If such a language does exist I assume it would be difficult to teach or learn.
Tamil grammar and phonetics is built on the concept of மாத்திரை (roughly translated to metre or measure, surprisigly the words மாத்திரை and metre are phonetically close).
The ancient Tamil grammar text தொல்காப்பியம் (Tolkappiyam) has the following:
கண் இமை நொடி என அவ்வே மாத்திரை
literally translated to 'The metre is the blink of an eye'.
There are letter groups that are based on how long the phenome must be uttered:
- குறில் (Kuril) is the subset of letters that have மாத்திரை 1 (One metre)
- நெடில் (Nedil) is the subset of letters that have மாத்திரை 2 (Two metre)
There are are other groups of 0.25, 0.5, 1.5 மாத்திரை (metre).
For eg: கல் (stone, study: homonymns) vs. கால் (leg, quarter: homonyms) - The difference in pronunciation of these words is in how long each letter is spoken. Of course, Tamil has different letter forms for the different phonetics and the rules governing how long each phenome must be uttered. If those phonetic rules are broken, word semantics change (although the written word has a contextual meaning). Since the example words are homonyms themselves, meaning is disambiguated based on context.
- eg: இளமையில் கல் -> Study when young
- eg: இது ஒரு விலைமதிப்பற்ற கல் -> It is a precious stone
- கல் தடுக்கி விழுந்தான் -> He tripped on a stone and fell
- கால் தடுக்கி விழுந்தான் -> He tripped and fell
show that the only difference is in how long the first phenome in the first word is uttered. It changes the meaning of the sentence completely.
Although that is not how we talk about it, many languages use length of segments as a distinctive, meaningful property, for example Logoori kuvura 'to lack', kuvuura 'to reveal'. The vowel in kuvuura takes longer to pronounce, so you could say that it is slower. Another way in which there can be a fast vs. slow difference is withe speech rhythm. We sort of wave this in English with 'latest' and 'latex', where the two syllables in 'latest' are packed together into a single speech unit called a foot, and are spread out into two of those units. There are a number of languages spoken in Cameroon and Nigeria which use this as a distinctive means of forming words. Estonian is famous for using both distinctive length of vowels, as well as distinctive grouping of syllables into feet, which results in three degrees of quantity. Then finally, in North Saami, there is an interesting feature known as allegro formation, where in certain grammatical contexts you say words quickly. For example the imperative verb has to be said quickly, and that's how you can tell the difference between an imperative and a negative, at least in the verb part. Or, phrases sound different from compounds because in compounds, the sub words are said quickly.