In this article we are going to learn what it takes to uncover the Listeners’ Likes and dislikes from a whole new perspective. This article is part of a larger 23-part class about music, sound, and consciousness I have been developing called “REtuning the BOdy through ENjoyment of Music And Mind.”
Have you ever wondered if there are any studies specifically on “dissonance” ratios in music? Have you instantly turned off a YouTube music video you were listening to within only a few seconds because it sounded horrible to you? Of course, we all have. We do not find that beat pleasurable. Dissonant ratios are sounds with imperfect tonality…they have a relative “roughness” to their pitch and timbre. We dislike dissonance, or do we really?
There are very few studies trying to uncover what people consider dissonant because as astonishing as it may seem nearly every musician, mathematician and philosopher runs away from the subject. Let’s get to know this subject a little and why this happens.
I believe humanity is recovering from an agenda conceived during the medieval ages to mandate rules for how and what is allowed to be produced in music and sung in choirs. Essentially, the anti-pagan agenda sparked a “forgetting” of what was once considered consonant and what was felt as dissonant in music. What tones can and cannot be played…the police-state of the auditory control of humanity. And for good reason too.
By hiding the free study and use of harmony in one’s life a person may not gain the necessary understanding to reveal to them self a deeper and subconscious knowledge of SELF and connect the harmonic ratios ever-present in Nature in their daily life. This actually may relate to the ego-complex and dissonance itself. A real-life example cold be when someone tells you they love you but they have a sinister smile on their face. Their actions and facial expression do not “match up” with their statement. You and I both wouldn’t believe they actually love us and instead, that they are lying. This would create a dissonance between us in that moment. The tone-of-voice they used to say I love you also is a signal, not to mention the volume of their voice when telling us.
Going all the way back to Ptolemy (1oo A.D.) and prior musical harmony and “consonance” was the capstone quality essential to all music. It was the bearing, the primary gear of how musicians determined if the song was in a masterful resonance and the emotions the music would draw people into experiencing inside themselves. This Consonance Created was not arbitrary: it is determined by a strict law and is immutable as the color series of the rainbow is inside every person at different vibrating ratios (endocrine system and chakrahs). Back in the day JUST Intonation was the tuning method most often using the harmonic series, which are consonant ratios of sounds found in Nature. For example; 1:1 (the fundamental), 2:1 (the octave), 3:2 (the perfect fifth), and 4:3 (the perfect fourth).
Dissonance can be heard, if you will, as the “roughness” or “beats between the harmonics.” The measure of roughness, aka dissonance, is often weighted toward certain intervals because of the prevailing musical-conditioning of the times. The signals we can equate to having a dissonant quality are often calculated by adding together two sine-waves, or harmonic spectra could be another name, to sum up the “roughness” of all the signals in the spectrum under observation.
Amazingly, the tones when coupled together using harmonic spectra, e.g. the net effect of the roughness between all the harmonics being played, produces a graph with notches of consonance exactly at the intervals I mentioned above. The intervals or ratios the musicians all across the ages and cultures have continually uncovered again and again seen above.
In 1965 a paper entitled “Tonal Consonance and Critical Bandwidth,” by researchers Plomp and Levelt suggest “…that the difference between consonant and dissonant intervals is related to beats of adjacent partials.” In addition to the consonance and dissonance aspect of the study they also addressed the role that “critical bandwidth” plays in music. They tested the critical bandwidth by analyzing two songs; one from J.S. Bach and one from A. Dvořák. What they did was to calculate the way in which the intervals were spread out as the function of the frequency, and a number of harmonics were also taken into account. The study discovered that critical bandwidth, or put another way, the “density” of the simultaneous partials, changes its characteristics and affect because of changes in frequency in the same way as the densities of the multitude of partials. There is a strong correlation between how the harmonics vibrating in their overtones “match up” with the partial harmonic frequencies.
Each different type of musical instrument, including human beings and all the ways we can use our voice, make their own complex tones. The discovery in the 1600’s that the tones of musical instruments are composed of partials gave rise to an alternative explanation of consonance. Certain harmonics in the whole sound spectrum produce discernible tones, and overtones, bringing to bear the clarity and strengths of those notes. This so-called strength of the note, in terms of its pitch or “likability” and consonance, is called a partial.
The partial is the lowest possible harmonic frequency which is heard as the musical “pitch” of a note and created by the vibrations traveling over the whole length of a real string, or air column. Typically the frequency of each partial may be calculated by multiplying the fundamental frequency, say 55 hertz, by the number of the note it is in progression with e.g. 55hz=1, 110hz=2, 165hz=3, 220hz=4, etc. Each harmonic inside of the whole vibrating string combine instantly into a steady tone in our ears as the tone color quality forms into its timbre, it’s quality or character; i.e. its strength, and becomes perceived by the listener.
Plomp and Levelt (1965) state, “we assume that the total dissonance of such an interval is equal to the sum of the dissonances in EACH PAIR OF ADJACENT PARTIALS…these presuppositions are rather speculative. In this way, the curves were computed for complex tones consisting of 6 harmonics and shows how the consonance of some intervals, given by simple frequency ratios, depend on frequency.”
Uncovering the Listeners’ Likes and dislikes as you can now see it is a deep topic with many rigorous examples of how the partials of harmonics, the fundamentals, and overtones are all eluding to similar phenomena even though the Listeners’ body and mind is “hearing” sounds, not the math or terminology behind the song or frequency.
Summing up for now when I think about sound waves I imagine them “matching up” inside my hearing perception. There are perfect consonance harmonics (1:1, 1:2, 2:3, 3:4) and even imperfect consonance (4:5, 3:5, 5:6, 5:8) and these “likes” are not an invention of me, but the characters actors, allies, and villains in the sound domain itself. Auditory cognition and subjectivity of course play into this. Dissonance is the consolidation of the shadow of sound whereby other genres of vibration may influence our “dislikes.” Musicians secretly decide what shape the world is!!! Read more about how Hydrogen as a WHOLE OCTAVE unto Itself.