d. The frequency of 25 ​half-steps above middle C is 
  
enter your response here cps.
​(Round to the nearest integer as​ needed.) 

To calculate the frequency of a note that is 25 half-steps above middle C, we use the formula for the frequency of a note based on half-steps:

\[
f = f_0 \times 2^{n/12}
\]

Where:
- \(f_0\) is the frequency of middle C (usually 261.63 Hz),
- \(n\) is the number of half-steps above middle C,
- \(f\) is the frequency of the new note.

Here, \(n = 25\) and \(f_0 = 261.63\). Plugging the values into the formula:

\[
f = 261.63 \times 2^{25/12}
\]

Let's calculate this.The frequency of a note 25 half-steps above middle C is approximately **1109 Hz**.

Do you have any questions or would you like further details?

Here are 5 related questions to explore:
1. What is the frequency of a note 12 half-steps above middle C (an octave)?
2. How do half-steps relate to the musical scale?
3. What is the formula for calculating frequencies of notes below middle C?
4. How does the equal temperament system affect musical tuning?
5. What are some common frequencies in the audible range for musical notes?

**Tip:** Remember that moving by 12 half-steps doubles the frequency, as it represents one octave!

The frequency of 25 half-steps above middle C is ​​enter your response here cps. (Round to the nearest integer as needed.)

Learn how to calculate the frequency of a note 25 half-steps above middle C using the exponential growth formula. This solution involves music theory and the relationship between half-steps and frequency, ideal for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation