**Introduction**

In this experiment (Frequency Relationship of Notes in Musical Harmony), we will be determining whether the musical notes in harmony have any kind of mathematical relationship between their respective frequencies.

We hypothesised that there would be no mathematical relationship of notes with frequency in an interval. In this experiment, we will examine intervals between keys.

**Aim**

To check whether the musical notes in harmony have any mathematical relation in the ratio between their frequencies.

**Theory**

1. The simultaneously occurring pitches, frequencies, and chords are termed harmony.

2. It is often referred to as the vertical aspect of music.

**Requirements**

1. Flute

2. Electronic Keyboard

3. Headphones jack

4. Oscilloscope

5. Notebook

**Procedures**

**Step 1:** Stimulate a flute by setting up an electronic keyboard configuration.

**Step 2:** Connect the oscilloscope’s output channel to the keyboard’s output signal with a headphone jack.

**Step 3:** Adjust the horizontal timezone and vertical signal gain as required on the oscilloscope.

**Step 4:** For each of the eighteen chromatic sequences, measure the signal period in a chromatic sequence.

**Step 5:** For each of the eighteen chromatic sequences (C, C#, D, D#, E, F, F#, G, G#, A, A#, B, C, C#, D, D#, E), the result of the key direct measurement of the time interval is two times the actual period. On the keyboard, the first note C is an octave above the middle C.

**Step 6:** From the raw data, calculate the frequency and the actual respective signal for each of the 30 notes.

**Step 7**: Tabulate the ratio between twelve possible intervals (minor 2nd, major 2nd, so on) frequencies within an octave for the fifteen keys (C, C#, D, D#, E, F, F#, G, G#, A, A#, B, C, D and E).

**Step 8:** Record your observations.

**Observation**

1. For the notes in an octave, we observed that the 6 intervals (minor 3rd, major 3rd, perfect 4th, perfect 5th, major 6th, and perfect Octave) out of 12 intervals were surely in harmony.

2. Four (minor 2nd, augmented 5th, minor 7th major 7th) were not in harmony.

3. Two intervals (major 2nd and minor 6th) were marginally in harmony.

4. We found that between two notes, there was always a certain specific ratio that is independent of the actual frequency (pitch tone) or actual key.

**Result**

1. The first and the second note must have a certain ratio in their frequency.

2. Our hypothesis is right in which we assumed that the note in harmony would not have a mathematical relationship in the ratio between frequency.

**Precaution**

1. Take help in using an oscilloscope

2. The Oscilloscope should be working properly.

3. Record the observation carefully.

**Conclusion**

In this experiment, we determined whether the notes in harmony have any kind of mathematical relationship in the ratio between their frequencies.

**Viva Questions with Answers**

**Q.1 What was the aim of your experiment?**

ANS. We aimed to determine whether the notes in harmony have a mathematical relationship in the ratio between their frequency.

**Q.2 What was your hypothesis?**

ANS. We hypothesized that the notes in harmony are independent of the frequency.

**Q.3 Is your hypothesis correct?**

ANS. Yes, we find that the notes in harmony do not have a mathematical relationship in the ratio between their frequency.

An Indian nuclear physicist, founding director, and professor of physics at the Tata Institute of Fundamental Research.

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