Musical Scales

Like sound ascending a musical scale, the radiance increases, passing even beyond the frequency visible to spirit, until all is absolute blackness, yet pervaded with the iridescence of a raven s plumage. Here, within the thrice-radiant Darkness of Ain, you are alone with the Alone, the All-One. 

The relationships between the layers are ratios. They describe numerically the vibrations of the three essential notes in the music scale the whole note, which had a ratio of one to two the perfect fifth, which has a ratio of two to three and the perfect fourth, which has a ratio of three to four. Together with the four physical layers, these musical layers provide seven layers altogether. Like the ziggurat the Tetractys had seven layers, but here numbers have replaced the gods as emanations. To fill out the musical scale Pythagoras devised four other notes and created the Western diatonic scale with seven notes. Pythagoras believed that the seven notes captured the sound of each of the seven planets—the music of the spheres—and he used the seven vowels of the Greek alphabet to denote them. 

Some answers may be obtained from smaller bacterial, mitochondrial, and chloroplast ATP-dependent proteases. Cells of E. coli contain at least nine proteases, which have been named after the musical scale as Do, Re, Mi, Fa, So, La, Ti, Di, and Ci.450 451 Most are serine proteases but two, Ci and Pi, are metalloproteins. Protease La (Lon protease, encoded by gene Ion) has attracted particular attention because the hydrolysis of two molecules of ATP occurs synchronously with cleavage of a peptide linkage in the protein chain 452 This enzyme, as well as protease Ti (more often called CIp, for caseinolytic protease),451453 454 is ATP-dependent.451... 

Sir Isaac Newton not only compared the seven colors of the visible spectrum to the seven major notes of the musical scale but also did experiments with light and discovered that the human mind s perception of color requires only three colors red, green, and blue. White light is a mixture of these three colors. 

Another study was designed to determine how neural circuits are organized to provide a perception of sound. Specifically, Williamson wanted to find whether individuals have a tone map across the auditory cortex—that is, whether tones of different frequencies evoke neural activity at different locations. While Williamson s subjects listened to notes of a scale, the sensors hunted for magnetic field variations, and the researchers were able to monitor the movement of nerve impulses from cell group to cell group inside the brain. It appeared that the brain assigned equal numbers of neurons to each octave of the musical scale, much like the arrangement of keys on a piano. This... 

Some answers may be obtained from smaller bacterial, mitochondrial, and chloroplast ATP-dependent proteases. Cells of E. coli contain at least nine proteases, which have been named after the musical scale as Do, Re, Mi, Fa, So, La, Ti, Di, and Most are serine... 

John Newlands noticed that the properties of elements repeated in a manner similar to an octave on a musical scale (A, B, C, D, E,... 

In 1863, John Newlands (1837-1898) created a table of elements grouped by atomic weight and by chemical characteristic. Newlands noticed that in an eight-column table, the first and eighth element in a row resembled each other. This relationship then repeated, so that the fifteenth resembled the first and eighth. He called this the law of octaves, borrowing the idea from musical scales. 

The human ear also does not hear all sounds equally. Very low and very high notes sound more faint to one s ear than do 1000-Hz sounds of equal strength. This is the way ears fimction. The human voice in conversation covers a median range of 300-4000 Hz. The musical scale ranges from 30 to 4000 Hz. Noise in these ranges sound much louder than do very low or very high pitched noises of equal strength. 

In his book Odours, Fragrances and Cosmetics (1865), S. Piesse developed theories that related specific odours to notes on a musical scale in an attempt to categorize the spectrum of smells, whilst in 1890 Atkinsons produced one of the first books on perfume technology, essentially concerned with the production of absolutes by the cryo-scopic removal of fats. Perfumery was beginning to be investigated in depth. 

The. next step was taken when John A. It, Newlands published a series of articles2 in which attention was directed to the fnut that when the. elements are urranged in tlu order of utomie weight, the eighth element, resembles the first. On account of the resemblance to the musical scale this genera liz,at ion was known as the Law of Octaves. An examination of Newlands table shows some inconsistencies, due at least in part to his failure to leave spaces for undiscovered elements. There is much to admire in Newlands contribution, in spite of his inability to provide satisfactorily for the elements of higher atomic weight. 

Two years later, J. A. R. Newlands, in England, listed the first seven elements as hydrogen, lithium, beryllium, boron, carbon, nitrogen, and oxygen, like the notes in a musical scale. Each of the seven stood at the top of a group of elements with similar properties. Newlands called his arrangement of elements into seven groups the law of octaves. ... 

Returning now to ancient Greece, we find that the Pythagoreans recognised the existence of definite numerical relationships between the notes of musical scales and so number became associated in their minds with harmony. Moreover, they considered that the positions and movements of the celestial bodies were subject to numerical laws,... 

The evidence that musical scales and planetary motion both obeyed the same numerical rules was simply too attractive to discount as coincidence and nobody dared to contradict the interpretation of the masters. 

In this chapter, we will report on six basic concepts of multicriteria optimization. Just as the three primary colors (red, yeUow, and blue) can produce an infinite number of pictures and the seven basic notes of the musical scale (do, re, mi, etc.) can produce an infinite number of songs, the six basic concepts we will describe should allow the reader to generate an infinite number of models to solve the complex multiple-criteria decision problems. The six basic concepts are ... 

Among the elements, however, not only does the period length vary, but ako the periodicity is not exact. The elements within any column of the periodic table are not exact recurrences of each other. In this respect, their periodicity is not imhke the musical scale, in which one returns to a note denoted by the same letter, which soimds hke the original note but is definitely not identical to it, being an octave higher. 

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