Question

Music Math: Which note is equivalent in duration to all of the following rhythmic values together?
quarter note plus sixteenth note plus sixteenth note plus quarter note plus eighth note plus quarter note.

Answer 1

To find the equivalent duration of the given rhythmic values, we need to convert each note into a common unit, typically using the quarter note as a reference.

1. **Quarter note** = 1 quarter note
2. **Sixteenth note** = 1/4 quarter note (because 4 sixteenth notes make up a quarter note)
3. **Sixteenth note** = 1/4 quarter note
4. **Quarter note** = 1 quarter note
5. **Eighth note** = 1/2 quarter note (because 2 eighth notes make up a quarter note)
6. **Quarter note** = 1 quarter note

Now we can sum these values:

\[
1 \, (\text{quarter note}) + \frac{1}{4} \, (\text{first sixteenth note}) + \frac{1}{4} \, (\text{second sixteenth note}) + 1 \, (\text{quarter note}) + \frac{1}{2} \, (\text{eighth note}) + 1 \, (\text{quarter note})
\]

Calculating this:

- Combining the quarter notes: \(1 + 1 + 1 = 3\) quarter notes
- Combining the sixteenth notes: \(\frac{1}{4} + \frac{1}{4} = \frac{2}{4} = \frac{1}{2} \, \text{(which is also equivalent to an eighth note)}\)
- Adding the eighth note: \(\frac{1}{2} + \frac{1}{2} = 1 \, \text{(which is also equivalent to a quarter note)}\)

Now we will sum all the quarter notes together:

\[
3 + 1 = 4 \, \text{quarter notes}
\]

Therefore, the total equivalent duration of the rhythmic values combined is **4 quarter notes**.