Leído entre: Jun 5, 2010 – Jul 1, 2010 (26 días).
Lo que me gustó: la primera mitad, cuando habla de teoría musical, los procesos físicos detrás de los sonidos y la música, el análisis de los sonidos producidos por diferentes instrumentos. Un poco dentro de la segunda mitad, cuando habla de la relación entre el sonido y el cuarto donde se genera (reverberación, cómo la afectan los materiales y dimensiones, y las consecuencias de cambiarlos).
Lo que no me gustó: la segunda mitad, donde empieza a dar muchos números y tablas con poca utilidad para personas que no son ingenieros acústicos, donde habla de mediciones de sonido (que no es inherentemente aburrido, pero no me gustó cómo lo trata). Tampoco me gustó que le dio muy poco espacio al oído en sí, y a la transmisión del sonido al cerebro una vez que está en el oído (pero como el autor bien menciona, no es algo que se entienda muy detalladamente). Y el final... simplemente no se siente como final.
En general: recomendable para personas que disfrutan de la música y que gustan de entender los por qués de las cosas (aunque no culparía a nadie de dejarlo inconcluso después de la mitad). Recordar las clases de física de la prepa/carrera (ondas, vibraciones en cuerdas, ondas estacionarias en tubos, etc.) ayuda bastante a entender y apreciar los primeros capítulos.
Amazon lo tiene aquí.
Notas y citas:
Cases such as those just mentioned, in which there are only two or four beats to the second, do not usually produce an unpleasant sound. Indeed certain registers of the organ, such as the "voix celeste" and the "unda maris", produce the effect deliberately by the device of each note having two pipes, which are purposely put sufficiently out of tune with one another to give two or three beats a second. The voix celeste is usually constructed of string-toned pipes. Its fantastic name notwithstanding, it attempts to represent the slightly undulating sound heard when the strings of an orchestra play in unison; the undulations arise in part from the "beats" which must necessarily occur since the instruments can never be in perfect tune with one another, but in still greater part from a more subtle cause which we shall discover when we study violin tone in detail. The still more fantastically named unda maris usually consists of flute-toned pipes, and bears some resemblance to voices singing in attempted but imperfect unison. These undulations of sound endow organ tone with a certain quality of life and motion which is otherwise wanting. (p48-49)
Indeed it is a general rule that beats sound unpleasant when the number of beats per second is comparable with the frequency of the main tone. (p49)
Los nombres de los harmónicos de una nota (incluyendo 2 hacia abajo): Sub-octave, Quint, Fundamental, Octave, Twelfth, Fifteenth, Seventeenth, Nineteenth, Twenty-second
The timbre depends only on the relative energies of the various harmonics and not on their phase-differences. Differences of phase produce no effect on the ear. This is known as Ohm's law, having been discovered by G. S. Ohm (1787-1854), the discoverer of the still better known electrical law.
The second harmonic adds clearness and brilliance but nothing else, it being a general principle that the addition of the octave can introduce no difference of timbre or characteristic musical quality.
The third harmonic again adds a certain amount of brilliance because of its high pitch, but it also introduces a difference of timbre, thickening the tone, and adding to it a certain hollow, throaty or nasal quality, which we may recognise as one of the main ingredients of the clarinet tone [...].
The fourth harmonic, being two octaves above the fundamental, adds yet more brilliance, and perhaps even shrillness, but nothing more, for the reason already explained. The fifth harmonic, apart from adding yet more brilliance, adds a rich, somewhat horn-like quality to the tone, while the sixth adds a delicate shrillness of nasal quality.
As the table on p.73 shews, all these six harmonics form parts of the common chord of the fundamental note, and so are concordant with this note and with one another. The seventh harmonic, however, introduces an element of discord; if the fundamental note is c', its pitch is approximately b[flat]''', which forms a dissonance with c. The same is true of the ninth, eleventh, thirteenth, and all higher odd-numbered harmonics; thees add dissonance as well as shrillness to the fundamental tone, and so introduce a roughness or harshness into the composite sounde. The resultant quality of tone is often described as "metallic", since a piece of metal, when struck, emits a sound which is rich in discordant high tones. (p87)
We found that when a stretched string is plucked at its middle point, the second and fourth harmonics are absent from the sound produced, whereas if it is plucked at some other point, these harmonics are present.
The second and fourth are, however, the harmonics which above all others impart clearness and brilliance to the tone, so that the note given out by the plucked string will be deficient in these qualities. It will have a rather hollow, nasal quality, reminiscent perhaps of the tone of a clarinet or a stopped organ-pipe, since the tones of both of these consist mainly of odd-numbered harmonics. This seems to suggest that the quality of tone emitted by a string depends on the point at which we pluck or strike the string, and harmonic analysis (p.78) proves that this is so.
The middle point of a string is a node for all even-numbered harmonics and a loop for all odd-numbered harmonics, so that if we excite a string at its middle point, all the even-numbered harmonics, including the octave, super-octave and all higher octaves, will be missing from the sound produced (the result already obtained), while all the odd-numbered harmonics will be present in their maximum strength. In the same way we see that if we excite a string at a point a third way along its length, the third harmonic will be missing, but the second (octave) and fourth (super-octave) will be fairly strong, giving a clear brilliant tone. If we excite the string a quarter way along, the second harmonic will be heard in full strength but the fourth will be entirely missing, while the third and fifth will appear, but weakly. (p89)
Talking about violin playing and how the bow pulls the string, until it cannot hold it anymore and the string goes back to its position, overshoots, and is again trapped by the bow that keeps pulling in the original direction:
Each time that the bow loses its grips on the string, as well as each time that it resumes this grip, the vibration of the string undergoes a sudden change in phase. Thus, if two violins are playing in unison, the difference in phase of their two vibrations changes repeatedly, so that the sounds they emit may reinforce one another at one instant, but enfeeble one another at the next (p.39). Thees frequent alternations of loudness cause the "beating" or undulating effect which is characteristic of string playing in unison, even when they are perfectly in tune with one another. (p102)
Helmholts shewed that the strength of the various harmonics must always be in the ratio od 1:1/4:1/9:1/16:etc, whatever the point at which the string is bowed.
No matter where the string is bowed, the first, third, fifth and other odd-numbered harmonics occur in the same strength as in a string plucked at its middle point, but the second, fourth, sixth and other even-numbered harmonics, instead of being completely absent, are present in full strength, with the result that the bowed string has a fuller, more brilliant and richer tone than the plucked string. (p102-103)
The string may be bowed anywhere from a seventh to a fifteenth, but is usually bowed at a ninth or tenth, of its length from the bridge —more in piano passages, and less in forte passages. If it is bowed sul ponticello —i.e. close up to the bridge— the bow does not lie over any nodes except those of very high harmonics, so that moderately high harmonics are produced in full strength, and the note has a metallic sound. (p103-104)
Talking about the body of the violin:
Its free vibrations are of high pitch, and as many of them coincide in frequency with harmonics of the notes produced by the strings, these particular vibrations may be much reinforced by resonance. It is their presence that gives the instrument its peculiar tone or timbre. Such a group of frequencies is known as a "formant". (p104)
Backhaus has examined the frequencies of the body vibrations of a first-class Stradivarius, and finds that the majority are fairly evenly distributed between 3200 and 5200. In other violins the frequencies are usually lower and also less evenly distributed. (p104)
The fact that the speed of sound varies with the temperature entails important practical consequences. We have seen that the period of vibration of a column of air is proportional to the time sound takes to travel over the length of the column. If the air is warmed, sound travels faster and the period becomes less. It follows that the pitch of all wind instruments is raised when temperature rises, or when they are taken into a warmer atmosphere. This explains why the instruments of an orchestra must be tuned afresh each time the temperature changes. Before a concert the tuning is performed in the concert hall itself, so that the various instruments will be in tune with one another in the actual air in which they are to be played, and, for the same reason, the players of wind instruments breathe into their instruments before tuning them. (p120)
When the wind or a blast of air encounters a small obstacle, little whirlwinds are formed which are the exact counterparts of the whirlpools which are formed when a stream of water strikes a rock. There is a steady flow of air in front of the obstacle, and a steady train of whirlwinds behind it. These whirlwinds are formed on the two sides of the obstacle alternately; as soon as one comes into existence, it begins to drift away in the general current of air, thus making place for others which are formed in turn behind it.
When whirlwinds are formed by the wind streaming past an obstacle of any kind, the formation of each little whirlwind gives a slight shock, both to the obstacle and to the air in its neighborhood. If the wind blows in a continuous steady stream, these shocks are given to the air at perfectly regular intervals. We may then hear a musical note — it is what is often described as the "whistling of the wind", or the "wind whistle". Its pitch is of course determined by the frequency of the shocks to the air, and this is the number of whirlwinds formed per second. (p126)
Then Helmholtz (1862) developed a theory of consonance and dissonance in terms of beats — a theory which has been much discussed and criticised [sic], but still holds the field to-day. We have already seen that C and C# sound badly together because they make unpleasant beats. In the case of wider intervals, such as C and F# there are no beats to be heard, either pleasant or unpleasant, but Helmholtz asserted that C and F# sound badly together because certain of their harmonics (e.g. g' and f'#) make unpleasant beats. On the other hand C and G sound well together because few of their harmonics beat badly: [...] indeed many harmonics are common to both notes. (p157)
In time, however, the idea must have occurred to sing or play two or more notes at once — possibly because it was impossible for men and boys to sing together in the same pitch, or possibly because on-part music began to pall. [...] from now on it was important that two or more notes of the scale could be sounded together without undue dissonance. Even to-day, many of the races which have not advanced beyond homophonic music —as for instance the Arabs, Persians and Javanese— use scales whose notes are not at all consonant; the dissonance is harmless because two notes are never heard together. On the other hand, even primitive races whose music is polyphonic use scales in which most intervals are consonant. (p161)
La secuencia de la que habla (F-C-G-D-A...) es la de "perfect fifths".
By stopping at different places in the sequence F-C-G-D-A-..., we obtain the various scales which have figured in the music of practically all those races which have advanced beyond the one-part music of primitive man.
The first three notes of the sequence C, F and G formed the main tones of the scale of ancient Greece. If we proceed as far as five notes C, D, F, G, A we have the pentatonic scale in which a considerable amount of Chinese and ancient Scottish music is written, as well as much of the music of primitive peoples in Southern Asia, East Africa and elsewhere; transpose it a semitone up, and we have the scale provided by the black keys of the piano — hence the fact, beloved of school-children, that many Scottish melodies, "Auld Lang Syne", etc., can be played without touching the white keys at all, and that almost any sequence of notes strummed on the black keys sounds like a Scottish melody. On taking the first seven notes, we have the ordinary diatonic scale, which seems to have been introduced into Greece in the middle of the sixth century B.C., was standardised [sic] by Pythagoras, and has remained the normal scale for western music ever since. (p164)
Plato tells us, for instance, that the Lydian mode (our modern major mode!) was specially associated with sorrow; it and the closely associated Ionian mode, which only differed from it in b[flat] replacing b, were also the modes of softness, relaxation, self-indulgence, and even drunkenness. The Dorian and Phrygian modes on the other hand were —so he tell us— associated with courage, the military spirit, temperance and endurance. Because of this association, Plato would have permitted only the Dorian and Phrygian modes to be employed in his ideal republic, the Lydian and Ionian modes being prohibited. (p180)
When we compare two scales in major keys with one another, we find that, unless the tuning is that of equal temperament, the octave is still divided into its seven intervals by slightly different steps, and the question is whether this slight difference is perceptible to the trained musical ear, and if so, whether it has an appreciable influence on the emotional qualities of the music.
Many musicians, including Berlioz, Schuman and Beethoven, seem to have believed that both questions must be answered in the affirmative. We find Beethoven writing of B minor as a "schwarze tonart", describing Klopstock as "always maestoso — Db major", changing the key of a song in an effort to make it sound amoroso in place of barbaresco, and so forth.