"In organ pipes, of a certain calibre, very sensitive waves occur at intervals; as according to the character of the sound evolved; but on a combination of resonators composed of brass tubes of more than nine in number, a wave of sound, induced by certain chords passing over them, produces high vortex action of the air enclosed in them. The vibration of tuning forks induces alternate condition of the air that surrounds them, if in open atmosphere; but quite a different action presents itself when the forks are exercised in resonating tubes, set to thirds of the ((mass chord) they represent. Then high vortex action is the instant result. Vibrators cannot be set promiscuously in tubes, and get such results, any more than a musician can render a musical composition on the violin before tuning it." [Appendix I]

The chord-scales may be either major or minor, or may be found in a sweetly mingled condition; a piece may be wholly major or wholly minor, but not wholly chromatic. Chromatic chords do not usually succeed each other, but come into diatonic compositions for the purpose of producing certain effects peculiar to them, or by solving difficulties which may arise in composition. They are used as musical condiments to spice or sweeten a passage; but nobody makes pudding all of spice or sugar. The structure, character, and progression of the various chord-scales will be found so amply set forth in several parts of this work that it is not necessary to enlarge further in this place. [Scientific Basis and Build of Music, page 69]

Helmholtz falls into a mistake when he says- "The system of scales and modes, and all the network of harmony founded on them, do not seem to rest on any immutable laws of Nature, but are due to the aesthetical principle which is constantly subject to change, according to the progressive development of taste." It is true, indeed, that the ear is the last judge; but the ear is to judge something which it does not create, but simply judges. Nature is the maker of music in its scales and modes. The styles of composition may vary with successive generations, and in the different nations of men; but the scientific basis of music is another thing. It is a thing, belonging to the aesthetic element of our being and our environment; it is under the idea of the beautiful, rather than the idea of the useful or the just; but all these various aspects of our relation to creation have their laws which underlie whatever changes may be fashionable at any period in our practice. If the clang-farbe of a musical tone, that is, its quality or timbre, depends on the number and comparative strength of the partial tones or harmonics of which it is composed, and this is considered to be the great discovery of Helmholtz, it cannot be that the scales and modes are at the caprice of the fickle and varied taste of times and individuals, for these partials are under Nature's mathematical usages, and quite beyond any taste for man's to change. It is these very partials or harmonics brought fully into view as a system, and they lead us back and back till they have brought us to the great all-prevading law of gravitation; it is these very partials, which clothe as an audible halo every musical sound, which constitute the musical system of sounds. [Scientific Basis and Build of Music, page 78]

Thus chord tends toward chord, and note leans toward note, and it has to be considered whether the attraction of affinity or proximity be strongest while working out the charming effects of a composition. [Scientific Basis and Build of Music, page 92]

The relations which music has to mechanics, the sphere of centers; to geometry, the sphere of measures; and to arithmetic, the sphere of numbers, show how deeply seated music is in the nature of things, and how independent it is of the will or choice of the musician. His composition may take any form his inspiration may suggest; they are subject to him; but as to the nature of music and its laws, he must keep himself subject and obedient to them. Music is of the aesthetic; but the aesthetic is of the nature of things. [Scientific Basis and Build of Music, page 92]


In passing from one key to another in the fellowship of keys in a composition, the new key grows out of the top of the dominant and converts the old dominant into a tonic. The dominant and subdominant being at the opposite extremes of the key, with the tonic between them, are not related by affinity. This want of affinity makes an opening in the system for the new chord to come in by, and it, being related by affinity to the chord of the old dominant, which is now the new Tonic, comes in and establishes itself and the new key for the time. It is this gap between subdominant and dominant, along with the affinity existing between the new key and the old dominant, which makes this musical event to be so gracefully accomplished. This is what is called natural modulation, the passing for a time into another key in the course of a composition; and its abundant and habitual use in music, even in the simplest chorales, shows how natural and acceptable it is. The young student will find illustrations in the second lines of the Psalm tunes - Watchman, Sicily, Tranquility, Eaton, Birmingham, Jackson, Bethel, Bedford, and Sheffield. Take Watchman, for example, and let the young student follow carefully, noting each chord of the little passage, which we shall analyse for his help. It is by such practice that he will become by-and-by familiar with the kinship of keys and the legitimate resources of harmony. [Scientific Basis and Build of Music, page 93]

In the opening of the third measure the tune returns to its own key by striking the tonic. This case is a very simple illustration of how a composition will move with perfect naturalness in more keys than one, the keys so grow out of each other, and may either merely snatch a passing chord from a new key, or pass quite into it for a phrase or two, or for a whole measure, then return as naturally, either by a smooth and quiet or by a strongly contrasted turn, according to the chords between which the turn takes place. In such modulation there may or there may not be marked a sharp, , or , in the air itself; the note which Nature raises in the new key may occur in one of the other parts of the harmony. In Watchman it is A, the fourth, which is altered; from being it is made . The change which takes place in the sixth of the scale, which is C in Watchman, is only one comma, the ratio of 80 to 81, and it slips into the new key as if nothing had happened. No mark is placed to it, as the comma difference is never taken notice of, although it is really and regularly taking place, with all the precision of Nature, in every new key. It is, however, only the note which is altered four commas, which is marked by a sharp, , or , as the case may be. [Scientific Basis and Build of Music, page 94]

This plate is a representation of the area of a scale; the major scale, when viewed with the large hemisphere, lowest; the minor when viewed the reverse way. It is here pictorially shown that major and minor does not mean larger and smaller, for both modes occupy the same area, and have in their structure the same intervals, though standing in a different order. It is this difference in structural arrangement of the intervals which characterizes the one as masculine and the other as feminine, which are much preferable to the major and minor as distinctive names for the two modes. Each scale, in both its modes, has three Fifths - subdominant, tonic, and dominant. The middle fifth is the tonic, and its lowest note the key-note of the scale, or of any composition written in this scale. The 53 commas of the Octave are variously allotted in its seven notes - 3 of them have 9 commas, 2 have 8, and 2 have 5. The area of the scale, however, has much more than the octave; it is two octaves, all save the minor third D-F, and has 93 commas. This is the area alike of masculine and feminine modes. The two modes are here shown as directly related, as we might figuratively say, in their marriage relation. The law of Duality, which always emerges when the two modes are seen in their relationship, is here illustrated, and the dual notes are indicated by oblique lines across the pairs. [Scientific Basis and Build of Music, page 106]

Fig. 4 is a setting of the minor and the major chord-scales, showing how they stand linked by notes in common in their direct sequence from dominant minor to dominant major. To each of the six chords is placed the first chromatic chord, showing how it resolves in its three-fold manner by 1, 2, and 3 semitonic progressions in each mode, and by 1 and 2 notes in common variously in each mode; and here again the law of duality is seen in its always symmetrical adjustments. Duality, when once clearly and familiarly come into possession of musicians, will be sure to become an operative rule and test-agent in composition. [Scientific Basis and Build of Music, page 121]

schools on the hill of Sion—'out of Sion hath God appeared in perfect beauty.' So long as this principle was recognised in musical academies, there were composers of the highest class; devoid of it, the highest order of compositions disappeared." "Power over music does not depend solely on the mere agreement of 'how to do it.' The student in song will never learn the perfection of beauty except from the preparation of the heart. To make a real musician, there must be a sense of the ever-presence of the Creator of all beauty. The boy-musician must begin his day with prayer, and end it with praise. This made Handel, Bach, Haydn, and Mozart. Music is neither dram nor sweetmeat, neither sensual nor intellectual. It is made so now; but in this order of music there is neither joy nor love, thankfulness nor reverence." [Harmonies of Tones and Colours, Fragments from Dr. Gauntlett's Last Note-book, page 51]

Created by Dale Pond. Last Modification: Thursday April 8, 2021 03:30:47 MDT by Dale Pond.