Pedagogy / Harmony 101 / Root Position



Academic harmony starts with Triads, considering them complete chords.
      MusicNovatory starts with Tetrads, considering them complete and fundamental chords,
           with Triads incomplete forms of Tetrads.
 With this new approach, you will understand Triads for the first time.
      Give it a try, you won't regret it.

Getting Ready

Intruduction
We hope that our indications will be both clear and helpful.
      Let usknowif they are not.
 Each lesson, on a separate page, will have its specific instructions,
           the first lesson remaining as simple as possible.
      This first lesson is, however, fairly long,
           because there are many ways of producing Triads in Root Position,
                so take it easy, one step at a time.
 You will be asked to take links to the encyclopedic pages of the site.
      Do not read more than is absolutely necessary and come right back to this page.
 The most important thing is to realize, at all times,
      the relationship between Triads and the fundamental Tetrads from which they come.
           Good luck ! We hope you enjoy it !

This should take a week or two
While the rest of the class is building Triads,
      on each of the 7 degrees of the major scale,
      by stacking thirds over the root,
      producingI,ii,iii,IV,V,vi,vii,
           (1 major, 2 minor, 2 major, 1 minor, and 1 lonely diminished Triad),
 we will be building Tetrads,
      in eachFRAME(fifth) of the Diatonic Window,
      placing aMEDIAN(third) inside theFRAME,
      and aMOTRIX(seventh or sixth) outside theFRAME,
           (3 major chords below and 3 minor chords above, with the TONIC chord in the center of each group).

Start with Tetrads

The structure of Tetrads
All Tetrads are built the same way.
      This is whereHarmony starts.
           Don't forget to come back.

The disposition of Tetrads
Tetrads are disposed in the series of fifths,
      in what we call aDiatonic Window.
           Don't forget to come back.

The Major Mode
You will find here the 4 Tetrads in the nucleus of the mode (the 3 major chords),
      and what we call the 2 "swings" which exist between these 3 major chords.
           You will note that we call this theDiatonic Major Mode
               because there is also a Chromatic Major Mode which we will see later.
 Looking at the nucleus should be enough,
      you might find the tail confusing and it is not really required for now.
 Remember that Tetrads can resolve in either direction (a fifth up as well as a fifth down)
      depending on theMOTRIX(sixth or seventh) which it possesses.
           Don't forget to come back.

Orbits
We have another way of identifying chord components according to their degree of tension.
       Have a look.
           Don't forget to come right back,
                you probably do not need at this time
                     the further material starting with “Voice Disposition”.

Then Produce Triads

With Swings

The Swing with Voice-leading A
This is one of the most precious jewels of harmonic structure, a real diamond.
 WhenVoice-leading Ais applied to the sharpening TONIC (C6) or to the DOMINANT (G7)
      this 4-voice canonic swing appears all by itself !
           Don't forget to come right back, the beginning of Voice-leading A is all you need.

Let's see what this natural canon Voice-leading A Swing can do for us.
      Remember that it has no rhythmic structure, it can start and end at any time.
           As you copy it, you may add a few extra chords (from the beginning) at the end,
                to clearly see all the possibilities that can be taken from it.
           We strongly recommend that you insert the orbit number beside each note
                in all your preliminary Orbit Line sketches,
                     removing them only in the final performance disposition that you hand in.
We will now generate series of Triads in Root Position
      and you will be in a good position to evaluate -
           1. not only how complex Triads are compared to Tetrads,
                being either Real or Deceptive,
           2. but also how complex Triads can be in Root Position,
                the Root Position of Real Triads being the same as for the Original Tetrad,
                but the Root Position of Deceptive Triads NOT being the same as for the Original Tetrad,
                     having either the sixth of the Tetrad in the Bass (for sixth Tetrads),
                     or the third of the Tetrad in the Bass (for seventh Tetrads).
      This will be much clearer when we see Triad inversions in the third lesson.
To clearly differentiate Real Triads from Deceptive Triads,
      we will indicate Real Triads with upper case Roman numerals
           and Deceptive Triads with lower case Roman numerals.
      At first, in these 2 Swings, it will seem as if -
           the major triads are indicated upper case (which they are), and
           the mInor triads are indicated lower case (which they are), but
                that is beacause all the major triads are Real Triads,
                and all the minor (and diminished) triads are Deceptive Triads.
      Our specific form of identification will be much clearer in the "circle".




Start building
1. On a large sheet of music paper,copy this swingin the top-left corner, and number it S1a.
      This is the TONIC/DOMINANT swing,I6-V7 , between C6and G7.
           Don't forget to inscribe the Orbit numbers in all the examples.
 2. Re-copy it a fifth lower (always in the same key) in the top-right corner, and number it S1b.
      You now have the COUNTER/TONIC swing,IV6-I7 , between F6and C+7.
           The Orbit numbers are exactly the same as in S1a.
 3. Below S1a, remove eachOrbit 3(seventh or sixth) from it, and replace it with anOrbit 0, indicated0(3),
      to produceReal Triads(IandV), and number it S2aR
           The Orbit numbers are still the same as in S1a, if you read within the parentheses.
 4. Beside S2aR, remove eachOrbit 0from S1a, and replace it with anOrbit 1, indicated1(0),
      to produceDeceptive Triads(viandvii), and number it S2aD.
           The Orbit numbers are still the same as in S1a, if you read within the parentheses.
      Come right back, you don't really need Voice-leading B now.
 5. Below S1b, remove eachOrbit 3(seventh or sixth) from it, and replace it with anOrbit 0, indicated0(3),
      to produce Real Triads (IVandI), and number it S2bR
           The Orbit numbers are still the same as in S1a.
 6. Beside S2bR, remove eachOrbit 0from S1b, and replace it with anOrbit 1, indicated1(0),
      to produce Deceptive Triads (iiand iii), and number it S2bD.
           The Orbit numbers are still the same as in S1a.
                In S2aR, S2aD, S2bR, and S2bD, notice where the Triads are in root position.
 7. Below S2aR and S2aD, choose only the triads in root position
           (first and second of S2aD, third and fourth of S2aR)
      and you have 4 Triads in root position (vi,vii,I, andV)
           with perfect doublings ("thirds" for the Deceptive Triads, roots for the Real Triads).
      However, there is a voice-leading problem where these 2 sections are pasted together,
           between theviiandITriads,
                where the 2 Ds (in the Alto and Tenor) both go to G when one should go to C.
           The solution is to send the Alto from D to C (and then to B) for perfect Voice-leading,
                with substitutions1(0)D and1(3)C (and resolution to Orbit2B), in the same voice.
           Number this S3aRD and write in the Triad Roman numerals (and Orbit numbers).
 8. Below S2bR and S2bD, choose only the triads in root position
           (first and second of S2bD, third and fourth of S2bR)
      and you have 4 Triads in root position (ii,iii,IV, andI)
           with perfect doublings ("thirds" for the Deceptive Triads, roots for the Real Triads).
      For perfect Voice-leading, don't forget the adjustment where the 2 sections are pasted together
           between theiiiandIVTriads, G, F, E, in the Alto voice.
                Number this S3bRD and write in the Triad Roman numerals (and Orbit numbers).
 In these 2 Swings, with Real and Deceptive Triads,
      you have the7 possible Triads, co-existing beautifully together.
Keep this page. Examples 7 and 8, S3aRD and S3bRD, furnish precious material in Root Position.

Analysis and Summary

Grouping of Triads
When we mocked the disposition of Triads on each degree of the scale (under “Getting ready”) -
       I,ii,iii,IV,V,vi,vii,
           (1 major, 2 minor, 2 major, 1 minor, and 1 lonely diminished Triad),
      we might have been a little hasty.
 Now that these 2 swings have given us precious insights, we see that -
      1. Triads on the first 4 degrees of the scaleI,ii,iii,IV
          all belong to the COUNTER/TONIC Swing,
                with the Real Triads (IandIV) at the ends,
                and the Deceptive Triads (iiandiii) in the middle,
                     with the Tetrad chords (I7 andIV6 ) alternating as we move up the scale.
      2. Triads on the last 4 degrees of the scaleV,vi,vii,I
          all belong to the TONIC/DOMINANT Swing,
                with the Real Triads (VandI) at the ends,
                and the Deceptive Triads (viandvii) in the middle,
                     with the Tetrad chords (V7 andI6 ) alternating as we move up the scale.
      NOTE that the Real TriadIappears twice -
           once at the very beginning (of the scale) in the COUNTER/TONIC Swing,
                part of theI7 Tetrad, the chord of C+7, and
           once at the very end (of the scale) in the TONIC/DOMINANT Swing,
                part of theI6 Tetrad, the chord of C6.

With a Complete Circle

The complete Circle is actually simpler than the preceding swings
           because the chords are all alike, all in the same direction (with sevenths).
      Here, we will be usingVoice-leading Calmost exclusively.
 The indication of Real Triads in upper case, and that of Deceptiive Triads in lower case,
      will be much more evident here, and very, very useful.
A circle may be composed uniquely of Real Triads (2. numbered C2R and 5. numbered C2Ra),
      but it is not possible to have 2 Deceptive Triads in a row in 4-voice writing,
           because 2 Orbit Lines would be using the same notes.
      It is only possible to alternate Deceptive Triads with Real Triads
           (3. numbered C2DR and 4. numbered C2RD).




Start building
1. At the top of a sheet of music paper, copy the Diatonic MajorCirclein Tetrads,
      complete with the 4 Orbit Lines and the Fundamental Bass, and number it C1.
           Don't forget to inscribe the Orbit numbers in each example, which will always remain the same.
 2. Below C1, remove eachOrbit 3(the seventh), and replace it with anOrbit 0, indicated0(3),
           (in this case, the root of each chord),
      to produce Real Triads (I,IV,VII,III,VI,II,V,I).
           Number this C2R and write in the Triad Roman numerals (and Orbit numbers).
      There are no crossings here and this may be disposed in open or close positions.
      The Fundamental Bass will assure Root Position for all Triads
           and one may eliminate either the second or the fourth Orbit Line.
 3. Below C2R,
      in the odd-numbered Tetrads of C1 (I7 ,VII7 ,VI7 ,V7 )
           remove eachOrbit 0(the root of each chord)
           and replace it with anOrbit 1(the fifth of the chord), indicated1(0),
                to produce Deceptive Triads (iii,ii,i,vii),
      in the even-numbered Tetrads (IV7 ,III7 ,II7 ) treat as in C2R (2.), indicated0(3),
                to produce Real Triads (IV,III,II).
           Number this C2DR and write in the Triad Roman numerals (and Orbit numbers).
      With the first Orbit Line in the Bass, all the Triads (iii,IV,ii,III,i,II,vii,I), will be in root position.
           NOTE - With the second Orbit Line zigzagging on the fifth of each chord,
                     it will constantly cross the third Orbit Line,
                and they should be placed in alternate performance voices, Tenor (2) and Soprano (3).
                     thereby placing the secondary notes in the outer voices (always a good idea).
           The Fundamental Bass cannot be used here,
                because the root must be removed from each Deceptive Triad.
      Place this disposition of C2DR (without the Orbit numbers) to the right of the original Orbit Lines.
 4. Below C2DR,
      in the even-numbered Tetrads of C1 (IV7 ,III7 ,II7 ) remove eachOrbit 0,
           and replace it with anOrbit 1, indicated1(0),
                to produce Deceptive Triads (vi,v,iv), and
      in the odd-numbered Tetrads (I7 ,VII7 ,VI7 ,V7 ) treat as in C2R (2.), indicated0(3),
                to produce Real Triads (I,VII,VI,V).
           Number this C2RD and write in the Triad Roman numerals (and Orbit numbers).
      With the third Orbit Line in the Bass, all the Triads (I,vi,VII,v,VI,iv,V,I), will be in root position.
           NOTE - The third and fourth Orbit Lines will cross
                     and should be placed in alternate performance voices, with the fourth line in the Alto.
                The first Orbit Line could advantageously be in the Soprano,
                     placing the secondary notes in the outer voices, and producing a closing cadence.
           The Fundamental Bass cannot be used here,
                because the root must be removed from each Deceptive Triad,
                     but part of it will appear in the last 2 chords.
      Place this disposition of C2RD (without the Orbit numbers) to the right of the original Orbit Lines.
 5. Here is an interesting possibility with only Root Position Real Triads using Voice-leading A.
      Start by copying theCircle with Voice-leading Ain Tetrads,
           with the 3 canonic Orbit Lines and the Fundamental Bass (leaving out the first line with only fifths),
                and number it C1a.
           Don't forget to inscribe the Orbit numbers.
      Then in the 3 upper voices, remove eachOrbit 3(the seventh),
           and replace it with anOrbit 1(the fifth of each chord) , indicated1(3),
                     rather than with anOrbit 0(the root of each chord) as we did previously, indicated0(3).
           Number this C2Ra and write in the Triad Roman numerals.
                NOTE that this voice-leading uses the "Common Tone rule-of-thumb".
      The Fundamental Bass will assure Root Position for all Triads,
                gradually descending as the upper 3 voices rise.
           There are no crossings here and this may be disposed in open or close positions.
Keep this page. All 4 examples furnish precious material in Root Position,
      2. C2R and 5. C2Ra with only Real Triads,
      3. C2DR and 4. C2RD with alternating Real and Deceptive Triads.

With Extended Swings

InSwings, we were dealing with 2 Tetrads "facing each other" withMOTRIXs directing each to the other,
           which just "swing back and forth" between the two adjacentFRAMEs,
      the original TONIC/DOMINANT Swing, C6-G7, and also the COUNTER/TONIC Swing, F6-C+7.
 In aCircle, we were dealing with Tetrads in the same direction, with the sameMOTRIX,
      constantly moving from one Swing to the next, constantly changing theCOMMON TONE,
           without ever establishing a Swing.
 In theI7 ,IV6 ,I6 ,V7 ,ITetrad chord pattern,
      the Circle chords ofI7 andI6 (C+7and C6) transport us from theIV6 Swing to theV7 Swing,
                in what we call an Extended Swing between the three adjacentFRAMEs.
           It will evidently be possible, with more Circle chords, to extend Swings even further.
      The restrictions of writing uniquely in Root Position will be quite severe here,
           and we will limit ourselves to one process of generation, without Deceptive Triads,
                which evolves directly from the preceding work.




Start building
1. We will start where the Circle example 5. C1a left off,
      using the Voice-leading A Circle with the Tetrad Fundamental Bass, and only Real Triads,
           applying the "Common Tone rule-of-thumb" voice-leading between the Triads.
 2. From 5. C1a , copy the Triads ofIandIVat the beginning,
           and the Triads ofVandIat the end, numbering this CS1.
      This is how we will "navigate" between the Real Triads of our newI,IV,I,V,ITriad chord pattern,
           always returning to the original disposition of our TONIC Triad.
 3. For our upper 3 Orbit Lines, let's arbitrarily choose theFRAMEdisposition of the TONIC Triad,
           the notes C, E, G (reading from bottom to top).
      Applying the voice-leading seen in 2. with a higher position forI-IVand a lower position forV-I,
           the first Orbit Line will consist of the notes G, A, G, G, G,
           the second Orbit Line will consist of the notes E, F, E, D, E,
           the third Orbit Line will consist of the notes C, C, C, B, C,
           with the Tetrad Fundamental Bass C, F, C, G, C, assuring the Root Position of each Triad.
                Number this CS2R.
           Don't forget the Orbit numbers.
      There are no crossings between the 3 Orbit Lines
           and they may be disposed in any order in open or close position.
 4. Using theITriad to pass from one Swing to the other,
      is not the only way of making this transition.
           Removing theITriad in the middle of theI,IV,I,V,Ipattern,
                leaves us with the traditionalI,IV,V,Ipattern,
                     passing directly from theIVto theV,
                          with perfectly suitable voice-leading.
                Number this CS2Rx.

Analysis and Summary

Explaining the Triad Progression from IV to V
Let's start by going back to the original Tetrad progression fromIV6 toV7 .
      The TetradsIV6 andII7 each possessexactly the same notes
               with the Primary and Secondary notes inverted -
           the TetradIV6 with Primary notes F, C, and Secondary notes A, D, and
           the TetradII7 with Primary notes D, A, and Secondary notes F, C.
      TheIV6 Tetrad has a Real Triad ofIVand a Deceptive Triad ofii, and
      theII7 Tetrad has a Real Triad ofIIand a Deceptive Triad ofiv.
 What really happens here is that the Real Triad ofIVhas been transformed into a Deceptive Triad ofiv
     without correcting the doubling of the note F which was fine for theIV
          but not for theivwhere the correct doubling should have been the note A (see Circle 4. C2RD).
      In the Triad ofIV, the note F substituted for theMOTRIXD,
           which becomes theCOMMON TONEon Dm7to G7.
                It is perfectly logical for the note F to go to the note D which it was replacing.

Doing Your Homework

We have tried to estimate what your homework will be like,
      and given you the tools we feel you will need,
           in the 3 pages of Swings, Circles, and Extended Swings.
 If you need extra help, with more details for specific work,
      let usknowwhat you need.

Isolated Progressions

You may be asked to write, in four voices (SATB), different arrangements of harmonic progressions,
           using only triads in root position.
      First let's see what you have available -
           1. Take out your 3 pages of Swings, Circles, and Extended Swings.
           2. You should find the Triad progression you are looking for in these pages,
                possibly several times.
           3. Change the disposition of the Orbit lines to get different "arrangements",
                especially by inverting the Soprano and Tenor voices.
           4. This is where you will discover that
                 Swings and Circles are the "building blocks" of Harmony
                    and that most progressions (and chord patterns) will be found within them.
           5. You will be dealing with a variety of possibilities.

Real and Deceptive Triads
Let's look at these different possibilities -
      (a) 2 Real Triads, from 2 different Tetrads,
           presented as a Triad progression by fifth, in all 3 pages.
      (b) 2 Deceptive Triads, from 2 different Tetrads,
           presented as a Triad progression by ascending second in the Swings.
      (c) the Real Triad of one Tetrad followed by the Deceptive Triad of another Tetrad,
           presented as a Triad progression by ascending second in the Swings,
           but also as Triad progressions by descending third in the Circles.
      (d) the Deceptive Triad of one Tetrad followed by the Real Triad of another Tetrad,
           also presented as a Triad progression by ascending second, in Swings and Circles.
      (e) the Real Triad followed by the Deceptive Triad of the same Tetrad,
           will look like a Triad "progression" by ascending or descending third.
      (f) the Deceptive Triad followed by the Real Triad of the same Tetrad,
           will also look like a Triad "progression" by ascending or descending third.
      These last 2 cases (e) and (f) are not present in your 3 pages,
           but will be explained in 3. of the following paragraph "Triad Progressions".
     We suggest that you start with the assumption that the Tetrads are in the major nucleus (V7 ,I6 ,IV6 ,I7 ),
           unless you find something that suits your fancy in one of the Circle examples.

     Now let's see how your homework is presented to you
           and help you to identify Real and Deceptive Triads -

Triad Progressions
      1. Triad progressions by fifth are between 2 Real Triads
          by ascending fifth there are 2 progressionsI-VandIV-I
               which you will find in the Swings, at the end of 7. S3aRD and 8. S3bRD,
                as well as in the Extended Swings, in the center of CS2R,
           by descending fifth there are all 7 possible progressionsI-IV-VII-III-VI-II-V-I
               which you will find in the Circle, in 2.C2R and 5. C2Ra
                     (with Voice-leading C and with Voice-leading A respectively).
       2. Triad progressions by second have at least 1 Deceptive Triad involved,
          by ascending second there are all 7 possible progressions,
                 I-ii-iii-IVin 8.S3bRD,V-vi-vii-Iin 7.S3aRD, both in the Swings,
                 iii-IV,ii-III,i-II,vii-I, in 3. C2DR,vi-VII,v-VI,iv-Vin 4. C2RD, both in the Circle, as well as
                 iv-Vin CS2Rx in the Extended Swings.
           by descending second, triad progressions in Root Position are never totally successful,
                     and remain awkward at best,
                because one of the 2 Triads should preferably be in First Inversion,
                     as we will later see in Lesson 3.
           Deceptive Triads resolve by "caving in", with the root and fifth moving toward each other,
                thus always forcing the Bass voice to move by ascending second.
           If the first Triad is Real, we have more leeway.
       3. Triad progressions by third are usually the 2 Triads of the same Tetrad,
               which may be presented in either order, Real-Deceptive or Deceptive-Real.
           A classical example is theI-iii-IVprogression
                in which we have the Real and Deceptive Triads of theI7 Tetrad
                     followed, evidently, by the Real Triad of theIV6 Tetrad.
                The following disposition is particularly popular, with good reason -
                          In the Soprano, the notes C-B-A, Orbit Line0(3)-3 / 2
                         In the Alto, the notes E-G-F, Orbit Lines2-1 / 1
                         In the Tenor, the notes G-G-C, Orbit Line1-1 / 0
                         In the Bass, the notes C-E-F, Orbit Lines0-2 / 1
                    In each voice, the notes of the Real and Deceptive Triads both resolve perfectly.
                     The Secondary Notes of the Tetrad, E and B, are in the extreme voices.
                     The Bass has the Root of each Triad, Real and Deceptive.
                          The Deceptive Triad could precede the Real Triad in theiii-I-IVprogression.
                Further examples will be seen later inComposition 3.
                    in which each Tetrad of a Circle is presented by both its Real and Deceptive Triads.
           However, we have found examples of Triad Progressions by descending third in the Circle -
                 IV-ii,III-i,II-vii, in 3. C2DR, and
                 I-vi,VII-v,VI-iv, in 4. C2RD,
                     in which the Real and Deceptive Triadsare in 2 different Tetrads.

Analysis and Summary

Voice-leading Resolution of a Deceptive Triad
          Example -iitoIoriitoiii(Dm to C or Dm to Em)
 1. First resolve the "cave-in" lines, the Root ascending a step and the Fifth descending a step,
      producing an interval of a third on the following Triad of resolution.
           D to E and A to G, producing the third EG.
 2. The 2 "thirds" of the Deceptive Triad are free,
      one will go by step to double the appropriate note of the following Triad,
           F to G, and
      the other will go by skip of a fourth (or fifth) to the note which completes the following Triad,
           F to C for the progressioniitoIor F to B for the progressioniitoiii.
 3. The disposition in the performance voices (SATB) is up to you -
      D to E will give you Root Position for the Triadsiitoiii, and
      F to C will give you the Fundamental Bass for the TetradsIV6 toI7
          but the Triadiiwill be in first inversion (with F in the Bass).

Voice-leading Resolution of a Real Triad
          Example -ItoiiorItoIV(C to Dm or C to F)
 1. First resolve the third without a skip (only by step or by remaining on the same note),
           E to F or to D forItoii, E to F forItoIV,
 2. The Root and Fifth (either one may be doubled) are free to produce
      the 2 missing notes of the following Triad, as well as its appropriate doubling.
 3. Check for consecutive or exposed fifths and octaves
      as you dispose the lines in the performance voices.

A Given Bass

You may be asked to add three parts (Soprano, Alto, and Tenor) to a given Bass,
           using only triads in root position.
 This should not be too difficult because the Bass Voice will indicate the root of each triad.
      1. Inscribe the Roman numeral of each triad below the Bass voice
           and proceed as you did in the "Isolated Progressions" section,
                especially the "Triad Progressions" paragraph.
      2. Identify the Real and Deceptive Triads
           and work out the Orbit Lines for the 3 upper voices.
      3. First, choose the Orbit Line best suited to the Soprano voice,
           one which has nice melodic contours,
                which has the tonic note at the end but preferably not in the middle.
      4. Then dispose the other 2 Orbit Lines in the Alto and Tenor Voices.

Composition

You may be asked to "compose" something for 4 voices (Soprano, Alto, and Tenor and Bass) -
           This should be fun. You can choose material from any of your 3 pages.




More building
     1. In the page of Swings -
           First, take example 7. S3aRD and repeat it (vi-vii-I-V-vi-vii-I-V)
           then, remove the secondviand add aIat the end (vi-vii-I-V-vii-I-V-I).
                You should be able to dispose the last chord to come to a definitive ending.
           Finally, transpose this to a more suitable key for performance, in F or G.
      2. In the page of the Circle -
           Just paste examples 3. C2DR and 4. C2RD together and leave it in C.
                The first example, cadencing weakly (vii-I), forms what we call the Antecedent Phrase,
                     while the second, the Consequent Phrase, cadences strongly (V-I),
                          which is normal and desirable (iii-IV-ii-III-i-II-vii-I, I-vi-VII-v-VI-iv-V-I).
      3. Also in the page of the Circle with examples 3. C2DR and 4. C2RD -
                Instead of pasting them together, end to end,
           use both the Real and Deceptive Triads of each Tetrad in only 1circle,
                interlocking the 2 examples to produceI-iii / IV-vi-VII-ii / III-v-VI-i / II-iv-V-vii / I.
           This should not be too difficult -
                In the Bass voice, start with the Bass of C2RD and insert the Bass of C2DR,
                In the Alto voice, start with the Tenor of C2RD (8va) and insert the Soprano of C2DR,
                In the Soprano voice, start with the Soprano of C2RD and insert the Alto of C2DR (8va),
                Keep the Tenor of C2DR in note-values of double length with each odd note 8va.
                     The Soprano and Alto voices are in canon.
           Finally, transpose this to Bb, a more suitable key for performance.
      4. Also in the page of the Circle -
           Take example 5. C2Ra and leave it as is in C.
      5. Also in the page of the Circle -
           Take example 5. C2Ra and leave it in C, but making the following changes -
                place it in 3/4 time, with aQuarter notepick-up and aHalf noteat the end,
                change the Real TriadsVIIandIIto Deceptive Triadsiiandiv,
                     producing the chord patternI / IV-ii-III / VI-iv-V / I,
                with the appropriate adjustments to the 4 voices on the 2 Deceptive Triads -
                     the Bass Voice will have the root of each Triad,
                     the Soprano Voice will return to its original form in C1a,
                     the Alto Voice must leave the D and the F (now in the Bass),
                     the Tenor Voice must make the1(0)substitution (replace the Root by the Fifth).
      6. In the page of Extended Swings -
           First, take the Orbit Lines of the beginning of example 2. CS2R (I-IV-I-V)
                and add the Orbit Lines of 3. CS2Rx (I-IV-V-I), one Orbit Line Lower than those of CS2R,
                     so that the lines all go down a little during the completeI-IV-I-V-I-IV-V-I.
           Then, choose the Orbit Line which "closes" (ends on the tonic note C), place it in the Soprano,
                and place the 2 other lines in the Alto and Tenor, in close position.
           Finally, transpose this to a more suitable key for performance, in F or G.
      7. It is possible to do something quite neat to the previous example by borrowing from the Circle page.
           The fifth chord ofI-IV-I-V-I-IV-V-Iis a Real Triad ofI,
                which can easily be replaced by its corresponding Deceptive Triadiii,
           producingI-IV-I-V-iii-IV-V-I,
                and you can see how to voiceV-iii-IVin either 3. C2DR or 4. C2RD of the Circle page.
                     The last 3 chords of 3. C2DR give the correct notes for the Orbit Lines
                          (without the # on the F).
           NOTE how this "improves" both the Soprano and Bass voices,
                leaving the Alto and Tenor voices unobtrusive and even smoother.

We hope that our indications have been both clear and helpful.
      Let usknowif they have not.

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