I'm amusical - I cannot discriminate between higher and lower pitch even when there is a large difference between them. I want my child to develop musical abilities. I know that an out-of-tune piano can affect the development of absolute pitch recognition, would a parent who sings out-of-tune have the same effect? I find it difficult to get the tune right even for simple nursery rhymes such as twinkle twinkle little star.
Unlikely, because unless your child has a genetic reason for being unable to distinguish pitches (which you apparently may, if what you say is true), he or she will soon learn to identify the inaccuracies in your singing.
For example, there has been some noise about bilingual families and a fear that the non-native parent will "infect" the child with bad grammar, but it turns out the children tend to learn quickly and can soon tell that one parent speaks incorrectly sometimes. Eventually non-family sources of language will dominate anyways.
To that note, if you play any recorded music or movies/television, every note in that music will be rigorously tuned to its exact pitch. So there will be plenty of chances to hear properly tuned music if you live in a typical household. I wouldn't really worry about damaging your child's hearing skills at all. But why not do some activities with a pitched instrument such as a piano, or take your child to musical activities? If you're concerned, just make sure you spend time listening to recorded music at home.
You should pay attention to your singing.
Tone-deafness is a result of a disconnection between what are you hear and what you produce. It is generally fixable through conscious attention.
I work developing musical training computer games for children.
My mother sang to me as a child, and she is tone-deaf. I also learned to sing in a tone deaf manner. We learn by copying.
I subsequently spent thousands of hours playing the piano, but my early training (basically to NOT pay attention to the sounds I am making) retarded my musical development. That caused me much suffering.
It was only in my 30s that I trained myself consciously to sing correctly, it has been hard work. I taught myself to sing accurately using a solfege system.
I fixed such things as gradual pitch drift, incorrect intervals such as getting a fourth, fifth, octave muddled up, squashed thirds.
It is a blessing for your child that you are conscious enough to enquire.
You should find your child a teacher, who can teach them to sing. This should be the first instrument everyone learns upon, it is our natural inbuilt instrument. To try and bypass it is stupid. Chopin said "If you wish to play, you must first learn to sing."
If your child has a good teacher, you don't need to worry about damaging their musicality. (Note: It is difficult to find a good music teacher. And a bad one will do more harm than good. So choose carefully!)
If the child doesn't, you do. Even by abstaining from singing, your child will learn to perceive the world as you do by a million subtle cues. The way you use words, the way your eyes will move, the way your physical form follows conscious intent. And the set of conditions that led to your own disconnection may well be transferred to the child. Maybe you are primarily a visual person, this is your primary perception and the root of your attention. It's quite easy to see if someone is primarily a visual person. The renowned 19th century music teacher Evelyn Fletcher Copp (the first teacher to systematically impart Absolute Pitch to her child students) said that when a parent brought a prospective new student to see her, she would look closely and ascertain how the child primarily perceives the world (visual, auditory, kinaesthetic, logical, emotional, etc).
It's worth remembering that these balances can be adjusted. Imbalance can show proclivity which is to be encouraged. But at the same time weaknesses should be addressed.
If someone is strongly primarily visual, maybe practising music in a pitch dark room would encourage them to rebalance.
PS Someone commented earlier that music is unlike language, it is something artificial. This is an ignorant statement. It has been demonstrated to be an intrinsic component of spoken language. Diana Deutsch (a world-famous researcher of Absolute Pitch) demonstrated (in a public lecture) the presence of the diatonic scale in spoken language, by time-stretching and looping short phrases of spoken word. We use this scale to communicate (subliminally for most of us) at an emotional level.
It may be, genetically, that your child has inherited your amusicality. You won't know for a while. In fact, if only you listen to it, then you'll never know! Children tend to believe that their parents are inscrutable, so your out of tune singing may be acceptable as the right way to your child. This will then oppose renditions by others, giving a bit of a dilemma. I say far better to not try to sing to your child - there are multiple other better ways to communicate. If, for instance, you weren't good at spelling, when your child has to learn words for a test, would you spell badly whilst trying to help?
It occurs to me in reading all the answers posted so far (by well meaning members of the community offering what they perceive to be useful advice) that the ONLY answer that seems correct is: We don't actually know how singing dissonant off pitch musical phrases to an infant during the very early stages of language development might affect their future ability to recognize or reproduce what we consider the proper notes within a particular key.
I don't know if there have been any scientific studies on this. But I do know, that science has proved that language development and word recognition comes at a very early age and begins before the development of the ability to reproduce the words that are recognized.
And we know that learning multiple languages is much easier for younger children and the ability to learn new languages diminishes as we get older. I actually have a relative who speaks both Russian and English with equal aplomb at the age of two, because her mother speaks Russian and English to her. If I tried to learn to speak Russian, it would take years of intense study before I could even develop the vocabulary of this two year old.
So unless someone can cite some scientific evidence to support either a yes or a no, I feel it may be misleading to answer either way.
The safest thing to do in my opinion would be to both sing to your child (a mother's voice is "music to a child's ears"), but also play recorded music for your child - just to be on the safe side.
I think a very safe answer is that interacting with your child is much more important than worrying about unknown risks linked to parental tone deafness.
Give and take, have a conversation, sing, smile, dance to the beat of music, and don't hold back - add rich emotional dynamics with your face while you interact with your child. Make sure the musical experience positive even if you are only playing a drum. Try a peek-a-boo style game to get your child to guess the key you hit on a xylophone and take turns.
If (certainly an if) a musical developmental window exists, then the only sure fire way to miss it would be through absence.
Don't worry, if the child has the skill, he/she will soon be able to tell the difference between your singing and a perfect tune singing.
In addition to that, establishing an emotional communication with your child is more important than anything else. Rather than blocking yourself from singing, provide access to good quality music besides that. So that you don't prevent your child establishing emotional communication skills which may be very beneficial if he/she develops interest in any creative process in the future.
Just keep an easy and natural access to hearing and playing music around and don't force anything, that would be sufficient. Proper education is something you should think of later according to his/her capabilities. (I assume we are talking about the first few months).
Again no worries, in time it will learn many things that you are not capable of.
what about tone and pitch?
I am fully bilingual in Mandarin and English. I sing pentatonic traditional chinese music as well as Italian arias. I can't say that I can detect middle eastern or indian music to be out of tune. I think they have smaller intervals than us and very very small range.
Linguists will say that language acquisition works best prior to age 11. After that, you probably have a very hard time speaking Chinese the way I do. (I spent 11 yrs in Taiwan and 30 yrs in US). I am a little different. My English is without accent and my Spanish is overwhelmingly convincing for an asian person. When I hear a 'foreigner' speak Chinese, their intonation is horrible. We can understand it when they speak a full sentence, but when speaking short phrases it can be embarrassingly incomprehensible for both speaker and listener.
It is quite obvious that tone is culture/immersion thing and is trained at early pre-pubescent age....
(Sorry I am probably mixing 3 discussions thread into one)
Like the story of Jane (movie with Jodie Foster), who grew up in isolation with her mother who suffered from brain damage that impaired her speaking ability, one probably should be wary of what they want to expose their very impressionable child to....