So what exactly are the pitches of the harmonic series and how do we describe them?

We’ve already developed some tools with which we can begin to go about doing so. We know that a sound is a series of pressure waves, caused by a vibration, that oscillate with a certain frequency in hertz. When someone hears two or more pitches simultaneously, or in rapid succession, the perceived character of that sound is based on a ‘snap’ assessment of the difference between the two frequencies. In other words, we perceive a discrepancy between two frequencies and instantly translate that into an emotional and aesthetic response. The mathematical difference in frequency at the core of that response can be described using ratios.

Let’s start from the ground up. What is the simplest musical interval, and ratio, that we can come up with?

1:1

Simple. This much is the same as that much. This is equal to that. These two things are the same. Equal parts flour and equal parts water.

Rama perceives a sound at 200hz. He then hears another sound at 200hz. These two sounds stand in a 1:1 relationship with each other. They are the same pitch, otherwise known as a musical ‘unison’.

The first member of the harmonic series, known as the first partial, stands in a 1:1 relationship with itself, and will serve as a constant reference point as we ascend. It is the lowest pitch produced by a vibrating string, and it is therefore also known as the fundamental.