**Ramsay**

"lower effect than the fifth; the seventh, B, has a higher effect than the sixth; but the eighth, C, has a lower effect than the seventh. If the effects of notes or chords depended wholly on the mathematical primes by which they are measured and located, or the ratios inherent in them, then the effects of the tonic, subdominant, and dominant chords would have been alike, for these chords are measured by exactly the same primes, and have exactly the same ratios. It is the position of the tonic chord which gives it its importance and not any special primes by which it is produced, nor any special ratios inherent in it. Notes by the power of 2 have a pure unmixed and invariable character. Notes by the first, second, and third powers of 3 have different degrees of centrifugal force; and the character of the notes produced by the first power of 5 depends on the character of the notes from which they are derived. The final character of notes and chords is determined by the amount of force which they have acquired from the way in which they have been derived, and from their position in the system. And no matter where these notes may be afterwards placed, like chemical elements, they never lose their original forces and tendencies. What Tyndal says of the inorganic chemical elements of the brain is true of the inorganic notes of music, "They are all dead as grains of shot." It is the organic state which gives the notes and chords their gravities and levities, and these two tendencies, the one upward and the other downward, constitute the vital principle of music. It is true that the **mathematical operation** is required to give birth and life to music, and that the **mathematical system** gives the knowledge of causes down to the law of gravitation, yet the artistic effects are fully realised from the tempered system deriving its organic harmony from this vital principle of music. The centrifugal tendencies of the notes of the subdominant, are too strong to be at all disturbed by the system being tempered. The enormous power of these chords corrects the effect which might otherwise arise from tempering, as the enormous power of the sun corrects the perturbations of the planets." [Scientific Basis and Build of Music, page 29]

The vitality of the notes depends on their specific gravities and levities. As the tempered system does not in any way alter the position of the notes of the **mathematical system**, and as it is their specific gravities and levities which give the notes their vitality, when the one is not changed neither is the other. The gravities and levities of the notes change when the notes change their position in the system. They may indeed have the same names, but they are no longer the same notes. [Scientific Basis and Build of Music, page 43]

See Also

**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**