use the symbol ^ to represent a skipped note. Now the above scale becomes

Do ^ Re ^ Mi Fa ^ So ^ La ^ Ti Do

Count how many notes you see there, either named notes or skipped notes which are designated by a "^". You get... 13. Ah, but don't count the top Do. OK, so now that makes 12 unique notes in the western scale.

Well, so what? More next week!

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