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1. Standard Guitar Tuning (EADGBe) and Mersenne Vibrational Laws

In 1636, French mathematician and music theorist Marin Mersenne published Harmonie universelle. In it, he described his experiments with vibrating strings.

Today, these are summarized in the ideal string model, f = 1/(2L) × √(T/μ). L is the vibrating length in meters, and T is the tension in newtons, N.

The letter μ is the linear mass density, in kilograms per meter, kg/m. The frequency decreases if the length or the square root of the linear density increases.

It increases with the square root of the tension.

Mersenne describes these experiments in Book III of Harmonie universelle, published in Paris in 1636. He compares the length, tension, thickness, and pitch of strings.

Today's equation expresses that relationship for an ideal string. It is not a direct quote or a formula copied from his treatise.

f = 1 / (2L) × √(T / μ)

The Six Strings, in Hertz

Concert pitch takes A4 = 440 Hz as a reference, according to ISO 16. In standard tuning, the six open strings of the classical or acoustic guitar span two full octaves.

Between the 3rd and 2nd strings, there is a major third. Between the other adjacent strings, there are perfect fourths.

Wavelengths are approximate for sound in air at 343 m/s and are calculated with λ = v/f. These are not the vibrating lengths of the strings. ISO 16:1975 specifies A4 = 440 Hz.

2. The 8 Fundamental Open Chords and Pivot Finger Biomechanics

In classical and popular guitar pedagogy, eight open positions form the technical foundation. These are called open chords.

They utilize open strings, which vibrate freely. This gives them a resonant sound and requires little effort from the left hand.

Sor's Méthode pour la Guitare, published in Paris in 1830, is a primary source on early 19th-century technique. His instructions on instrument, hand, and finger position help in studying economy of motion.

This summary is not a literal quote from Sor.

When changing from C to A minor, your index finger remains on the first fret of the second string. Your middle finger stays on the second fret of the fourth string.

Your ring finger moves from the third fret of the fifth string to the second fret of the third string. This is called a pivot finger.

You keep a note or a finger when the next position allows it and only move what is necessary. This helps with coordination but does not eliminate effort or guarantee a continuous sound on its own.

3. Rameau Fundamental Bass and the Circle Progression (I - vi - ii - V7)

In 1722, French composer and theorist Jean-Philippe Rameau published his Traité de l’harmonie réduite à ses principes naturels. It changed the way music was understood in the West.

For Rameau, chords are not randomly stacked intervals. They are governed by the attraction of the “fundamental bass.”

The diatonic harmonic circle, as it is called in popular teaching, is a good example.