**Ramsay**

"While Mr. Ramsay was meditating on these teachings of the great mathematician, Euler, and studying these notes and their vibrations, he was led to discover that *the order of quantities above F, when taken below B, constitutes the Minor System. This was the discovery of the Law of Duality in Music.* This Law of Duality in Mr. Ramsay's hands asserts an importance not second even to the **Law of Mathematical Ratios** which rules in the genesis of the notes." [Scientific Basis and Build of Music, page 8]

Fig. 1 - The pendulums in this illustration are suspended from points determined by the division of the Octave into Commas; the comma-measured chords of the Major key being **S**, 9, 8, 9, 5; **T**, 9, 8, 5, 9; **D**, 8, 9, 5, 9. The pendulums suspended from these points are tuned, as to length, to swing the **mathematical ratios** of the Diatonic scale. The longest pendulum is F, the chords being properly arranged with the subdominant, tonic, and dominant, the lowest, center, and upper chords respectively. Although in "Nature's Grand Fugue" there are 25 pendulums engaged, as will be seen by reference to it, yet for the area of a single key 13 pendulums, as here set forth, are all that are required. It will not fail to be observed that thus arranged, according to the law of the genesis of the scale, they form a beautiful curve, probably the curve of a falling projectile. It is an exceedingly interesting sight to watch the unfailing coincidences of the pendulums perfectly tuned, when started in pairs such as F4, A5, and C6; or started all together and seen in their manifold manner of working. The eye is then treated to a sight, in this solemn silent harp, of the order in which the vibrations of sounding instruments play their sweet coincidences on the drum of the delighted ear; and these two "art senses," the eye and the ear, keep good company. Fig. 2 is an illustration of the correct definition of a Pendulum Oscillation, as defined in this work. In watching the swinging pendulums, it will be observed that the coincidences [Scientific Basis and Build of Music, page 104]

See Also

**Ratio**
**three mathematical primes**
**chromatic scale**
**chromatic**
**flat**
**Law of Mathematical Ratios**
**mathematical intonation**
**Mathematical Relations are Constant - page 125**
**mathematical scales**
**mathematical system**
**On the Partial Differential Equations of Mathematical Physics**
**Ramsay - PLATE VIII - The Mathematical Table of Majors and Minors and their Ratio Numbers**
**Ramsay - PLATE XXII - Mathematical Table of the Twelve Major Scales and their relative Minors**
**Ramsay - PLATE XXIII - The Mathematical and Tempered Scales**
**Ramsay - PLATE XXVII - The Mathematical Scale of Thirty two notes in Commas, Sharps and Flats**
**scale of mathematical intonation**
**semitone**
**semitonic progression**
**sharp**
**tempered key**
**tempered scale**
**tempered system**
**three mathematical primes**