**Ramsay**

"These three combinations of the three primary ratios, when taken together with 1 as unity, produce ten different quantities and motions - 1, 2, 3, 5, 6, 9, 15, 18, 27, and 45; and by producing the octaves of these **primes** and products, dividing by 4 for the **quantities**, and multiplying by 2 for the motions^{2} up to 64, we have 15 additional quantities and motions - 4, 8, 10, 12, 16, 20, 24, 30, 32, 36, 40, 48, 54, 60, and 64." [Scientific Basis and Build of Music, page 16]

"The numbers which express the motions of these twenty-five **quantities** have among themselves nineteen different ratios, or rates of meeting; and when these ratios are represented by the oscillations of twenty-five pendulums, at the number of 64 for the highest one, they will all have finished their periods, and meet at one for a new series. This is an illustration, in the low silence of pendulum-oscillations, of what constitutes the System of musical vibration in the much higher region of vibrating strings and other elastic bodies, and determines the number of undeveloped sounds which form the harmonious halo of one sound, more or less faintly heard, or altogether eluding our dull mortal ears; and which determines the number of sounds which, when developed, constitute the System of musical sounds." [Scientific Basis and Build of Music, page 16]

The law of gravitation is the law of Music as well as of Astronomy. The cycles of the *distances*, that is the *intervals*, in Music correspond to the cycles of the *periods* in Astronomy. In Astronomy the distances and **quantities** of matter are primary, and determine the periods; in Music the periods and **quantities** are primary, and determine the distances or intervals. In Astronomy the *distances* are commensurable; in Music the *periods* are commensurable. In Astronomy the periods are incommensurable; in Music the distances or intervals are incommensurable. In Astronomy, because the simplicity is not in the periods, the conjunctions are very few at one time; in Music, because the simplicity is in the periods, the conjunctions are very many at one time. And herein lies in the one case the harmony and permanence of the solar system, and in the other case the harmony and beauty of the musical system. The periods and distances in Astronomy and Music are inversely related. [Scientific Basis and Build of Music, page 30]

Well, how are we to get the true minor scale? There is a remarkable fact, and a beautiful one, which suggests the method. Such is the economy of Nature, that from one system of proportion employed in two different ways, in the one case as periods of vibrations and in the other as **quantities** of strings, everything in Music's foundation is produced. It is a remarkable fact that the numbers for the lengths of the strings producing the major scale are the numbers of the vibrations producing the minor scale; and the numbers for the lengths of the strings for the minor scale are the numbers of the vibrations of the notes of the major scale. Here Nature reveals to us an inverse process for the discovery of the minor scale of notes. [Scientific Basis and Build of Music, page 31]

When the major scale has been generated, with its three chords, the subdominant, tonic, and dominant, by the primary mathematical ratios, it consists of forms and orders which in themselves are adapted to give outgrowth to other forms and orders by the law of duality and other laws. All the elements, orders, combinations, and progressions in music are the products of natural laws. The law of Ratio gives **quantities**, form, and organic structure. The law of Duality gives symmetry, producing the minor mode in response to the major in all that belongs to it. The laws of Permutations and Combinations give orders and rhythms to the elements. The law of Affinity gives continuity; continuity gives unity; and unity gives the sweetness of harmony. The law of Position gives the notes and chords their specific levities and gravities; and these two tendencies, the one upward and the other downward, constitute the vital principle of music. This is the spiritual constitution of music which the Peter Bell mathematicians have failed to discern: [Scientific Basis and Build of Music, page 37]

It runs in all the polarities of Nature. Music, as belonging to Nature - as one of the things which the Great Numberer hath created - is under this Law of Duality as well as that of mathematical ratios and other laws. The *Law of Duality* in *music* gives the *major and minor systems*. As the major is derived from certain primes in ratios *ascending*, and the minor from the same primes in the same ratios *descending*, they are *inversely* related; and these diatonic scales have in the responding parts exactly the same **quantities**. But as multiplying by 3 three times gives the framework of the major system in the ascending genesis, and dividing by 3 three times gives the framework of the minor system in the descending genesis. They are in this view also *directly* related. The Law of Duality in music emerges into view from the genesis [Scientific Basis and Build of Music, page 42]

It is in their *inverse relations* that the major and the minor are equal. Every note, chord, and progression in the one has its reciprocal or corresponding note, chord, and progression in the other. This is the *Law of Duality*. And this general law of Nature is so deeply rooted in music, that is the numbers which represent the vibrations in the major system be made to represent **quantities** of string, these **quantities** will produce the minor system (beginning, of course, with the proper notes and numbers); so that *when the quantities are minor the tones are major, and when the quantities are major the tones are minor*.

^{1}[Scientific Basis and Build of Music, page 44]

Such is the economy of Nature, that from *one system of proportions employed in two ways* - in the one case as periods of vibrations, and in the other case as quantities of strings - everything in music is derived. The numbers which are the periods in the one are the numbers which are the **quantities** in the other. And abundantly throughout Creation reigneth the Law of Duality, which thus reigneth here in this region of most perfect response.^{2}[Scientific Basis and Build of Music, page 44]

In getting the length of a string, in inches or otherwise, to produce the scale of music, any number may be fixed on for the unit; or for the vibrations of the root note any number may be fixed on for the *unit*; but in the *fractions* which show the *proportions of the notes of the scale*, there is no coming and going here; this belongs to the invariables; there is just one way of it. Whatever is not sense here is nonsense. It is here we are to look for the truth. The numbers which express the **quantities** and the numbers which express the motions are always related as being of the same kind. The fractions bring their characters with them, and we know by this where they come from. 1/4 of a string gives a note 2 octaves above the whole string, no matter what may be its length; 2 has exactly the same character as 1; 2/4 gives the note which is 1 octave above the whole string; but in the case of 3/4 here is a new ingredient, 3; 3/4 of a string gives a note which is a *fifth* below the [Scientific Basis and Build of Music, page 75]

The root of the subdominant is F, in the key of C major; and the top of the dominant is D. The difference between these two notes at the top and bottom of the chord-scale, is the **quantity** which two octaves is more than three fifths; it is the ratio of 27 to 30, a comma less than the minor third whose ratio is 5 to 6. [Scientific Basis and Build of Music, page 76]

"Dividing the octave into twelve semitones is a near approach to the mathematical **quantities**, and this saves the musical artist from *errors in tone* - at least to any extent; but it does not save from *errors in judgment*. In the case of G#, for example, not one of the reasons given for the use of the *sharp seventh in the minor scale* is a correct one. A touch of nature makes the world akin, and a touch of the Law of Duality balances everything in music." [Scientific Basis and Build of Music, page 99]

This plate sets forth the essential duality of the musical system of vibrations. It is a remarkable fact that the numbers of the vibrations of the major mode are the numbers for the string proportions of the minor mode; and vice versa, the string proportions in the major are the numbers of the vibrations in the minor. We have, however, to see that we use the proper notes and numbers; we must know the secret of Nature. This secret rests in the duality of the notes, and begins from the two D's. The center of gravity of the musical system of vibrations is found in the comma space between the |two D's as they are found in the genesis of the two modes. In these |two D's the vibration number and string proportions are nearly identical. Starting from this point as the center of gravity in the [Scientific Basis and Build of Music, page 118]

**Werner Heisenberg**

In quantum mechanics, the Heisenberg uncertainty principle states by precise inequalities that certain pairs of physical properties, such as position and momentum, cannot be simultaneously known to arbitrarily high precision. That is, the more precisely one property is measured, the less precisely the other can be measured.

Published by Werner Heisenberg in 1927, the principle means that it is impossible to determine simultaneously both the position and the momentum of an electron or any other particle with any great degree of accuracy or certainty. This is not a statement about researchers' ability to measure the **quantities**. Rather, it is a statement about the system itself. That is, a system cannot be defined to have simultaneously singular values of these pairs of **quantities**. The principle states that a minimum exists for the product of the uncertainties in these properties that is equal to or greater than one half of the reduced Planck constant (Ä§ = h/2Ï€). (wikipedia)

See Also

**approximation**
**cycles per second**
**DIRECT OBSERVATION UNRELIABLE**
**first comparison and combination of quantities**
**Frequency**
**Heisenberg uncertainty principle**
**laws of quantities and motions**
**Observation**
**order of quantities**
**Period**
**quantities and motions**
**quantities of strings**
**quantities**
**Ramsay - Duality in Quantities of Strings and Vibrations**
**relative quantities**
**Time**
**unit of quantities**