Measures of Music and Fractions

Date: 01/13/99 at 21:00:42
From: Prince
Subject: Transcribing measures of music

Hello Dr. Math,

Can you explain how to transcribe 8 measures of sheet music into 
fractions? I need to include staff, punctuation, time stamp, sharps, 
and flats.

Thank you, Prince

Date: 01/14/99 at 13:09:19
From: Doctor Mike
Subject: Re: Transcribing measures of music

Hello,   
   
I cannot tell for sure what kind of answers you need, but here is a 
start. 

I assume you have the sheet music already. When you look at a 
particular note in a measure, one thing you can ask is "What fraction 
of a whole measure is that note?" You do not have to consider the 
sharps and flats to answer this, but you do need to know the time 
signature.
   
Let's look at a few. The most common time is "four-four," which is 
written as 4 with another 4 under it: 4 beats to a measure with a 
quarter note (1/4 note) getting one beat. Another frequent example is 
"six-eight," which means 6 beats to a measure with an eighth note 
(1/8 note) getting one beat.  
   
Let's focus on six-eight because the numbers are different. What 
fraction of the measure is an eighth note? This is the same kind of 
situation as where you cut a pie up into 6 equal slices. One slice is 
1/6 of the whole pie, and 2 slices make 2/6 or 1/3 of the pie. If you 
take one slice away, 5/6 of the pie is left. You remember that, right? 
It's the same with the measures of six-eight music. An eighth note is 
1/6 of the measure; a quarter note is the same as 2 eighth notes, so it 
is 2/6 or 1/3 of the measure. A dotted quarter note is the same as 3 
eighth notes, so it is 3/6 or 1/2 of the measure.  
   
Let's say the six-eight time measure has a dotted quarter, followed 
by a regular quarter note and finally an eighth note. These would be 
1/2 of the measure, 1/3 of the measure, and 1/6 of the measure, 
respectively. One way to check your work is to make sure all the 
fractions add up to 1, because "all of" the measure is the fraction 
1/1:
   
   1/2  +  1/3  +  1/6  =  3/6  +  2/6  +  1/6  =  6/6  =  1    
   
That's all I'll say for now. I hope this helps. If you need more, or
if I did not answer your real question, just write back.  

- Doctor Mike, The Math Forum
  http://mathforum.org/dr.math/