MODULATION: PIVOT CHORDS - Harmonic Wheel
MODULATION: PIVOT CHORDSAPPLICATIONS OF THE HARMONIC WHEEL
CONTENTS2The Modulation consists in changing from one Key toanother.To do that, it is common to use a Pivot Chord, whichis a chord that belongs to both keys, and then thenew key is affirmed by a Cadence, which mayconsist, simply, in the chords V7 I.In this presentation, an explanation is given on how toobtain the pivot chords between two keys, using theHarmonic Wheel.For the sake of simplicity, only consonant pivot chordsare considered, that is, Major or minor. 2009 www.harmonicwheel.com
CHORDS OF A GIVEN KEY3Every Major or natural minor key contains 6 consonantchords: 3 Major and 3 minor.On the Harmonic Wheel, these 6 chords are inside acurved rectangle and they are placed taking intoaccount their affinity.For example, in the C Major / A minor key these 6chords appear in the following arrangement:DmAmEmFCG 2009 www.harmonicwheel.com
CHORDS OF A GIVEN KEY4 2009 www.harmonicwheel.com
CHORDS OF A GIVEN KEY5Remember that the scale tonic is indicated withand the rest of the notes with.Traditionally, the modulation is studied with the aidof the cycle of fifths, where the keys are sortedaccording to their key signatures.On its own, the Harmonic Wheel is a much morecomplete representation than a cycle of fifths, sinceit gives a panoramic view of chords and keys, aswell as the existing relationships among them. 2009 www.harmonicwheel.com
MODUL. C MAJOR TO G MAJOR6Suppose that we modulate from C Major to GMajor and want to know the pivot chords, that is,the chords common to both keys.The common practice is to keep to the followingprocedure:1) To write the notes of the C Major scale andsuperimpose 2 thirds on each of them.2) To do the same with the G Major scale, butstarting this scale with note C.3) To find the chords common to the two keys. 2009 www.harmonicwheel.com
MODUL. C MAJOR TO G MAJOR7Chords of C Major and G Major:Now, we have to see which of these chords arecommon to the two keys. 2009 www.harmonicwheel.com
MODUL. C MAJOR TO G MAJOR8Chords common to C Major and G Major:CEmG 2009 www.harmonicwheel.comAm
MODUL. C MAJOR TO G MAJOR9However, the Harmonic Wheel gives us a much moresimple procedure.On it, we observe that tonic G is placed one positionaway to the right of tonic C, so the chords of GMajor will also be one position away to the right ofthose of C Major.In the next figures, the C Major scale has beenrepresented in dark blue, while G Major scale hasbeen represented in light blue. Rapidly, we see thatthe pivot chords are: Am C Em G. 2009 www.harmonicwheel.com
MODUL. C MAJOR TO G MAJOR10 2009 www.harmonicwheel.com
MODUL. C MAJOR TO G MAJOR11 2009 www.harmonicwheel.com
MODUL. C MAJOR TO D MAJOR12 If we now want to modulate from C Major to DMajor, we again have two procedures:The common one, which consists in writing the twoscales, superimposing thirds and comparing theresulting chords.By means of the Harmonic Wheel, by simplyobserving that tonic D is placed two positions awayto the right of tonic C, so the chords of D Major willalso be two positions away to the right of those ofC Major. 2009 www.harmonicwheel.com
MODUL. C MAJOR TO D MAJOR13Common procedure:Now, we have to see which of these chords arecommon to the two keys. 2009 www.harmonicwheel.com
MODUL. C MAJOR TO D MAJOR14Chords common to C Major and D Major:EmGWith the Harmonic Wheel, it is much simpler: 2009 www.harmonicwheel.com
MODUL. C MAJOR TO D MAJOR15 2009 www.harmonicwheel.com
MODULATION TOWARDS THE FLATS16Let us now see two examples of modulation towardsthe flat region, by using the Harmonic Wheel: Modulation from C Major to F Major. In the next twofigures, it is clearly seen that the pivot chords are:Dm F Am C. Modulation from C Major to B b Major. As can beseen in the figure following the previous ones, thepivot chords are: Dm F. 2009 www.harmonicwheel.com
MODUL. C MAJOR TO F MAJOR17 2009 www.harmonicwheel.com
MODUL. C MAJOR TO F MAJOR18 2009 www.harmonicwheel.com
19MODUL. C MAJOR TO B b MAJOR 2009 www.harmonicwheel.com
20MODUL. D b MAJOR TO B MAJORFinally, let us consider a more complicated example:the modulation from D b Major to B Major.As can be seen in the next figure, finding the pivotchords with the traditional method is not easy at all.However, we rapidly find the solution by using theHarmonic Wheel:Eb m Gb 2009 www.harmonicwheel.com
21MODUL. D b MAJOR TO B MAJORTraditional procedure:Finding the pivot chords in this representation is noteasy at all. But in the Harmonic Wheel, it is: 2009 www.harmonicwheel.com
22MODUL. D b MAJOR TO B MAJOR 2009 www.harmonicwheel.com
FINAL CONSIDERATIONS23Additionally, the Harmonic Wheel allows us to easilycheck that “if two keys are more than 2 accidentalsapart, there is not any consonant pivot chord”. This iswhat occurs, for instance, when going from C Major toA Major or to E b Major.This statement, however, is difficult to prove by writingchords on a staff.In these cases, we need other procedures to modulate.For example, using the Neapolitan sixth chord, alteredscales, deceptive cadences, etc. 2009 www.harmonicwheel.com
FINAL CONSIDERATIONS24All these modulation procedures correspond to the socalled Diatonic Modulation.But there exist, in addition, the so called Chromaticand Enharmonic modulations.As the harmonic and melodic minor scales are alsorepresented on the Harmonic Wheel, and therelationships between chords and keys are alwaysshown as well, the use of the Harmonic Wheel makesit much easier to study any kind of modulation. 2009 www.harmonicwheel.com
called Diatonic Modulation. But there exist, in addition, the so called Chromatic and Enharmonic modulations. As the harmonic and melodic minor scales are also represented on the Harmonic Wheel, and the relationships between chords and keys are always shown as well, the use of the Harmonic Wheel makes it much easier to study any kind of modulation.
9/18/2016 9Nurul/DEE 3413/Modulation Types of Modulation Pulse Modulation Carrier is a train of pulses Example: Pulse Amplitude Modulation (PAM), Pulse width modulation (PWM) , Pulse Position Modulation (PPM) Digital Modulation Modulating signal is analog Example: Pulse Code Modulation (PCM), Delta Modulation (DM), Adaptive Delta Modulation (ADM), Differential Pulse
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Modulation allows for the designated frequency bands (with the carrier frequency at the center of the band) to be utilized for communication and allows for signal multiplexing. Amplitude modulation (AM) is an analog and linear modulation process as opposed to frequency modulation (FM) and phase modulation (PM).
Types of Modulation 6 Flynn/Katz 7/8/10 Analog Modulation Amplitude Modulation, AM Frequency Modulation, FM Double and Single Sideband, DSB and SSB Digital Modulation Phase Shift Keying: BPSK, QPSK, MSK Frequency Shift Keying, FSK Quad
10.3 Analog Modulation Schemes 10.4 Amplitude Modulation 10.5 Frequency Modulation 10.6 Phase Shift Modulation 10.7 Amplitude Modulation And Shannon's Theorem 10.8 Modulation, Digital Input, And Shift Keying 10.9 Modem Hardware For Modulation And Demodulation 10.10 Optical And Radio Frequency Modems 10.11 .
The green octave: Low string chords (C2-B2) Major & Minor chords triggered by velocity The blue octave: Low, Mid, High chords played together (C1-B1) Major & Minor chords triggered by velocity Dynamics: The mod wheel gives you further possibilities to adjust the dynamics and enables you to mix sustain and tremolo chords.
Creating a Pivot Table Create the Pivot Table using Data Pivot Table Create from the menu bar. If the list to be analyzed is in a spreadsheet table, select only one cell within this list. Calc recognizes and selects the list automatically for use with the Pivot Table (Figure 2). Figure 2: Selecting the source data for the Pivot Table
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