The following is an extract from my FREE PDF document of scale and arpeggio exercises for jazz trombone. I am publishing part of the introductory notes here because it might be of interest to others who have posted similar articles.
An important aspect of harmony in jazz improvisation is the matter of related scales. All diatonic chords are served by the notes of the particular key or mode. The 3rd and 7th functions of a chord are most characteristic and will acquire emphasis in melodization where it is desired to reaffirm the underlying harmony. The 5th acquires significance in diminished, leading note 7th and augmented chords.
Melodization has to accommodate both the chord itself and the prevailing key, which may be in the form of the nominal key, temporary modulation or a ‘tonal cell’ (the llm7 > V7 progressions that abound in jazz and standard songs).
Modal harmony will tend to avoid using chords foreign to the scale that destroy its purity so the forms of melody/harmony correlation will be mainly diatonic, except where altered upper functions occur (e.g.♭9, #9, #11).
With chromatic chords, the related scale will generally be the one from which the chord is borrowed so that, for example, a Bb7 chord will probably be related to the scale of Eb major, in which it forms the dominant chord.
(If we play the scale of Eb beginning on Bb, which may not necessarily be the case in real music, we obtain the Mixolydian mode which is another way of viewing the subject.)
Augmented triads and the many variations of the augmented 7th chords are related to one of the two forms of the whole tone scale (exercises 41/43).
Diminished 7th chords are often melodized by a scale comprising alternating whole tones and semitones (exercise 37). String of Pearls is probably the most appropriate name for these scales. Since dim7 chords resemble ‘flattened’ ninth chords with roots omitted, the scales can be used with these chords, also. Just as there are three dim7 chords, there are three of these scales, too.
Some writers have attempted to define a related scale for all chords, no matter which. In my opinion, those who advocate extending the list of scales are rebels without a cause because we already have the option to use notes in continuity or in simultaneity. In other words, if we take the notes of a chord and spread them through time we produce a melody, or scale, and if we take the notes of melody, or a selection from the melody, and use them in simultaneity, we produce a chord. Of course, neither of the results will necessarily be acceptable in their raw state but that doesn’t alter the principle.
But, rather than dismiss the idea out of hand, let’s look at it in more detail.
Two notes in continuity or simultaneity form a melodic or harmonic interval respectively. Three or more notes of different pitch moving stepwise in the same direction are required to generate scalewise motion.
An online search using ‘related scales’ as a search term quickly reveals a bewildering number of scale/chord associations. The problem is that we may require up to 6 notes of different pitch, the exact number depending on the starting point and the number of degrees in the scale, to define a scale type (i.e. before the characteristic note or notes occur). In addition, most tunes regularly feature chord changes at the bar or half-bar, placing severe constraints on the space available to incorporate such differently identified scales in a melodic line whilst, at the same time, ensuring smooth harmonic connections (which may already have required the insertion of unessential notes).
Tunes intended to be played at a fast tempo (e.g. Limehouse Blues) have less active harmonic changes (thereby providing more musical space) but the velocity itself will become our enemy, anyway, because rapid changes in tonality are difficult to listen to and the subtleties of the additional scale identities will become lost.
Another important fact, that’s often overlooked, is that our awareness of tonality exists both simultaneously and continuously so that the tonality of the approaching bar (or half-bar) may sometimes be anticipated (you might, for example, play a b♭ as an unessential note over a G7 chord if the note plays a prominent part in the approaching bar). Anyone who has attempted to play jazz lines over a chord sequence will have experienced the occurrence of notes in the melodic line that contradict the harmony, and the difficulty of avoiding them without destroying melodiousness (and performing theoretical back-flips in order to justify their actions).
Because of the above considerations I concluded that the best solution was to limit the list of related scales when I produced the scales/chords document but I am open to debate.
Regarding the absence of the various minor scales: the modes, including the Aeolian (natural minor) occur during the stepwise permutations in the major scale exercises. Jazz lines are concerned with the tonality of the underlying harmonies and, when we add to that the many factors involved in playing solo lines that are musical in effect, jazz musicians will rarely avail themselves of the different forms of the minor scale in creating their music.
‘Master your instrument, master the music and then just play’