Harmonic Wheel - Level 2 Foundations of Harmony
Transcript of 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.