As a music theory expert, I can provide you with a detailed explanation of the frequency of G sharp. The frequency of a musical note is determined by its vibrational frequency, which is the number of cycles per second that a wave completes. This is measured in Hertz (Hz). In Western music, we use a system called equal temperament to tune our instruments. In equal temperament, the octave is divided into 12 equal parts, each called a semitone.

The reference point commonly used for tuning is the A above middle C, which is set at a standard frequency of 440 Hz. This is known as the concert pitch A4. From this reference point, we can calculate the frequency of other notes, including G sharp.

To calculate the frequency of G sharp, we need to understand its position relative to A4. G sharp is the seventh semitone above middle C in the chromatic scale. In an equal temperament system, each semitone is a fraction of the octave. Specifically, the ratio of the frequencies of two adjacent semitones is the twelfth root of 2, which is approximately 1.059463.

Starting from A4 at 440 Hz, we can calculate the frequency of G sharp by multiplying the frequency of A4 by the twelfth root of 2, six times (since G sharp is six semitones above middle C). The calculation is as follows:

\[ \text{Frequency of G sharp} = 440 \times (2^{1/12})^6 \]

Using a calculator to compute this value, we get:

\[ \text{Frequency of G sharp} \approx 440 \times 1.059463 \times 1.059463 \times 1.059463 \times 1.059463 \times 1.059463 \times 1.059463 \]
\[ \text{Frequency of G sharp} \approx 415.305 \text{ Hz} \]

It's important to note that this calculation assumes equal temperament and a standard tuning of A4 at 440 Hz. There are historical variations in tuning systems and concert pitches, which can affect the exact frequency of G sharp. For example, in the Baroque period, the concert pitch was often lower, around 415 Hz, which would result in a slightly lower frequency for G sharp.

Moreover, different instruments and different musical traditions may use slightly different tuning systems, which can also affect the frequency of notes. However, for most modern Western music, the calculation provided above will give you a very accurate frequency for G sharp.

In conclusion, the frequency of G sharp in an equal temperament system with A4 tuned to 440 Hz is approximately 415.305 Hz. This frequency is fundamental to understanding the physics of sound and the structure of Western music.

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When calculated in equal temperament with a reference of A above middle C as 440 Hz, the frequency of the G? semitone is approximately 415.305 Hz. See pitch (music) for a discussion of historical variations in frequency.read more >>