Question

MAKE A DECISION Which note would you expect to have a higher frequency? Explain your reasoning. (a) Musical note \(\mathrm{E}\) one octave above middle \(\mathrm{C}\) (b) Musical note \(\mathrm{D}\) one octave above middle \(\mathrm{C}\)

Short answer

The musical note E one octave above middle C will have a higher frequency than the musical note D one octave above middle C.

Step-by-step solution

Understand Musical Alphabet and their Frequencies

In Western music, the musical alphabet goes from A to G. Afterwards, it begins again at A. Because the note E comes after the note D in the musical alphabet, it will have a higher frequency than D. Musical notes that are to the right and thus 'higher' on a piano keyboard for instance, will have higher frequencies.

Compare the two notes

In our specific case, we are comparing E and D that are an octave above middle C. Using the principle from Step 1 - knowing that E comes after D in the musical alphabet - E will have a higher frequency than D.

Key concepts

The Musical Alphabet in Western Music

Understanding the musical alphabet is the foundation upon which we explore the world of music theory and sound. In Western music, the musical alphabet comprises seven unique notes: A, B, C, D, E, F, and G. The sequence is cyclical, which means upon reaching G, it restarts at A again.

In terms of their place on a standard piano keyboard, these seven notes are represented as white keys. Each note stands for a particular pitch, and when played in sequence from A to G, it creates an ascending scale, with each successive note having a higher pitch and frequency than the one before.

The relationship between the notes is consistent, defining the harmony and melody of the music we hear. Variations such as sharps and flats add complexity, allowing for the full chromatic scale that gives composers a rich palette of tones to work with.

Octaves in Music

An 'octave' in music is a unit of pitch interval that separates two notes, each with a frequency double, or half, of the other. For example, if one note has a frequency of 440 Hz (hertz), the note an octave above it would have a frequency of 880 Hz, and the note an octave below would be at 220 Hz.

An octave encompasses the complete cycle of the musical alphabet. Due to the logarithmic nature of human hearing and the structure of musical scales, an octave above any note sounds distinct yet harmoniously resonant with the original note.

Significance of Middle C

The note 'middle C' is often used as a reference point in music because of its central location on the piano keyboard. When we talk about notes an 'octave above' middle C, we're referring to the same note in the next higher sequence of the musical alphabet, pitched eight notes above middle C on the grand staff. Notes within the same octave are used to create chords and melodies, weaving the fabric of a musical piece.

Frequency Comparison in Music

When comparing frequencies in music, especially between notes of the musical alphabet, it's critical to consider both the sequential order of notes and their octaves. Frequencies in music increase as you move up the musical scale. This means that if we compare two notes, the one that comes later in the musical alphabet and/or is in a higher octave generally has a higher frequency.

For example, the note D that lies an octave above middle C will undoubtedly have a higher frequency than D in the middle octave. However, when comparing a D to an E in the same octave, even though they’re next to each other, E will have a higher frequency because it comes after D in the musical alphabet sequence.

Understanding this principle of frequency comparison is not just theoretical; it's the basis for tuning instruments and the creation of harmonious music. Instruments are tuned to specific frequencies to ensure that when different notes are played together, they are harmonically pleasing to the ear. This harmony is rooted in the mathematic and acoustical relationships between the frequencies of notes.