I mentioned that I discovered a magic method of memorizing intervals in my 24-hour workout post last week. I was doing exercises on my interval trainer, which tests recognition of the interval between two named notes or of the note a specified interval above or below another note. I was testing myself with all intervals between all the natural notes, thinking I would do well to have these ingrained before introducing accidentals. That's when my idea hit.
I noticed that I could instantly recognize thirds, probably from reciting notes in chords (Fmaj7: F A C E, G7: G B D F, etc.). Consequently, I could quickly identify a sixth as the inverse of any third. I wondered if I could do this with other intervals. It's actually quite easy, as there are only 3 such inverse pairs: seconds and sevenths, thirds and sixths, fourths and fifths. I know my ABC's up to G, so seconds are taken care of. And I memorized the cycle of fourths long ago for jazz.
Seconds clockwise, sevenths counterclockwise:
C B D A E G F
Thirds clockwise, sixths counterclockwise:
C A E F G D B
Fourths clockwise, fifths counterclockwise:
C G F D B A E
The key is to get a cycle without accidentals rolling off my tongue (or mind) without thinking. I did this with thirds on a road trip last year. I endlessly recited a cycle of thirds to myself while driving. It helps to periodically emphasize a note to learn the cycle from every point instead of repeating a set of 7. (Every 3: C e g B d f A c e G b d F a c . . . Every 5: C e g b d F a c e g B d f a c . . .) So I can spit these off about as fast as I can speak. I'm now working on that with seconds and fourths. It will help to know them backwards, so I'll get to that soon.
Although the cycles contain no accidentals, they do contain altered intervals: major and minor seconds, major and minor thirds, perfect and augmented fourths. Knowing which interval is between every adjacent pair is as important as memorizing the cycle.
Once these cycles are memorized backward, forward, outward, inward, bottom to the top, I should have a much easier time on the interval trainer. With any 2 given notes, I need to identify which cycle they're from, which direction, and the specific type of interval between them (i.e. major or minor third). Ideally, these steps would be taken instantly, without thought. After that, some easy math with accidentals might be required (i.e. the low note is sharped, so the interval is a semitone smaller). Presto.
I made a new preset called "All Natural" on the interval trainer, with the above ideas in mind. Who has other methods of visualizing intervals? Shapes on guitar? Piano keys?