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I suspect that I will not use the right terminology here. Apologies in advance.

Is there a word for the phenomenon in which speakers of a language treat two different sounds as equivalent, even though they can hear the difference between them?

One situation in which this occurs a lot is when speakers of the same language have different accents (e.g. from different regions, economic classes, etc.), and these accents pronounce some corresponding sounds differently. The speakers can hear the difference, but they treat the sounds as equivalent.

(For examples, certain dialects of Spanish pronounce the word jamón (tr: ham) like xaˈmon, while others pronounce it like haˈmoŋ. In other words both the initial and final sounds differ between the two versions. Most native speakers can hear these differences, but they disregard them; that is, they treat xaˈmon and haˈmoŋ as the same word.)

Is there a name for this equating of sounds that are perceptibly different?

Note that the phenomenon I'm referring to here should not be confused with the case in which someone is unable to hear the difference between two sounds.

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Yes, this term is Allophone.

Here's some background, briefly:

  • A language has concept of phoneme. It is a concept, not a sound;
  • People produce phones;
  • A listener then maps a phone they hear to a phoneme;
  • All different phones that a native speaker would map to the same phoneme are called allophones.

Take English /k/.
Unvoiced plosive consonants are usually aspirated in English, so many words would have /k/ produced as [kʰ], as in "cat".
However, in some cases, it stays unaspirated [k], as in "mark".
/k/ can also undergo other transformations, like palatalization in "thank you".

People of different dialects produce same phoneme differently.
Furthermore, even the same person produces the same phoneme slightly differently every time. In addition, sound can be distorted significantly or frequencies can be cut off, like when using a broken telephone or handy loudspeakers.
Nevertheless, an English listener maps all mentioned phones to the /k/ phoneme.

Note that the phenomenon of Allophone is strictly language-specific. Many languages, like Thai, make a clear difference between [k] and [kʰ], and they are never interchangeable.

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    I think you're abusing the term "allophone", since the conditioning environment is social and not positional. Instead, "free variation" comes closer, since it is more of a sociolinguistic concept. – user6726 Jun 30 '18 at 1:57
  • "Free variation" is a confession of ignorance; everybody has their own phonology, and allophones don't come close to recording the actual variation. – jlawler Jun 30 '18 at 3:07
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    Indeed, this is not a case of allophony. Allophones are a matter of phonology, not sociolinguistics. They're in view when there is complementary distribution in the phonological structure (not when there is identical distribution in the phonological structure and complementary distribution in the social structure).It's true that this is normally called free variation, even if the term doesn't explain anything. – Luke Sawczak Jun 30 '18 at 16:04
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I don't know of a specific term for this, but Edward Sapir (1925) presents this situation in his "C and D languages": two languages that are phonetically different but have a similar phonemic patterning. One can apply the same reasoning to two different dialects. Here is an example taken from Dresher (2009:62) enter image description here

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It happens. I don't know of a good word. Assuming the SPE analysis for convenience, in English in a latinate word, at the end of an unstressed word-initial unstressed syllable, /e/ can often be either tense or lax. Examples: "eliminate", "deliberate" (v.), "revise", "preliminary", "demonic". The difference in other contexts is phonemic, so presumably people can hear the difference.

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