Fractions of Musical Notes

Date: 10/14/97 at 12:10:49
From: Jeremie Rancier
Subject: Adding notes

I'm in band, and I can't figure out how many notes are in two 
sixteenth notes plus eighth notes with five quarter notes.

Your math friend,
Jeremie Rancier

Date: 10/31/97 at 11:13:57
From: Doctor Melissa
Subject: Re: Adding notes

Hi Jeremie -

You haven't said how many eighth notes there are, or whether any of 
these are tied together, or what time signature you're working with, 
and I assume you want to know how many beats there are altogether. So 
here's a shot at an answer... and you may need to find someone to look 
at the piece with you!

Musical notes are named like fractions: a whole note divided in two 
makes two half notes, just as one divided by two makes 1/2. A quarter 
note divided in two makes two eighth notes, just as 1/4 divided by 2 
makes 1/8. An eighth note divided in two makes two sixteenth notes, 
just as 1/8 divided by 2 makes 1/16. 

In terms of time, four quarter notes take the same amount of time as a 
whole note. (Just as there are four quarters in a dollar!) And, as you 
might suspect, sixteen sixteenth notes take up the same amount of 
time as a whole note. Eight sixteenth notes would take up the same 
amount of time as a half note, and it would take only four to fill the 
time a quarter note takes.

Now as for beats, check the time signature in your music: is it 4/4? 
(Are there two fours on top of each other at the beginning of your 
piece?) If so, there are four beats to a measure (that's the top 
number), and the quarter note "gets the beat"(that's the bottom number 
- if the bottom number is an 8, then an 8th note is one beat, and so 
on.)

Assuming the time signature is 4/4, 5 quarter notes would be five 
beats, an eighth note would be half a beat (multiply by however many 
you have - 2 eighth notes would be one beat, and so on. 

You might want to check our fractions FAQ, which has some Dr. Math 
answers to previous fractions questions at the bottom, at 

  http://mathforum.org/dr.math/faq/faq.fractions.html   
 
A sixteenth note would be 1/4 of a beat, so four would be one beat. 

It is sometimes helpful to draw (lightly, in pencil!) connections over 
various notes: connect two 16th notes so you know what's equal to an 
eighth, then connect the connections to see what's equal to a quarter, 
and so forth.

If any of these are tied together, that is, they have an arch over 
their stems but not actually touching them (like a slur, but with a 
number over the arch), then they are meant to be "squeezed" into that 
different number of beats! So if you have four beats in a measure, and 
a half note takes up two of them, but you have three quarter notes 
tied together for the rest of the measure, you need to "squeeze" the 
three beats into the space of two. (That's especially difficult with 
folks like Chopin, who write a lot of "runs" in odd rhythmic phrasing, 
so you have to do things like fit seven notes evenly into four 
beats...)

Is this more or less than what you wanted to know? :-) Write back if 
you need more help, and we'll see what we can do. Good luck and good 
music!

-Doctor Melissa,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/