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I have made good progress in identifying most ascending intervals up to the octave, but am really struggling with the tritone, min 6th and maj 7th.

All three sound dissonant and very similar.

Is there a trick/method for correctly identifying them?

I recommend relating them to two stable intervals that you certainly already know: the perfect fifth and the perfect octave.

When you hear a given interval, sing in your mind a perfect fifth from the original pitch. If the second pitch played is a half step "smaller" than the perfect fifth, you know it's a tritone; if it's a half step "larger," you know it's a minor sixth.

(Note that I'm using "smaller" and "larger" so as to be agnostic in terms of direction; in an ascending interval, the tritone will be below the perfect fifth, but it will be above it in a descending interval.)

The same strategy is true for the major seventh: find your orientation by singing a perfect octave, and if the given interval is a half step smaller, you have a major seventh.

I know that sounds like an extra step, and you want immediate recognition. But for this stage of the learning process, that's okay! The more you do this extra step, the quicker this immediate recognition will come to you. These are tough intervals, so it's going to take a little bit of work.

Tritone is pretty dissonant, so works well in Blues! Check out 'Maria', from West Side Story. First two notes make that tritone.

Major seventh is easily found going straight to the octave, as in 'Somewhere Over the Rainbow' and dropping a semitone. Which is exactly what the melody does. Just as the opening three notes of 'Bali Ha'i'.

Minor sixth is the upside down version of major third. 'Half a Pound of Tuppeny Rice' starts with a maj3, so invert it, there's the m6. I think most would say that m6 isn't dissonant, but it's in the ear of the beholder.

I respectfully disagree with the suggestion of combining multiple familiar intervals as a way for getting to an unfamiliar interval. If you bear with me I'll try to explain why and give you a practical demonstration of a better way of overcoming the challenge of unfamiliar intervals.

1. Breaking down an unfamiliar interval into multiple familiar interval doesn't take you very far.

Please note: there's nothing wrong in doing that, and in fact it's a valuable exercise in itself. But it does NOT help you very much toward the goal of mastering the interval, especially compared with other much easier and more effective methods. (See demonstration below)

For example, think of this. Suppose someone says they can't recognize minor thirds. And so we advise them to think a major second, and then add a minor second, and there you go. But then again, anyone with minimum of musical experience and common sense will probably say, "come on, don't do that, just practice minor thirds, it's not that hard, practice a bit and you'll get it". I think this is what most experienced musicians would advise.

And so, why should things be different if the unfamiliar interval is a sixth rather than a third, or anything else?

So, breaking down an interval in smaller steps, or reaching it by a roundabout way, or thinking of a song with that interval -- it's all fine but can never be the solution you're really looking for.

The question is then: OK, so how do I master those unfamiliar intervals?

Let's answer that.

2. You need to practice each interval directly, a lot

As simple as that. The reason why you can recognize a major second easily, and think of it easily in your head, is because you already used it a lot, knowing what it was. You are extremely familiar with it. And the reason why, for example, you cannot just as easily instantly recognize a minor sixth, or promptly think of it in your mind, is that you have not consciously used it a lot. If you have been using seconds consciously all your (musical) life, but you have hardly ever consciously used sixths -- of course there will be a big difference there.

3. You can turn an unfamiliar interval into a familiar one with focused practice

I'll try to demonstrate what I mean by "focused practice". This can be done in many ways. Here I'll do it one way that I've used and refined a lot over time.

Let's say you want to truly familiarize with and master the tritone interval.

According to everything I've said above, what you need to do is to (1) listen to the tritone a lot, and (2) practice hearing the tritone in your mind a lot.

If you do these two things enough, there is no other possible outcome other than you mastering that interval.

I'll describe you two ways of doing that in practice, using the ascending tritone interval as the subject.

4. Demonstration of tritone familiarization

In the below video, you'll be hearing random notes on the piano, followed a tritone interval starting from those notes.

After you hear each note, see if your brain can tell you the pitch of the second note of the interval.

As you do that, DON'T TRY TO THINK OF THE INTERVAL BY STEPS! Either your know it directly, or not. It's OK either way.

Keep listening to the starting notes and the subsequent intervals.

Even if in the beginning you didn't have a clue about tritones, after maybe a few minutes of listening, your brain will start to anticipate the sound of tritone intervals.

You can even leave the video playing in a loop, in the background. You don't even have to pay attention continuously to every note. Just let your brain gradually and naturally absorb the feeling and the sound quality of that interval.

Once again, do NOT think of the interval with intermediate steps, or in a roundabout way. Either you know it directly or not (yet) and it's OK both ways.

After a while, or if it's too hard to follow, take a break and try again later or the next day.

If you do this enough, in a relatively short time you will have the sound of the tritone permanently established in your ear. You will not confuse it with anything else.

Whenever you will hear a tritone in a melody, the interval will jump out at you. And whenever you will need to think of it, it will be enough that you think of one note in your mind, and have the intention of hearing a tritone up, and your brain will instantly and precisely generate that interval for you in your head.

Here's a video that demonstrate this type of exercise, done with a software called Multilateral Ear Trainer:

Full disclosure, I worked on developing that software and I'm affiliated with the project. In fact for many years I also answered users' questions about it, and because of that I'm fairly familiar with the typical ear training challenges of musicians at different levels. These suggestions are based on this experience.

If you (OP but also others) find the video useful, I can make similar ones for other intervals, let me know.

5. Alternative tritone familiarization exercises

A similar familiarization exercise can be done by playing on your instrument.

Play a random note. Then imagine a tritone up, if you can. Then play the interval, like in the video above. By playing the interval you will know how accurate you were in your head.

Continue for a few minutes: play a random note, think of the interval, play the interval.

If you cannot think of the interval at all, just play the intervals for a while. After a bit your brain will start to catch up.

Again, do not use roundabout ways to think of the interval. Either you can think of it directly, or play it so you can hear it. After a while, it'll come. It's really only a matter of hearing it and using it consciously a sufficient number of times.

All you need to do, ultimately, is to hear and think of the interval in a focused way a sufficient number of times. Your brain will do the rest.

6. Additional points

Each interval must be trained individually as explained above, or in some other way that yields similar results.

Ascending and descending intervals must be trained separately. For example, tritone up and tritone down are two different beasts, each needs its own training.

About using roundabout ways to think of intervals is fine, do it whenever you need. But to seriously master any interval, only a direct approach like the one described here will do.

If you play the piano, you can enrich the exercise by adding other notes to the starting note. In this way you also learn to hear and generate the intervals in your head not only in "laboratory conditions", but also with a musical context.

In case of the software used above, there is an option to add background chords to the exercise, for the same reason, i.e. to train the ear within a musical framework rather than in aseptic conditions, so to speak. But in the beginning you should start with the pure interval and nothing else.

If you have the chance, it's good to practice these intervals with different instrument sounds (e.g. if you play with a synth, or if you use the software, change the sound from time to time) but it's not a critical factor.

Bottom line, even just a few minutes of well-directed training can give you a level of interval mastery that even years of playing without paying direct attention to this issue could ever do for you.

Lastly: ear training is a long-term thing. You cannot cram. You can do just a little, and do it often, and you'll get great results.

I hope this helps someone :)

Differentiating tritone, min 6th and major 7th intervals

this would be very easy if you‘d practice like this little boy:

Never mind, this was just a joke ...

There are several ways to improve relative pitch and ear training:

1. Play a brass instrument: There you‘ll have always to estimate an interval - otherwise you wouldn’t be able to play the correct tone (in opposite to a keyboard of a piano or computer where you just press a key). This habit will become interiorisized as an automatism.




2. Make a collection of the first interval of well known tunes (this methode is most used in schools and also promoted here in the answers you already got and in the jazz book of mark levine. ( Just like Tim suggests I always mentionened „Maria“ and „over the rainbow“ as a help to intonate the diminished fifth respectively the M7.)

https://flypaper.soundfly.com/tips/interval-cheat-sheet-songs-to-help-you-remember-common-intervals/

3. Note that the intervals you struggle with are chromatic approaches to perfect intervals (5th and 8th). As you say you got them, so you have to practice to sing and hear the half tone leading from the +4 and the maj. 7 and the min. 6 to the 5th and the 8th.




4. Instead of analyzing the interval as 2 succeeding tones try to identify them (auditive) in a chord of 2 tones or in a triad.




5. Characterisize and name the intervals by your own and unique, individual and personal impression. (certainly you‘ll remember how you were able to identify the b7 in the final chord of a blues: so solaso ta (ta=b7), before you knew that it is named a blue note)




6. My way to success - aside that I played tenor horn before I started piano playing - was: practicing to imagine the scale before singing the interval by going back to the root do: do re do mi do fa do so do la do ti do do.




7. Repeat this patterns: do so la so, do so lu so (lu = la flat), do do(8) ti do, do so fi so (fi = fa sharp) singing, playing, imaging



8. 
   

   Invent some own short tunes (like the beginning of songs) with the repeating the motive e.g.: do-fidoso-dosofidoso-fisofidoso-do.

   
   
   

   (I‘ve got to admit: the latest methodes were the most succesful ones to me.)