harmonic wheel - level 2 foundations of harmony

8/11/2019 Harmonic Wheel - Level 2 Foundations of Harmony

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HARMONIC WHEEL: UTILITIEShttp://www.harmonicwheel.com

In the next 2 large sections the main utilities of the Harmonic Wheel are explained in detail. They

have been written in a simple and friendly way so as to be useful even for the layman. In fact a

summary of main musical concepts is given, which may serve as an introduction to Music

Theory and Harmony for anyone interested in this subject.Thus all the concepts are explained

in the simplest cases !for example in the " #a$or %ey& and the rest of them are solved

automatically with the aid of the Harmonic Wheel. In this development a big effort has been made

to logically connect all the concepts to give the theory a solid and unified structure.

All the explanations are given without using the musical notation, for it is unnecessary in this

approach.'nly one example of it is presented in one of the last chapters. (evertheless it is

strongly recommended to learn it for it is one of the few languages having the status as a universal

language along with the mathematical language the symbols for the physical units and the symbols

for the chemical elements. #oreover once the contents of this Web page are ac)uired it will be

easier to understand this system of script.

*ven for those people having musical %nowledge this new way of connecting musical concepts will

result very interesting. +nd particularly those musicians who play monophonic or percussion

instruments will find, in Level , a very useful summary of Harmony foundations, which may

be sufficient to satisfy their real professional needs thus avoiding the necessity of readingcomplex and extensive texts.

The contents have been organi,ed into 2 -evels:

Level ! is devoted to fundamental aspects of Music Theory. This level deals with the musical

notes the intervals the #a$or and minor scales and the %eys. The Harmonic Wheel allows us to

easily obtain the interval between any two notes as well as the notes belonging to any #a$or or

minor scale being it natural harmonic or melodic along with their corresponding %ey signature. +s

novelty the Harmonic Wheel gives a complete and panoramic view of the existing relationships

among all the %eys. While the cycle of fifths shows the %eys on a line !one dimension& the

Harmonic Wheel shows them on a surface !two dimensions&. o besides the cycle of fifths the

changes of mode are also visible which are not in the cycle of fifths. Thus a real MA" #$ TH%

&%'(is achieved.

Level is devoted to the foundations of Harmony. This level deals with the construction of #a$or

minor +ugmented and diminished chords as well as all possible note chords that can be obtained

by superimposing #a$or and minor thirds. Then the existing relationships among the different

types of chords are explained by means of scales. 'n the Harmonic Wheel all these chords have a

simple graphical representation. This fact facilitates us to obtain the notes composing them that is

their arpeggios. 'n the other hand this instrument allows us to obtain automatically all the chordsassociated to any #a$or or minor scale. This function is named )H#*+ $-+%*. +s novelty the

particular representation of notes and consonant chords on the Harmonic Wheel explains
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graphically the construction of the #a$or scale its relationship with its relative minor scale and the

most important characteristics of their associated chords. +ll these things are difficult to see even in

the conventional musical script. #oreover than%s to this %ind of representation it is easy to

determine which chords are more or less affine to any given scale. 0inally some special scales

containing 1 and 3 notes are explained along with their associated chords.


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LEVEL 2: FOUNDATIONS OF HARMONY

http://www.harmonicwheel.com

9. MAJOR AND MINOR CHORDS

+ )hordis a set of 4 or more notes that sound simultaneously. In a similar way as we saw with the

intervals there are some combinations of 4 notes that when played together produce a sensation of

harmony, rest and stability. They are the so5called )onsonant )hordsand there are only two types

of them: Majorand minor )hords. The rest of the chords are +issonant.

+ Major )hordis built by superimposing a # 4 rdand a m 4rdintervals on a note which is called

the *oot. +nd a minor chordis built by superimposing first a m 4rdand then a # 4rd.

Thus for example the " #a$or chord is composed by notes " * 67 and the + minor chord is

composed by notes + " *. In both cases it can be seen that between the first note !that is the

root& and the last one there is a 8 1 thinterval !" 9 6 in the first case and + 9 * in the second one&

which ma%es these chords especially stable. The " #a$or chord is simply represented by "; while

the + minor chord is represented by +m;.

Those people who play polyphonic instruments such as piano guitar etc. must learn to play these

types of chords as well as other types that will be described in the next chapters. #oreover they

must learn to play the notes composing these chords successively both ascending and descending

what is %nown as Arpeggios. 'n the contrary those people who play monophonic instruments

such as trumpet saxophone etc. can only play the arpeggios but not the chords. +nyway both the

former and the latter must learn to recogni,e the different types of chords by ear;.

'n the Harmonic Wheel the )onsonant )hords that is Major and minor chords are shown in

*%+ and are placed inside curved triangles. The notes composing these chords that is their

arpeggios are placed $ust at the vertices of these triangles.

In 0ig.


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0igure


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10. AUGMENTED AND DIMINISHED CHORDS

+n Augmented )hordis a 4 note +issonant chord built by superimposing two # 4rdintervals.

Thus for example the " +ugmented chord is composed by notes " * 6 . +s can be seen there

are no 8 1thintervals between these notes but an + 1 th so this chord is unstable and produces a

sensation of tension. The " +ugmented chord is represented by "=;.

'n the Harmonic Wheel the Augmented )hordsare represented by the spiral red lines. In 0ig.


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'n the Harmonic Wheel the diminished )hordsare represented by the radial red lines. In 0ig.


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11. FOUR NOTE CHORDS

Ap to now we have explained the construction and graphic representation of #a$or minor

+ugmented and diminished chords !in this last case with 4 and notes&. These chords include all

possible chords built by superimposing two #a$or o minor 4 rdintervals. +nd as we have seen allof them have a very simple geometric shape on the Harmonic Wheel.

The superimposition of three #a$or o minor 4 rdintervals gives 3 possibilities. However the case of

three #a$or 4rdsresults in an +ugmented chord which has only 4 different notes and has been

studied in the last chapter. The other B possibilities actually correspond to note chords but the

case of three minor 4rdsresults in a diminished chord which has been studied in the last chapter

too. o we shall go on with the construction and graphic representation of the remaining types of

chords. They have been grouped by couples in order to show the existing symmetries. In all cases

the ?oot of every chord has been mar%ed with and the rest of the notes with .

(ow besides of the 4rdand 1thintervals a Bthwill appear between the first and the last note in each

chord. ?elating to the symbols used to represent the chords the most simple as well as universally

accepted ones have been chosen. 8articularly the symbol B; is used to indicate the minor B thand

the symbol ; for the #a$or Bth. 0rom now on we shall not repeat that the enharmonic notes not

following the series of 4rdintervals must be discarded as it has already been mentioned several

times.

+ Major 2th)hordis a note chord built by superimposing a # 4rd a m 4rdand a # 4rdintervals

!in this se)uence&. Thus for example the " #a$or B thchord is composed by notes " * 6 >. This

chord is represented by " ;.

+ minor 2th)hordis a note chord built by superimposing a m 4rd a # 4rdand a m 4rdintervals

!in this se)uence&. Thus for example the + minor Bthchord is composed by notes + " * 6. This

chord is represented by +mB;.


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0igure


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0igure chords on the Harmonic Wheel.

+n Augmented, Major 2th)hordis a note chord built by superimposing two # 4rdand one m

4rdintervals !in this se)uence&. Thus for example the " +ugmented #a$or B thchord is composed

by notes " * 6 >. This chord is represented by "= ;.

+ minor, Major 2th)hordis a note chord built by superimposing one m 4 rdand two # 4rd

intervals !in this se)uence&. Thus for example the + minor #a$or B thchord is composed by notes

+ " * 6 . This chord is represented by +m ;.


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0igure


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12. CHORDS AND SCALES

Ap to now we have studied the chords as if they were independent to each other that is without

saying which chords are related with which other chords. 6enerally a melody consists of notes

belonging either to a #a$or or to a minor scale. 'n the other hand each melody usually has anaccompaniment that is normally composed by notes belonging to the same scale as the melody.

+nd also in a general sense this accompaniment consists in chords built by superimposing 4 rd

intervals !#a$or or minor& on every scale degree.

Thus for example a musical passage written in " #a$or will have an accompaniment that in most

cases will be formed by the chords shown in Table . In that Table both 4 and note chords have

been considered.

Table . " #a$or scale and 4 and note chords associated to this scale.

" #a$or scale I " II @ III * IC 0 C 6 CI + CII >

4 note chords I " II @m III *m IC 0 C 6 CI +mCII >m!

1&

6*

"

+0

@

>6

*

"+

0

@>

6

*"

+

0@

>

note chords I " II @mB III *mB IC 0 C 6B CI +mB CII >

>

6

*"

"

+

0@

@

>

6*

*

"

+0

0

@

>6

6

*

"+

+

0

@>

The musical system of script provides us with an easy and compact way for representing both the

melodies and the chords. +s an example the information in Table is again shown in 0ig.


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0igure ut if we consider the + harmonic or melodic minor scales some different chord types will then

appear. The 4 and 1 note chord types appearing in Major and minor scales are precisely all

those studied in chapters 5 to !!.

The tas% of adding chords to a melody is %nown as harmoni6ation of melodiesand represents an

important part in the study of Harmony. #a$or and minor scales besides serving us to create

melodies as well as providing the most suitable chords to accompany them are the %ey to relate

chords among them for the chords associated to any Major or minor scale always form a set of

chords which are affine among them.

When tal%ing about scales and their associated chords it is worthwhile to clarify the difference

between Tonic and ?oot. The Tonic is the first note of a scale; !that is the I degree& and the ?oot


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is the first note of a chord; !that is the note above which the 4rd intervals are superimposed&.

Therefore in a #a$or or minor scale there is only one tonic but there are B roots one for each

chord associated to the scale. These B roots are precisely the notes of the scale. The chord whose

root is the tonic of the scale is called Tonic )hord. o if considering 4 note chords the tonic chord

in the " #a$or scale is "7 and the tonic chord in any + minor scale is +m.

#n the Harmonic 7heel, the consonant chords are always grouped by couples formed by a

Major chord and its relative minor chord. And each of these couples is assigned the 8ey

signature that would correspond to these chords if they were tonic chords. (o, each Major or

minor chord also represents a 8ey.This fact allows us to directly obtain the %ey signature

associated to any #a$or or minor scale as was done in "hapter B.

Dnowing the chords associated to any #a$or or minor scale for any number of accidentals in the

%ey signature is therefore a corner stone to harmoni,e melodies. +nd because it may result very

complex in the Harmonic Wheel a very simple system to obtain all the chords associated to any

scale has been implemented as will be seen in the next "hapter. #oreover moving a series of notesor chords from one %ey to another is also a complex operation that can be easily performed by using

this instrument. This operation is named Transpositionand is )uite common in #usic. However

the transposition of notes should be mentally performed which re)uires the study of their

associated rules and much practice as well.


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13. CHORD FINDER AND THE MAJOR-MINOR SYSTEM

In the last chapter it was pointed out that %nowing the chords associated to any scale is extremely

important and we also saw the big difficulties related to it. If we go bac% to Table or 0ig. m! 1& did not appear in this analysis

for it is not a consonant chord but a dissonant one.

-oo%ing at 0ig.


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necessary to form 4 Major chords in intervals of " :ths one /central0 chord and, with respect

to it, one regressive and one progressive chord.This provides this set of B notes with a strong

cohesion and unity and establishes the particular succession of whole and half steps among them as

well. #oreover with the same B notes we can form other 4 minor chords in intervals of 8 1 ths too:

one central chord and with respect to it one regressive and one progressive chord. These facts

$ustify both the existence of the #a$or and its relative minor scales and at the same time confer

these two modes a supremacy with respect to the other 1.

+s we saw the representation of notes and chords provided by the Harmonic 7heel allows us

to easily understand which is the underlying relationship connecting the 2 notes composing a

Major scale, that is to say, which is the origin of its particular succession of whole and half

steps, the reason why two relative modes are established, the Major and the minor, and which

are the main characteristics of the chords associated to them.+ll this information is not visible

in other %inds of representations even in that of 0ig.


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due to the graphic nature of the scale and chord representations, it is very simple to determine

which chords are nearer to or further from a given scale that is if they contain some notes

belonging to the scale or on the contrary they are completely unrelated to it.


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14. PENTATONIC SCALES. PROPERTIES

When tal%ing of the " #a$or scale in "hapter


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0rom these graphic representations it is easy to understand the two most important properties of

this type of scale:


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1. DIMINISHED SCALES AND THEIR ASSOCIATED

CHORDS

+ diminished scaleis composed by eight notes in alternating intervals of half and whole steps

!HW&. Thus for example if we begin with note > the following diminished scale is obtained:

> diminished scale !HW&

@ue to the existing symmetry in this scale from its 3 notes can be considered the tonic: > @ 0

and 6 . Its representation on the Harmonic Wheel is very simple for it corresponds to 2

consecutive radii !0ig. 22&. +nd the possible tonics are the notes contained in the left radius.

!?emember that the notes located at the ends of each radius are repeated&.

0igure 22. @iminished scale representation.

+ diminished scale can also be defined as an 3 note scale in alternating intervals of whole and half

steps !WH&. Asing this definition and beginning with note " yields

" diminished scale !WH&

@ue to the existing symmetry in this scale again from its 3 notes can be considered the tonic. In

this case: " * 0 and +. +nd because the " diminished scale !WH& has the same notes as the >

diminished scale !HW& its graphic representation is newly that in 0ig. 22 but its possible tonics


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correspond now to the right radius. It is easy to prove that there are only 4 different diminished

scales.

*very diminished scale contains 3 consonant chords and includes for each of them its

corresponding relative chord !#a$or or minor& and itsparallel chord!that is the one obtained by

changing the mode&. 0urthermore it contains every diminished chord formed by considering any

note of the scale as the root.

The diminished scales are widely used in modern music and $a,,. +nd particularly in

improvisation techni)ues.


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1!. HE"ATONIC SCALES AND THEIR ASSOCIATED

CHORDS

The Hexatonic scalesare those having notes. (ext the two most important types of hexatonic

scales are described.

+ 7hole Tone scaleis composed by notes in intervals of one whole step. Thus for example if

we begin with note " the following Whole Tone scale is obtained:

" Whole Tone scale

@ue to the existing symmetry in this scale any of its notes can be considered the tonic. Itsrepresentation on the Harmonic Wheel is very simple for it corresponds to 2 non5consecutive spiral

lines !0ig. 24&. It is easy to prove that there are only 2 different Whole Tone scales.

+ Whole Tone scale has no consonant chords but it contains every +ugmented chord formed by

considering any note of the scale as the root. #oreover it contains every @ominant B thchord with

+ugmented or diminished 1th that is the B! 1& and B! 1& chords which are formed by considering

any note of the scale as the root. 0or example if we consider " as the root the "B! 1& and "B! 1&

chords are obtained.


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0igure 24. Whole Tone scale representation.

+n Augmented scaleis composed by notes in alternating intervals of


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0igure 2. +ugmented scale representation.

Hexatonic scales but mainly the Whole Tone scale are widely used in modern music and $a,,. +nd

particularly in improvisation techni)ues.

harmonic wheel - level 2 foundations of harmony

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