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Shrill notes are said to be "high", and rumbles are said to be "low". Humans seem to metaphorically map frequency to the vertical axis, and in the cultures that I know of, high frequency is considered "up".

  • Is this a universal phenomenon? Are there any cultures that map it upside-down, or in a completely different way? (For example, smaller objects tend to produce higher pitches. Are there any cultures that say that a pitch is "small" instead of "high"?)
  • Does this convention pre-date the scientific understanding of sound waves?
  • If it is universal (or nearly so), is there any neurological hard-wiring that would cause that mapping?
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Humans technically don't perceive frequencies, they perceive pitch. According to Wikipedia:

the idiom relating vertical height to sound pitch is shared by most languages.

citing a 1930 article by Pratt, which in turn says that:

Stumpf has found that adjectives meaning high and low (or words closely related in meaning) have been applied to tones in almost every known language.[2] But why should tones be characterized as high or low? Do these characteristics refer to differences in spatial height and depth? The answer to this second question has been almost without exception in the negative. A high tone does not mean a tone which is high in space. The phrase is merely figurative, and must be accounted for in terms of secondary criteria such as, e.g., the apparent localization of high vocal tones in the head and low ones in the chest. The composer Berlioz makes sport of such explanations and reminds his readers that high and low tones for the pianist lie in the horizontal directions of right and left and that the violoncellist must reach downward to produce high tones, and suggests that those composers of opera who use descending passages for a person falling downstairs have stupidly transferred to the tones the arbitrary downward character of the printed notes on the staff. And yet Stumpf, convinced that there can be no intrinsic height and depth in tones, has felt obliged to argue that here again some associative mechanism, strangely obscure and elusive, has been at work. Even Wundt was forced to agree with Stumpf in calling these terms metaphorical when applied to tones [3], and most psychologists who have given the matter any thought have expressed similar views [4].

[2]: C. Stumpf, Tonpsychologie, 1883, I, 192 ff.

[3]: W. Wundt, Grundzüge der physiologischen Psychologie, 1910, 11, 78.

[4]: J. Redfield, Music: a Science and an Art, 1928, 42 ff.

All these sources are pretty dated alas.

There are however some newer papers on this; e.g. Fernandez-Prieto et al. (2017) which do qualify such statements, e.g.:

Higher frequency and louder sounds are associated with higher positions whereas lower frequency and quieter sounds are associated with lower locations. In English, ‘‘high’’ and ‘‘low’’ are used to label pitch, loudness, and spatial verticality. By contrast, different words are preferentially used, in Catalan and Spanish, for pitch (high: ‘‘agut/agudo’’; low: ‘‘greu/grave’’) and for loudness/verticality (high: ‘‘alt/alto’’; low: ‘‘baix/bajo’’). Thus, English and Catalan/Spanish differ in the spatial connotations for pitch. To analyze the influence of language on these crossmodal associations, a task was conducted in which English and Spanish/Catalan speakers had to judge whether a tone was higher or lower (in pitch or loudness) than a reference tone. The response buttons were located at crossmodally congruent or incongruent positions with respect to the probe tone. Crossmodal correspondences were evidenced in both language groups. However, English speakers showed greater effects for pitch, suggesting an influence of linguistic background.

They also cite an older review paper (Cassanto, 2013) which highlights a similar studies (co-authored by Cassanto) on Dutch vs Farsi:

Like English, Dutch describes pitches as ‘high’ (hoog) or ‘low’ (laag), but this is not the only possible spatial metaphor for pitch. In Farsi, high pitches are ‘thin’ (nāzok) and low pitches are ‘thick’ (koloft). Dutch and Farsi speakers’ performance on non-linguistic pitch reproduction tasks reflects these linguistic differences (Dolscheid, Shayan, Majid, and Casasanto 2013). Participants were asked to reproduce the pitch of tones that they heard in the presence of irrelevant spatial information: lines that varied in their height (height interference task) or their thickness (thickness interference task). Dutch speakers’ pitch estimates showed stronger crossdimensional interference from spatial height, and Farsi speakers’ from the thickness of visually presented stimuli. This effect was not explained by differences in accuracy, or in musical training. When trained to talk about pitches using Farsi-like metaphors (e.g. a tuba sounds thicker than a flute) for 20-30 minutes, Dutch speakers’ performance on the non-linguistic thickness interference task became indistinguishable from native Farsi speakers’. Experience using one kind of spatial metaphor or another in language can have a causal influence on non-linguistic pitch representations. [...]

infants as young as four months old are sensitive to the height-pitch mapping found in Dutch-speaking adults (but not in Farsi-speaking adults), and also to the thickness-pitch mapping found in Farsi-speaking adults (but not in Dutch-speaking adults; Dolscheid, Hunnius, Casasanto, and Majid 2012). There is no need, therefore, to posit that using linguistic metaphors causes people to construct these mappings de novo.

A somewhat similar paper on infants, perhaps with stronger claims is from Walker et al., 2010:

Stimulation of one sensory modality can induce perceptual experiences in another modality that reflect synaesthetic correspondences among different dimensions of sensory experience. In visual-hearing synaesthesia, for example, higher pitched sounds induce visual images that are brighter, smaller, higher in space, and sharper than those induced by lower pitched sounds. Claims that neonatal perception is synaesthetic imply that such correspondences are an unlearned aspect of perception. To date, the youngest children in whom such correspondences have been confirmed with any certainty were 2- to 3-year-olds. We examined preferential looking to assess 3- to 4-month-old preverbal infants’ sensitivity to the correspondences linking auditory pitch to visuospatial height and visual sharpness. The infants looked longer at a changing visual display when this was accompanied by a sound whose changing pitch was congruent, rather than incongruent, with these correspondences. This is the strongest indication to date that synaesthetic cross-modality correspondences are an unlearned aspect of perception.

Cassanto and colleagues also develop a Hierarchical Mental Metaphors Theory (HMMT) according to which

correlational mental metaphors develop in two stages, the second of which may extend throughout the lifetime. The mental metaphors that adults typically use are specific instances of more general families of mappings. These families may be evident in behavior from infancy, and reflect regularities in humans’ experiences of the physical and social world, many of which may be universal. As children are exposed to peculiar aspects of their languages, cultures, or even their own bodies, certain mappings from a given source-target family become strengthened through repeated use, which weakens ‘sibling’ mappings as a consequence. The result is that people tend to think in language-specific, culture-specific, or body-specific mental metaphors: Relativity emerges from universals. [...]

One prediction of HMMT is that specific source-target mappings should be easy to activate via linguistic training so long as they are members of one of the families of source-target mappings encoded in our minds (over phylogenetic or ontogenetic time) on the basis of observable sourcetarget correspondences in the world. Mappings that are not members of a pre-linguistically established family (and that do not reflect correlations in our experience) should be relatively hard to activate via training, because these mappings would need to be created, not just strengthened.

In a test of this prediction, Dutch speakers were trained to used a thickness- pitch mapping that is the reverse of the mapping found in Farsi, and in the natural world: thin=low and thick=high. These ‘reverse-Farsi’ trained participants received the same amount of training as the participants trained to use the Farsi-like mapping. Whereas Farsi-like training had a significant effect on participants’ nonlinguistic pitch representations, reverse-Farsi training had no effect (Dolscheid et al. 2013). Thus, brief linguistic experience caused participants to use the thickness-pitch mapping that reflects correlations between thickness and pitch in the world (and is evident in prelinguistic infants). Yet, the same amount of linguistic experience was not effective at instilling the opposite thickness-pitch mapping, which has no obvious experiential correlates, and is therefore not predicted to be among the pre-linguistically established space-pitch mappings.

That's referring to the same paper as the first citation in the previous quote. Oddly this experiment isn't summarized in the paper's abstract, but does appear in the paper (as Experiment 4). Cassanto has a free pdf of that paper as well.

A 2014 PNAS paper by Parise et al. proposes that the low-high pitch metaphor has a natural basis in the elevation of the sources of such sounds in nature.

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    $\begingroup$ Fascinating references — thanks! Dated is good: Tonpsychologie is out of copyright. French and Chinese use "high/low", like English. It seems like many languages use partial mappings, though. German uses "high/deep". The Greeks and Romans used "sharp/heavy", which carries over to Spanish/Catalan. Sanskrit used one word for treble/loud, but separate words for bass vs. soft. Good observation by Berlioz about cartoon falls. There is definitely something going on cognitively, even if it's not always linguistically consistent. $\endgroup$ – 200_success Sep 30 '18 at 7:45
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    $\begingroup$ Parise 2014 seems to give a pretty plausible explanation for the origin of the mapping: the human ear is designed to enhance perception of treble sounds from above and bass sounds from below, to optimize for where those frequencies tend to come from. $\endgroup$ – 200_success Sep 30 '18 at 8:06

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