The first thing I notice is that I was correct in assuming Helmholtz was one of the people they were disagreeing with. I suppose this is all reasonable from a scientist's point of view? Perhaps my commentor Joel could weigh in here. But I find a lot of things perplexing. First of all, the opening sentence: "To date, no consensus exists in the literature as to theories of consonance and dissonance." What literature are they referring to? Certainly not the theoretical literature in music that abounds in discussion of consonance and dissonance. By "theories" of consonance and dissonance they must be referring to theories of the listener's reception or perception of consonance and dissonance. OK. Then they refer to the "frequency relationships between the harmonics of music chords". What this means is unclear. A chord in music is the simultaneous sounding of two or more notes. Typically chords are triads or tetrads. Yes, every note, in a chord or alone, has harmonics, that is, the overtone series, but what the "frequency relationships between the harmonics of music chords" is, is a mystery to me. Most of the rest I find unclear as well. But perhaps that is due to my ignorance of the scientific context.
Consonance and Pitch.By McLachlan, Neil; Marco, David; Light, Maria; Wilson, SarahJournal of Experimental Psychology: General, Jan 7 , 2013, No Pagination Specified.AbstractTo date, no consensus exists in the literature as to theories of consonance and dissonance. Experimental data collected over the last century have raised questions about the dominant theories that are based on frequency relationships between the harmonics of music chords. This study provides experimental evidence that strongly challenges these theories and suggests a new theory of dissonance based on relationships between pitch perception and recognition. Experiment 1 shows that dissonance does not increase with increasing numbers of harmonics in chords as predicted by Helmholtz's (1863/1954) roughness theory, nor does it increase with fewer pitch-matching errors as predicted by Stumpf's (1898) tonal fusion theory. Dissonance was strongly correlated with pitch-matching error for chords, which in turn was reduced by chord familiarity and greater music training. This led to the proposition that long-term memory templates for common chords assist the perception of pitches in chords by providing an estimate of the chord intervals from spectral information. When recognition mechanisms based on these templates fail, the spectral pitch estimate is inconsistent with the period of the waveform, leading to cognitive incongruence and the negative affect of dissonance. The cognitive incongruence theory of dissonance was rigorously tested in Experiment 2, in which nonmusicians were trained to match the pitches of a random selection of 2-pitch chords. After 10 training sessions, they rated the chords they had learned to pitch match as less dissonant than the unlearned chords, irrespective of their tuning, providing strong support for a cognitive mechanism of dissonance.
Here is how a musician and composer looks at consonance and dissonance. All intervals are divided up into consonant and dissonant, but the line between them has changed over time. If we go back far enough, every interval except the perfect ones (fourth, fifth and octave) was considered more or less dissonant. In actual use this meant that while you could use other intervals, you couldn't end with anything other than a perfect one. Dissonances like thirds and sixths, had to be passing. Later on, thirds and sixths were accepted as consonant, though the minor third was often not considered suitable in a final chord, so a major third was substituted resulting in a tierce de Picardy. As chords with an added seventh developed, found very useful for the added tension they provided cadences, the seventh and tritone were used more and more--though again, they were used in a chord normally passing to a consonant tonic harmony: GBDF (the tritone lies between the B and the F) going to CEGC. The most dissonant intervals have always been the tritone and the minor second, but we find them in constant use during the whole common practice period. However, for most of this period they were used in specific ways and resolved in specific ways. In the late 19th and early 20th century, their use became more and more frequent and the resolution more and more ambiguous until finally the whole notion of consonant and dissonant was tossed out with the development of 12-tone music.
What I find problematic with the researcher's approach is that they seem to take no account of the context. But I can't imagine understanding anything much about consonance and dissonance without context. A C major triad can sound harsh and dissonant in just the right (or wrong!) context. Here is the beginning of the Piano Sonata op 106 by Beethoven, nicknamed the "Hammerklavier" which begins with a simple B flat chord, though sounding quite bold and 'crunchy':
It's all in the context...