Re: Equal Temperament
- From: Stephen Calder <calder9@xxxxxxxxx>
- Date: Tue, 30 Aug 2005 09:11:52 +1000
FirstAlternate wrote:
For a start, that's not what the charts say. One of them gives C# without Db, showing the difference between C# in equal temperament and C# in" just" tuning. It may help to know that the A=440 Hz frequency is ARBITRARY. It was not accepted as being standard pitch until 1939! Before that the value of A floated around at up to 30 Hz below that value.As a matter of physics, distances between notes in a scale in any particular key depend on certain intervals being maintained. As a result, strictly speaking, C# is NOT the same as Db, but equal temperament makes them the same.
Interesting info, but I still see the frequencies for C# and Db listed as being the same on all these charts (277.18Hz for C#/Db above middle C) It seems to me that if they are are different, someone would have measured their respective frequencies. What am I not grasping here?
Having said that, consider a length of vibrating pipe, the archetype of a non-voice musical instrument. A pipe twice as long will vibrate exactly half as fast and sound an octave lower. We learned to cut holes in the pipe so that different lengths of it could be made to vibrate, giving different notes. The ratios between the notes in the scale based on a a particular note (the whole length of the pipe) are, as a matter of physics, whole-number ratios (the overtone series). A half, or 1/2 is an octave higher, a third or 1/3 is a fifth above the fundamental, 1/5 is a third (four semitones) above the fundamental, and 1/6 is a fifth above the fundamental. Played together (on different pipes of the same fundamental length) the fundamental, the 1/5 and the 1/6 form a major chord.
Imagine that we set up a pipe this way so that it plays the notes of a C scale based on any arbitrary value of C. Now play a D on this pipe and then construct another pipe whose fundamental is based on the D note of the first pipe. The D pipe will not be exactly in tune with the C pipe for notes other than D (and possibly some others whose overtones happen to match). To make them play in tune, the distances between the holes (ie effective length of the vibrating columns) must be adjusted to equal temperament.
-- Stephen Byron Bay, Australia .
- References:
- Equal Temperament
- From: Stephen Calder
- Re: Equal Temperament
- From: FirstAlternate
- Equal Temperament
- Prev by Date: Re: OT Good Thoughts Needed
- Next by Date: Re: OT Good Thoughts Needed
- Previous by thread: Re: Equal Temperament
- Next by thread: Re: Equal Temperament
- Index(es):
Relevant Pages
|
