Musical Intervals Research Articles

It all starts with music – musical intervals in neonatal crying

ABSTRACTBackground: Having had ample opportunity to become acquainted with their mother’s voice melody in the womb, newborns have been found to exhibit salient ‘musical’ elements in their own cry melodies. Musical interval-like substructures have also been observed in young infants crying. The aim of the study was to answer the question of whether interval-like substructures regularly occur in crying. Method: Here, we studied for the first time, a total of 2740 cry utterances from 58 healthy, term-born infants at a mean age of 3 days. Results and Conclusion: The study demonstrated that intervals are regularly occurring in crying with the semitone being the prevailing interval. No sex differences were found.

A Comparative Study of Sassanid, Qajar and Contemporary Phonetic Systems

Comparison among the phonetic of people in different eras helped us to find a better understanding of their culture. Also we can use this approached to predict the future phonetic. In this paper we study the difference among phonetic of people in the present period, Qajar era and Sassanid era. 2000 people in Tehran are selected randomly. Because Tehran is the capital of Iran, and the people from all over different parts of Iran are gathered in Tehran, this sample can be considered as the sample of Iranian people. From each one a speech is recorded. Using the VST instrument, these speeches translated to a harmony and a consensus harmony is considered as the harmony of current people’s phonetic. By Simulation of the speech of the people in Qajar era the harmony of speech of that ear is simulated. Finally by using the 504 Gushehes and Radif of Iranian Avaz, which is generated in Sassanid ear, the harmony of the people in this era is simulated. By comparison of these three harmonies, we obtained a significant different between the harmony of current era and Sassanid era, which is in the basic musical interval. These differences between now and Qajar era is in the upper fifth musical interval. It is shown that during the last 1500 years there exist 2.5 blind musical deviations between harmony of current phonetics and Sassanid Harmony phonetics. This deviation from Qajar era until now is 0.5 blind musical interval. Our results show that the deviation in the harmony of Iranian phonetics from the phonetics of the people of last century is more with respect to the people in the ancient time.

FMRI Mapping of Brain Activity Associated with the Vocal Production of Consonant and Dissonant Intervals.

The neural correlates of consonance and dissonance perception have been widely studied, but not the neural correlates of consonance and dissonance production. The most straightforward manner of musical production is singing, but, from an imaging perspective, it still presents more challenges than listening because it involves motor activity. The accurate singing of musical intervals requires integration between auditory feedback processing and vocal motor control in order to correctly produce each note. This protocol presents a method that permits the monitoring of neural activations associated with the vocal production of consonant and dissonant intervals. Four musical intervals, two consonant and two dissonant, are used as stimuli, both for an auditory discrimination test and a task that involves first listening to and then reproducing given intervals. Participants, all female vocal students at the conservatory level, were studied using functional Magnetic Resonance Imaging (fMRI) during the performance of the singing task, with the listening task serving as a control condition. In this manner, the activity of both the motor and auditory systems was observed, and a measure of vocal accuracy during the singing task was also obtained. Thus, the protocol can also be used to track activations associated with singing different types of intervals or with singing the required notes more accurately. The results indicate that singing dissonant intervals requires greater participation of the neural mechanisms responsible for the integration of external feedback from the auditory and sensorimotor systems than does singing consonant intervals.

FMRI Mapping of Brain Activity Associated with the Vocal Production of Consonant and Dissonant Intervals

The neural correlates of consonance and dissonance perception have been widely studied, but not the neural correlates of consonance and dissonance production. The most straightforward manner of musical production is singing, but, from an imaging perspective, it still presents more challenges than listening because it involves motor activity. The accurate singing of musical intervals requires integration between auditory feedback processing and vocal motor control in order to correctly produce each note. This protocol presents a method that permits the monitoring of neural activations associated with the vocal production of consonant and dissonant intervals. Four musical intervals, two consonant and two dissonant, are used as stimuli, both for an auditory discrimination test and a task that involves first listening to and then reproducing given intervals. Participants, all female vocal students at the conservatory level, were studied using functional Magnetic Resonance Imaging (fMRI) during the performance of the singing task, with the listening task serving as a control condition. In this manner, the activity of both the motor and auditory systems was observed, and a measure of vocal accuracy during the singing task was also obtained. Thus, the protocol can also be used to track activations associated with singing different types of intervals or with singing the required notes more accurately. The results indicate that singing dissonant intervals requires greater participation of the neural mechanisms responsible for the integration of external feedback from the auditory and sensorimotor systems than does singing consonant intervals.

Differences in sound perception are reflected by individual auditory fingerprints in musicians

Musicians have been reported to show significant inter-Individual differences in elementary hearing functions, sound perception mode, musical instrument preference, performance style, as well as more complex musical abilities like absolute- and relative pitch perception, and auditory imagery. However, it remains unexplored how individual elementary hearing functions and corresponding musical abilities are inter-connected and to what extend they reflect individual differences in the musical behavior of musicians. Using a combination of five listening tests and assessing resulting psychoacoustic parameters, we were able to determine individual auditory fingerprints on the single subject- and group level. 93 musicians (49 professionals and 44 amateurs) were individually tested for: frequency discrimination threshold, holistic and spectral sound perception, absolute pitch perception, relative pitch perception (musical interval recognition), and musical imagery (AMMA). On the individual level, our results show that auditory fingerprints differ remarkably between subjects. On the group level, using PCA and cluster analysis, we found four main components represented significantly different in the three characteristic clusters of subjects. Taken together, our findings suggest that inter-individual differences in the auditory fingerprint reflect the high variability of individual sound perception and may have crucial impact on specific musical preference, style and performance of musicians.

Sensory cortical response to uncertainty and low salience during recognition of affective cues in musical intervals.

Previous neuroimaging studies have shown an increased sensory cortical response (i.e., heightened weight on sensory evidence) under higher levels of predictive uncertainty. The signal enhancement theory proposes that attention improves the quality of the stimulus representation, and therefore reduces uncertainty by increasing the gain of the sensory signal. The present study employed functional magnetic resonance imaging (fMRI) to investigate the neural correlates for ambiguous valence inferences signaled by auditory information within an emotion recognition paradigm. Participants categorized sound stimuli of three distinct levels of consonance/dissonance controlled by interval content. Separate behavioural and neuroscientific experiments were conducted. Behavioural results revealed that, compared with the consonance condition (perfect fourths, fifths and octaves) and the strong dissonance condition (minor/major seconds and tritones), the intermediate dissonance condition (minor thirds) was the most ambiguous, least salient and more cognitively demanding category (slowest reaction times). The neuroscientific findings were consistent with a heightened weight on sensory evidence whilst participants were evaluating intermediate dissonances, which was reflected in an increased neural response of the right Heschl’s gyrus. The results support previous studies that have observed enhanced precision of sensory evidence whilst participants attempted to represent and respond to higher degrees of uncertainty, and converge with evidence showing preferential processing of complex spectral information in the right primary auditory cortex. These findings are discussed with respect to music-theoretical concepts and recent Bayesian models of perception, which have proposed that attention may heighten the weight of information coming from sensory channels to stimulate learning about unknown predictive relationships.

A Beginner's Guide to the Musical Scales of Cyberwar

This article is a beginner's guide to the 'musical scales' of cyberwar. Using the analogy of a piano keyboard, it aims to promote an understanding of what constitutes a use of force in cyberspace and how a state may lawfully respond. To help achieve this, the article utilizes the concept of Middle C and musical intervals known as octaves to explain the range of permissible state conduct during times of conflict. By juxtaposing the law of war with a keyboard, the process of how states evaluate the scale and effects of a cyber operation, and determine a basis for resorting to a use of force under the Law of Armed Conflict, can be more readily conceptualized. And if music is indeed, the universal language of mankind, then by encouraging society to learn about the law of war, we can collectively better strategize ways to mitigate conflict in this domain.

Musical intervals under 12-note equal temperament: a geometrical interpretation

Musical intervals in multiple of semitones under 12-note equal temperament, or more specifically pitch-class subsets of assigned cardinality ($n$-chords) are conceived as positive integer points within an Euclidean $n$-space. The number of distinct $n$-chords is inferred from combinatorics with the extension to $n=0$, involving an Euclidean 0-space. The number of repeating $n$-chords, or points which are turned into themselves during a circular permutation, $T_n$, of their coordinates, is inferred from algebraic considerations. Finally, the total number of $n$-chords and the number of $T_n$ set classes are determined. Palindrome and pseudo palindrome $n$-chords are defined and included among repeating $n$-chords, with regard to an equivalence relation, $T_n/T_nI$, where reflection is added to circular permutation. To this respect, the number of $T_n$ set classes is inferred concerning palindrome and pseudo palindrome $n$-chords and the remaining $n$-chords. The above results are reproduced within the framework of a geometrical interpretation, where positive integer points related to $n$-chords of cardinality, $n$, belong to a regular inclined $n$-hedron, $\Psi_{12}^n$, the vertexes lying on the coordinate axes of a Cartesian orthogonal reference frame at a distance, $x_i=12$, $1\le i\le n$, from the origin. Considering $\Psi_{12}^n$ as special cases of lattice polytopes, the number of related nonnegative integer points is also determined for completeness. A comparison is performed with the results inferred from group theory.

Three Poems

photo : susanna hsing Three Poems by Kiriu Minashita Rhythm Lucretius’s atomic rain falls gradually above daily congestion, wetting my earlobes with noise. I’ve swallowed the good parts of several drops sleepy dissonance. On one side, the trembling world, a forest of umbrellas. Beyond dreams of homeostatic noise and air compressors, a serene garden of flowers. Little dog with a rising bark. Little woman smacking it. Little pellets of rain that stain into my hair Little courtyard of an elementary school Little voices humming If you listen closely to those voices’ noises, there’s vivid rhythm. Poison is stirred into your s-igh. Several bags of air float at the street corner. Then, the traffic signal rottens with each breath. What is here is only red rust, and ev· ery· one gets a· long. I sever today’s date that falls toward heaven from the spaces between the stones WORLDLIT.ORG 45 that give sound to the sighing of my feet. Soon, the day becomes dark tidying up a snug line of ice-contrails. When you call, I’m at the base of the Universal Building in Nakano where I build a mountain range in the exaggerated spaces of required etiquette. I look up. Right in the middle of a bright frozen darkness the greedy overflowing sun laughs at me, straining my ears, amazed. Humid in Tokyo The first and last stops on the Chuo Line are the beginning and ending of a story I completely miss while napping. Furious freezing rain angles up from the ground, cutting wires and cinder blocks diagonally. The gap between buildings zoned for ma· xi· mum per-floor den· si· ty is bathed in metal blessings. From the cloud-seam, instead of sky, I see words in musical intervals. A street vendor says the painters who fill the Void have finished their installation. The vendor whispers, a hexagonal color wheel in one hand. In the agora in front of the convenience store, the conveniently un· em· ployed assemble drink eat smoke trash smile. Happy to oblige the om· in· ous yel· low sign· board: In· ten· ded For Com· mer· cial Use smile. That guy living in a cardboard box must be wri· ting some kind of un· seen poem, you say, smile. The world is sunny. Frozen and sunny, the sun trembling and rattling. Pleasantly sunny while trembling. In a sunny spot on a sunny afternoon, weddings, death notices, to· night’s ap· pe· ti· zers are lined up neatly, then tossed. The end-of-the-world catastrophe keeps coming gently. Every time I step into a hole in the road, I see the setting sun of the world. Still, I can’t tell if I’m seeing things, or hear· ing things? Right away, a change of key— today, the beat correlated to my pulse in 6/8 time. I hear voices— Tokyo Humidity for Sale, sing the vendors, in perfect pitch. Festival of Water My view is blocked by ice driz· zle rising from asphalt. The lines of (what should be) earth are endless, twis· ted up. At the feast (intra festum) 46 WLT MARCH–APRIL 2017 cover feature dystopian visions WORLDLIT.ORG 47 we keep quivering with the sun’s rays like growing plants. Pascal’s human misery, on a personal day. For example: the way a hunger artist disregards the round dance of life*— At the heart of its roar, the world is always sparkling in the stillness before the end. Flood the stores of de· sic· ca· ted days, draw the boundary once more. You leave behind a wet trail lit by sunshine. If I look the world is glaring, stretching and elongating. In the end, the world is expanding: wave of heat, smokescreen of water. But I’m interrupted by the shadow of a giant question mark falling straight down. Will the day end in a feast of broad daylight? Or will it sink into spray? (How biz· zare) right before my eyes, I see wetness that didn’t fall as rain. Not the water of the rain that strews the road with sorrow. But you, left behind. Translations from the Japanese By Eric E. Hyett...

Three Poems

photo : susanna hsing Three Poems by Kiriu Minashita Rhythm Lucretius’s atomic rain falls gradually above daily congestion, wetting my earlobes with noise. I’ve swallowed the good parts of several drops sleepy dissonance. On one side, the trembling world, a forest of umbrellas. Beyond dreams of homeostatic noise and air compressors, a serene garden of flowers. Little dog with a rising bark. Little woman smacking it. Little pellets of rain that stain into my hair Little courtyard of an elementary school Little voices humming If you listen closely to those voices’ noises, there’s vivid rhythm. Poison is stirred into your s-igh. Several bags of air float at the street corner. Then, the traffic signal rottens with each breath. What is here is only red rust, and ev· ery· one gets a· long. I sever today’s date that falls toward heaven from the spaces between the stones WORLDLIT.ORG 45 that give sound to the sighing of my feet. Soon, the day becomes dark tidying up a snug line of ice-contrails. When you call, I’m at the base of the Universal Building in Nakano where I build a mountain range in the exaggerated spaces of required etiquette. I look up. Right in the middle of a bright frozen darkness the greedy overflowing sun laughs at me, straining my ears, amazed. Humid in Tokyo The first and last stops on the Chuo Line are the beginning and ending of a story I completely miss while napping. Furious freezing rain angles up from the ground, cutting wires and cinder blocks diagonally. The gap between buildings zoned for ma· xi· mum per-floor den· si· ty is bathed in metal blessings. From the cloud-seam, instead of sky, I see words in musical intervals. A street vendor says the painters who fill the Void have finished their installation. The vendor whispers, a hexagonal color wheel in one hand. In the agora in front of the convenience store, the conveniently un· em· ployed assemble drink eat smoke trash smile. Happy to oblige the om· in· ous yel· low sign· board: In· ten· ded For Com· mer· cial Use smile. That guy living in a cardboard box must be wri· ting some kind of un· seen poem, you say, smile. The world is sunny. Frozen and sunny, the sun trembling and rattling. Pleasantly sunny while trembling. In a sunny spot on a sunny afternoon, weddings, death notices, to· night’s ap· pe· ti· zers are lined up neatly, then tossed. The end-of-the-world catastrophe keeps coming gently. Every time I step into a hole in the road, I see the setting sun of the world. Still, I can’t tell if I’m seeing things, or hear· ing things? Right away, a change of key— today, the beat correlated to my pulse in 6/8 time. I hear voices— Tokyo Humidity for Sale, sing the vendors, in perfect pitch. Festival of Water My view is blocked by ice driz· zle rising from asphalt. The lines of (what should be) earth are endless, twis· ted up. At the feast (intra festum) 46 WLT MARCH–APRIL 2017 cover feature dystopian visions WORLDLIT.ORG 47 we keep quivering with the sun’s rays like growing plants. Pascal’s human misery, on a personal day. For example: the way a hunger artist disregards the round dance of life*— At the heart of its roar, the world is always sparkling in the stillness before the end. Flood the stores of de· sic· ca· ted days, draw the boundary once more. You leave behind a wet trail lit by sunshine. If I look the world is glaring, stretching and elongating. In the end, the world is expanding: wave of heat, smokescreen of water. But I’m interrupted by the shadow of a giant question mark falling straight down. Will the day end in a feast of broad daylight? Or will it sink into spray? (How biz· zare) right before my eyes, I see wetness that didn’t fall as rain. Not the water of the rain that strews the road with sorrow. But you, left behind. Translations from the Japanese By Eric E. Hyett...

Momentum in music: Musical succession as physical motion.

Metaphors involving motion have shaped discussion and understanding of for millennia. Rothfarb (2001, p. 927) points out that ever since ancient times authors have identified motion as a functional aspect of Perhaps the most famous example is the so-called music of the spheres in which Kepler in Harmonices Mundi attempted to connect planetary motion with numerical ratios of musical intervals (Balbi, 2008). St. Augustine in Da Musica defined as scientia bene modulani, which translates as knowledge of correct (MacInnis, 2015), and Rameau's Treatise on Harmony refers to collisions of sounds (Christiansen, 2004). More recently, Shove and Repp (1995) concluded can represent natural forms of motion, Clarke (2001, 2005) concluded the relationship between and motion provides an important part of music's impact and meaning, Eitan and Granot (2006) considered how was associated with bodily movement, and Phillips-Silver (2009) concluded a link between and movement was pervasive in human experience. Consistent with this, Larson (2012) suggested an important metaphor in our conceptualization of is Musical Succession is Physical Motion. Indeed, Larson (2012, p. 50) noted is hard to imagine a term that describes physical motion that has not been, or could not be, applied to music, and he provided many examples of spatial and motion metaphors in (e.g., melodies moving by steps or leaps, melodic contours ascending or descending, presence of passing and leading tones; see also Johnson & Larson, 2003).The purpose here is to review data and theories regarding whether the mental representation of embodies a dynamic of motion. Production of typically requires motion of some sort (e.g., vibration of a string, reed, or drumhead; changing configurations of open [not pressed] and closed [pressed] keys on a musical instrument, etc.), and so in a trivial sense, arises from motion. However, and motion are complex concepts, and not every type of motion is necessarily a potential source of music. Rather than reviewing the relationship between and motion in general, the goal here is simpler: to consider the relationship between and a single consequence of motion, momentum. It is suggested that the mental representation of exhibits momentum-like effects that share many properties with momentum-like effects in other domains of perception, cognition, and behavior. Part 1 explores the notion of musical motion and considers Larson's discussion of musical forces in general and musical inertia in particular. Part 2 reviews information on different (nonmusical) momentum-like effects and considers whether musical inertia is consistent with these effects. Part 3 examines implications and consequences of musical momentum, and considers dynamic representation and functional architecture, an emphasis on extrapolation across time, auditory streaming and perceptual grouping, auditory kappa and tau effects, naive physics of forces, and which aspects of might map on to different components of momentum. Part 4 provides a brief summary and conclusions.Part 1: Music and MotionIt has long been thought that is related to motion (for reviews, see Eitan & Granot, 2006; Phillips-Silver, 2009; Rothfarb, 2001; Shove & Repp, 1995). Motion of a physical object results from physical forces, and the existence of analogous musical forces associated with musical succession in Western tonal was proposed by Larson (2004, 2012; Larson & van Handel, 2005). In Part 1, the idea of musical forces, and the properties of a specific musical force-musical inertia-are considered.Musical Succession and Physical MotionWhat is it that moves in music? Indeed, the idea of musical motion is something of a puzzle, in that unless the source of the (e.g., performer, loudspeaker) is physically moving, the per se does not actually physically move (see Larson, 2012; Zuckerkandl, 1956). …

On Zwicker tones and musical pitch in the likely absence of phase locking corresponding to the pitch.

It was assessed whether Zwicker tones (ZTs) (an auditory afterimage produced by a band-stop noise) have a musical pitch. First (stage I), musically trained subjects adjusted the frequency, level, and decay time of an exponentially decaying diotic sinusoid to sound similar to the ZT they perceived following the presentation of diotic broadband noise, for various band-stop positions. Next (stage II), subjects adjusted a sinusoid in frequency and level so that its pitch was a specified musical interval below that of either a preceding ZT or a preceding sinusoid, and so that it was equally loud. For each subject the reference sinusoid corresponded to their adjusted sinusoid from stage I. Subjects selected appropriate frequency ratios for ZTs, although the standard deviations of the adjustments were larger for the ZTs than for the equally salient sinusoids by a factor of 1.0-2.2. Experiments with monaural stimuli led to similar results, although the pitch of the ZTs could differ for monaural and diotic presentation of the ZT-exciting noise. The results suggest that a weak musical pitch may exist in the absence of phase locking in the auditory nerve to the frequency corresponding to the pitch (or harmonics thereof) at the time of the percept.

More about monaural noise edge pitch

Lowpass noise with a sharp spectral cutoff generates a monaural noise edge pitch (MNEP) that listeners match with a sine tone having a frequency somewhat below the noise cutoff frequency (negative pitch shift). If the MNEP is a proper musical pitch, listeners should be able to identify musical intervals made using only the MNEP stimulus. Open-set MNEP experiments in the edge-frequency range of 600-2400 Hz found that four out of four listeners with musical training correctly identified octaves, fifths, fourths, and major thirds, proving that the MNEP is a musical pitch. The MNEP can be heard for edge frequencies at least as low as 100 Hz, but the negative pitch shift becomes larger than a semitone, consistent with a timing model of the MNEP having a fixed integration time. If the MNEP reflects the expected quasi-periodic timing response of the auditory system to a sharp spectral edge, the pitch should become inaudible if the edge frequency becomes too high for neural synchrony—expected to be about 5000 Hz. Sine tone pitch matching experiments showed that such a limit clearly applies for most listeners, but less clearly for others. [Work supported by the USAFOSR.]

The Music of the Spheres

The integration of music and science is embodied in the music of the spheres, the ancient concept that the universe is ordered in a manner consistent with principles of musical harmony. This idea boasts a long history, from the teachings of Pythagoras (ca. 600 BC) through Isaac Newton in the eighteenth century, and makes a fascinating interdisciplinary topic accessible to middle and high school students. Several music-science correlations are explored, including the mathematical commonalities between musical intervals and planetary orbits. The article includes teaching suggestions and student activities.

Facing pitch: Constructing associations between space and pitch leads to better estimation of musical intervals

Mental-spatial representations are often used for processing quantities and magnitudes such as numbers or pitch. The present study investigates whether the active creation of associations between space and pitch magnitude leads to a better estimation of the distances between pitches (musical intervals). Non-musicians performed an aurally presented comparison task in which musical intervals had to be estimated both before and after a training phase. Experiment 1 shows that the experimental group participants who were given the opportunity to establish associations between space and pitch (by means of spatial visualizations presented during training) improved significantly regarding their skill of estimating musical intervals compared with a control group without exposure to spatial visualizations during training. Experiment 2 replicated these findings, and a supplementary experimental group showed that the establishment of these associations is hindered when, additionally to pitch, task-irrelevant information about the point in time at which a tone is played during a trial, is also presented spatially during training (which does not decrease performance in training). We found that explicitly creating associations between space and pitch leads to a better estimation of the size of musical intervals, and we conclude that using analogies between space and pitch, e.g., in aural training in music education, is an efficient way to train the perception of pitch distances between musical notes.

Music intervals in speech: Psychological disposition modulates ratio precision among interlocutors’ nonlocal f0 production in real-time dyadic conversation

Drawing on the notion of musical intervals, recent studies have demonstrated the use of precise frequency ratios within human vocalisation. Methodologically, these studies have addressed human vocalisation at an individual level. In the present study, we asked whether patterns such as musical intervals can also be found among the voices of people engaging in a conversation as an emerging interpersonal phenomenon. Fifty-six participants were randomly paired and assigned to either a control or a low-trust condition. Frequency ratios were generated by juxtaposing nonlocal fundamental frequency (f0) productions from two people engaged in each given dyadic conversation. Differences were found among conditions, both in terms of interval distribution and precision. These results support the idea that psychological dispositions modulate the musical intervals generated between participants through mutual real-time vocal accommodation. They also underscore the inter-domain use of musical intervals.

Students’ performance when aurally identifying musical harmonic intervals: Experimentation of a teaching innovation proposal

The aim of the study was to measure the performance reached by students ( N = 138) when aurally identifying musical harmonic intervals (from m2 to P8) after having experienced a teaching innovation proposal for the Music Conservatories of Catalonia (Spain) based on observational methodology. Its design took into account several issues, which had been detected previously as being conflictive. The teaching innovation proposal was tested during an academic year in six Catalan Music conservatories, specifically in Music Theory classes in the first year of a 6-year professional course. A quasi-experimental pre-test/post-test design was used. The existence of a control group gave a reference point for the measured results before and after an intervention period. By the end of the teaching–learning process, it was established that the performance of the participants had improved, resulting in statistically significant differences in favour of the experimental group.

Efficacy of musical intervals on psychological parameters: a randomized controlled trial

Efficacy of musical intervals on psychological parameters: a randomized controlled trial

Neural activity related to discrimination and vocal production of consonant and dissonant musical intervals

Background: Relationships between musical pitches are described as either consonant, when associated with a pleasant and harmonious sensation, or dissonant, when associated with an inharmonious feeling. The accurate singing of musical intervals requires communication between auditory feedback processing and vocal motor control (i.e. audio-vocal integration) to ensure that each note is produced correctly. The objective of this study is to investigate the neural mechanisms through which trained musicians produce consonant and dissonant intervals.Methodology: We utilized 4 musical intervals (specifically, an octave, a major seventh, a fifth, and a tritone) as the main stimuli for auditory discrimination testing, and we used the same interval tasks to assess vocal accuracy in a group of musicians (11 subjects, all female vocal students at conservatory level). The intervals were chosen so as to test for differences in recognition and production of consonant and dissonant intervals, as well as narrow and wide intervals. The subjects were studied using fMRI during performance of the interval tasks; the control condition consisted of passive listening.Results: Singing dissonant intervals as opposed to singing consonant intervals led to an increase in activation in several regions, most notably the primary auditory cortex, the primary somatosensory cortex, the amygdala, the left putamen, and the right insula. Singing wide intervals as opposed to singing narrow intervals resulted in the activation of the right anterior insula. Moreover, we also observed a correlation between singing in tune and brain activity in the premotor cortex, and a positive correlation between training and activation of primary somatosensory cortex, primary motor cortex, and premotor cortex during singing. When singing dissonant intervals, a higher degree of training correlated with the right thalamus and the left putamen.Conclusions/Significance: Our results indicate that singing dissonant intervals requires greater involvement of neural mechanisms associated with integrating external feedback from auditory and sensorimotor systems than singing consonant intervals, and it would then seem likely that dissonant intervals are intoned by adjusting the neural mechanisms used for the production of consonant intervals. Singing wide intervals requires a greater degree of control than singing narrow intervals, as it involves neural mechanisms which again involve the integration of internal and external feedback.

A case study approach involving string harmonics to reinforce concepts of standing waves, superposition, and musical intervals... as well as the scientific process

A combined classroom/lab activity is described that employs a modified Interrupted Case Study approach to reinforce concepts of standing waves, superposition, and musical intervals. Students work cooperatively, with guidance from the instructor, to investigate the behavior of a plucked string. The activity is structured as a sequence of tasks that encapsulate the scientific process, requiring the application of critical thinking skills and knowledge from earlier classes. Students working in small groups propose a hypothesis about the behavior of a string that is plucked, drawing upon previous studies of superposition and standing wave behavior in a driven string. After a class discussion, one hypothesis is chosen as the basis for further inquiry. Each group then formulates specific testable predictions, with the constraint that only a mounted string (sonometer), finger, and ears be used in any experiment. After discussion, the class chooses a subset of these predictions to test. Groups formulate a detailed procedure (generally involving creating harmonics on the string), carry out the experiment, and interpret their results. Conclusions are shared among the class.