I think its time to discuss the nuts of bolts of music, so here I am focusing on the frequency of A at 432 Hz and how we arrive at such a number. We knew this centuries ago, so I am just refreshing us all as to why it is important in today’s world with a particular focus on aligning ourselves with the natural world as we move ever forward in our evolution.

The Harmonic series are the overtones that occur when any note is played, and the 27thnote in that series, if the first was C, is A. Octaves of **27**are **54**, **108**, **216**and **432**. Hence the reason why it is becoming popular again. Let’s breakdown the number 432 into its factors:

A = 27 = 3 squared x 2 = 54 x 2 = 108 x 2 = 216 x 2 = 432 = 3 squared x 2 to the fourth

So, **432 = 2 x 2 x 2 x 2 x 3 x 3 x 3**

Next, lets look at the interval of an augmented 4thor #4. The ratio of an augmented 4this 1.414 or more commonly known as √2. Now this is where it gets interesting. When the interval of an augmented 4th is viewed in the circle of fifths, the two notes are at the opposite sides of the circle exactly 180 degrees apart. (See diagram).

Notice that the line from C to F# is straight across the circle, or more correctly known as the diameter. That is also known as the diagonal of a square:

(See second diagram. Picture the note C at one corner when the line ends and F# at the other.)

The diagonal of a square has the ratio of **1: √2 **so this means that the augmented 4threpresents the diagonal of a square or the diameter of a circle. Now, the frequency of an augmented 4th above **432 Hz**:

432 x √2 = 610.94 which is the frequency of **D#**, the augmented 4th above A. So, D# in the system of natural phenomena which takes as its starting point the harmonic series, which is observable all across the universe, is now represented as:

610.94 = 2 to the fourth x 3 cubed x √2

So whenever you are playing an interval of an augmented 4thin 432 Hz you are implying the mathematical fundamental principle of: **2 to the fourth x 3 cubed x √2**

Tell me, which do you think has most meaning and therefore benefit to us as musicians and as a species, **432 **or **440 ?**

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