I'm not a music teacher and I'm not the greatest sight reader, but I'm going to take a whack at this - probably not adding much to what's already been said:
The problem starts when I read music using intervals and miss playing
accidentals of the key I am in.
There seems to be a fundamental error in this sentence: If you are not playing the notes of your scale correctly according to the key signature (not called accidentals when they are part of the key signature), you are not really using intervals - just an approximation of them: You know that from a line to a space, or vice versa, is a 2nd, from a line to a line or a space to a space is a 3rd, etc. But that's only part of the interval - the size or quantity. An interval also has a quality: Major, Minor, Diminished, Augmented or Perfect, but you're not reading that at all - which is exactly your problem: If you see E->F, without knowing the key is Eb and the E is flatted, you are seeing a Minor 2nd. Only when you know the key signature can you read the interval correctly: A Major 2nd.
The upshot from this is that your 'intervals' approach to reading is incorrect - it's not giving you the correct result because you are not reading all the music that's written. It might seem faster to you, but what good is that when you're not reading the music correctly - only reading half of the music? It's like taking a shortcut that leads you to the wrong destination.
IMO that is your problem in a nutshell. Hopefully, what I'll say now will help you fix it:
I knew quite a bit of theory before I learned how to sight-read properly to play from a sheet. I took some guitar lessons (a long time ago) and learned how to read from a sheet and play. The instructor taught me using note recognition only - no intervals, no mnemonics, no counting lines and spaces - he forced me to recognize the notes using a few landmarks on the staff. I drilled for a few months with that system - we used mostly flash cards that showed only one note at a time and a key signature - no intervals. After a few months I was an almost decent reader of bass and treble clefs.
After the first few lessons, because I knew some theory, I realized that learning to recognize and read 'intervals' would be a great shortcut, and I was lazy - didn't want to do all those drills.
I mentioned my idea to my instructor. He was a pro who was constantly working as a free-lancer, always running off to a gig - because he was a great reader. His response: No - you need to read the notes - just read the notes - read the notes in front of you, just like you read English off a page.
I didn't think too much about why, I just did what he told me to do, and I haven't thought about it much since then. But this question helps me understand his method:
If you're trying to identify 'intervals' on a sheet, you're occupied with analyzing the patterns on the page, not the notes themselves. But if you're not focusing on a note, how can you determine if it's sharp, flat or natural? That only happens if you are compelled to name the note: C
is a different name that C#
. E
is a different name than Eb
, etc.
I am tired of websites asking me to memorise the order of flats/
sharps and key signatures - I have done this already and am quite
comfortable with it. I even practice scales and play them comfortably.
The problem starts when I read music using intervals and miss playing
accidentals of the key I am in.
It's because you know the key signatures, but you are not using that knowledge when you read, as stated above - you are only reading part of the music that's written. The key signatures give you the proper names for the notes in a particular key. The staff effectively changes with the key signature. If you're just reading the 'intervals' based on the pattern you see on the page, but you don't actually know what the notes on the staff represent in that key, you're going to get them wrong.
Think about it this way: By reading 'intervals' off the staff, you're actually going backwards, because the notes determine the intervals.To get the intervals right, you need the notes.
So: My answer is you need to break the habit of reading intervals first. You must learn to read the notes themselves - they determine the intervals - that's what the key signature teaches you, but your insistence on reading the intervals off the page makes you neglect the key signature. Naturally you make mistakes with your sharps and flats.
I can say from experience that after you do that for a while, since you know your scales, if you are interested in the intervals at all - depending on the genre and on your own personal need to understand the music you're playing better - they will start popping into your head immediately as you read the notes.
Consider that the musical alphabet has only 7 letters, plus the flat, sharp and natural signs, and there are only 9 notes on the staff. English has 26 letters and some languages have many more letters. So learning to recognize the musical notes isn't going to be very hard: You've already mastered a far more difficult language: English.
As far as reading itself goes: What @TimH said in his answer sounds good to me:
I think for really good sight readers interval reading is one of the less used tools. They come to a point where there is an almost direct map between the note on paper and the physical key on the keyboard which they can reach almost entirely by feel.