Consonant Intervals Research Articles

Core principles of melodic organisation emerge from transmission chains with random melodies

Music is a product of both biological and cultural evolution. Cultural transmission is the engine of cultural evolution and may play a role in the establishment of musical universals. Here, we examined how transmission dynamics can shape melodic features in music. Specifically, we tested whether random melodic seeds, in their transformation, take on properties known to characterise music within or even across cultures. Using an iterated learning paradigm, we investigated the transmission of random melodic seeds through a chain of non-musician participants (N = 64). We found that melodies reproduced vocally between “generations” became more similar to known musical scales, exhibited a predominance of consonant intervals, and reduced the number of scale degrees used. Additionally, we observed the previously documented tendency for large intervals to be followed by a change in direction, as well as features common to both music and speech including phrase-final lengthening and the Zipfian distribution of signalling units. As participants' vocalisations converged towards greater memorability, they exhibited decreased entropy, and their contours became smoother and more consistent. Finally, certain short melodic patterns became prominent motifs within the incipient musical “traditions” simulated by the chains. These emerging features may reflect a process shaped by (i) cognitive bottlenecks such as learnability; (ii) statistical properties of the processes and structures involved in inter-generational vocal transmission; but also by (iii) idiosyncratic cultural artefacts specific to the lab samples employed. Overall, our results demonstrate that fundamental aspects of melodic structure emerge naturally through the process of cultural transmission, as simulated in the lab.

Impact of Japanese L1 Rhythm on English L2 Speech.

The study aimed to examine whether L1 speech rhythm affects L2 speech by assessing how the speech rhythm of Japanese L2 English speakers differed from native speakers. We chose Japanese and English because they differ markedly in the phonological properties that likely contribute to speech rhythm. Speech rhythm was measured by the variability of vowel and consonant intervals using rate-normalized rhythm metrics (VarcoV and VarcoC; nPVI-V and nPVI-C) and %V. The study utilized recordings of spoken sentences in English by 10 native Australian English speakers; and in English and also in Japanese by 10 native Japanese speakers (who had limited experience in speaking English). Experiment 1 compared the rhythm of L1 English (by measuring 1,750 vowels and 3,093 consonants from 20 sentences) and L1 Japanese (1,923 vowels and 2,097 consonants from 10 sentences). The results showed that for all measures, Japanese had reduced durational variability in both consonant and vowel intervals compared with English. In Experiment 2, we examined the rhythm characteristics of L1 and L2 English using 40 sentences (including the 20 in Experiment 1). The results showed that vowel and consonant intervals were less variable in L2 (Japanese English) than in L1 (Australian English) speech, mirroring the results of Experiment 1. Overall, the results are consistent with the proposal that L1 (Japanese) speech rhythm influenced L2 (English) speech.

The ripples of consonant intervals and chords arising in different tuning systems

Pure consonances are combinations of exact multiples of a fundamental frequency, particularly with the factors 2, 3, and 5. They give rise to the consonant intervals (octave, perfect fifth, and major and minor thirds) and consonant chords (major and minor). However, these kinds of consonances are only achieved in just intonation, which does not produce beats or ripples, that is, their envelopes are constant. On the contrary, other tuning systems, such as Pythagorean, meantone, or N-tone equal temperaments, which slightly differ from just intonation, actually produce beats or ripples, that is, the corresponding envelopes oscillate and, acoustically, resemble a vibrato in amplitude. In this paper, the envelopes of consonant intervals and chords are modelled mathematically by approximate formulas. They contain one variable for the intervals and two variables for the chords. The formulas include deviations of one full trigonometric period, thus being valid for any tuning system. In the case of intervals, the corresponding ripples are obtained by following a line (1D) at a specific velocity and, in the case of chords, by following a line on a graph (2D) at specific velocity and direction. The corresponding audio files considering pure tones are also obtained.

Nonspecific hebbian neural network model predicts musical scales discreteness and just intonation without using octave-equivalency mapping

This study continues investigating the consonance-pattern emerging neural network model introduced in our previous publication, specifically to test if it will reproduce the results using 100-fold finer precision of 1/100th of a semitone (1 cent). The model is a simplistic feed-forward generic Hebbian-learning generic neural network trained with multiple-harmonic complex sounds from the full auditory sound spectrum of 10 octaves. We use the synaptic weights between the neural correlates of each two-tone from the said spectrum to measure the model’s preference to their inter-tonal interval (12,0002 intervals), considering familiarity as a consonance predictor. We analyze all the 12,000 intervals of a selected tone (the tonic), and the results reveal three distinct yet related features. Firstly, Helmholtz’s list of consonant intervals re-emerges from the synaptic weights of the model, although with disordered dissonant intervals. Additionally, the results show a high preference to a small number of selected intervals, mapping the virtually continual input sound spectrum to a discrete set of intervals. Finally, the model's most preferred (most consonant) intervals are from the Just Intonation scales. The model does not need to use cross-octave interval mapping due to octave equivalence to produce the said results.

Local minima of dissonance functions

When the same sound is produced simultaneously with two different fundamental frequencies, auditory roughness is observed. If the first sound is fixed and the fundamental frequency of the second is varied continuously, auditory roughness also varies continuously. A vowel sound is distinguished by its spectral envelope – which is independent of the fundamental frequency. This is a motivation to define the metric space of timbres. Each timbre is associated with a dissonance function which has local minima at certain intervals of local consonance related to the timbre. This is related to the music-theoretical notion of consonant intervals and scales. For the subspace consisting of all timbres with an interval of local consonance at a chosen point β, the main theorem describes certain points on the boundary by the vanishing of one-sided derivatives of dissonance functions at β.

Lengthening and shortening processes in Korean

This study examines the duration of Korean lax and tense stops in the prosodic word-medial position, their interactions with nearby segments, and the phonological implications of these interactions. It first examines the lengthening of consonants at the function of the short lax stop. Experiment 1 shows that the sonorant C1 is significantly longer before a short lax stop C2 than before a long tense stop. Experiment 2 shows that the short lax stop C1 cancels the contrast between the lax and tense obstruent at C2, making them appear as long tense obstruents (Post-Stop Tensing Rule). We suggest that such lengthening phenomena occur in Korean to robustly preserve the contrastive length difference between C and CC. Second, this study examines the vowel shortening, known as Closed-Syllable Vowel Shortening, before a long tense stop or before the consonant sequence. Experiment 3 suggests that it be interpreted as temporal adjustment to make the interval from the onset of a vowel to the onset of the following vowel of near-equal length. Conclusively, we suggest that Korean speech be planned and controlled with two specific intervals. One is the duration of contrastive consonant intervals between vowels, and the other is the duration from the onset of a vowel to the onset of the following vowel.

Is consonance attractive to budgerigars? No evidence from a place preference study

Consonant tone combinations occur naturally in the overtone series of harmonic sounds. These include sounds that many non-human animals produce to communicate. As such, non-human animals may be attracted to consonant intervals, interpreting them, e.g., as a feature of important social stimuli. There is preliminary evidence of attraction to consonance in various bird species in the wild, but few experimental studies with birds. We tested budgerigars (Melopsittacus undulatus) for attraction to consonant over dissonant intervals in two experiments. In Experiment 1, we tested humans and budgerigars using a place preference paradigm in which individuals could explore an environment with multiple sound sources. Both species were tested with consonant and dissonant versions of a previously studied piano melody, and we recorded time spent with each stimulus as a measure of attraction. Human females spent more time with consonant than dissonant stimuli in this experiment, but human males spent equal time with both consonant and dissonant stimuli. Neither male nor female budgerigars spent more time with either stimulus type. In Experiment 2, we tested budgerigars with more ecologically relevant stimuli comprised of sampled budgerigar vocalizations arranged into consonant or dissonant chords. These stimuli, however, also failed to produce any evidence of preference in budgerigar responses. We discuss these results in the context of ongoing research on the study of consonance as a potential general feature of auditory perception in animals with harmonic vocalizations, with respect to similarities and differences between human and budgerigar vocal behaviour, and future methodological directions.

Perceived Tension, Movement, and Pleasantness in Harmonic Musical Intervals and Noises

Perceived valence, tension, and movement of harmonic musical intervals (from the unison to the octave presented in a low- and high-register) and standard noises (brown, pink, white, blue, purple) were assessed in two studies that differed in the crossmodal procedure by which tension and movement were rated: proprioceptive device or visual analog scale. Valence was evaluated in both studies with the visual analog scale. In a preliminary study, the proprioceptive device was calibrated with a psychophysical procedure. Roughness of the stimuli was included as covariate. Tension was perceived higher in dissonant intervals and in intervals presented in the high register. The higher the high-pitch energy content in the standard noise, the higher the perceived tension. The visual analog scale resulted in higher tension ratings than the proprioceptive device. Perception of movement was higher in dissonant intervals, in intervals in the high register, and in standard noises than in musical intervals. High-pitch spectrum noises were associated with more sense of movement than low-pitch spectrum noises. Consonant intervals and low-register intervals were evaluated as more pleasant than dissonant and high-register intervals. High-pitch spectrum purple and blue noises were evaluated as more unpleasant than low-pitch spectrum noises.

ENTROTUNER: A Computational Method Adopting the Musician’s Interaction With the Instrument to Estimate its Tuning

Archeomusicologists commonly use methods based on the physical properties and the relative tuning system of a musical instrument in order to estimate its tones. However, because the musician often alters the tones’ frequency, for example, while playing in wind instruments by means of embouchure or by stressing the string in string instruments, the current methods that neglect the musician’s interaction with the instrument cannot provide solid results. In this work, we introduce ENTROTUNER, a computational method, based on mathematical optimization, to more accurately estimate the generated tones by considering: the instrument as a sound production mechanism, the relevant musical scale(s), and the musician’s interaction with the instrument. We simulate this interaction as a system that, by following tuning rules, aims to maximize the partials’ overlap (harmonicity), coded as entropy’s minimization of the aggregated tones’ spectrum. Last, we put ENTROTUNER into practice for the ancient Greek wind instrument Aulos. The results reveal that, compared with the traditional methods, ENTROTUNER highlights increased harmonicity (entropy decreased by 0.341bits), eleven additional consonant intervals, as well as 47.8% more tuning quality for the musical instrument.

Consonance perception beyond the traditional existence region of pitch.

Some theories posit that the perception of consonance is based on neural periodicity detection, which is dependent on accurate phase locking of auditory nerve fibers to features of the stimulus waveform. In the current study, 15 listeners were asked to rate the pleasantness of complex tone dyads (2 note chords) forming various harmonic intervals and bandpass filtered in a high-frequency region (all components >5.8 kHz), where phase locking to the rapid stimulus fine structure is thought to be severely degraded or absent. The two notes were presented to opposite ears. Consonant intervals (minor third and perfect fifth) received higher ratings than dissonant intervals (minor second and tritone). The results could not be explained in terms of phase locking to the slower waveform envelope because the preference for consonant intervals was higher when the stimuli were harmonic, compared to a condition in which they were made inharmonic by shifting their component frequencies by a constant offset, so as to preserve their envelope periodicity. Overall the results indicate that, if phase locking is indeed absent at frequencies greater than ∼5 kHz, neural periodicity detection is not necessary for the perception of consonance.

A Study to Explore the Effects of Sound Vibrations on Consciousness

Sound is a form of energy produced by vibrations caused by movement of particles. Sound can travel through solids (such as metal, wood, membranes), liquids (water) and gases (air). The sound vibrations that reach our ear are produced by the movement of particles in the air surrounding the source of sound. The movement or vibration of particles produces waves of sound. Sound waves are longitudinal and travel in the direction of propagation of vibrations. The pitch of sound is related directly to its frequency, which is given by the number of vibrations or cycles per second. The higher the pitch of sound, the higher is its frequency, and the lower the pitch, the lower is its frequency. Human ear can hear sounds of frequencies ranging from 20 – 20,000 cycles per second (or Hertz – Hz). Sound waves can be visually seen and studied using 'Chladni' plates, which was devised and experimented by Ernst Chladni, a famous physicist with a passion for sound/music. In this experiment the source of sound is connected via a wave driver to the Chladni metal plate with fine sand strewn on it. The sound vibrations cause the plate to vibrate at the same frequency, which causes movement of the sand particles to form patterns of the sound generated. The visual patterns comprise of nodes or regions where the sand particles accumulate, and antinodes or regions where the sand particles drift away from. Each frequency of sound causes a particular pattern to be formed on the plate. The study of wave phenomena is also called 'Cymatics' (Raghu, 2016). Sound vibrations can come in contact physically through the body and have an effect on our consciousness at the mental, emotional and spiritual levels. Sounds that are musical can be categorized as consonant sounds that are pleasant, and dissonant sounds that are unpleasant or not so pleasant. Musical sounds are comprised of notes in increasing or decreasing order of pitch (frequency). The interval between notes can give rise to consonance and dissonance. Example, an interval of an octave -a range of seven notes - is said to be consonant, whereas an interval between adjacent notes can be dissonant. These are studied by experimenting with musical notes and intervals, their visual patterns and their effect on consciousness. While consonant intervals can cause happiness, joy, courage or calmness, dissonant intervals can cause tension, anger, fear or sadness, thereby affecting the emotional aspect of consciousness.

Early neural responses underlie advantages for consonance over dissonance

Consonant musical intervals tend to be more readily processed than dissonant intervals. In the present study, we explore the neural basis for this difference by registering how the brain responds after changes in consonance and dissonance, and how formal musical training modulates these responses. Event-related brain potentials (ERPs) were registered while participants were presented with sequences of consonant intervals interrupted by a dissonant interval, or sequences of dissonant intervals interrupted by a consonant interval. Participants were musicians and non-musicians. Our results show that brain responses triggered by changes in a consonant context differ from those triggered in a dissonant context. Changes in a sequence of consonant intervals are rapidly processed independently of musical expertise, as revealed by a change-related mismatch negativity (MMN, a component of the ERPs triggered by an odd stimulus in a sequence of stimuli) elicited in both musicians and non-musicians. In contrast, changes in a sequence of dissonant intervals elicited a late MMN only in participants with prolonged musical training. These different neural responses might form the basis for the processing advantages observed for consonance over dissonance and provide information about how formal musical training modulates them.

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.

Commentary: Cats prefer species-appropriate music.

Commentary: Cats prefer species-appropriate music.

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.

The Song of the Sirens

In Homer’s account of the adventurous journey of Odysseus, the song of the sirens was so appealing and tempting that it lured sailors to their deaths. Warned by the goddess Kirke, Odysseus overcame the trap by plugging his crew’s ears with wax. An archaeo-acoustical research expedition undertaken by members of Humboldt University Berlin made sound propagation experiments at the supposedly historical scene at the Galli Islands where it’s said that the sirens originally sung. At the site we broadcasted both synthetic signals and natural voices via loudspeakers in the direction Odysseus most probably should have approached the Siren’s island. Subjective listening as well as objective acoustic analysis of the recorded signals revealed evidence for a combination of site-specific acoustic effects, which may explain the nature and origin of the song of the sirens in Homer. The local arrangement of the three islands deforms the acoustic signals by amplification and by changes in timbre. Two female singers from the Berlin State Opera were asked to sing differently pitched musical intervals to be tested in the Li Galli environment. The experiment evinced that the first overtones (octave, fifth, and fourths) would be merged by the echo of the rocks; yet when singing pure thirds and less consonant intervals, which yield higher orders in the overtone series, the voices appear recognisable as being two. As a result, and particularly because Homer stresses the number of exactly two sirens several times, the evidence of our research supports the musicological theory for a rather early existence of enharmonic tunings and most prominently a two-part polyphonic singing of Greek songs. Given that the rocky formation of the Galli Islands most likely didn’t change during the geological tick of just 2,700 years, we conclude that there has been a real acoustic basis for the myth reported by Homer and that a “song of the Sirens”, most probably based on natural voices, was transformed by the particular acoustic conditions of the landscape in such a way that signals were amplified and sent out in one concrete direction. Based on these results, we continue to discuss further leading acoustic theories that offer new insights into the mythology and which were essential to motivate our expedition in the first place. After all, the question remains open what kind of beings the first emitters of the song might have been.

On the Relevance of Natural Stimuli for the Study of Brainstem Correlates: The Example of Consonance Perception.

Some combinations of musical tones sound pleasing to Western listeners, and are termed consonant, while others sound discordant, and are termed dissonant. The perceptual phenomenon of consonance has been traced to the acoustic property of harmonicity. It has been repeatedly shown that neural correlates of consonance can be found as early as the auditory brainstem as reflected in the harmonicity of the scalp-recorded frequency-following response (FFR). “Neural Pitch Salience” (NPS) measured from FFRs—essentially a time-domain equivalent of the classic pattern recognition models of pitch—has been found to correlate with behavioral judgments of consonance for synthetic stimuli. Following the idea that the auditory system has evolved to process behaviorally relevant natural sounds, and in order to test the generalizability of this finding made with synthetic tones, we recorded FFRs for consonant and dissonant intervals composed of synthetic and natural stimuli. We found that NPS correlated with behavioral judgments of consonance and dissonance for synthetic but not for naturalistic sounds. These results suggest that while some form of harmonicity can be computed from the auditory brainstem response, the general percept of consonance and dissonance is not captured by this measure. It might either be represented in the brainstem in a different code (such as place code) or arise at higher levels of the auditory pathway. Our findings further illustrate the importance of using natural sounds, as a complementary tool to fully-controlled synthetic sounds, when probing auditory perception.

How Different Are Our Perceptions of Equal-Tempered and Microtonal Intervals? A Behavioural and EEG Survey.

For listeners familiar with Western twelve-tone equal-tempered (12-TET) music, a novel microtonal tuning system is expected to present additional processing challenges. We aimed to determine whether this was the case, focusing on the extent to which our perceptions can be considered bottom-up (psychoacoustic and primarily perceptual) and top-down (dependent on familiarity and cognitive processing). We elicited both overt response ratings, and covert event-related potentials (ERPs), so as to compare subjective impressions of sounds with the neurophysiological processing of the acoustic signal. We hypothesised that microtonal intervals are perceived differently from 12-TET intervals, and that the responses of musicians (n = 10) and non-musicians (n = 10) are distinct. Two-note chords were presented comprising 12-TET intervals (consonant and dissonant) or microtonal (quarter tone) intervals, and ERP, subjective roughness ratings, and liking ratings were recorded successively. Musical experience mediated the perception of differences between dissonant and microtone intervals, with non-musicians giving similar ratings for each, and musicians preferring dissonant over the less commonly used microtonal intervals, rating them as less rough. ERP response amplitude was greater for consonant intervals than other intervals. Musical experience interacted with interval type, suggesting that musical expertise facilitates the sensory and perceptual discrimination of microtonal intervals from 12-TET intervals, and an increased ability to categorize such intervals. Non-musicians appear to have perceived microtonal intervals as instances of neighbouring 12-TET intervals.

Context Dependent Pitch Perception in Consonant and Dissonant Harmonic Intervals

Two experiments examined whether discrimination of component pitches in a harmonic interval is affected by the consonance or dissonance of the interval. A single probe pitch (B or C) was followed by a two note harmonic interval including that pitch (e.g., C then C-F# or C-G) or not including it (e.g., C then B-F# or B-G). On each trial, subjects indicated by key press whether the probe note was repeated in the following interval. The target note in the interval either matched the probe or differed by one semitone (B or C). The other note produced a consonant (e.g., perfect fifth) or dissonant (e.g., tritone) context for the target. Pitch discrimination was faster and more accurate in consonant intervals than dissonant, when the context note was higher than the target (Experiment 1), but there was no effect of consonance when the target was higher (Experiment 2). We conclude that the perception of the lower but not the upper pitch in a two note harmonic interval is affected by the interval’s consonance or dissonance. We discuss the results in terms of the theoretical framework of processing fluency and aesthetics proposed by Winkielman, Schwarz, Fazendeiro, and Reber (2003).