Updated scales and chords bootcamp for jazz trombone document now online. If you’ve already printed this you’ll only need the last four pages but I suggest printing out the ‘notes’ because there’s an extended explanation of why I believe it’s unnecessary to extend the list of related scales.
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.
FREE download of the complete file from the link at the bottom of the page at
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’ Charlie Parker.
I’ve compiled a free 56 page PDF scales and chords bootcamp for jazz trombone. The link is at the bottom of this page: http://www.arranging-composing.com/about.html
Errata: Page 55 text. Bar1: should read ‘ f# is an auxiliary note set a semitone away from g’ (not e).
It sounds like an attempt to spam the search results but please read on…
One of the features that causes the music of modern ‘masters’ to sound so fresh and different is the use of scales and chords that get away from the beaten track. Not only do they make use of unorthodox scales and their harmonies but they sometimes convert one into the other. At the risk of repeating myself, there are many hundreds of scales possessing 3, 4, 5 and six notes on each ‘root’. There are also 36 seven-unit scales including the familiar major and minor scales and their modal derivatives.
[In my opinion there is no such thing as a ‘diatonic’ scale. Music written where melodies and chords chiefly* use the notes of the scale in use (whatever scale it is – major, minor, modal, pentatonic, etc. etc….) is referred to as being ‘diatonic’, not the scale itself.]
Here’s how it all works:
Notes of harmonic progressions can be converted into melody and notes of melody (continuity) can be converted into harmony (simultaneity). The idea is that the raw materials haven’t changed, merely their presentation. Personally, I buy into this quite happily.
Of course, as soon as melody becomes harmony the ‘rules’ change. Chords, which may involve any combination of notes sounded together, are subject to acoustic considerations in order to maintain clarity, with wider intervals lower down and closer, more dissonant effects reserved for the higher register. This is how the natural harmonic series works and, although our systems of harmony evolved quite separately, the sonorous quality of orchestration nevertheless follows these principles. (Colouristic or percussive effects are likely to break this pattern.)
Arpeggio forms are the most obvious example of the melodic exploitation of chords but the technique can be refined, using unessential notes that respect the prevailing tonality or tonal ‘cell’. Just to be clear on this, a whole passage of harmony, all of its ‘voices’, can be used as notes of melody but, in the real world, care will be needed to achieve a musical result. We have to write a good tune.
More adventurous forms can take the two elements out of synch so that, for example, a melody from harmony x can be used over harmony n (and vice versa) but don’t expect to find yourself at Number One the following week. A case that succeeds in more orthodox surroundings is the anticipated ‘lead-in’ to the next passage in a composition, where the approaching tonality, say, at an abrupt modulation, is foreshadowed, even if there is a temporary ‘clash’ before the resolution.
The ‘rules’ also change when harmony becomes melody. A melody has the characteristics of trajectorial motion so that inertial and other qualities become apparent. It has a two-dimensional presence with the rising and falling in pitch representing the vertical dimension and the passage of time the horizontal. Human expectations are based upon our physical conditioning in everyday life and reactions to music follow suit.
A chord, on the other hand, can just ‘be’.
A warning here about the use of too many scale identifications; they can be counter-productive (just too much to remember).
For example, I recently did a bit of research into the pentatonic scale (the usual one that occurs on the black notes –there are many others) and discovered a list of them, each with its own name. And then I noticed they were all the same but each time starting on a different note (i.e. they were modal displacements). To those involved in Gaelic and Celtic music these categories can be important, especially since such music is rarely written and, like so much folk music, is handed down by skilled practitioners. Here in Britain the Alba TV station from Stornoway, Isle of Lewis, regularly broadcasts such styles. This is terrific stuff. Some of these bands really rock and the group cohesiveness is impressive. (Alba, as everyone knows, is the old name for Scotland.) An actual composition emerged from my research, which is the way things should work, of course. It’s called ‘Alba’, funnily enough, and can be found at:
The playback quality is kind of ‘OK’. I can explain. The live recordings lower down in the list would have benefited from extra rehearsal, in case anyone is interested, but time ran out. The band did amazingly well. I pride myself on the versatility of these pieces. No one would guess they were all composed by one person. Me.
[Los Jardines De Espana is computer-generated, too. There’s a minor glitch in the playback that would have required too much work to justify removing it but it doesn’t hurt too much. The process of creating this piece was analysed in a previous Blog and some people would find this interesting]
You can find it at:
Anyone researching chords and their related scales, with jazz improvisational improvement in mind, will have encountered the bewildering list of possibilities. It’s difficult to think on such a level. Added to this, ‘real music’ involves many surrounding features – harmonic, rhythmic, inflective–that can influence melodic characteristics in ways that can be difficult to quantify. In other words, as stated above, turning harmony into melody is a different ball-game. Knowledge of harmony, especially the sound of the harmony, together with a good ear, is arguably the most productive method of improvising over harmonies.
*I say ‘chiefly’ rather than ‘solely’ because the possibility of adding chromatic embellishment to most music without altering its essential form will generally exist.
We sometimes hear about orchestral, or harmonic, strata. As so often happens, in any field of endeavour, seemingly obscure and complex ideas actually exist all around us.
The idea is this: by treating large groups of sound as collections of smaller layers we not only achieve a more controllable method (especially of combining instrumental sections) but also introduce subtle changes in effect.
There’s nothing new in this. Take the simplest form of writing for an eight-piece brass section in the jazz orchestra or ‘big band’. It simply comprises one four piece ‘block’ harmony, trumpets, above another, an octave lower, from the trombones. This simple scheme, along with a few less obvious forms, was dealt with in more detail in a previous post:
Theoretically, it requires little further justification; it really works.
When, as frequently happens, we open up the trombone harmonies and/or use more active trumpet work above the more static trombones, we introduce refinements into the scheme.
The big band ensemble is another example. Typically (but not always) the brass will be in close position but the saxophones will be in open harmony, often carrying the bulk of the harmonic tension. Their richer sound enhances the effect which is to form an acoustic cradle for the brass to ‘sit’ in. Early arrangers arrived at these schemes without ‘schools’ to guide them, which makes their novelty all the more remarkable.
Occasionally, trumpets will ‘fan out’ into simpler chords in the high register, accentuating the feeling of ‘altitude’. For example, they might play a simpler form, which might be, say, a chord with added sixth – or even a simple triad with octave doubling of the melody. The harmonic fullness is carried down below in the trombones, or saxes and trombones. Exact doubling will be required down here to avoid stragglers in the blend, which will stick out at the expense of the surrounding parts (to cut a long story short). The compound effect will be that of the full chord, say, 13th, but the orchestral treatment introduces a different effect altogether than one that simply piles the chord upwards from the root. With smaller ensembles the latter method has to be used of course.
In the full orchestra, the present technique really comes into its own, with sections of homogenous instruments cohering together but, at the same time, combining to produce the ‘master’ harmonies.
A further and, I would say inevitable, development lies in the field of polytonality. Although the limit of this idea will be reached (in equal temperament) with a staggering twelve instrumental layers, with up to four parts in each, it’s more usual (because the listener’s auditory response has to be born in mind!) to show more restraint and limit the number of vertical strata.
It’s essential (I would say) to select equal intervals between each stratum in the compound group. Minor or major thirds (or their inverted forms) and fourths (or fifths) are easiest to manage. Chord transformations will generally be required to differ (i.e. we can’t just transpose groups from one stratum to another) because of the need to avoid overlapping but different activity between them, coupled with the effect of different tone colour, will alleviate this problem to an extent plus, as always, ‘logical’ tendencies have to be carried through in the movement of parts.
There are, as everyone knows, four minor chords and three major within the span of an octave, which can also be divided into six whole tones. These subdivisions limit the number of strata but the roots of more ambitious groups can exceed the range of the octave. Everything can be generalized, too, with semitone = 1 and building out systematically from there. The augmented fourth divides the octave exactly in half and this form of bitonality was a favourite with English comedian Les Dawson when he played the piano badly on purpose. You have to choose just the correct wrong notes for success in this area, if anyone is interested. Les was no fool. Oh, and by the way, it was used by ‘modern’ composers, too.
Although all this might seem, at first glance, to be a mechanical process, the procedure is no different to the subdivisions we all happily live with every day such as, for example, the habit of writing in the major and minor scales and the various modes, which are themselves selected from the full range of audible frequencies. In other words, the FBI won’t come knocking on the door. Strata harmony isn’t a Federal offence.
This kind of treatment often favours an open key signature and it might also be an idea to write the score in ‘concert’ rather than transposed, especially since each stratum might be in a different key (multiple strata can be diatonic, too). Have some pity for the conductor.
The result does not need to be a succession of sustained chords. All instrumental effects – alberti bass, oompah figures etc. etc. – are fine.
A melody will ideally be developed from the tonality of one stratum, generally, but not always, the highest, and contrapuntal schemes can be developed. To avoid the end product being hopelessly confusing, unessential notes require to be closely systemized. Pre-set patterns may be derived and I find that graphic diagrams can help keep a ‘handle’ on things and keep them tidy.
People will think you’re really clever when you present your arrangement but, to be fair, this type of architecture can be brain-wrenchingly difficult to ‘construct’. The trick is to be methodical in our working methods and not try to make too many different decisions at the same time. I find that, as I work, artistic selective processes begin to dominate, breathing ‘life’ into the music, generally in ways that would not otherwise occur.
Music written in this way can be very dissonant. The environment will form an important factor. An audience sitting in a palm court environment during a lunchtime concert will not expect to be scared to death but writing the background music for a film about a catastrophic volcanic eruption will be a different ball game altogether plus, as always, listeners differ in their musical awareness and their ability to assimilate extreme forms.
It’s a lonely business, being a composer.
A while ago I was standing in a bar with my son and a group of his friends. The juke box was pulsing out its message at very high volume. Now, I have very wide musical tastes and sitting in a trombone section right in front of five trumpets for much of my musical life means I’m no stranger to volume, either but my younger comrades perceptively picked up on the fact that I was approaching the boundary of my comfort zone. ‘Oh well, at least it’s got rhythm’ one of them reminded me, beating his fist on the bar top in time with the music to emphasise the point.
I didn’t want to wreck the atmosphere by pointing out that the thud, thud, thud of the music, which sounded like someone building a chicken pen, was merely the continuum, or scheme of reference, which gave meaning to the rhythms, so I simply said ‘That’s just the beat, not the rhythm’ and left it at that.
The most comprehensive treatise on this subject was surely the one written by Russian-born Joseph Schillinger who eventually landed in the USA and rose to the position of teaching some of the most respected musicians and composers around at that time, including George Gershwin.
Joseph has tended to be on the fringe of music education because, amongst other things, he attempted to create mathematical systems controlling ‘art production’ (to cut a long story short). For example, he claims that, had J.S. Bach been aware of his system, he would have achieved more consistent results! Such statements alienated many with the result that relatively few musicians, to this day, have availed themselves of the wealth of information and advice that is actually to be found in the two volumes that, together, comprise the ‘Schillinger System of Musical Composition’. I’m not sure if these books are still in print but I understand that Schillinger courses still exist.
If readers can ignore the naïve positivism that, to be fair, was typical of the era between the two great wars, there’s a wealth of important ideas and information in this publication. There are, understandably, in a monumental work of this kind (that had to be collated by editors after his early death), a number of errors in the text, including a couple of entire sections that are out of order. I shall be pleased to convey those I found to interested parties. It will save them a lot of time.
Joseph discovered that what we call ‘rhythm’ is the result of interference patterns between different periodicities. I still read statements that ‘we don’t understand rhythm’ (or words to that effect) but I’m convinced that he was right about this.
He goes on to show that rhythm not only governs individual phrases but it also gives shape to the order of formal sections, movements etc. Rhythm can also be serialized by means of permutations and patterns that give meaning to a subject that can become hopelessly subjective in the wrong hands. Do we go ‘doo-wap-be-doo-wap’ or should it be ‘der-doo-wap-be-doo-wap’? The point is that, relying purely on intuition, we might do it one way and then, later, do it another. Was there a reason for this or did we just not notice? The ‘choice’ might be governed by all kinds of circumstantial factors and this, to my tidy mind, just aint good enough.
My earlier blog on WordPress might be worth reading at this point: https://composerarranger.wordpress.com/2014/07/24/musical-form-why-do-we-need-it-and-where-does-it-come-from/
Google comes up with a wealth of information about Joseph Schillinger which will serve the reader better than this ‘introductory’ post, in fact there’s a very fair and, in my opinion, accurate assessment on Wikipedia.
It’s difficult to avoid comparisons with architecture when discussing musical form. Of course, music is a temporal medium, which raises important differences right away but the superstitious tendency to believe that music (because it is so abstract in nature) belongs in the realms of the inexplicable has done much to damage our efforts.
My own book is a hands-on, musician-to-musician journal that expects readers to roll up their sleeves and get their hands dirty but those who choose to approach the Schillinger System should realize that it is a scientific work and, as such, every statement has to be rigorously justified, sometimes with pages of lengthy examples. My only warning would be to avoid the belief that using the system is a short-cut to success (which Joseph never claimed!); a composer’s work still requires content, a word that I hope will suffice in the present context.
More than anything else, the system streamlines many down-to-Earth problems. For example, it becomes easy to predict when two or more schemes in composition will ‘come out even’. In fact, temporal planning becomes so manageable that it’s easy to understand why the system was so popular in Hollywood.
At the end of the day we shouldn’t think of ‘right’ and ‘wrong’ because Shillinger’s work represents a theory and theories, as we all know, remain in force until they are superseded. The most quoted example is Newton’s inverse square law of gravity. This theory evolved in the 17th century and is still used today every time we launch a spacecraft or put a satellite into orbit. We had to wait around 300 years for a man of equal stature to point out that the theory is required to be relativistic.
I believe many young composers are constrained by unnecessary inhibitions that develop during the learning process. I know I was, in my early days. My previous posts have dealt with some of these – parallels etc. – but there are others. Again, it’s important to establish an ‘overview’ which is where one of my favourite expressions once more comes in handy, which claims that our work must have ‘a clearly defined, strong artistic purpose’. It’s a catch-all argument, in a way, as long as the music lives up to the claim. It’s also a very powerful notion, because these Taboos can have a damaging effect on our efforts. A still, small voice, somewhere in the back of the head, suddenly steps up and whispers ‘You can’t do that’ and, without realizing it, we can find ourselves abandoning a course of action before it even begins to develop.
Crossed voicing, etc.
Textbooks on four part harmony teach us, correctly, to be wary of crossed parts. The main reason for this is that the linear flow of a harmonic continuum is disturbed when, say, a tenor part resolves to a note in the succeeding chord that is higher than, say, the alto part. In reality, crossed voices are always a sign something has gone wrong.
This advice is sound enough where the harmonic continuity is strictly homophonic (i.e. the vertical ‘cross-sections’ of all parts involve a sequence of similar durations). But where a continuity features melodic figuration of harmony involving split duration groups (greater mobility), it becomes very important to carry through the ‘logic’ of each part even if, by doing so, we have to cross an adjacent voice. Failure to do this will be disturbing to a performer, too, because the melodiousness of the part is adversely affected (it will feel wrong). The listener might also notice*, particularly where a non-homogenous group of instruments is employed (each part will stand out even more clearly).
*This is a difficult area. Although a listener may not necessarily be able consciously to identify and classify an error it doesn’t mean that his perception of ‘quality’ isn’t disturbed. Life for the critic would be very difficult were this not the case.
A similar ‘rule’ warns against overlapping parts where, for example, the top note of a pair of voices resolves down in such a way that the upper note of the two ends up being lower than the bottom note had previously been. I do this occasionally in energetic bass parts, either doubled in the octave or in perfect fifths (or both). Bass parts frequently leap about in this way. Extra force and energy can be generated by so doing.
Undesirable overlapping will most often occur in the case of inner voices. The top voice will generally be the melody, which is ‘given’, and the bass has the freedom just outlined, providing it remains at the correct distance from the other parts, in line with acoustic requirements (it stays out of the way).
Block harmony styles that are prevalent in jazz and early dance bands are a different matter. Because the voices are compressed to the max, decisions regarding part progressions are largely predetermined. Added to this, the linear movement of individual lines is disguised, especially since this style of orchestration mainly involves ‘choirs’ of homogenous instruments. This doesn’t mean that voice leading is unimportant; block harmony, although simple in principle, is capable of considerable refinement but traditional resolutions are often lost in the ‘blend’.
Exposed Octaves and Fifths
In the interest of brevity I refer the reader to the many texts on this subject regarding the traditional view. The opinion is commonly held that contemporary writers should not be unduly concerned by them but I’m not so sure, personally. Becoming used to something often involves a process of becoming insensitive, also. (Familiarity breeds contempt.)
The point I wish to make here is that, once more, effective solutions may involve a breach of the ‘rules’. A typical case would be in ‘doo-WAP!’ figures, where the exposed intervals give added weight to the target notes, enhanced by a rapid crescendo.
The bottom line in discussions of this nature is that we need a clear idea of what we’re trying to achieve and we need to possess knowledge of the dynamic forces that shape, not only music, but also actual physical systems in motion. This does not necessarily mean that music does not possess attributes that extend beyond the merely physical. It might but it might not. No one knows. I’ve had a number of fruitful conversations on here with Jonathan L Friedman and others on this subject:
The most discussed rule of doubling is probably the one regarding doubling the third of a major chord. There are so many exceptions to this rule that it is easier to refer to the only situation where doubling this function is objectionable, which is where the harmony comes to rest. Even here, I bet I could write a piece of music where even this transgression is allowable.
In orchestral arrangements, because instruments of a similar tone colour tend to cohere, mixing the various instrumental sections in the overall ensemble will frequently give rise to irregular doubling.
My very first post on here dealt with a common situation where doubled thirds are essential (in fact ‘permitted’ cases are virtually all unavoidable):
Another taboo is the placing of higher chordal extensions below lower ones but, again, this can work. In jazz arranging, I’ve more than once placed the ‘major seventh’ (i.e. b in the chord of C) below the root (c in this example), especially in the final chord of the composition. In this case, it would be positioned a major 7th interval below the top note c, with the other voices adapted to suit the occasion. The result is rather spicy but it works well in the right circumstances (style). Placing the 13th below the minor seventh (a below b flat in a C7 chord) is usually a no-no unless it occurs in rapidly executed block harmony, probably in one of the open position distributions. Sometimes smooth voice leading will lead us to such choices and the ‘offending’ note might be the melody duplicated in the octave, in which case it’s OK except, in some musical environments, when sustained.
The above examples feature those I could bring to mind at the time of writing. There are others but the ‘bottom line’ of this post is that unnecessary complications can occur as a result of the dogmatic approach that is so often used, when attempting to rationalize guidelines. As described above, situations where breaking a ‘rule’ is permissible often involve musical situations where the result is unavoidable anyway and expressive results can be achieved by wilfully flouting the rules.