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I really want to know what exactly the similarity between consonants depends on.

For me, the core might be the place of articulation, manner of articulation and voiced vs. voiceless. For example, b/p/t/d are all stop consonants, and they will sound similar to each other than comparing to other consonants.

But, are there any objective acoustic indicators to judge the similarity between the sounds? For example, formula, VOTs, or any other things? Would you please recommend me some researches about this question?

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What you're asking for is a synopsis of all of phonetics, which is kind of unmanageable in a simple SE Q&A. The first thing to do is set aside syllables and focus on segments: [pa] and [ba] are similar because of the similarity or [p] and [b] and the identity of [a]. You can work on understanding syllable similarity in terms of the similarity of the individual segments.

The classical work Preliminaries to Speech Analysis: The Distinctive Features and Their Correlates provides a phonological analysis of parameters of sound distinction and their acoustic correlates. Although the theory has been improved on since the book was published in 1951, it still provides the conceptual framework for answering your framework. Then, you would want to look at the descriptive taxonomy of the IPA which is the lingua franca for talking about types of sounds, and focus on specific kinds of classifications (many of which are already described in Preliminaries). The book The sounds of the world's languages then goes into more contemporary phonetic analysis of the IPA classifications of sounds.

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    The word ‘syllables’ seemed so out of place in the question that I’m almost entirely sure it was a mistake (should have been ‘sounds’). I’ve edited the question accordingly, so you may want to edit your first paragraph too. Oct 20 at 16:52

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