An elementary treatise on musical intervals and temperament1876 - 94 pagina's |
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An Elementary Treatise on Musical Intervals and Temperament (Classic Reprint) R. H. M. Bosanquet Geen voorbeeld beschikbaar - 2018 |
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Apotomè Pythagorica application approximate harmonic seventh approximately perfect fifths Bach Bach's beats called CHAPTER chords chromatic semitone clavichord common logarithm departure of twelve Diagram diatonic scale difference tone division dominant duodenes E. T. fifth E. T. semitones E. T. third effect eight fifths employed ENHARMONIC HARMONIUM enharmonic organ equal intervals equal temperament semitones error exact fifths fifths and thirds generalised keyboard harmonious music Helmholtz's Theorem instrument key relationship key-note keyed instrument Major Sixth major third major tone mean-tone system Minor Scale minor seventh Musical Association musicians nearly notation notes number of units old unequal temperament perfect third perfect-fifth systems pitch Poole's positive systems practical principal Pythagorean comma Pythagorean Semitone Regular Cyclical Systems Rule series of fifths seven octaves seven-fifths semitone sixth skhisma stop symmetrical arrangement system of 53 system of logarithms system of perfect theory twelve fifths upwards vibration numbers vibration ratio دو دو دو
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Pagina 45 - In all, the series of tones are arranged diagonally one beyond another, so "that the form of a chord of given key relation is the same in every key. But the notes are not all symmetrical, and the same chord may be struck in different forms according to the view which is taken of its key relationship."* They therefore possess the great advantage of similarity of manipulation, although this is quite different from that ordinarily taught. It would appear, however, that the new systems are far from difficult...
Pagina 60 - Regular systems are such that all their notes can be arranged in a continuous series of equal fifths. Regular cyclical systems are not only regular, but return into the same pitch after a certain number of fifths. Every such system divides the octave into a certain number of equal intervals. Error is deviation from a perfect interval. Departure is deviation from an ET interval. Intervals taken upwards are called positive, taken downwards, negative. Systems are said to be of the rth order, positive...
Pagina xi - ... system of notation which shall point out to the performer the ratio of the note he is to sound to its generator ; when genius shall have used all this new material to the glory of art — then it will be time enough to found a Theory of Harmony on a mathematical basis.
Pagina 51 - Turin ; an enharmonic harmonium, tuned according to the division of the octave into fiftythree equal intervals ; and the first of the now generally adopted upright pianofortes patented by Robert Wornum in 1811.
Pagina 21 - The disenthrallment of the professional, as well as the public mind, on this subject, has been slow and gradual. However, we have similar ignorance and superstition in other fields of medical research. The question of the causation of insanity, is one of the most important with which we have to deal.
Pagina 5 - Octave middle c' to treble c" beat once per second ; and make those which have their upper notes above treble c" beat three times in two seconds. Keeping the Fifth treble /' and treble c" to the last, it should beat once in between one and tico seconds.
Pagina 5 - Ellis, is much less variable in its results than the ordinary process of guesswork. It is this : — ' make all the Fifths which lie entirely within the Octave middle c' to treble c" beat once per second ; and make those which have their upper notes above treble c" beat three times in two seconds.
Pagina 53 - Generalized Key-board." An harmonium has been constructed which is arranged as follows : — The note \\\c is taken as the first note of the series, and receives the characteristic number 1. Then c is 4, and the remaining numbers can be assigned by the rules for the identifications in the system of 53 given above. A number of notes at the top of the key-board are thus identical with corresponding notes in the adjacent principal divisions on the right at the bottom, eg //c=6=\\cj.
Pagina x - MODERN music owes much of its beauty to the use of " doubtful chords;" that is, chords which belong equally to more than one key. Now, if an enharmonic scale were feasible, such chords .could not exist, because mathematical correctness of ratio would make every chord strictly in tune in one key, instead of allowing it to be somewhat out of tune in several keys. The whole of our musical literature, from the works of Bach to those of Wagner, would therefore be unavailable for instruments with an enharmonic...
Pagina x - The tempered scale is certainly out of tune, and will not bear to have its proportions exhibited to an audience with better eyes than ears, on a white screen ; but its sounds have nevertheless been a source of as real pleasure to all great composers, as of imaginary pain to certain theorists.