Related Scales; chord/scale relationships

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.

Dear USA, we don’t deserve this!

The anti-English* sentiment in Hollywood shows no sign of abating. With depictions of cowardice on the Titanic that, curiously, only involved the English and distortions of history in the script of Braveheart that should have won a special award for ingenuity, it was, perhaps, not as shocking as it might have been when the cyber attack on Sony prompted an American observer to comment that Sony had ‘done Neville Chamberlain proud’.

Huh?! What possible justification could there be for such a vicious side-swipe? They really can’t wait, can they?

I was born just as WW2 began and spent many nights huddled below stairs or in an Anderson dug-out in the garden as the Luftwaffe attacked a nearby armaments factory. Coventry was largely destroyed and many cities over here, including London (and Buckingham Palace), were badly damaged.

The Chamberlain I remember had the courage single-handedly to declare war on the most efficient fighting machine the world had ever seen even though he knew Britain was lamentably ill-prepared. Germany had been preparing for war for years, having trained pilots at gliding schools in defiance of the terms of the Treaty of Versailles. These pilots gained combat experience in the Spanish Civil War where the early Messerschmidt 109’s were also battle-tested.

By contrast, RAF pilots, some of whom were as young as 19 years of age, had around 5 hours experience each at the controls of early Spitfires before being sent to war!

Perhaps the observer could explain why we had to wait so long for American involvement if he feels so strongly about Chamberlain’s initial response to Hitler’s militarism. We should all bear in mind that Chamberlain wasn’t the only leader inclined to trust Hitler in those days. Members of our Royal Family were received as his guests. Vulgar upstart he may have been but he was very, very clever and knew exactly how to manipulate people.

Two world wars bled this little country dry and the cream of two generations of British manhood was wiped out. We still feel the ramifications of it all to this day.

* I refer to the ‘English’ (rather than to the British) since that is where most prejudice is directed.

Your help is urgently needed

[Nothing in this blog is concerned with ‘race’. Racial factors determine, for example, whether a person’s hair will be oval or round in cross-section and whether they will have a propensity to develop rickets or sickle-cell anaemia, etc. Characteristics may also be more than skin-deep with darker skinned people more likely to show an ebullient response whereas lighter skinned people are likely to be more reserved. Only scientific research can solve such problems, not rash outbursts. ‘Racism’ involves a deliberate attempt to engender disapproval of a group of people on the grounds of their ethnicity. Most so-called racial issues have little to do with race and involve cultural attitudes which, more often than not, have evolved from religious dogma.]

In recent posts I have attempted to justify my obsession with Islamic ambitions throughout the world because the opinions of my friends and colleagues is significant to me both personally and professionally. Fortuitously, three developments have come to my aid right on cue, providing an intriguing example of the idea of synchronicity in our affairs.

1) Firstly, a report from NASA reveals that, as a result of observations by the Kepler telescope during its lifetime, scientists are now able to calculate, not merely suggest, the possibility of finding sentient beings in the Universe. More than 8 billion Earth-like planets are said to exist in our own galaxy alone and spectroscopic examination of their atmospheres will search for signs of intelligent life.

The possibility has fascinating consequences for religions of all kinds and also for the idea of Heaven as being the final resting place for the virtuous. Many religions hold that places and buildings here on Earth have (by implication) universal significance. They have also taught about the eminence of man without stopping to think that beings would exist who are far more advanced than homo sapiens. If the Universe is infinite we would one day find a planet where pigs evolved to be the dominant species.

The proselytizing nature of Islam, in particular, will finally come to a dead end and Mecca will lose its essential centrality. The problem also arises regarding how beings on other planets would be able to face Mecca, anyhow, bearing in mind that planets all appear to be spinning.

2) Another report announced that a Church of England Bishop has suggested the Koran should be read at the coronation of Prince Charles because of the need to ‘embrace’ Islam. (I suppose Bishops, like the Liberal Democrats, can say what they like, within reason, because their ideas will never be put to the test.) Bearing in mind the fact that a Christian women is facing the death penalty in Pakistan because she committed blasphemy by drinking water from a cup also used by Muslims and that it is a crime for a Muslim to convert to Christianity – still punishable by death in some areas – surely Christians are entitled to look for some sign that Muslims are prepared to meet us half way (to integrate with us, in other words) before anyone, most especially a man who should know better, makes such an idiotic statement . The worrying thing is that Charles is likely to agree with the idea! It is nonsense to suggest we should embrace a religion whose adherents regard us with such disdain. Disdain always implies disapproval.

3) Closer to home, in my home town of Dudley, United Kingdom, Labour councillor Qadar Zada urged an end to “existing and future procurement of goods and services where there is a direct benefit to the State of Israel, including through the supply chain, subject to legal compliance with all relevant procurement, contractual, legislative and regulatory requirements… “.

The seven UKIP councillors in Dudley – the council’s third largest group – opposed the motion. The idea has now been dropped.

A similar motion was thrown out in Leicester.

I can’t understand how Israeli actions can be compared with the scale of Islamic atrocities. I suggest that, before judgments are made concerning Israel’s actions, consideration should be given to the fact that Israelis have lived with the daily dread of crude, home-made missiles being fired into their communities over many years. These missiles cannot be aimed or guided and those firing them have little concern for where they might land. I would like to hear opinions from my contacts in the USA regarding what the American response would have been had Canada or Mexico behaved the same way.

Returning to the title of this blog I would like to ask people to share and reblog this content, with links to Facebook and Twitter. At least we will be doing something.

The problem of closed-system ideologies

I have taken time off from the musical policy of my blog to describe my fears that the threat to world order posed by Islam is not being fully recognized. The matter is particularly important to those of us living in Britain because we live side-by-side with a problem that is being allowed to worsen because of the very tolerance for which Britain is famous throughout the world.

Prolonged and determined attempts to force the issue of a new mosque onto a reluctant majority in my home town of Dudley, United Kingdom, have caused me to ponder the wider implications of a steady, relentless, growth in Islamic influences.

Ideally, one would avoid unhelpful generalizations but, as I have described elsewhere, this cannot work.

Many people were shocked when Subway, a national chain of sandwich and snack shops, agreed to bow to pressure from Muslims to stop selling pork products and were prompted to wonder just how far such appeasement will go. Where will it stop? To further my intentions in writing this blog I would like to analyse the statement described below as a test-case. I have always regarded this statement and the incident to which it refers as being particularly worrying.

The following statement is by Leicester Federation of Muslim Organisations spokesman Yaqub Khan. He was referring to a collection of ceramic pigs displayed in a front window, perhaps rather mischievously, by a resident. Muslims have learned how easy it is to further their cause because of the prevailing tendency to emphasize tolerance and integration, a tendency that has encouraged positive discrimination to reach unacceptable levels. Their statements are frequently cleverly worded and require analysis in order to produce a counter-argument. Our decision-makers rarely have sufficient time to do this. They also feel constrained by the fear of possible recriminations and by accusations of racism or bigotry.

These matters have nothing to do with race. The problems presently discussed are of a cultural, not racial kind, and particularly relate to those aspects of culture that stem from religious dogma.

The statement

Mr Kahn said that more than 1,000 worshippers attending weekly Friday prayers at the nearby mosque passed the collection of pigs. He claimed that Mrs Bennett was aware of the potential for offence to be caused (it shouldn’t really matter) and explained that the pig is mentioned as being “unclean” in the Koran, and is regarded as an offensive animal by Muslims, who are forbidden from eating it.

“There are rules which, as good citizens, we have to observe. We are a multi-faith society and we, as Muslims, respect other faiths practised in this country, so I think, in return, they should respect ours. Something like this is taken very seriously by Muslims and it is a very sensitive area.”

A quote from the Koran “Let there be no coercion in religion” that was displayed alongside the pigs was also seen as provocative. Mr Khan said “The Koran is a sacred book. If that is placed in a window where pigs have been placed then that is even more offensive. It may be a trivial matter for some sections of the community but it has to be dealt with.”

Where do we go from here?

I decided to start as closely to the origin of this matter as I was able to venture and I decided that the existence or otherwise of a deity had to be the starting point. When ideas and principles are based on religious beliefs the existence of a deity has to be established in order for such ideas and principles to have meaning. Without such proof, beliefs become superstitions. Learned books have been written on this subject so I decided that, because both Deism and Atheism still exist, none of the previous attempts to find a solution could have been successful. I therefore decided that my own ideas would be based upon the following claim:

Because there is proof neither for nor against the existence of a deity the only satisfactory stance to assume is that of the Agnostic.

Of course, it could be argued that, since God created the Universe, he was able to create it any way He wished and therefore who are we to question His wisdom? Unfortunately, we go round and jump on again by following that line of thought so we have to try to find an objective approach if we are to avoid the potentially catastrophic results of belief systems.

Personally, I like the idea of God and the Afterlife and I would give anything to share in the instant panacea that such beliefs offer but, so far at least, I’ve been unlucky (but still open-minded). In the meantime I have to rely on my own inner strength and intelligence.

Having decided all this, I also decided, some time ago, that beliefs must be kept out of public life where they have no place. History provides so many examples of the failure of attempts to marshal our affairs by means of principles that are based on unsubstantiated beliefs. Beliefs divide people.

Mr Kahn’s claims

“…the pig is mentioned as being “unclean” in the Koran, and is regarded as an offensive animal by Muslims, who are forbidden from eating it.”

Eating pork that has not been properly prepared, especially in a warm climate where few people owned a fridge, would have been dangerous and I wouldn’t like to live in a pig sty, either. But does this represent Muslim views in their entirety? Of course it doesn’t. Billions of intelligent, ‘decent’ people eat pork every day so there can be no validity in the claim that pigs can be offensive for any reason other than the common sense reasons given above. My own claim is that, having created a religion which, in this case, has these ideas about pigs, surely followers of the religion choose to be offended. They cannot move on from this to inflict their ideas on others or to claim that respect for their views should automatically follow.

“There are rules which, as good citizens, we have to observe…”

I’m not quite sure what Mr Khan’s idea of a good citizen is but it is likely that the concept would have to be framed within constraints laid down by is Islam, a religion that does not have a particularly good record in this respect.

“We are a multi-faith society and we, as Muslims, respect other faiths practised in this country, so I think, in return, they should respect ours.”

A multi-faith society? Does he refer to the situation that prevails, where different faiths grudgingly co-exist or is he pointing to an ideal where different religious leaders might come together and join the best bits of all faiths into one? This is an unlikely prospect. In any other context it often works but not in a religious one. Do Muslims respect the views of others and, in any case, what do we mean by the word ‘view’, especially in this context? Should I be required to respect the views of others? Not necessarily. It depends on the particular views expressed.

Everything a Muslim does and thinks is governed by the presumed will of their God. To suggest that compromise is needed, in order that integration can take place, is to suggest that the will of God is less than perfect, otherwise, why would it require modification in order to fit with the requirements of others? It’s easy to see why Muslims adopted the path of claiming that their God is, quite simply, infallible and that, therefore, we should all abide by His rules, regardless of what non-believers may think. This notion is, of course, the root cause of the troubles we are dealing with currently.

‘Think’ is a significant word. Whether we are able to adopt religious views or not it is, to me, self-evident that the only way to achieve a level playing field for all, regardless of race, colour or creed, is by striving for solutions based upon objective reasoning, or as objective as we fallible beings are able to achieve. Other methods have failed. Badly.

“The Koran is a sacred book…

I always have trouble accepting the idea that physical objects, including the ‘graven images’ in some Christian churches, are anything more than that. A physical object, especially a building or a book, cannot be sacred. No matter how closely we analyse them it is likely that they will still reveal themselves to be lacking in any other determinable attributes and unless we can demonstrate, beyond reasonable doubt, that it is otherwise, we cannot impose our ideas on others and, by so doing, claim a lack of respect has been shown. Beliefs and religious notions dwell in the ‘hearts and minds’ of people, not in symbols, images or objects.

“… It may be a trivial matter for some sections of the community but it has to be dealt with.”

It is a trivial matter. The question of eating pork or not eating pork or, equally, of possessing ceramic pigs, or not, is intrinsically inconsequential and importance can only be ascribed to the acts on the basis of beliefs. If I enter a room and see someone poised, dagger in hand, ready to attack my friend it will be important to stop them. There is a difference.

I particularly dislike Mr Khan’s claim that the above problem “has to be dealt with”. No, it doesn’t. He must modify his views into a form that is more likely to allow the integration we all hear about so often. That’s the ‘truth’ of the matter. The suggestion that even a quote from the Koran is holy is quite unacceptable. The idea that there should be no coercion in religion is an idea that cannot be patented by Muslims. It is a principle we should all abide by. I believe it is fair to say that Muslims practise the ideal less the Christians do.

Returning to the unfulfilled requirement for proof of the existence of a deity I would like to make the following comments:

There was a fascinating link on Facebook recently which claimed that extermination in the Universe is the norm not the exception. Our fragile planet faces threats from near-Earth objects and from gamma ray bursts that would fry all of us, except the creatures in the deepest parts of the ocean. A massive volcanic eruption would plunge us into another Ice Age. The point is, the article claimed, that what is true for us is also true for every civilization in the Universe. Statistically, according to physicist Enrico Fermi, there must be many hundreds in our Galaxy alone. Now why would God go to all this trouble and then fix things in such a way that it all comes tumbling down?

And the idea of Heaven has always fascinated me. If all the creatures in the Universe, in all their unimaginable varieties, who have ever lived and all those who have yet to be born are promised a seat, if they behave, of course, then it must be a strange place.

‘Ah’ you say. ‘Off you go again, applying your puny human mind to the problem. God works in ways you can’t even imagine’. I wish I could believe that such opinions could possibly be helpful.

Our prospects

A former president of Pakistan has said militants from Islamic State are already operating in his country and warned the threat they pose is a global one.

They are well-armed and expertly led and show great prowess in the tactics and strategy of conflicts. They are also well funded. As I myself warned many years ago, captured American weapons, including tanks, are being used against us as they de-stabilize the region. The border town of Kobane is particularly significant because IS is hoping to de-stabilize Turkey, also. Turkey could easily become a fundamentalist Islamic state and, not only that, but IS is cleverly exploiting divisions between the Turks and the Kurds.

Islamist terrorists are also well-established in the African countries of Nigeria, Kenya, Somalia, Algeria, Tunisia and Libya. They also have ambitions in Iraq, Lebanon and parts of Palestine and Jordan. There are more than 25.000,000 Muslims in Indonesia in the Far East, a proportionate number of whom will inevitably become enemies of Christianity.

It is easy for us to believe that IS, the most dangerous of them all, poses no direct threat to European countries, apart from isolated terrorist incidents. After all, they wouldn’t stand a chance in a straight fight but this is terrorism, the ‘great leveller’, that we are dealing with.

We have already witnessed the temporary lock-down of the government in Canada as a result of an incursion by one man. In a similar way, attacks by small groups against key installations could create sufficient panic to affect share prices and even cause unemployment. Benefit systems might collapse leading to an increase in crime as people attempt to survive. The resulting chaos would be easy to exploit.

The current film about the life of brilliant mathematician Alan Turing is causing incredulity. Imagine predicting, at that time, that homosexuality, which was then a crime, would one day be commonplace, with politicians and public figures openly ‘coming out’. Similarly, my prediction that Britain is in danger of becoming an Islamic state might seem equally ludicrous. But it could happen and, as I see it, there is little to stand in the way of further erosion.

You won’t believe this in the USA…

There’s a firm belief amongst musicians that we should keep religion and politics out of the band room. In this context the ‘band room’ comprises the Internet and, especially, Facebook. So am I guilty? I’ve damaged a few friendships and even my business aspirations with my warnings about the growing menace of religious fundamentalism. The problem, as I see it, is so desperately important that we cannot continue to bury our heads in the sand as we Brits, especially, are prone to doing.

I was surprised to find a fellow blogger giving me support over my last blog concerning the hugely unpopular plan to build a mosque in my home town. To say that he doesn’t automatically agree with me is an understatement; he has been a fierce critic on many occasions.

He points out that, as the Muslim population increases, their demands will also grow. In my opinion, because of the well-established pattern of allowing their requests in the name of ‘tolerance’ and ‘respect’, there will be no constraints governing the number and nature of these complaints until they eventually bury the wishes of the indigenous population.

Readers in the USA, particularly, will find the following evidence difficult to believe. I wish it were not true, but it is:

No more bacon butties

Nationwide sandwich chain Subway removed ham and bacon from nearly 200 stores and offers halal meat only after strong demand from Muslims. 185 branches across UK and Ireland now sell halal meat only.

The ceramic pigs saga

A woman arrived at her home in Leicestershire to find police about to break into her house. They had a warrant because they had received complaints about ceramic pigs in her window from Muslim neighbours. They considered it was a public order matter and took about 17 of them. She was told not to replace them.

She had been targeted by youths since the death of Diana, Princess of Wales, when she decorated her house with red, white and blue flags.

A Muslim spokesman said that more than 1,000 worshippers attended Friday prayers at the nearby mosque and Mrs Bennett was aware of the potential for offence to be caused. (The pig is regarded as an offensive animal by Muslims, who are forbidden from eating it.) He also stated that there are rules which, as good citizens, we all have to observe. He pointed out that we are a multi-faith society and that since Muslims respect other faiths practised in Britain their views, too, should be respected.

I was in this area of the City Leicester a while ago, visiting friends who live on a typical English suburban estate. People were mowing their lawns and cleaning their cars. The difference was that the call to pray was being broadcast at very high volume over the area.

Leicester was the first city in the UK where the ethnic population exceeded the indigenous population in numbers. This links to my claim above, endorsed by my fellow blogger, that a rise in demands will follow a rise in numbers. This is why we cannot allow a nation within a nation to develop. Beliefs have to be kept out of public life. Achieving this aim is the only way to create a level playing field for all, regardless of race, colour or creed.

A critic on Facebook sneered ‘They’re coming to get you’. I pointed out at the time that it won’t work like that. There isn’t a conspiracy to take over the Country. These people are far too busy. It is abject appeasement that will leave the doors wide open.

Your Child’s education

Even more unbelievable is the fact that, when school inspectors visited a school in Birmingham, UK, they discovered that Muslim staff had enforced gender-separation on the pupils. This was against instructions given to them but, to be fair, the prospect of defying Muslim requests must be very intimidating.