In Ellis's "Translator's Notice"
he writes:
"Professor Helmholtz's book having taken its place as a
work which all candidates for musical degrees are
expected to study ..."
At this time, it was common for conservatories
to teach the anatomy of the voice to voice students,
and the anatomy of the hand to pianists.
Show ms for "Physiology and Music in the Late Industrial Revolution"
Is Helmholtz a trained musician?
The need to understand the why of consonant ratios.
"... but I am not aware that any real step was ever made towards answering the question: What have musical consonances to do with the ratios of the first six numbers? Musicians, as well as philosophers and physicists, have generally contented themselves with saying in effect that human minds were in some unknown manner so constituted as to discover the numerical relations of musical birations, and to have a peculiar pleasure in contemplating simple ratios which are readily comprehensible." [p.2, top]
Contrast with vision: we don't think that colors that go together are related by simple integer ratios
Helmholtz links his emphasis on sensation as the foundation for music theory with Hanslick's anti-representational esthetic
Cites Hanslick "... trimphantly attacked the false standpoint of exaggerated sentimentality, from which it was fashionable to theorise on music." [p.2 near middle]
"Music stands in a much closer connection with pure sensation than any of the other arts. The latter deal with what the sense apprehend, that is, with the images of outward objects ... Poetry aims most distinctly of all at merely exciting the formation of images, by addressing itself especially to imagination and memory, and it is only by subordinate auxiliaries of a more musical kind, such as rhythm, and imitations of sounds, that it appeals to the immmediate sensation of hearing." [p.2, near bottom]
"In this sense it is clear that music has a more immediate connection with pure sensation than any other of the fine arts, and, consequently, that the theory of the sensations of hearing is destined to play a much more important part in musical esthetics, than, for example, the theory of charoscuro or of perspective in painting. ... In music, on the other hand, no such perfect representation of nature is aimed at; tones and the sensations of tone exist for themselves alone, and produce their effects independently of anything behind them." [p.3 1st paragraph]
The influence of Johannes Mueller on Helmholtz's interest in the physiology of hearing:
On page 4 he talks about the physiology of hearing, and especially praises the advances made by Johannes Mueller. (Recall the Mueller was his freshman teacher at Berlin.)
Holds a very modern conception of perception:
"the laws according to which these sensations result in mental images of determinate external objects, that is, in perception [p.4 middle]
"In these first two Parts of the book, no attention is paid to esthetic considerations. Natural phenomena obeying a blind necessity, are alone treated. The Third Part treats of the construction of musical scales and notes. Here we come at once upon esthetic ground, and the differences of national and individual tastes begin to appear. Modern music has especially developed the principle of tonality, which connects all the tones in a piece of music by their relationship to one chief tone, called the tonic. On admitting this principle, the results of the preceding investigations furnish a method of contructing our modern musical scales and modes, from which all arbitrary assumption is excluded." [p.5 2nd-last paragraph]
"I was unwilling to separate the physiological investigation from its musical consequences, ... and the reader, who takes up my book for its musical conclusions alone, cannot form a perfectly clear view ... unless he has endeavoured to get at least some conception of their foundations in natural science." [p.5 last paragraph]
Visual renderings of sound vibrations:
"Fig. 6 is the copy of a drawing actually made in this way on the rotating cylinder of Messrs. Scott and Koenig's Phonautograph" [p.20]
Recall Thomas Edison's phonograph and Emil Berliner's grammophone.
Ohm showed that there is only one form of vibration that has no harmonics (the sine tone) [p.23]
Cocktail Party Effect:
"When several persons are speaking at once, we can generally listen at pleasure to the words of any single one of them ... Hence it follows, first, that many different trains of waves of sound can be propagated at the same time through the same mass of air, without mutual disturbance; and, secondly, that the human ear is capable of again analysing into its constituent elements that composite motion of the air which is produced by the simultaneous action of several musical instruments." [p.25]
Frequency analysis of tones same mechanism as segregation of instruments:
"the ear has to analyse the composition of single musical tones, under proper conditions, by means of the same faculty which enabled it to analyse the composition of simultaneous musical tones." [p.26, top]
Auditory Streaming:
A remarkable description on page 25 about waves on the ocean created by different activities, with a parallel drawn to the waves of sounds in a ballroom.
Almost exactly the analogy given 130 years later by Al Bregman.
Helmholtz is impressed by this capacity to segregate sounds: "I must own that whenever I attentively observe this spectacle it awakens in me a peculiar kind of intellectual pleasure, because it bares to the bodily eye, what the mind's ey grasps only by the help of a long series of complicated conclusions for the waves of the invisible atmospheric ocean." [p.25]
Helmholtz resonator (illustrated p.43).
Following pages describe sympathetic vibration. (Especially, sympathetic strings.) Gives example of making sounds into piano with an open lid.
Chapter IV. On the Analysis of Musical Tones by the Ear.
Importance of Transients:
"Such accompanying noises and little inequalities in the motion of the air, furnish much that is characteristic in the tones of musical instruments" [p.68]
Nevertheless, "we shall at first disregard all irregular portions of the motion of the air ..." [p.68]
Description of Helmholtz's "oscilloscope".
A grain of starch reflected light, viewed through a microscope. "Lissajous" figures. [pp.80-81]
Ear cavity and the human scream:
"Hence it follows that the human ear by its own resonance favours the tones between e'''' and g'''', or, in other words, that it is tuned to one of these pitches. These notes produce a feeling of pain in sensitive ears. Hence the upper partial tone which have nearly this pitch, if any such exist, are extremely prominent and affect the ear powerfully. This is generally the case for the human voice when it is strained, and will help to give it a screaming effect." [p.116]
What is not included in your reading: Helmholtz's theory of the fibers in the cochlea responding to sounds using sympathetic resonance; hearing out individual partials occurs in cochlea
"Combinational Tones, which were first discovered in 1745 by Sorge, a German organist, and were afterwards generally known, although their pitch was often wrongly assigned, through the Italian violinist Tartini (1754), from whom they are often called Tartini's tones. [p.152]
demonstrate combination tones using two recorders
Sorge & Tartini only knew about what Helmholtz calls "differential tones"; On page 153; Helmholtz notes "The second class of summational tones, having their pitch number equal to the sum of the pitch numbers of the gernating tones, were discovered by myself." [p.153]
difference tones are generally louder than summation tones [p.153]
sum and difference tones are generated between all of the harmonics [p.153]
Helmholtz resonators are useless, because the combination tones are generated solely in the ear [last line, p.153]
Helmholtz notes that: sum and difference tones between the sum and difference tones was first described by Hallstroem. [bottom p.154]
"Were they not generally so weak on most instruments, they would give rise to intolerable dissonances." [middle p.156]
"Now it so happens that in the construction of the external parts of the ear for conducting sound, there are certain conditions which are peculiarly favourable for the generation of combinational tones. First we have the unsymmetrical form of the drumskin kitself. Its radial fibres, which are externally convex, undergo a much greater alteration of tension when they make an oscillation of moderate amplitude towards the inside, than when the oscillation takes place towards the outside." [2nd paragraph, p.158]
"But a more important circumstance, as it seems to me, when the tones are powerful, is the loose formation of the joint between the hammer and anvil. If the handle of the hammer is driven inwards by the drumskin, the anvil and stirrup must follow the motion unconditionally. But that is not the case fo the subsequent outward motion ..." [3rd paragraph, p.158]
"Since the human ear easily produces combinational tones, for which the principal causes lying in the construction of that organ have just been assigned, it must also form upper partials for powerful simple tones ... Hence we cannot easily have the sensation of a powerful simple tone, without having also the sensation of its harmonic upper partials." [3rd paragraph, middle p.159]
Are beats just slow combination tones? NO: In Chapter VIII (pp.159-) Helmholtz describes beats (which happen in all mediums), and distinguishes them from combination tones (which arise only in non-linear mediums).
In modern terms, combination tones result in tonotopic excitation of the corresponding frequencies evoked by non-linear distortion. Whereas, beats cause amplitude changes that modulate the entire basilar membrane. Said another way, from the perspective of Licklider's duplex perception of pitch, combination tones represent \fIplace\fR-related interference, whereas beats represent \fItiming\fR-related interference.
Helmholtz draws attention to the importance of recognizing that beats and combination tones are independent phenomena, even the beats and difference tones have the same frequency:
"Most acousticians were probably inclined to agree with the hypothesis of Thomas Young, that when the beats became very quick they gradually passed over into a combinational tone (the first differential). Young imagined that the pulses of tone which ensue during beats, might have the same effect on the ear as elementary pulses of air (in the siren, for example), and that just as 30 puffs in a second through a siren would produce the sensation of a deep tone, so would 30 beats in a second resulting from any two higher tones produce the same sensation of a deep tone. Certainly this view is well supported by the fact that the vibrational number of the first and strongest combinational tone is actually the number of beats produced by the two tones in a second. It is, however, of much importance to remember that there are other combinational tones (my summational tones), which will not agree with this hypothesis in any respect,* but on the other hand are readily deduced from the theory of combinational tones which I have proposed (in Appendix XII). It is moreover an objection to Young's theory, that in many cases the combinational tones exist externally to the ear, and are able to set properly tuned membranes or resonators into sympathetic vibration,* because this could not possibly be the case, if the combinational tones were nothgin but the series of beats with undisturbed superposition of the two waves. For the mechanical theory of sympathetic vibration shews that a motion of the air compounded of two simple vibrations of different periodic times, is capable of putting such bodies only into sympathetic vibration as have a proper tone corresponding to one of the two given tones, provided no conditions intervene by which the simple superposition of two wave systems might be disturbed; and the nature of such a disturbance was investigated in the last chapter.* Hence we may consider combinational tones as an accessory phenomenon, by which, however, the course of the two primary wave systems and of their beats is not essentially interrupted." [pp.166-167]
"The most penetrating roughness arises even in the upper parts of the scale from beats of 30 to 40 in a second." [middle p.171]
Helmholtz concludes that beating at 33 Hz is the roughest sounding; beating at less than 6 Hz is tolerable and at more than 132 Hz is imperceptible. [p.171]
"Consonance is a continuous, dissonance an intermittedn sensation of tone." [near bottom p.226]
Helmholtz provides a remarkably modern and accurate account of the prohibition against parallel fifths and octaves:
"The harmony was a secondary consideration, the melodic progression of the individual voices was the principal matter. Hence it was necessary to take care that each voice should stand out clear and distinct from all the others. The relation between the importance of harmony and melody has certainly altered essentially in modern music; the former has attained a much higher independent significance. But, after all, perfection of harmony must arise from the simultaneous performance of several voices, each of which has its own beautiful and clear melodic progression, and each of which therefore moves in a direction that the hearer has no difficulty in understanding. On this rests the prohibition of consecutive Fifths and Octaves. [The progression by octaves] is allowable when it is intentionally introduced for a whole melodic phrase, but it is not suited for a few notes in the course of a piece, where it can only give the impression of reducing the richness of the harmony by an unskilful accident. Now in this respect the nearest to an Octave are the Twelfth, and its lower octave, the Fifth. Hence, then, consecutive Twelfths and consecutive Fifths partake of the same imperfection as consecutive Octaves." [p.359]
False Relations. "The meaning of this rule is, probably, that the singer would find it difficult to hit the new tone which is not in the scale, if he had just heard the next nearest tone of the scale given by another singer." [top p.362]
An understanding of the contextual limits of these rules. "All these rules were essentially intended for the old ecclesiastical music, where a quiet, gentle, well-contrived, and well-adjusted stream of sound was aimed at, without any intentional effort or disturbance of the smoothest equilibrium. Where music has to express effort and excitement, these rules become meaningless." [p.362]
Helmholtz's aesthetics.
Hanslick. [pp.362-371]
First to turn attention away from physical acoustics to the structure of the ear.
First to understand "perception" as the subjective reconstruction of the objective world.
First to distinguish "sensation" from "perception".
First to draw attention (experimentally rather than theoretically) to the inaccuracies of sensory systems (e.g. used microscope to identify distortions in animal eyes)
Invented tools to examine sensory systems, including opthalmoscope, Helmholtz resonators, a simple oscilloscope.
First to describe "summation tones" (along with the "difference tones" described by Tartini and Sorge.
Explained the nature of combination tones through his theory of the non-linearity of the ear.
Recognized that combination tones generate sensory dissonance.
First to describe the ear as a frequency analyser.
First to describe the cocktail party effect.
First to describe the phenomonon of auditory streaming.
First to describe the importance of transients in sounds.
First to recognize the difficulty of hearing truly pure tones.
First to recognize the relationship between ear canal resonance and the human scream.
First to distinguish beats from combination tones.
First to recognize that 33 beats per second causes dissonance, without regard to register.
First to provide modern and accurate account of the prohibition against parallel fifths and octaves.
Important students:
Wilhelm Wundt (1832-1920)
"Helmholtz failed to answer ... why we hear complex tones as unanalyzed" (Green & Bulter, 2002; p.260)
sympathetic vibration of fibers in the cochlea
This document is available at http://dactyl.som.ohio-state.edu/Music829F/descript.F.html