gdritter repos when-computer / 927080c
Modified conclusion of temperament post Getty Ritter 8 years ago
1 changed file(s) with 2 addition(s) and 2 deletion(s). Collapse all Expand all
+2
-2
drafts/temperament-and-tuning.telml less more
231231
232232 \table{
233233 \tr{ \th{ frequency } \th{ cents } \th { change in cents } }
234 \tr{ \td{ 400.00 Hz } \td{ 0.00 cents } \td{ } }
234 \tr{ \td{ 400.00 Hz } \td{ 0.00 cents } \td{ +100 cents } }
235235 \tr{ \td{ 423.78 Hz } \td{ 100.00 cents } \td{ +100 cents } }
236236 \tr{ \td{ 448.98 Hz } \td{ 200.00 cents } \td{ +100 cents } }
237237 \tr{ \td{ 475.68 Hz } \td{ 300.00 cents } \td{ +100 cents } }
251251
252252 It's a pretty convenient system, and it's in pretty wide use today: at the very least, it's how a lot of people think about tuning. In practice, a number of instruments can't use equal temperament \em{exactly} because of physical limitations on the instrument itself, and singers tend to use something closer to the Pythagorean tuning (because it's easier to make your voice go up a perfect fifth than an ever-so-slightly-imperfect fifth) but we tend to treat equal temperament as the ideal tuning for most modern instruments.
253253
254 I have more things to say, but this post is already a bit long, so I'm going to split the rest of this material into a separate post. Next time: \em{microtonal music}!
254 That's the high-level overview of where twelve came from: it's has its roots in Pythagorean tuning, where it made sense to only include twelve tones, and our current system of equal temperament came from a reasonable compromise that ironed out some of the rough edges in Pythagorean tuning. Of course, there are still more tunings and temperaments to discuss—including some very interesting systems that result in more than twelve tones!—but this post is already a bit long, so I'm going to split the rest of this material into a separate post. Next time: \em{microtonal music}!