Chapter 2: The localization of frequencies on the vertical axis
2.1 Theorization
As mentioned in the introduction to this research, the postulate to be verified is:
“ to each of the three main frequency fields, or perceived pitches (low, medium and acute), our auditory-perceptive system associates a position on the vertical (y) axis of the three-dimensional coordinates in relation to the frequency field, or pitches, involved: the low frequencies are read towards the 0 of the y axis, medium ones at the midpoint and high ones at the positive apex of the same axis”.
When I talk about reading the frequency field, and/or the heights, or, equivalently, the perception of these on the vertical y axis, I mean not which part of our body they possibly set in vibration, or similar things, but rather, from where, geographically, we hear the sound arrives. The quotation marks on we feel are a must because we have said it is a phenomenon of perception, therefore an interpretation given by us of a physical event and must be experienced as such.
In fact, what was stated in the starting postulate can partly find scientific validation if we refer to the tonotopic maps previously described and in which the brain preserves every characteristic frequency for it in a group of cells close to each other, recalling their positioning during the of their recognition. If the theory according to which the high frequencies are written at the top in Brodmann’s area 41 (auditory cerebral cortex) and the low ones are written further down, the relationship with what is said in the postulate is if nothing else fascinating.
Referring, however, to the HRTF transfer function (exposed in relation to the duplex theory), one might ask, given the ability of our body to behave as a filter and in particular of the auditory pinnae, head and trunk, whether this characteristic does not also intervene in the localization of the sound not only due to the different positioning of the sound source, but also due to its different frequency content. That is, if sounds with different perceived heights and the same positioning in three-dimensional space are translated into a sort of auditory images (similar to those theorized by McAdams and Bregman) that are different and linked to the task of an imaginary spatial localization correlated, precisely, only to their difference in terms of frequency.
Both constitute fascinating theses but which, apart from the possible reading given of the localization event based on the frequency content, do not fall within the aims of this experiment for which the only objective is to verify or not the postulate given at the start.
2.2 What awaits us
Of course, it is much simpler to expect a listener to tell us whether the sound source is placed on the right rather than on the left, above rather than below or, even, at what distance it is located and whether it is placed forward or behind. This is, in fact, a daily auditory experience and has now been acquired over the thousands of years of evolution of the human species. A more complex and delicate thing is to try to receive an answer to the question we have asked ourselves because this requires not only a higher level of attention to listening, but also one that calls for more complex mental and analytical superstructures. The most effective way to overcome this problem is to rely on the intuition that each of us possesses and therefore let the listener subjected to the experiment put his own into play through some simple experimentation protocols described later.
The expectations deriving from the experimentation are the simple verification or disavowal, through collection of data and their statistical reading, of the starting theorization. We must now decide what the statistical-percentage limit is below which the initial thesis should be considered failed.
Two factors come into play in this evaluation:
purely mathematical: it would be normal to set this limit to values lower than 51% (50% represents the legal possibility that an event is true or false, so for it to be definitely true it is necessary to exceed this limit)
contextualization of the experimentation: let’s not forget that we are dealing with topics related to auditory perception and in which emotional, psychological factors etc. come into play in addition to the possible environmental variations during the experimentation phase. All this tends, in my opinion, to lower the on-site limit by 51% in a mathematically unquantifiable manner (as happens in many other psychoacoustic experiences) and which I have determined (by common sense) to be around 40%.
To support this choice of mine, I recall what happens in a similar experience which concerns the emotional perception of musical intervals such as, for example, the sixth. For a part (statistically significant but almost always less than 50%) this represents an impulse towards something, an emotional leap but, the remainder of the statistical pie is experienced as a void, something that alone has no emotional meaning. So isn’t all the theorization about the perception of musical intervals, harmonies, colors expressed differently depending on the position of the tone within its circle or, even, the different coloring that some of us associate with different timbres, true?
It could also be, perhaps one day it will be discovered that everything is the result of trips by intellectuals in the sector or whatever else, for me, for now, remains real data mathematically describable even if not in absolute terms.
A final point for reflection concerns the number of tests to be performed in order to assume a statistical truth here too. Usually, the higher this number, the more reliable the experimentation is, but we also need to deal with the reality of things and with the time available.
In fact, while a quantity of even 100 tests carried out or more, perhaps with people of different social and cultural backgrounds and even of different origins, would be, in my opinion, a desirable minimum, for the moment we will be satisfied with a much lower number knowing full well that , by doing so, we would only have trendy masks of the event.
2.3 Implementation protocols
Environmental protocols: usually in scientific experiments we try to create an environment suitable for containing the experiment that is functional for the purpose and all tests are carried out in the chosen environment. In our case, the salient point is the verification of a perceptive experience lived in everyday life and, therefore, in the most disparate environmental situations. I therefore opted not to create that single laboratory environment (which would have contradicted everyday life understood as constant in the philosophy of the experiment but, at the same time, variable because it was part of the personal experience of the test participants). There are, however, minimum conditions to be respected and to be taken into account during the data analysis phase:
The size and characteristics of the room in which the test sounds are listened to should be such as not to induce particular reverberation phenomena (approximately T60 between 0.6 and 0.9 sec) especially with regard to the first reflections induced by the environment which can be responsible for spots virtual sound source localization. Even the presence of extremely characteristic environmental resonance peaks should be avoided and, if nothing else, reported on the test sheet.
The tests were designed for reproduction via loudspeakers although the use of ear monitors or headphones (for something else that happened during the tests) can open up a further analytical front. In any case, the minimum quality required for listening is a frequency response that goes at least from 80Hz to 10KHz, the optimal one is from 40Hz to 20KHz. The positioning of the speakers is also important: they must be at ear height and at a distance from the listener which I have determined, from experience, as H*4 where H is the height of the speaker containing the speakers. This is to avoid, especially in the case of speakers with woofer or bass reflex, middle range and tweeter, a marked effect of the origin of sounds with a different frequency range if the listener is too close to them (respect this condition even in the case of horizontal and non-horizontal arrangement). vertical of the speakers as sometimes happens).
The listener must be placed at the center of the radiating field of the speakers (stereo point) even if almost all of the sounds used are monophonic. This is to avoid any anomalous reflections as much as possible, especially in the case of pure sinusoids.
Execution protocols: the execution of the experiment requires reflection on at least two salient points:
Listening to each of the individual files (audio tracks in the case of playback via audio CD) must be single, that is, the track already listened to must not be repeated. This has the aim of obtaining information from the listener that is as close as possible to an instinctive reaction such as that which we normally experience in daily life when we perceive the origin of an acoustic event in our environment. Any repetition could, in some way, compromise the instinctiveness of perception by filtering the experience through analytical parameters which would distance us from the search for its naturalness.
There must be sound control during the performance in order to make the volumes of the individual tracks of the three test CDs perceptually equal. In fact, the amplitudes of the individual sounds used for the experience are the same given that it would have been possible to adapt them to the Fletcher-Munson curves but, impossible to modulate them depending on the different environmental response and on the speakers (especially consumer ones) which present characteristics frequency response significantly different from type to type. I therefore chose to obtain the leveling of the perceived loudness in an artisanal manner by resorting, precisely, to the direction of the sound operated either by the executor of the experiment or by a technician.