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The Geography of the Piano and the Symmetry of the Hands: New Ways with Old Scales

Margaret Brandman

Introduction The topics for discussion in this paper are: 1) The application of right brain faculties of ‘spatial relationships’ and ‘visualisation’ and ‘gestalt’ to learning the keyboard geography.

2) The interval approach which assists the performer to combine the visual, aural and tactile aspects of music allowing a pianist to feel the space and the geography or topography of the keyboard.

3) The symmetry of the hands and fingering commonality - the main clues and sub-clues for fingering scales and arpeggios. 4) The application of these concepts to scale patterns, modal patterns and transposition – making connections between scale and chord shapes using the concept of photographic negatives. 5) The discussion of speed learning techniques for major, minor and modal scale patterns. To conclude the practical application of these ideas is shown in a section of a piece written for the symmetry of hands and keyboard layout.

Method Music Mind Map

I will begin by showing this Music Mind Map (see Diagram 1) to put you in the picture ‘so to speak’. The mind map displays left and right brain abilities and how they can be applied to the learning of music.

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Diagram 1: Original Design, M. Brandman

A balanced teaching system will ideally incorporate all of these aspects. However today, as time is short, I will speak about the application of only some of them. The left brain faculties are words, logic, numbers, linearity, lists and analysis. Two of the applications of these left brain side faculties would be the logical sequencing of material in a teaching program and analysis of compositions. .

The abilities attributed to the right brain include:

• Spatial relationships, • seeing the whole view of a topic – German word for this is ‘gestalt’ • colour • rhythm • imagination • and visualisation.

The first of the Right Brain abilities is the aspect of Spatial relationships:

• when you approach music from the point of view of the space between

two notes - you are necessarily thinking of intervals.

• The interval approach helps a player combine the visual, aural and tactile aspects of music.

• It allows a pianist to feel the space and the geography or topography of

the keyboard.

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Interval Tree

Diagram 2 shows the many applications that an understanding of intervals can assist with. I don’t have time to explain this tree in detail at the moment, but it is on my website if you care to delve into it.

Diagram 2 – Original Design, M. Brandman

The main branch I wanted to point out is the lowest branch on the right which shows scale patterns and transposition. In the following discussion I will explain some easy ways for pianists to memorise scale patterns for use in exam situations or when improvising a melody line.

In my teaching, the right brain abilities of colour, rhythm and imagination. are engaged in many different ways, but it is the topic of visualisation and whole view (German word –gestalt) as applied to the keyboard patterns I wish to focus on at this time

According to researcher John Ball the smallest brain element is the PATOM – a collection of pattern matching atoms and therefore the brain is a

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pattern matching machine, not a processing machine. In my teaching I approach many topics from the whole view.

A smallest brain element is the patom, a collection of pattern-matching neurons. The brain is a collection of patoms. The brain is a pattern-matching machine, not a processing machine. The brain creates order out of chaos by learning patterns, and then by using these patterns in novel ways. (From ABC Science Show- Rockham’s Razor, John Ball in conversation with Robyn Williams.) Here is an interesting piece on how the brain comprehends the whole.

Aoccdring to rscheearch at Cmabridge uinervtisy, it deosn’t mttaer in what oredr the ltteers in a word are, the olny ipmoetnt tihng is that the frist and lsat ltter be at the rghit pclae. The rset can be a tatol mses and you can still raed it wouthit a porbelm. This is bcuseae thehuamn mind deos not raed ervey iteter by istlef, but the word as a wlohe. Just Amzanig! Dno’t you aegre? (The Bell magazine published by Stainer and Bell, UK.)

Grand View

Now here is how the entire twelve major scale patterns can be seen in one (gestalt) view. I call this the Grand View (Diagram 3)

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Diagram 3 – Pictorial Patterns for Keyboard Scales & Chords, M. Brandman

Notice how the patterns seem to grow with the addition of black notes as you go down the column. It is easy to remember the scale by making connections between the patterns.

As every Major and minor scale has seven different notes – you can

decode their patterns into chunks of three and four notes, to easily find the fingering for the scales.

Viewing the patterns in this Grand View enables one to find the various

chunks which are used for scale fingering. For instance for the scales of BbEbAb& Db majors, the left hand needs to

use a chunk of three fingers to begin these four scales – followed by a chunk of four.

While for CGDA&E majors the right hand needs to a chunk of three

fingers for the first three notes of these scales, followed by a chunk of four. A Major Scale

Here are some more curious facts about the keyboard topography or geography. In Diagram 4 you can see the pattern for A major scale- notice the black notes on the third, sixth and seventh positions of the scale. The black notes are the notes C sharp, F sharp and G sharp.

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Diagram 4 – Pictorial Patterns for Keyboard Scales & Chords, M. Brandman

Ab Major Scale

Now lets look at the scale of Ab major – placed directly under the pattern

for A Major scale (Diagram 5A)

Diagram 5A – Pictorial Patterns for Keyboard Scales & Chords, M. Brandman

Ab major- has four black notes and now you can see that now the left over white notes are C – F and G . I call this phenomenon – photographic negatives.

There are three more sets of scales which do this, which you can see

further down on the right hand slide. (Diagram5B)

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Diagram 5B – Pictorial Patterns for Keyboard Scales & Chords, M. Brandman

I would now like to demonstrate a way of taking guesswork out of scale patterns using the whole view or ‘Gestalt’ approach. I begin with asking the student to ‘block out’ the scale pattern – beginning with all white notes, and then introducing the black notes, in key signature order.

This system allows the whole pathway of the scale to be seen at one time,

eliminating the mistakes likely to occur when finding scale notes one at a time. The picture – can be used as a reminder of the shape of the scale that has been blocked out. This way the scale is taught both kinesthetically and visually. The sound of course is used as a means of checking that the correct notes have been played, when the scale is played in single notes. Chord Shapes

Lets look now and some aspects of Chord Shapes where again you can also see the phenomenon of photographic negatives. In this picture, the shapes of the major chords, set out around the circle of fifths. (Diagram 6)

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Diagram 6 – Pictorial Patterns for Keyboard Scales & Chords, M. Brandman

At one end you have the ‘all white’ chords, and at the opposite end ‘the all blacks’ (I call this the New Zealand chord – named after their football team ‘the All blacks).

On the right hand side you can see the chords with white on the outside

and black in the middle. I compare these to sandwiches – white bread with a black filling- What sort of sandwiches do you eat? Maybe you eat Parwill sandwiches ( remember Marmite – its rival in the 1930’s was ‘Pa’ will!). You all know this product now as Vegemite’!

Notice that on the opposite side – there are black bread sandwiches with

cheese! Fingering Commonality (Db major and F # major)

Lets look now at the aspect of the symmetry of the hands which comes into play when playing the scales and finding a suitable fingering. (Diagram 7)

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Diagram 7 – Pictorial Patterns for Keyboard Scales & Chords, M. Brandman

When searching for the fingering for scales a number of features appear, if you view the scales, once again- in chunks.

In the scales which use all the black notes, the standard fingering, places

the long fingers on the black notes, while the shorter thumbs play the white notes It just so happens, that when you play the group of two black notes, the

same two fingers are used in both hands. Can any pianists in the audience hold up both hands showing the two fingers used for these notes please? - There you have it – The Peace Sign. (Diagram 8)

Diagram 8 – Personal Photograph, M. Brandman

To play the set of three black notes – which fingers do we use? - now that’s the boy scout salute. (Diagram 9)

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Diagram 8 – Photograph of Scout Group

I call this phenomenon ‘Fingering Commonality’.

Another fingering commonality occurs when we play the two white notes in Eb major scale . The set of fingers is two and one: I call the unit ‘twenty-one’. (Diagram 9).

Diagram 9 – Pictorial Patterns for Keyboard Scales & Chords, M. Brandman

Another instance is the fingering commonality ‘43’ which occurs on the two black notes in this same scale. (Diagram 9). You can see these chunks, outlined in dotted red boxes on this map of the Eb Major scale.

In this two-octave version of G major scale, you can see the fingering unit

‘4 1 4’ at the centre of the scale. I find that if you think of the whole unit ‘ RH ‘4’ – thumbs together LH ‘4’ it helps with the tricky change-over section into the next octave. The 4’s in this scale are the main clues. There are also some sub-clues: - I have an association with the number three and the colour green as the words have a similar soung. Rather than adding more finger numbers to this picture of the scale pattern, the piano keys which are played using finger three in both hands at the same time, are coloured in green on the diagram. Also the red line added around the centre two notes of the scale, shows where the 21’s are used. (Diagram 10)

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Diagram 10 – Pictorial Patterns for Keyboard Scales & Chords, M. Brandman Pictorial Patterns

Diagram 11 also shows the Major scale and its related minor – offset

underneath it beginning on the 6th note. If you compare the top pattern to the next, you can see that the natural minor scale has exactly the same notes as the slice of the major scale above, while the Harmonic and Melodic Minor forms have variations shown by the dotted black lines.

Diagram 11 – Pictorial Patterns for Keyboard Scales & Chords, M. Brandman

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A quick way to teach minor scales, is to block out the major scale – then find the sixth note as the tonic of the minor scale. Then juggle the fingers down to grab the first six notes, and transfer the 7th note to the lower end of the scale, as well as another tonic.

Minor Scale Package: begin with the blocked out version of the

natural minor, then find the altered notes for the Harmonic and Melodic versions, while still blocking out the scale. Then play them in this sequence - NHNM

Modes

If you take any two octave Major scale, and play it beginning on another degree of the scale, you can easily play the modes. This graphic shows how this can be done. (Diagram 12)

Diagram 12 – Pictorial Patterns for Keyboard Scales & Chords, M. Brandman

Some time back I was puzzling over the way in which to capture the similarities and differences in pairs of notes played in a contrary motion scale. One morning, in one of those early morning half waking states, I came up with the idea of how to show them. (Diagram 13)

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Diagram 13 – Pictorial Patterns for Keyboard Scales & Chords, M. Brandman

The picture on the left shows two scale patterns which are symmetrical (E

major and Eb major) - you can easily see where the white and black notes match up.

On the first slide on the right you can see A major scale,: - the centre four

notes of the scale are symmetrical, while the second and second to last notes are an odd-pair (that is black and white) – plus you can see that the names of the notes in the first odd pair, swap around when they appear as the second to last pair.

In contrast, B major scale has an odd pair crossing over in the middle.

This idea occurs in F Major scale as well, and in Bb major. Arpeggios

Diagram 14 shows the Arpeggio patterns for all root position major and minor arpeggios,.

The red dotted boxes show where fingering commonality is used.

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Diagram 14 – Pictorial Patterns for Keyboard Scales & Chords, M. Brandman

Conclusion

I hope you enjoyed viewing these amazing patterns and learning to think of the scales in chunks to help fingering.

I have included a short piece which I wrote to demonstrate a symmetrical scale. There are only two places on the keyboard where you can play a contrary chromatic scale and have exact black and white matching notes. They are D and Ab.

This one begins on D, and as the pattern of the notes on the keyboard for

the first section of the piece is symmetrical, therefore the fingers used are matching fingers in both hands.

This piece is called Spider on the Mirror. It was first published in my book

‘Twelve Timely Pieces’. It has since been published in the AMEB’s Australian

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Anthology – Preliminary to Fourth Grades and set as an examination list piece for the AMEB Grade 3. Attachment 1. (Contemporary Piano Method, Twelve Timely Pieces, Margaret Brandman).

About the Author Margaret Brandman is a pianist, music educator, author and composer . She has written over 50 music education resources, ranging from materials for piano, theory and ear-training to the high school text, Accent on Music. Margaret has composed a great deal of music for piano. Several of her compositions are set as examination list pieces for the AMEB and ANZCA. She presents professional development seminars for studio music teachers throughout Australia and performs both written and improvised music. Contact Details Contact Details: Margaret Brandman Address: 22 Margaret Street, Newtown, NSW 2042 Australia Phone/Fax +61 (0) 2 9557 8058, Mobile 0414 185 193 Email: margaretbrandman@yahoo.com.au Website: www.margaretbrandman.com

References Brandman, M. S. (2001). Pictorial Patterns for Keyboard Scales & Chords.

Jazzem Music, Glenbrook, Australia. Rockham’s Razor with Robyn Williams, ABC Radio National, 16/01/2000 ‘The Bell’ Magazine, Stainer and Bell publications, UK Brandman, M. S. Personal Photograph of family member. Photograph of Scout Troup used with permission of New South Wales Scouting

Association. Brandman, M. S. (1999). Contemporary Piano Method – Twelve Timely Pieces,

Jazzem Music, Glenbrook, Australia

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Attachment 1