Question

MAKE A DECISION Assume the pattern shown on the piano continues. Which note would you expect to have a higher frequency? (a) Musical note \(\mathrm{D}\) one octave above middle \(\mathrm{C}\) (b) Musical note \(G\) one octave above middle \(C\)

Short answer

Musical note \(G\) one octave above middle \(C\) would have a higher frequency.

Step-by-step solution

Understand the Octave Principle

When moving up by an octave in music, the frequency of a note is doubled. This applies to all musical notes, including D and G.

Analyze the Position of the Notes on the Piano Keyboard

Looking at a piano keyboard, it can be seen that the musical note G is to the right of the musical note D. Simply put, G is higher than D.

Apply the Principle to the Specific Notes

The given notes are both one octave above middle C, which means they are in the same octave. Since they are in the same octave and G is to the right of D on the keyboard, G will have a higher frequency.

Key concepts

Octave Principle

The octave principle is a fundamental concept in the study of music, particularly when it comes to understanding how musical notes relate to one another in terms of their frequencies. An octave is the interval between one musical pitch and another with half or double its frequency. Essentially, if you start at any note and move up by 12 keys on a piano keyboard (which includes both white and black keys), you reach another note that sounds remarkably similar but is higher in pitch.

For instance, if you have the note middle C (usually denoted as C4 in scientific pitch notation), and you move up to the next C (C5), you've moved up by one octave. Scientifically, you've doubled the frequency of the original middle C. This relationship holds true for any note: moving up one octave always results in a doubling of frequency, while moving down reduces the frequency by half. Therefore, understanding this principle helps in predicting the frequencies of notes in the same octave and how they compare with one another.

Musical Notes

Musical notes are the building blocks of melody and harmony in music. They are symbolic representations of sound pitches and have specific names and placements on the staff in written music. The modern music scale is based on a pattern of 12 different pitches or notes, and these pitches repeat in a pattern across different octaves. These 12 pitches include seven alphabetically named notes—A, B, C, D, E, F, G—and five additional notes that come from the sharps and flats which are signified by black keys on the piano. For instance, between notes A and B, there's an A sharp (A#) or B flat (Bb), depending on the musical context – yet they represent the same pitch.

Each pitch has a distinct frequency, and it is the combination and sequence of these notes that create music. Knowing the names and sequence of these notes is critical because it allows musicians to communicate and play music together by following the same structure.

Piano Keyboard Frequencies

The piano keyboard is an excellent visual and practical representation of the relationship between musical notes and their frequencies. Each key on a piano corresponds to a specific musical note and thus a specific frequency. Middle C, for example, generally sits near the center of the keyboard and is a reference point for pitch — often set at a frequency of 261.63 Hz.

As you move to the right on the keyboard, each subsequent key represents a note with a higher pitch and frequency, progressing through the pattern of natural notes and sharps/flats. Conversely, as you move to the left, the frequencies decrease. This linear arrangement of keys makes it relatively simple to understand how musical intervals, such as octaves, work. The frequencies of the piano keys follow a geometric sequence; thus, every time you pass 12 keys (an octave), the frequency of the notes doubles. Having a grasp of the correlation between keys on a piano and their frequencies can greatly help musicians in tuning instruments, composing music, and understanding the science of sound.