(work in progress)
It's a craft.
I was inspired by the post on rhyming dictionaries et al. Rhyming dictionaries have their use.
Pat Pattison's songwriting course on coursera.org changed my view on rhyming (http://www.patpattison.com/news/). There are not only perfect rhymes, there are many kinds of rhymes, and they are all useful for different purposes. Some may not be considered rhymes, but then they are just imperfect rhymes. They are useful.
The perfect rhymes will probably land on a final voiced syllable to be obvious, and should match perfect rhymes in different verses, I feel.
(By the way, when I say vowels and consonants in the following, I am talking about phonetic sounds, not ortographic characters.)
VOWEL RHYMES: Murder-further.
Not the best, but if it's placed centrally in two separate lines, you might not notice it at all, yet you feel it subconsciously. You feel that the two lines are sewn together at that point.
.............. murder ............. standard
.............. further ............. pandered
Murder-further is a rhyme, of sorts, because of -ur- and -er. Standard-pandered is a much better rhyme, so it's placed in a prominent place. Further-murder could be criticized if it were placed there, especially if it matches a perfect rhyme in a different verse, but as it is, you can get away with it, claiming it is accidental. You don't even have to match this silly non-rhyme in the next verse. Oh, actually you probably would want to, but you could choose any other rhyming technique in that spot in the next verse.
The less perfect the rhyme, the less the need to match in the next verse.
Cook-take, moon-bean. Of course, you might use cook-cake, moon-mean. A proper (perfect) rhyme would include both consonants and vowels: Cook-took, mean-seen. Again, a simple consonant rhyme may not be the best choice finally in a line, but it could work wonders centrally.
The better and the longer the match, the more perfect the rhyme. Mood-food is perfect, mad-card not perfect, but it's a consonant rhyme, and it's slightly better than mad-food. But if mad-card is placed finally in a line and compared directly with the perfect smart-dart in a different verse, the difference will be noted.
Notice the A sounds in mad and card. They are different. In the latter, the r changes the quality of the a sound. The rhyme may be good enough for some purposes, not good enough for others.
To illustrate the idea of vowel qualities, remember how Tom Lehrer rhymed Harvard with discovered ("discavered"). He had to tweak it to make it work (and he achieved a comical effect thereby). So arv and cov are definitely not the same vowel quality.
A vowel, then, is vowel quality + length.
Same vowel quality, same length = perfect vowel rhyme.
Different vowel qualities = less perfect vowel rhymes.
Different length = cringeworthy rhymes.
English has quite a number of vowel qualities, and usually, perhaps always, they can be pronounced short (cut) or long (chord) (and if that is not an example of exactly the same vowel quality, short resp. long, then I apologize). The length of the vowel should match, unless you want to achieve a comical effect, and the reason is, it affects the rhythm. (When we sing, all vowels are usually long, you can sing short vowels long, but they should still fit. It should be rhythmic when you read it out loud.)
Danish has a plethora of vowels, with 14 (17?) vowel qualities which can usually be pronounced in three different ways: long, short, or with the glottal stop. I am not saying that to brag, it's true, and other languages have even more vowel qualities, so shut up. I am just putting things in perspective. Japanese has five, Greenlandic three. It's not a competition.
I could list the 14 different Danish vowel qualities, but what good would that do you. You need to figure out which ones exist in your language. Furthermore, you need to pair them up and decide for yourself which pairs are closer (usually synonymous with better). I think that mad-card is closer than mood-card, and sad-mad is identity. But you be the judge of that.
English has more consonants than Danish. I have to think to make many of the voiced sounds, such as badge; it may come out like ba-atch.
Again, there are perfect and less perfect rhymes, and they serve different purposes. You need to create or obtain a list of all the (phonetic) consonants in your language, and you need to pair them up and decide which are closer and to what degree they can substitute for each other. S and Z are close (unvoiced-voiced; same relation as F and V), SH a little further away. TCH is an unvoiced version of DG(E), but the former is combined with a short vowel, the latter with a long one (is my impression). M and F are quite different. N, being voiced, shares some qualities with M.
But please, don't let this be a stumbling stone for your songwriting. When I say "you need to," I don't mean for your next song. I mean for your songwriting career.
(All for now. I may follow up later with a piece about practical rhyming for songwriters.)