Here is an example of an altered scale. it uses 7 different notes per octave, just like a good old fashioned major scale, and it is made up of tone and semitone steps. The steps are in a slightly different order, thats all. The altered scale goes by various different names, most commonly "melodic minor", which is a pretty dire term for it, as it is often played in a non-minor context and isn't the same as a classical melodic minor scale anyway. You're probably used to the terminological problems of jazz by now, so we'll leave it there to fester for a while.
I'm going to suggest some possible uses for this scale which will add colour and sophistication to your solos and make you sound like Herbie Hancock or Wayne Shorter, or at least might impress next week's tutor.
I've tried to avoid getting too theoretical: the idea is that you should try these out - the examples I've chosen are in the New Real Book (Sher).
The discussion below relates to the above scale, and examples, in concert pitch, so you'll have to transpose the scale for your own instrument. However, for the benefit of those with Bb instruments I've done a transposed version. Apologies to alto and bari players.
Firstly, use it over the half-diminished chord. Get out your New Real Book and turn to that old favourite "Autumn Leaves". In bar 5 you will see a chord of Ami7b5; in other words a half diminished chord. This is an ideal chord to play this altered scale over, and you get plenty of chance to try it in "Autumn Leaves", because it comes up again in bar 13, 17 and 25. The effect of playing the altered scale is to change the Bb into B natural. The B flat is a bit dull here, and the B natural spices it up no end.
Another great use for the scale is over an F7 chord, giving a F7#11 sound. This doesn't go too well when the F7 is leading to a Bb tonic, it is best used in the key of G or C (you don't get quite so many F7s in these keys, so it's not something that occurs in every number). Of course, if the chord is actually notated F7#11, thats a dead give-away! Try it on "Darn That Dream" bars 5, 13 and 29. Again, the B natural is the interesting sounding note.
In different keys, it can be used on the second bar (and bars 10 and 26) of "Don't Go To Strangers" (Eb7#11), bars 10 and 26 of "Weaver of Dreams" (Bb7#11), bars 10 and 26 of "There Will Never Be Another You" (Db7#11), or bars 4, 12 and 28 of "We'll Be Together Again" (D7#11).
There are loads of other examples. Perhaps best known, though, bars 3-4, 11-12, and 27-28 of "Take The A Train" (D7#11).
For my third example, the altered scale can be used over a dominant 7th type chord of B7. This is probably the commonest application, and "altered" chord and "altered" scale are often used to mean this particular use.
I particularly like it over the dominant on III or VI, for example the E7 (III) or A7 (VI) in bars 3-4 and 5-6 of "All of Me" (in the key of C). But before you rush off to try this out, you can't play the altered scale I've shown here, it's in the wrong key. It goes with B7.
Sometimes the chord will be notated B7alt, or have the alterations #5, #9 or b9, which is a strong hint to use the altered scale. But you needn't always play the altered scale in these cases.
As an example in the right key, try "Early Autumn" bars 2, 10 and 26. In other keys there are plenty of opportunities to use the altered scale, B7 is a bit rare in standards.
Used in its minor form, the scale is like a scale of C melodic minor (ascending) and fits harmoniously wherever a minor chord is used as a tonic - like "Solar" by Miles Davis, or the second bar of "My Funny Valentine" (not in the New Real Book, but you may know it).
In the examples I've given, I've tried to stick to the particular scale I've written out, the one with 6 white notes plus Eb (in concert), but there are 11 other altered scales, obtained by transposition, which gives plenty of opportunity to annoy the neighbours practising them all.
(Or how to astound your friends with your extensive knowledge of arcane jazz terminology...)
Getting back into the quagmire of nomenclature, I've studiously avoided saying the scale "starting on" a certain note, as I'm a great believer in scales starting wherever you happen to be at the time. In fact, when used in a theoretical discussion, it is likely that the term "scale" means a set of notes, and probably an associated root. The order in which they are played is really only of significance in examination syllabi.
The same set of notes is used in the four examples over four different roots: A, F, B and C.
Most people call this scale the "melodic minor" or "jazz minor" scale, reserving the term "altered scale" (if it is used at all) for the third use described above. The first use would be described as the "6th mode of the melodic minor", the second as the "4th mode of the melodic minor", and the third as the "7th mode of the melodic minor", because A, F and B are the 6th, 4th and 7th notes of C "melodic" minor.
It is actually the same as the ascending classical melodic minor scale. The classical melodic minor when descending is the same as the aeolian (which is not an altered scale - it is a mode of the good old major scale).
The third use described above is also often known as the "super locrian" scale, or the "diminished whole-tone" scale (because it starts off like a diminished scale, then ends in whole-tone steps.
Another way of describing the first scale is as "locrian #2" because it is like a locrian scale with root A, but with the second note sharpened. Similarly, the second example could logically be called "mixolydian #4" or "lydian b7", but is quite commonly called the "lydian dominant". Phew! Try to learn all these terms, so you can use them at workshops to imply that you are party to the most arcane secrets, and regularly discuss obscure points of theory with Herbie Hancock and Wayne Shorter via email.
You may have noticed that there are 3 other possible roots to go with this scale - in other words, what happens if you play it over chords whose roots are D, Eb or G? Yes, there are more ways to use altered scales. Even more ways to name them. I've left myself the opportunity for a sequel!