Volume IV, Issue 1, Spring 1997

Table of Contents

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The Musical Infant and the Roots of Consonance

Threads of Music in the Tapestry of Memory

Matters of Opinion
The Neurobiology of the Benefits of Music

Briefly Noted
Wellness, Survival, Music and the Arts
Melodic Therapy Changes Brain Activation and Promotes Language Recovery After Brain Damage

Recent Publications of Special Interest

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The Musical Infant and the Roots of Consonance
Copyright © 1997 Norman M. Weinberger
and the Regents of the University of California. All Rights Reserved.

"The square of the hypotenuse is equal to the sum of the squares of the two opposite sides." That is what I remember best from high school geometry. And one other thing; this theorem was the gift of the Ancient Greek mathematician and philosopher Pythagoras, (circa 600 B.C.). Not as well known, but of foundational importance in music, are Pythagoras' experiments on the vibrations of strings. Vibrating strings were known to produce tones. When Pythagoras divided such a string into two unequal parts, not surprisingly, each shortened string produced its own note. The pitch of each was higher than the pitch of the entire string. More importantly, Pythagoras found that when the lengths of the two parts were related by simple ratios like 2:1 and 3:2, they produced tones that sounded good together. We call these tones "consonant." Conversely, dividing a vibrating string into two parts related by a complex ratio (e.g., 45:32) produced two tones that were regarded as "dissonant." For example, a ratio of 3:2 produces a consonant perfect fifth (e.g., C and G). In contrast, a ratio of 45:32 produces the dissonant "tritone", (e.g., C and F#), an interval of three whole tones that was regarded as unacceptable and dangerous in the Middle Ages, the "Diabolus in musica."(1)

What are the origins of music? Most people assume that music is only a cultural phenomenon. However, there is accumulating evidence that music has deep biological roots. In previous issues of MRN, we have summarized many of these findings.(2) Pythagoras is probably the first person to hold that simple mathematical relationships reflected universal properties of nature.(3) Hence, to him, the consonance of certain tones (and the dissonance of others) was neither culturally-based nor accidental. Rather, consonance was "natural." But in modern times, a different view has prevailed. Consonance is thought to reflect preferences that are based on experience with a particular musical culture. It has no absolute basis in nature.

Investigation of this issue has proven to be difficult. How does one determine whether consonance has some fundamental biological priority over dissonance?(4) Perhaps the first step is to clarify what is meant by "priority." Most researchers mean that objective behavioral measurements would reveal better perceptual processing of consonant tonal intervals than dissonant intervals. For example, the auditory system of the brain would be sort of "tuned" to respond to simple-ratio intervals better than to complex ratio intervals (e.g., C-G vs. C-F#).

This hypothesis has been tested by E. Glenn Schellenberg (University of Windsor) and Sandra E. Trehub (University of Toronto). College students listened to a repeatedly presented five tone melody consisting of two alternating tones that had a certain pitch relationship (consonant for some groups, dissonant for other groups). At some unknown time, the melody was changed. Subjects had to detect the changes either from consonant to dissonant or the converse, from dissonant to consonant intervals. The basic idea is as follows. Suppose that there is a biological bias for consonant tone pairs, i.e., they are more distinctive (the Pythagorean ideal), than dissonant tone pairs. Then it should be easier to notice changes from consonant pairs than changes from dissonant tone pairs. In fact, these were the results. The subjects did better on discriminating changes from tones having simple ratios to tones with complex ratios than vice-versa.

However, since adults were tested, it is possible that the effects were due to prior learning. That is, adults might find it easier to process consonant intervals because of extensive experience with standard tonal music that is based on consonant intervals. To check this possibility, Schellenberg and Trehub repeated the experiment with six year olds, who had no musical training and much less musical experience. The results were the same.(5)

Once again, those who argue for a cultural basis of special status for consonance can argue that even six year olds had enough experience with music to render the biological interpretation suspect. Therefore, the authors performed similar experiments with six to nine month old infants. The idea is that the absence of a special status for consonant intervals would support a cultural basis for consonance but the presence of a processing advantage would strongly support the biological origin for consonance. Testing had to be somewhat different for such young, pre-verbal subjects. But it was equally objective. The infants sat on their mothers laps and when they were looking straight ahead, tone sequences were played from a speaker located off to one side. If the infant turned and looked at the speaker during the time a change in melody occurred (i.e., consonant to dissonant or the reverse), then she or he was rewarded by the illumination of an animated toy. Again, the findings were the same; infants processed consonant intervals better than dissonant intervals.(6) Moreover, this bias for consonance occurred both for harmonic intervals (two tones presented simultaneously) and for melodic intervals (two tones presented in sequence). The ubiquity of the consonance effect underscores its importance.

In short, the perceptual advantage of consonant intervals over dissonant intervals is present at all age levels tested, in particular it is present in infants who can hardly be said to have had much opportunity to learn about tonal music.

The findings support the conclusion that the privileged status of intervals that have simple frequency ratios over those with complex frequency ratios is the result of a biological bias. Thus, consonance and dissonance are not simply determined by culture. It should be pointed out that this processing advantage may make it easier to comprehend tonal than atonal music. This is not to say that people cannot do the latter, but only that it is likely to be more difficult. The evolutionary processes (e.g., potential selective advantages) and the brain mechanisms (e.g., auditory system circuitry) that underlie consonance are not yet known. Nonetheless, the findings to date are themselves "consonant" with the view that music is not only a cultural phenomenon but that it has quite definite origins in the way that the human brain evolved.

-- N. M. Weinberger

(1) Harvard Dictionary of Music (2nd ed.), (1969), W. Apel (Ed.), Cambridge: Belknap Press, p. 230.

(2) See for example "The Musical Infant" and "Matters of Opinion", (Spring 1994); "Musical Building Blocks in the Brain" (Fall, 1994); "The Earliest Music Lessons" (Spring, 1995); "Sing, Sing, Sing" (Fall, 1996).

(3) For an early delineation of this position see Lundin, R.W. (1947). Toward a cultural theory of consonance.  J. Psychol., 23, 45-49.

(4)There are several extensive discussions of this issue, the complete details of which cannot be covered in this brief essay. The interested reader may wish to consult sources such as Burns, E.M. and Ward, W. D. (1982), Intervals, scales, and tuning. In D. Deutsch (Ed.),  The Psychology of Music. New York: Academic Press, pgs 241-269.

(5) Schellenberg, E. G. and Trehub, S. E. (1966). Children's discrimination of melodic intervals. Develop. Pscyhol., 32, 1039-1050.

(6) Schellenberg, E. G. and Trehub, S. E. (1966). Natural musical intervals: evidence from infant listeners. Psychol. Science, 7, 272-277. There were appropriate controls for other factors, such as the fact that head-tuning at the wrong time was not rewarded, etc. For a more complete description of this method and its use to determine pitch and contour perception, see " The Musical Infant", MRN, Spring 1994.

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Threads of Music in the Tapestry of Memory
Copyright © 1997 Norman M. Weinberger
and the Regents of the University of California. All Rights Reserved.

In the early fog-shrouded morning, a large group of scuba divers, clad in full gear, gathers on a beach. They soon divide into two equal groups, each apparently with an instructor. Half enter the ocean and disappear beneath the waves; the others gather round their instructor on the beach. After 30 minutes or so, only half of the ocean divers emerge from the surf; immediately they are replaced by half of the divers from the beach group. It is only then that the casual observe realizes that this is no ordinary scuba lesson. In fact, it is not a scuba lesson at all.

What are memories? How are they stored? How are they recalled? The scuba divers are helping to answer these questions. And, perhaps surprisingly, the answers ultimately involve music.

But for now, the divers continue their activities for another 20 minutes; then all of the ocean divers pop up to the surface and finally wade onto the beach. The instructors perform a quick tally of the results, to be later checked in the laboratory. They seem pleased. Another dimension of memory has been identified. The scuba divers are indeed scuba divers but the instructors are psychology professors, and an experiment has just been completed. During the first 30 minutes, both groups were shown the same list of words, on slates. After half of each group exchanged places, all divers were tested to recall as many as possible (writing on their own slates).

This was an experiment to determine how memories are recalled. Specifically, it studied "context-dependent-memory" (CDM). The question is, "To what extent is recall affected by the 'context' (in this case underwater vs. on the beach) of remembrance?" Is recall better or worse when recall occurs in a different place than the original context of learning?

In fact, it seems to be worse. Scuba divers who both learned and recalled in the same context (ocean-ocean and beach-beach) recalled more words than scuba divers who learned and recalled in different places (ocean-beach and beach-ocean).(1) The results show that memory systems in our brains don't act like tape recorders. Rather, the original learning seems to include (or "encode") the contextual background as well as the "main events".

Context-dependent-memory has been studied in many situations. Music turns out to be an important contextual element. For example, Steven M. Smith of Texas A&M University examined the role of background instrumental music. First, subjects viewed a list of words, one at a time. Two days later, they were given a test in which they simply had to recall as many of the learned words as possible. Like the scuba divers, learning and recall took place in the same or different context, but in this case the contexts were musical. There were three conditions during learning for different groups: a Mozart piano concerto (K491 in c) , a jazz piece ("People Make the World Go Around" by Milt Jackson), or a quiet background. During the recall test, groups were subdivided so that they received either the same music (or quiet) that was present during learning or different music (or quiet).

Recall was best when the music was the same during learning and recall than when the pieces were changed; quiet during both times did not aid memory. The worse recall when musical context was changed was found to be due to a memory process, rather than to possible distraction. These findings show that background music can enter into memory and aid recall, when it is simply present and not necessarily consciously attended. So a memory is somewhat like a complex weaving, composed of major patterns and also background strands. Hence, the title of this essay: music is a "thread" in the "tapestry" of memory.

Regular readers of MRN may themselves recall a previous essay "Elevator Music: More Than It Seems"(Fall, 1995). There, we pointed out the ubiquity of background music and its ability to alter consumer behavior, social perceptions and mood. And the effect of music on mood was a special subject in a later issue (MRN, Spring 1996). Is it possible that music enters into memory through its effects on mood?

Eric Eich and Janet Metcalfe at the University of British Columbia addressed this issue.(2) They played different compositions to induce different moods, the latter being self-rated by the subjects. A happy mood was induced by playing excerpts from Mozart's Eine Kleine Nachtmusik or Divertimento #136 [K number not given]. Albinoni's Adagio in G Minor or Barber's pour Cordes" were used to produce a sad mood. Subjects rated their moods every few minutes on a mood scale. When they had reached at extreme (very happy or very sad, in different groups), they learned word associations. Recall 48 hours later was done with the music that was concordant or discordant with the mood during learning. The main finding was that recall was worse when the moods were different. So music-induced mood is a thread in the tapestry.

While moods induced by music can enter into the storage and assist the recall of memories, there are also specific aspects of the music itself that can constitute other "threads". William Balch, Kelly Bowman and Lauri Mohler of The Pennsylvania State University investigated the effects of music genre and musical tempo in a series of experiments.(3) First, different groups learned words during one of four instrumental pieces: slow jazz (from "How Long Has This Been Going On?" by Fox, Worth and Cowan); fast jazz (from "Sing, Sing, Sing" by Benny Goodman); slow classical (from Mozart's clarinet concerto in A,); and fast classical (Tartini's "Devil's Trill"). The four groups were subdivided into many groups for the recall test, which received the same or different music compared to the learning condition. The different music was made as different as possible, e.g., a change from slow jazz to fast classical. When tested for word recall, there was a music-dependent result. As might be expected, recall was aided when the music was the same, worse when it was different.

However, reduced recall with different music could be due to different features of the music. For example, learning under fast jazz but recalling under slow classical involves simultaneously changing two features, tempo and genre. Are these equally important? In a second experiment the authors restricted changes to either tempo (e.g., slow jazz to fast jazz) or genre (e.g., slow jazz to slow classical). The results were surprising. Changing tempo impaired recall but changing genre did not.

Balch and Lewis followed this up by a more direct test of the effects of tempo.(4) They played exactly the same pieces in the same or different tempo during recall. Again, they found recall was better with the same tempo, worse with a change in tempo. The authors also checked the effects of changing only timbre by presenting the same selection at the same tempo, with synthesized piano or brass performance. Changing the timbre had no effect. They also found that tempo, but not timbre, could affect mood.

The importance of tempo might be due to the very surprising finding that the general public, not only musicians, appear to have an absolute memory for tempo. Levitin and Cook of Stanford University found that when adult subjects sang popular songs from memory and their tempos were compared with recordings of the same songs, most "performances" had essentially identical tempos.(5)

Overall the research literature shows that background music, itself not a part of a conscious learning task, enters into memory for the material learned. Moreover, recall is better when the music present during learning is also present during recall. Furthermore, tempo appears to be an important component of music's intrusion into memory. Finally, music's effect in altering mood plays a key role.

Of course, extensive research is required to achieve a more complete understanding of the role of music in daily memory and its implications. For example, studying with music may actually impair recall without similar music. In any event, the studies to date reveal that memories are complex constructions consisting of many strands. Learning obviously doesn't guarantee recall but music correctly integrated into the learning experience may well assist it.

--- N. M. Weinberger

(1) Godden, D.R. and Baddeley, A.D. (1975). Context-dependent memory in two natural environments: On land and underwater. British J. Psychol. 66, 325-331. The description of the experiment is accurate in essentials but slight liberties have been taken with some details of the scene.

(2) Eich, E. and Metcalfe, J. (1989). Mood dependent memory for internal versus external events. J. Exper. Psychol., Learn., Memory & Cognition, 15, 443-455.

(3) Balch, W. R., Bowman, K. and Mohler, L. (1992). Music-dependent memory in immediate and delayed word recall. Memory & Cognition, 20, 21-28.

(4) Balch, W.R. and Lewis, B.S. (1996). Music-dependent memory: the roles of tempo change an mood mediation. J. Exper. Psychol., Learn., Memory & Cognition, 22, 1354-1363.

(5) Levitin, D. J. and Cook, P.R. (1996). Memory for musical tempo: additional evidence that auditory memory is absolute. Perception & Psychophysics, 58, 927-935.

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Matters of Opinion
Copyright © 1997 Norman M. Weinberger
and the Regents of the University of California. All Rights Reserved.

The Neurobiology of the Benefits of Music

The following opinions about music are based on the reports of scientific studies. This does not mean that the opinions carry the same importance as the results of such studies themselves. They are simply opinions, intended to provoke thought and sometimes perhaps even argument, but ultimately to energize and enlarge thought and action on music

In this column of the last issue of MRN (Fall, 1996), I discussed two views on music, "purism" and "utilitarianism". The "purists" hold that music should be studied only because of its intrinsic values. The "utilitarians" hold that any benefits extrinsic to music also form the rationale for music education and music making. I come down on the "utilitarian" side. But I would like to think that as research on music, human behavior and the brain progresses from its still rather limited base (compared, for example, to research on language), a coalescence of these positions will emerge. But this is likely to develop only with greatly expanded research in music and ultimately will depend on a generally advanced view of the role of music in the human condition.

As long as music is viewed basically as relatively unimportant, an educational philosophy can argue that you can "take it or leave it". In contrast, to the extent that research finds that music has as substantial a biological basis as language, and is part and parcel of human nature, then it would make no educational sense to continue to treat it as a frill. [The same logic holds for the other Arts but this column focuses on music.]

Given the growing body of evidence that music has biological bases (e.g., "The Musical Infant and the Roots of Consonance", this issue), one would like to know the neurobehavioral effects of music. My purpose here is to provide such a sketch.

First, let's begin with an emerging neurobiological fact. The functional connections between brain cells (neurons) are their synapses. Active synapses are strengthened; inactive synapses are weakened.

Second, let's consider major components of the human brain/mind.

Sensory and Perceptual: auditory, visual, tactile, kinesthetic

Cognitive: symbolic, linguistic, reading

Planning Movements

Motor: fine muscle and gross muscle coordination

Feedback and Evaluation of Behaviors

Motivational/Hedonic (pleasure)



Third, and I think the major point here, making music engages all of these components. These will not be discussed in detail here. I hope that readers will go through this list and ask themselves the relation of music to each of these brain functions. Just think about everything that one does while playing from a score.

Finally, some speculative conclusions that can serve as a first approximation to better understand how music interacts with the brain.

Making Music "exercises" the whole brain and mind.

Making Music can strengthen synapses in all brain systems.

Making Music increases the brain's capacity and resources by increasing the strength of connections among its neurons.

This "sketch" provides a starting point for considering the effects of music on the brain that would be the neural substrates of effects of music on cognition and behavior. Whether or not research on such effects influences educational philosophy and practical decisions about the role of music in curricula, understanding the substrates of music should illuminate both music itself and the workings of the brain and mind.

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Briefly Noted
Copyright © 1997 Norman M. Weinberger
and the Regents of the University of California. All Rights Reserved.

Wellness, Survival, Music and the Arts The processes that contribute to health and longevity are of great interest. A recent publication provides evidence that attendance at cultural events, reading and making music or singing in a choir are associated with both health and longevity. Dr. Lars Olov Bygren and co-workers at the Department of Social Medicine in the University of Umeå in Sweden studied 12, 675 people, selected as a random sample of the Swedish population. The age range was 16-74 years. They were interviewed first in 1982-83 and followed-up until the beginning of 1992. Many variables were studied. As might be expected, smoking, long term disease and lack of exercise were associated with increased mortality. When all other variables were controlled for, the authors found that involvement in cultural events, reading and music were related positively to longevity (British Medical Journal, 1996, vol. 313, pgs. 1577-1580). Interestingly, educational level was not related to these effects. The authors are appropriately cautious about drawing strong conclusions. Additional demographic studies should be of great interest, particularly to determine if such positive relationships hold across cultural groups.

Melodic Therapy Changes Brain Activation and Promotes Language Recovery After Brain Damage Music therapies are in widespread use for a variety of behavioral and neurological problems. When positive effects are obtained on behavior, the brain mechanisms involved remain a mystery. Now comes evidence that a certain type of music therapy has behavioral benefits via measurable changes in brain function. Dr. Pascal Belin and his associates, working at the Service Hospitalier Frederic Joliot in Orsay and other institutions in France report that Melodic Intonation Therapy (MIT) promotes recovery from aphasia, a severe language disorder subsequent to stroke. MIT involves speaking in a type of musical manner, characterized by strong melodic (two notes, high and low) and temporal (two durations, long and short) components. Reporting in the December 1996 issue of Neurology (vol. 47, pgs. 1504-1511), Belin et al studied seven patients who had a lengthy absence of spontaneous recovery. They also evaluated the effects of MIT on the brain by measuring relative cerebral blood flow (CBF) and PET scanning during hearing and repetition of simple words and of "MIT-loaded" words. MIT produced recovery of speech capabilities. Of great interest, a critical regions of the brain was activated by "MIT-loaded" words but not regular words. This is Broca's Area in the left hemisphere, known for over 100 years to be critically implicated in language and speech. The authors believe that the reactivation by MIT of Broca's Area was critical to recovery of speech. These findings provide enormous promise for both the treatment of aphasia and understanding the role of music in normal and abnormal brain function.

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Recent Publications of Special Interest

Children and Education

Gardiner, M.F., Fox, A., Knowles, F., Jeffrey, D. (1996) Learning improved by arts training. Nature, 381(n6) 580: 284.

           Abstract: The authors investigated the effect of a music and visual-arts curriculum that emphasized sequenced skill development on visuospatial reasoning with 96 1st graders (aged 5-7 yrs old). Of subjects with previous First-Grade Metropolitan Achievement Test scores, those in the test arts classes started behind controls, but after 7 months of training they had caught up on reading and were ahead on learning mathematics. It is suggested that the pleasure of arts promotes the acquisition of skills, which in turn motivates the acquisition of other difficult skills. [See Editor's Note, MRN Fall 1997 (IV-2) for Authors' summary]

Rauscher, F. H., Shaw, G.L., Levine, L.J., Wright, E.L., Dennis, W.R., Newcomb, R.L. (1997). Music training causes long-term enhancement of preschool children's spatial-temporal reasoning. Neurological Research, 19: 2-8.

           Abstract: Predictions from a structured cortical model led the authors to test the hypothesis that music training specifically enhances spatial-temporal reasoning. Thirty-four children received private piano keyboard lessons, 20 children received private computer lessons, and 24 children provided other controls. Four standard, age-calibrated, spatial reasoning tests were given before and after training; one test assessed spatial- temporal reasoning and three tests assessed spatial recognition. Significant improvement on the spatial-temporal test was found for the keyboard group only. No group improved significantly on the spatial recognition tests. The improvement on the spatial-temporal task suggests that music training produces long-term modifications in underlying neural circuitry in regions not primarily concerned with music. The authors propose that an improvement of the magnitude reported may enhance the learning of standard curricula, such as mathematics and science, that draw heavily upon spatial-temporal reasoning.

Music Perception, Cognition and Behavior

van Egmond, R., Povel, D-J., and Maris, M. (1996). The influence of height and key on the perceptual similarity of transposed melodies. Perception and Psychophysics, 58:1252-1259.

           Abstract: In two experiments, the perceptual similarity between a strong tonal melody and various transpositions was investigated using a paradigm in which listeners compared the perceptual similarity of a melody and its transposition with that of the same melody and another transposition. The paradigm has the advantage that it provides a direct judgment regarding the similarity of transposed melodies. The experimental results indicate that the perceptual similarity of a strong tonal melody and its transposition is mainly determined by two factors: (1) the distance on the height dimension between the original melody and its transposition (pitch distance), and (2) the distance between keys as inferred from the circle of fifths (key distance). The major part of the variance is explained by the factor pitch distance, whereas key distance explains only a small part.


Plenger, P.M., Breier, J.I., Wheless, J.W., Ridley, T.D., Papanicolaou, A.C., Brookshire, B., Thomas, A., Curtis, V., and Willmore, L.J. (1996). Neuropsychologia, 34:1015-1018.

           Abstract: The present study was conducted to determine whether material-specific memory for unfamiliar tonal patterns could be demonstrated for the right temporal lobe during the intracarotid sodium amytal procedure (IAP). Thirty-one patients with intractable complex partial seizures associated with either left temporal lobe epilepsy (LTLE) or right temporal lobe epilepsy (RTLE) underwent assessment of memory for tonal patterns during a baseline phase and right and left cerebral hemisphere anesthesia during IAP. Patients were presented unfamiliar tonal patterns which were later selected from a set of distracter patterns. Findings indicated that there was no difference between LTLE and RTLE patients during injection of the right cerebral hemisphere suggesting no specific involvement of left mesial temporal structures. However, a significant effect was noted during left injection with the LTLE group performing significantly better than the RTLE group. This latter finding supports a specific role of right mesial temporal lobe structures in mediating memory for music.


Zimmerman, L., Nieveen, J., Barnason, S., Schmaderer, M. (1996). The effects of music interventions on postoperative pain and sleep in coronary artery bypass graft (CABG) patients. Scholarly Inquiry for Nursing Practice, Summer, 10:171-174.

           Abstract: The purpose of this experimental study was to determine the effects of second and third day postoperative music interventions (music, music video) on pain and sleep in 96 postoperative patients having CABG surgery. The McGill Pain Questionnaire (MPQ) was administered before session 1 and after session 2, and results indicated that Sensory, Affective, and Present Pain Intensity subscales showed no group difference for pain; however, pain decreased from Day 2 to Day 3 for all three groups. For the evaluative component of pain, those in the music group had significantly (F[2,93] = 4.74, p < .05) lower scores on postoperative Day 2 than the rest period control group. Effects of the intervention on sleep as measured by the Richard Sleep Questionnaire indicated that the video group had significantly (F[2, 92] = 3.18, p < .05) better sleep scores than the control group on the third morning. These findings lend some support for selected music interventions.

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Forthcoming Events

First International Conference on Music in Human Adaptation, will be held November 15-17, 1997 at The Hotel Roanoke & Conference Center in Roanoke, Virginia. Topics will concern subjects pertinent to music in human development, adaptation and function. There will be presentations of papers, workshops and panel discussions. For further information contact: Daniel J. Schneck, Virginia Tech, ESM Department, Mail Code 0219, Blacksburg, VA 24061-0219, voice: (540) 231-5626, fax: (540) 382-0915 or (540) 231-4574, e-mail: adanielj@vtvm1.cc.vt.edu or Dorita Berger, Connecticut Music Therapy Alliance, Post Office Box 473, Norwalk, CT 06850-0473, voice and fax: (203) 853-4426.

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Back Issues of MuSICA Research Notes

Back issues of MRN are available. If you would like to receive any or all of them, please write, email or call:

N.M. Weinberger
Center for the Neurobiology of Learning and Memory
University of California Irvine
Irvine CA 92697-3800
Tel: (714) 824-5512

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MuSICA on the WEB

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"For a few moments music makes us larger than we really are, and the world more orderly than it really is...As our brains are thrown into overdrive, we feel our very existence expand and realize that we can be more than we normally are, and that the world is more than it seems. That is cause enough for ecstasy."-- from Music, the Brain and Ecstasy by Robert Jourdain (William Morrow & Co., New York:1997)


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