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Bichordal harmonic musical intervals and effects on overall satisfaction
Bichordal harmonic musical intervals and effects on overall satisfaction
Joshua Gibson
Ryde Secondary College
Abstract
Bichordal harmonic intervals are a universal construct across all musical systems, and have critical roles in the perception of harmony and melody. This study aimed to establish whether there was a difference in the satisfaction achieved across all 12 possible bichordal harmonic intervals in the twelve tone scale, supported by literature investigating relevant concepts in music theory, and the emotional effects of different bichordal harmonic intervals on the individual. Individuals ranked each bichordal harmonic interval in terms of satisfaction in a survey, and both ANOVA: Single Factor and Post-hoc test was performed to determine if there was a difference in the satisfaction recorded across the bichordal harmonic intervals, and where it occurred most prom inently. A significant difference in satisfaction of BI’s was identified most strongly between dissonant and consonant BI’s, with major and minor BI’s also showing differences in satisfaction but less extensively. There was a significant difference identified, most predominantly in dissonant bichordal harmonic intervals, indicating that there was a relationship between the satisfaction achieved and the bichordal harmonic interval being played. Further studies on a more culturally diverse scale could benefit in creating a universal argument, instead of supporting predominantly Western culture.
1 Literature review
1.1 Introduction
Bichordal harmonic musical intervals (BI’s) relate to the playing of two tones simultaneously. The literature suggests harmonic musical intervals and emotional response are linked together, however, the specific contentment an individual feels after hearing a harmonic music interval remains a point of research that has been neglected with a lack of methodical, sound studies (Costa et al 2000) in musical literature, alternatively using musical theory. In this project, concepts such as dissonance and consonance will be explored using quantitative and qualitative data collected from a first-hand investigation, to form a specific link between musical tension (a musical lack of a resolution) and overall contentment. This literature review will draw on studies conducted within the last 40 years, which remains a current time interval for musical research. These articles will provide important understanding of concepts involving harmonic musical intervals, and arguments relating to the relationship between harmony and subjective and objective musical perceptions. Bichordal harmonic musical intervals will be referred to in terms of the upper note played in terms of the fundamental tone.
1.2 Background information
Consonance occurs when the upper harmonics (the additional frequencies in a tone that support a fundamental frequency) between the two tones of the BI’s match with each other, producing a pleasing tone (Zentner and Kagan, 2002). Contrarily, dissonance is characterised by the upper harmonics of the two tones clashing with each other, producing an displeasing overall BI tone. In order to achieve a more consonant BI, the ratio between the fundamental tone (f0) and the upper note (f) must be as small as possible (eg. a ratio of 2:1 (the octave) would be more consonant than a ratio of 4:3 (a perfect 4th)). Stolzenburg (2014) relates the harmoniousness of a BI with the periodicity of the function it creates, and different tuning systems can create different measures of harmoniousness . They relate pitch perception to four key measures: consonance, dissonance, instability, and roughness. Alternatively, Chailey (1985) presents an additional cultural frame that impacts the perception of pitch, and as an extension, different BI’s.
1.3 Limitations
The limitations of experiments conducted by the literature will be discussed. Overall, there was very basic consideration of the impact of aural disorders on the result of the experiment. Zentner and Kagan (2002) conducted research into the perception of consonance and dissonance in infants, and encountered issues of restlessness in 5 of the subjects, and removed them from the data set without accounting for possible reason. The other literature typically just made a note of inexperience such as Costa et all (2000), vaguely identifying the participants of the experiment as experts and naive. Another outstanding issue that existed in the literature was a generally severe lack of representation and diversity in the population being examined. Zentner and Kagan (2002) used used only caucasian infants aged 4 months and younger (although the effect of a cultural barrier would almost be negligible in this case), Costa et al (2000) had a disproportionate number of females to males, and Jacoby et al (2019) had the aim of addressing universal components of musical systems and only provided one group of nonWestern musicians. The main issue that arose from this was the favour for Western musical intervals, impacting an ability to produce empirical evidence of universal perceptions of harmony, demonstrating a gap in the literature.
1.4 Strengths
The literature successfully was able to some extent meet the aim of the experiments, which revolved around the relationship pitch perception, and then BI’s in a narrower scope, and the psychological responses that was created from that, such as emotional connections made by Costa et al (2000). The methodology of all the literature discussed was very similar except for Stolzenburg (2014) who did not even refer to human perception, which may not have met the aim as effectively, however the calculations for an objective sense of consonance and response to harmony could have balanced this issue out. Zentner and Kagan (2002) successfully achieved their aim, though some qualitative statements such as infants making vocalisations at dissonant pitches were immediately recorded as a lack of contentedness. They also used a habituation paradigm which demonstrated a greater holistic understanding of their area of research. Jacoby et al (2019) explicitly targeted the effect of the cultural frame, which the other literature did not cover as strongly, and given the recency of the article, may suggest that these considerations may be observed more frequently. They also differentiated musicians and non-musicians and provided a clear criteria for this, necessary as without a criteria the terms musician and non-musician would be too vague to assess.
1.5 Conclusion
Overall, the literature suggests that there is at least a substantial relationship between BI’s and music perception, with Costa et al (2000) relating emotions to the perception of BI’s, Zentner and Kagan (2002) identifying a difference in perception of consonance and dissonance in infants, Jacoby et al (2019) identifying key features across music systems that remain constant, and Stolzenburg (2014) creating systems that model perceptions of pitch perception.
2 Scientific research question
Do musical intervals in the 12-tone scale elicit specific responses to an individual’s sense of satisfaction?
3 Scientific hypothesis
Null hypothesis: There is no significant relationship between an individual’s sense of comfort and harmonic musical intervals.
Alternate hypothesis: There is a significant relationship between an individual’s sense of comfort and harmonic musical intervals.
4 Methodology
4.1 Ethics Statement
The Head of Science at Ryde Secondary college was consistently consulted in the research conducted, ensuring that the experiment was ethically sound, and that possible issue that could arise were effectively mitigated. The participants were given a UUID, which meant that their responses were anonymous and that personal bias would not be affected in the data analysis stage. A protected word document was used to log the names of participants and their given UUID, allowing for the data to be
retracted from the database if they desired. The participants also had to sign a consent form, which outlined what they were expected to do, and how their data would be used. A script was also strictly stuck to, ensuring that every participant received the same information. This created equally informed consent across all the participants, and ensured that the results were reliable.
4.2 Exposure to bichordal intervals
To assess the relationship between BI’s and satisfaction, individuals were exposed to all of the possible BI’s using the same root note, and had to score their level of satisfaction on a semantic differential scale from 1-9 on a survey, 1 being extremely unsatisfied, and 9 being exceedingly satisfied. In order to reduce the bias formed from ‘extremely,’ having negative connotations, ‘exceedingly’ was used instead. Odd numbers were also used instead of even numbers to differentiate responses more easily.
The BI’s were played from a Piano app on an iPhone 11, in the 4th octave, the middle octave of a traditional piano. The experiment took place in quiet, outdoor areas, and participants with music theory understanding were told not to attempt to work out the BI being played, reducing the bias that rose from musical experience. 16 participants took part in the experiment, which was performed on the grounds of Ryde Secondary College, and only involved students. The order of the BI’s being played was transcribed to a traditional music score (see Figure 1), to make it easier to perform the intervals as they were in a mixed order to prevent bias from subconsciously forming a melodic link between the BI’s.
4.3 Data Analysis
The data was cleansed of a student who was subjected to too many external factors such as school bells ringing, close-proximity conversation, and other sensory distractions.
An ANOVA: Single factor and post-hoc Tukey’s HSD test was performed, using a p-value < 0.05, as the goals of the experiment were to assess whether there was a difference among the different BI’s and the satisfaction achieved. The data from the Tukey’s HSD test was then presented in a matrix due to the large quantities of pairs formed from the 12 data sets.
5 Results
Figure 2 displays the averages of the confidence intervals for each BI, in order (from minor 2nd to octave). Intervals on the more extreme sides of consonance and dissonance tended to have a smaller confidence interval, indicating that there was more clustering of higher end scores with less deviation from the mean. However, the octave which was theoretically meant to be the most consonant of all the BI’s had a confidence interval that was larger.
In Table 1, a post-hoc Tukey’s HSD was performed and presented in a matrix after an ANOVA test returned a p-value <0.05, with a confidence interval set at 95%, rejecting the null hypothesis. The alternative hypothesis was accepted, meaning that there was a difference in the levels of satisfaction across some or all of the BI’s. The red text indicated that there was a statistically significant difference, and green indicated that was no statistically significant difference. The absolute distances from the means were also recorded.
The most significant difference in the satisfaction recorded occurred between the minor 2nd, and tritone, which were the two most dissonant intervals, and aligned with similar intervals that were also characterised as dissonant. The more consonant BI’s (perfect 4th and octave) however, had similarities in their satisfaction with other intervals, demonstrating identical relationships in terms of the intervals they were similar with, and were distinguished from.
Table 2 compares the differences in p-values between the minor 2nd, the most unsatisfying interval, and the perfect 4th, the most satisfying interval (the octave was not chosen as the standard deviation was significantly higher). The minor 2nd presented differences in all but the major 2nd and tritone, and the perfect 4th was similar to 5 out of 12 of the total BI’s, with a p-value of 1 with the octave indicating there was no difference in satisfaction other than by chance. Thus, it could be concluded that more consonant intervals could be distinguished from the second BI’s (minor and major), minor third, and seventh BI’s (major and minor).
6 Discussion
6.1 Cadences
The levels of satisfaction achieved by the specific intervals being played do not demonstrate a clear link looking visually from the matrix. However, upon applying musical theory, and the classification of specific intervals with other theoretical concepts in relation to pitch and harmony, a pattern begins to emerge. Cadences, a more complex music theory concept, provide some reasoning for the data in terms of the resolution. This concept examines the way two chords interact with each other, and highlights the different roles chords play in ending phrases. For example, half cadences are characterised as ending on a V chord, or having a root played 7 semitones above the tonic. They are distinguished as sounding incomplete, and are resolved through playing a vi (lowercase indicates a minor chord) chord or a diminished 7th chord. The Minor 7th interval, related to the diminished 7th chord, has a different function for satisfaction with a p-value < 0.05. From this, a relationship between BI’s and melodic phrasing can be established.
6.2 Order of BI’s
In terms of resolution, the order of the intervals being played could have also formed some inaccurate results. Placing the most theoretically unsatisfying BI (minor 2nd) towards the end would have made participants less aware of the scale, and could have been amended by placing the minor 2nd closer to the beginning of the test. Placing the octave, theoretically the most satisfying BI may have produced more accurate results on the upper end of the scale. Some students with music experience noted that there was a conscious need for an interval to resolve, and when this did not occur it was unsatisfying. However, given the parameters of the experiment with musical theory not being allowed to be applied, the effect of this was self-mitigated by the participants themselves. The placement of the minor 2nd after the tritone, the two most theoretically dissonant intervals, may have produced a stronger bias towards ranking an interval lower than desired due to a subconscious comparison between the interval that was played before. The interval order could have been better composed had there been a more selective process of the order in which the intervals were played, rather using a randomised number generator to attempt to reduce the bias formed by preconceptions of resolution.
6.3 Consonance and Dissonance
Consonance and dissonance have both been identified as vital factors to consider in the formation of BI’s, providing reasoning for key trends that occurred in the data, such as the most dissonant intervals (minor 2nd and tritone) lying outside of the distributions for the majority of the other BI’s. However, the ability to predict the satisfaction achieved by the more consonant intervals, particularly the octave was less obvious. The perfect 4th and octave both had the same mean (7.1) but the confidence intervals in the perfect 4th was smaller than the octave, which should have been inversely the case following consonance and dissonance theorem. This may have also been affected by a smaller sample size, and more students with musical experience possibly skewing the data with subconscious bias.
6.4 Major and Minor intervals
In terms of the satisfaction formed by the major and minor intervals, it would be expected that major intervals would have higher means of satisfaction, and minor intervals would have lower means of satisfaction. This trend did appear in the data, though there were some exceptions. The minor third appeared to be the most divisive out of all the BI’s, having the largest standard deviation (2.3), and a mean of 5.0. Minor chords, which rely on the minor third BI’s for their distinctive quality, are often used in order to create resolution, such as the vi chord to resolve a half cadence as discussed above. Such exposure to this BI being used to resolve, and their inherent minor quality, could have created a conflicting perception of satisfaction, thus producing mixed results. The minor 6th also had results that did not align with the understanding of minor and major intervals, behaving more like a major BI in that it aligned with similar major BI’s. Further, from the Tukey’s HSD, the minor 6th did not align with the satisfaction of exclusively dissonant intervals (minor 2nd and tritone), behaving similarly to the satisfaction achieved by the minor third.
6.5 Implications for research
This project suggests the possibility of future endeavours in the study of music in relation to science. Examining popular music scores from key historical music periods such as romantic, classical, contemporary, and baroque music, and further investigating the attitudes towards specific BI’s, and the relationship between BI’s and overall satisfaction could be mapped out over time to explore social, cultural and universal attitudes towards music. Student satisfaction during school time could further be mitigated by implementing the BI’s that are most satisfying for school bells, to assist students in feeling more supported and enthusiastic in engaging in their education. This could increase overall student achievement, and promote greater participation in extracurricular activities.
6.6 Limitations of this study
A specialised music room was going to be used for this study, being sound-proof and having access to a piano that could play pure tones through a high quality speaker. However, due to scheduling issues, accessing this room for extended periods of time was impractical. The study being performed outside, though in quiet areas would have been affected by outdoor stimulus such as wind, leaves rustling, and background chatter from extended distances, possibly producing inconsistent results. The phone playing the BI’s was also very weak in terms of volume of the sound produced, further creating issues in perception.
7 Conclusion
The present study aimed to examine whether there was a significant difference between bichordal harmonic intervals and their effects on satisfaction. A difference was supported in the satisfaction achieved by specific bichordal harmonic intervals (p=1.18E-21), with more dissonant BI’s being perceived significantly less satisfactory than more consonant BI’s. The more consonant intervals had generally similar levels of satisfaction towards other consonant intervals, becoming more obvious the more consonant a BI was. This could have been due to the purpose that dissonant BI’s have, which is to create tension and consonant intervals, which are typically meant to produce greater comfort and a sense of resolution. A BI’s role in affecting cadences had an understated impact on the rating of satisfaction measured, examined through half cadences and perfect cadences.
Consonance and dissonance, and major and minor intervals were the main indicators of a BI’s level of satisfaction, however there were minor deviations from expected results derived from the theory behind these concepts. The octave and perfect fourth were identified as the most satisfying (however the perfect 4th had a lower standard deviation) , and the minor 2nd and tritone were conversely the least satisfying of all the BI’s. Some future directions for this research could be to investigate the role of bichordal harmonic intervals throughout key historical periods, and use this to produce more sound genre-blending musical compositions. This research could also be applied in the design of school bell melodies, using BI’s that were more supported to be satisfying through the research, increasing the wellbeing and productivity of students.
Reference list
Costa, M., Ricci Bitti, P. E., & Bonfiglioli, L. (2000). Psychological Connotations of Harmonic Musical Intervals. Psychology of Music, 28(1), 4–22. University of Bologna. https://doi.org/10.1177/0305735600281002
Jacoby, N., Undurraga, E. A., McPherson, M. J., Valdés, J., Ossandón, T., & McDermott, J. H. (2019). Universal and Non-universal Features of Musical Pitch Perception Revealed by Singing. Current Biology. CellPress. https://doi.org/10.1016/j.cub.2019.08.020
Stolzenburg, F. (2015). Harmony perception by periodicity detection. Journal of Mathematics and Music, 9(3), 215–238. Taylor and Francis. https://doi.org/10.1080/17459737.2015.1033024
Zentner, M. R., & Kagan, J. (1998). Infants’ perception of consonance and dissonance in music. Infant Behavior and Development, 21(3), 483–492. Harvard University. https://doi.org/10.1016/s0163-6383(98)900212
