Studying or practicing Ear Training?  If you're a musician, you should be.  You'll find my Palm software Ear Trainer invaluable.  Also, I teach guitar lessons in Orange County, CA.  (See OCGuitarLessons.com)

If the two notes in an interval are the same, it's called a first or unison.  The next larger intervals are a minor second, a major second, a minor third, a major third and so on.

You'll notice that the second and the third have a quality described here:  minor or major (the latter being a slightly larger interval than the former).  Most intervals are this way, but not all of them.  The intervals that can be minor or major are so because in the conventional scales and chords they frequently vary between those two qualities or interval sizes.  (Besides the second and third, intervals that can be minor or major are the sixth and the seventh.)  Some intervals, however, usually do not vary, and are considered to have one default quality or interval size, which is called perfect.  The intervals that are usually perfect are the fourth, fifth and eighth.  (The latter is also called an octave.)

Next after the major third is the perfect fourth.  Between the perfect fourth and the perfect fifth is an interval sometimes called a tritone, because its size is that of three consecutive "tones".  (A "tone" is the size of a major second, and a "semitone" that of a minor second.)  Alternatively, the interval of the tritone may be called an augmented fourth or a diminished fifth, depending on the musical context.

After the perfect fifth is the minor sixth, then the major sixth, minor seventh, major seventh and the perfect eighth or octave.

When two notes are an octave apart, those two pitches have the same name.  In other words, if either of them is a "C", then the other is also a "C", just in a different octave.  The frequencies of two notes an octave apart have the ratio of 1:2, i.e. the higher of the two notes has twice the frequency of the lower.  For this reason, the two notes both stimulate the mechanism of the ear very similarly, and this close similarity in harmonic effect is why the note names simply repeat every octave.

Intervals have a similar repetition in each octave, though their names don't repeat.  If the interval of a minor second were enlarged by an octave, it would become a minor ninth, the major second would become a major ninth, the minor third a minor tenth and so on.  Intervals smaller than an octave are called simple, and those larger than an octave are called compound.  A simple interval can be compounded by adding an octave to it, e.g. the compound major third is the major tenth.  Likewise, a compound interval can be simplified by reducing it an octave, e.g. the simple perfect eleventh is the perfect fourth.  Most applications will only require familiarity with the first octave, but it will eventually be useful to memorize which pairs of intervals simplify and compound to each other:

Following are the common symbols, full names and some alternative symbols for the intervals. ("b" is the symbol for "flat", which means lower.  "#" is the symbol for "sharp", which means higher.  The minor intervals are sometimes called "flat" instead of "minor", but the major ones aren't called "flat" or "sharp" in this context.  "Sharp" usually applies only to making the fourth higher than perfect.  Other terms for altering the otherwise-perfect intervals are augmented [aug.] and diminished [dim.].)

The intervals simplify and compound as follows:

A well-trained ear is essential to good musicianship, no matter what the application.  Many amateurs may remain ignorant of this aspect of musical study, but all talented musicians have a good ear, whether by chance development or deliberate training.  However, truly fulfilling the abilities of any musician's ear is greatly accelerated by deliberate training.

There are two major categories of aural recognition:  (1) the absolute recognition of the pitch of a note, which is called Perfect Pitch; and (2) the recognition of the exact difference between any two particular notes, which is called Relative Pitch.  Perfect Pitch is very rare, very difficult (though possible) to develop and enables a very different perspective of music than usual, akin to suddenly seeing color where everyone else is seeing only a grayscale.  For the overwhelming majority of people, music composition, performance and audition never involve Perfect Pitch.  For that reason and others, Relative Pitch is probably more important, and its development is the exclusive charge of the Palm software Ear Trainer.

Relative Pitch is indispensable for identifying musical structures, whether in the inscription of existing music, the analysis of compositions by ear, identification of fellow bandmates' expositions and/or identification of music heard mentally while writing or expressing in real-time.  Relative Pitch is just as indispensible for the mental construction of musical structures:  whether their symbols be read or remembered by name, called for by bandmates in preparation for or during performance, or put in service to conceptual exploration while composing or performing improvisation.  In fact, the deliberateness of the harmony of any musical performance may be considered dependent upon the performer first hearing the intended pitches in the mind's ear, which are usually constructed therein entirely by the means of Relative Pitch.

The development of Relative Pitch requires repetitive drilling, but there is an effective mnemonic technique which can be employed to accelerate the results of such drilling, which is to associate each of the pitch intervals with a fragment of music that begins with that interval and which is already well-memorized.  This will allow you to recall the interval into your mind's ear by simply recalling the beginning of the music fragment.

The best fragments to use should be ones that you enjoy and know well and can therefore easily recall clearly, consistently and regardless of context.  If you were to go through all the music of your favorite band or bands, chances are good that you would discover a memorable fragment of music for most of the pitch intervals up to at least an octave, and this is highly recommended.

Following is an example of this mnemonic technique, utilizing the material of the classic Black Sabbath albums (during the original "Ozzy years"):

After the interval-fragment correlations are memorized, their utilization is simple:  Say you hear a particular interval you wish to recognize.  If the interval name or fitting music fragment doesn't come to mind right away, take a guess.  Suppose you guess the interval sounds like a fifth.  Following the example presented above, if Black Sabbath were one of your favorite bands, you would recall that the riff that begins with a fifth is the main one of the song "Electric Funeral".  Because you love this tune, you can easily recall the sound of this riff, basing its first note on the lower note of the interval in question.  If the riff's second note matches the higher note of the interval in question, then you know the interval in question is a fifth.  If it doesn't match, then you'll probably get it in one more guess.

Of course eventually your aural associations will become so well reinforced that you'll begin recalling the sound of the intervals without even bothering with the music fragments, but meanwhile this memory aid really is an effective stepping stone.

Another utilization is when you need to construct a pitch by ear:  Say your bandmate is singing a particular note and has requested that you sing the note a major third above it.  You'd recall that the musical fragment for that interval is Ozzy's main vocal in the tune "War Pigs".  In your mind, you would begin Ozzy's vocal melody on the note your friend is singing, and the second note of Ozzy's melody will be the major third you want to sing.  In other words, what you're doing is bringing to mind the lyric "Generals gathered in their masses...", and you're simply starting it with "Generals" on the note your friend is singing and then taking your note from the pitch of "gathered".

Of course, if Black Sabbath isn't your favorite stuff, figure out for each interval a music fragment from your personal favorite music.  (In time, interval-fragment correlations from the music of several great bands will be available here.)

 
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