Musical scale

“ It is a very remarkable fact that while the course of evolution is generally from simpler to more complex organisms, that of the musical scale is just the reverse. Primitive scales are highly complex, and involve intervals not appreciable by us as melody; with time they gradually become simpler; and in the diatonic scale, especially in its most modern developments, where the distinction between major and minor tends to become effaced, [15] we seem to have reached the limit, and the scale is reduced to the simplest possible numerical relations. ”

“ But since the seventeenth century our conception of music has gradually, from melodic, become harmonic; we hear vertically as well as horizontally; we hear the beauty of all chords as sounded together, and, unconsciously, we fill in the harmonies to every melody we hear. It would have been natural if the keyed instruments had adapted themselves to this altered musical conception, and had resigned the original conception of the scale to make way for harmonic conveniences. ”

“ since, again, they saw that the attributes and the ratios of the musical scales were expressible in numbers; since, then, all other things seemed in their whole nature to be modelled after numbers, and numbers seemed to be the first things in the whole of nature, they supposed the elements of numbers to be the elements of all things, and the whole heaven to be a musical scale and a number. ”

“ The art of illustrating the construction of the Musical Scale by means of certain syllables, so associated with the sounds of which it is composed as to exemplify both their relative proportions, and the functions they discharge as individual members of a system based upon fixed mathematical principles.
The laws of Solmisation are of scarcely less venerable antiquity than those which govern the accepted proportions of the Scale itself. ”

“ As they stand for the lowest notes of the scale, they are probably an addition, later than the rest of the system. At the upper end, again, the scale is extended by the simple device of using the same characters for notes an octave higher, distinguishing them in this use by an accent. The original fifteen characters, with the letters from which they are derived, and the corresponding notes in the modern musical scale, are as follows:
These notes, it will be seen, compose two octaves of the Diatonic scale, identical with the two octaves of the Greater Perfect System. ”

“ The Musical Scale is a series of eight notes, ascending by certain steps from the first or key-note to the octave above it, each of the notes being fixed by such distinguishable musical relations as we have spoken of above. ”

“ Moreover, if the diatonic major scale is thus suggested by nature, the minor scale with its flat third must be more artificial, and less likely to be universally adopted. Howbeit, the minor scale is especially popular, not only with several uncivilized races, but also with several who have cultivated the art of music to a high degree. Some of our most eminent composers have written perhaps more beautiful music in minor than in major keys. ”

“ The evolution of the musical scale should be of interest even to musicians who would not make the subject a study. How step by step our diatonic scale developed, how it has become what it is gradually by slow degrees—does anybody know? Certainly. Wise men in their libraries find much ”

“ Historically, however, the sense has developed from its stricter musical meaning of a scale (the recognized musical scale of any period) , originating in the medieval “great scale,” of which the invention has usually been ascribed to Guido of Arezzo (q.v.) in the 11th century. ”

“ As well might the carpenter or architect venture to dispense with scale, compass and square in their constructive labors, as that the composer should neglect beat, measure and rhythm, in his effort to realize a well-developed and intelligible design in the whole, or any part, of his composition. The beats and measures and phrases are the barley-corn, inch and ell of the musical draughtsman, and without these units of measurement and proportion, neither the vital condition of Symmetry nor the equally important condition of well-regulated Contrast could be clearly established. ”

“ A simple, clean-cut musical scale or systematized table of musical sounds. (2) Some definite manner of symbolizing sounds, so that they could be accurately expressed in writing. (3) A cultivation of the sense of hearing, in order that mankind might learn to distinguish between sounds that are discordant and those that sound well together; in other words, harmony.
We will begin with the scale, and review what we know of the Greek modes in order to show how they were amalgamated into our present octave system of scales. ”

“ It may be thought, perhaps, that the variety of senses ascribed to the word harmonia goes beyond what is probable. In itself however the word meant simply 'musical scale [24] .' The Pythagorean use of it in the sense of 'octave scale,' and the very similar use in reference to diagrams which represented the division of that scale, were antiquated in the time of Aristoxenus. The sense of 'key' was doubtless limited in the first instance to the use in conjunction with the names Dorian, &c., which suggested a distinction of pitch. From the meaning 'Dorian scale' to 'Dorian key' is an easy step. ”

“ It is like our five black keys on the piano, starting with F sharp. This is called the pentatonic scale, (penta, Greek word for five, tonic meaning tones) . This scale is a most amazing traveler, for we meet it in our musical journeys in China, Japan, Arabia, Scotland, Africa, Ireland, ancient Peru and Mexico, Greece and many other places. The reason we find these five tones popular must be because they are natural for the human throat. At any rate we know that it is difficult for the Indian to sing our scale. ”

“ And it is clear, especially from the specimens which Ptolemy gives of the scales in use in his time, that he was only endeavouring to systematise what already existed, and bring theory into harmony with the developments of practice. We must suppose, therefore, that the musical feeling which sought variety in differences of key came to have less influence on the practical art, and that musicians began to discover, or to appreciate more than they had done, the use of different 'modes' or forms of the octave scale. ”

“ If the lover of music is acquainted with the popular songs and dance-tunes of the Wallachians, or with the wild and plaintive airs played by the gipsy bands in Hungary, he need not be told that the Minor Scale with two Superfluous Seconds is capable of producing melodies extremely beautiful and impressive. ”

“ Those theorists who regard our diatonic major scale as the most perfect one, which ultimately must be universally accepted as the only true one, will probably not admit that under certain circumstances the sounding of one or other of its intervals a little "out of tune" may actually increase the beauty of a musical performance. ”

“ It is a truism that music is ruled by measure, but what I want you to perceive is quite a different interpretation, and that is that it was the measuring that ordered the music.
Those who, seeing the holes that are cut upon a common flute, or oboe, consider that in the origin of the instrument they were so done in order fitly to comport with a musical scale, are wrong in their supposition.
In the primitive making of a flute the holes were cut21 to suit the spread of the fingers, and the scales which followed as the result of the placing the holes, were accepted by primitive man ”

“ It is well known to those who have attended to the subject of musical ratios, that a fixed scale of eight degrees to the octave, which shall render all its concords perfect, is impossible. It has been demonstrated by Dr. Smith, from an investigation of all the positions which the major, the minor, and the half-tone can assume, that the most perfect scales possible, of which there are two equally so, differing only in the position of the major and the minor tone above the key note, must have one Vth and one 3d too flat, and consequently the supplementary 4th and VIth too sharp, by a comma. ”

“ The fixation of a definite interval-order which shall serve as the scale of their performances is the starting-point of Chinese musical theory. All the different pitches which are used in a given piece of music, taken together embody a certain set of intervals arranged in a certain order from low to high. The fact of scale in music is the fact that in general in the music of one age and race different pieces embody in this way the same order of intervals, or one or other of a few different orders. ”

“ It rests with you whether the piano shall be a musical instrument or not.
"A student who comes to me with a very poor touch must of course go back to first principles and work up. Such an one must learn correct movements and conditions of hands, arms and fingers; and these can be acquired at a table. Along with these, however, I would always give some simple music to play, so that the tonal and musical sense shall not be neglected.
"Of course I advise comprehensive scale practise; scales in all keys and in various rhythms and touches. There is an almost endless variety of ways to play scales. ”

“ The musical tones which these hard vibrating bodies gave out were the first determinations of pitch, and of the elements of the scale, which correspond to the natural partial vibrations of such bodies. "The human voice," Wallaschek<1> tells us, "equally admits of any pentatonic or heptatonic intervals, and very likely we should never have got regular scales if we had depended upon the ear and voice only. The first unique cause to settle the type of a regular scale is the instrument." ”

“ It appeared to me unnecessary to give definitions of musical terms made use of in the questions—such as interval, melody, harmony, etc.—which are to be found in every dictionary of the English language. Some terms, however, required an explanation to render them fully intelligible to those travellers who are but little acquainted with music. Of this kind are, for instance, the names of the different musical scales. The English missionaries, traders, merchants, consuls, and other residents in foreign countries, seldom possess any available knowledge of music. ”

“ How did man reach the conception of fixed scales? Here again opinions differ. Some consider that the extreme notes were fixed by the average compass of the human voice in impassioned speech, the interval being variously divided. Others claim that along with the vocal phase of music there was an instrumental side, and that the mechanical conditions in connection with instruments had bearing in the matter of organizing sounds into a scale; the rude, primitive trumpet of wood or bark, still found among forest tribes in South America and Africa, gives a series of harmonic notes. ”

“ It is unnecessary here to enter into the æsthetical reason for this; [1] it must suffice to state that all nations, at all times, who have made music, have agreed in adopting such a selection, although they have not always selected the same series of sounds. As a first step towards the selection all musical peoples appear to have appreciated the intimate natural relation between sounds which lie at that distance apart called an octave; and hence replicates of notes in octaves are found to form parts of all musical scales. ”

“ There are two obvious relations in which the scales employed in any system of music may stand to each other. They may be related as two keys of the same mode in modern music: that is to say, we may have to do with a scale consisting of a fixed succession of intervals, which may vary in pitch—may be 'transposed,' as we say, from one pitch or key to another. Or the scales may differ as the Major mode differs from the Minor, namely in the order in which the intervals follow each other. ”

“ This sharping of the G augments the natural interval from F to G, and, since this augmented interval is hard to sing, the F, too, is sometimes sharped, and the scale then becomes what we call the melodic minor. Nothing could be more indicative than this ‘melodic’ compromise of the power harmony has exercised over the development of music, for rather than do without the leading tone, which is itself an alteration of the natural scale, we alter the scale still further. Our melodic minor scale is therefore constructed to square with the harmonic need, a queer paradox. ”

“ For, in the first place, a settled scale is not only a vehicle for melody, it is also a means of modulation, and this latter function comes more into evidence as music becomes more complex and the need of modulation increases. ”

“ At other points the character and drift of the harmony is determined by quite a different principle—namely, that, the scale being conceived as indefinitely extended, the voices are agreed in selecting a particular section of it, the position of which determines not only the melodic character of each part but also the harmonic character of the whole, according to its greater or less remoteness from the scale in which major cardinal chords occupy a central position. ”

“ The student of some interesting modern developments will also speedily discover that the adoption of the so-called whole-tone scale as a basis of music is, except upon a keyed instrument tuned to the compromise of equal temperament, unnatural and impossible. ”

“ Of the many possible modes only two are used in our present system of music, the major and the minor. There is only one form of the major mode, and it is the one most people recall when they think of the scale. There are three forms of the minor mode, but of these the harmonic is the most frequently used. ”