Melody/Melo-Lines/Analysis

Procedures

There will be two classes of Procedures in this Method of Analysis -
     two Procedures of Analysis itself,
          one for the Melo-rhythm, and one for the Melo-harmony (the Chord Patterns), followed by
     two Procedures of Observation,
          one for the Entities, and one for the Symmetries.

Analysis of the Melo-rhythm
Melody is rhythmically structured as verse, not as prose,
     and should therefore be disposed on paper as verse, not as prose.
Passing from one staff-line to another should correspond to the breaths,
     and not when one runs out of space.

1. The first step of analysis will be to disregard whatever musical text we have before us,
     and establish ALL the rhythmic levels with Footsies.
          This will enable us to verify the position of bar-lines, especially at Level 0.
2. You may then wish to look at the Graphics again
     to refresh your memory concerning the "look" of the Rhythm.
3. Another look at the Melo-rhythm boxes might also be useful.
4. Placing bar lines of different "intensity" (dashed, single, double, triple, ... )
     helps to situate the larger Rhythmic Levels.
5. One must place the same number of Level 0 cells on each staff-line,
     only 1 cell if it is very subdivided,
     2 cells is the most common number, but
     there may be 4 cells if there are few subdivisions (notes).

Analysis of the Melo-harmony
Now that we have a well-disposed copy of our song,
     we can proceed to the genealogical process of retracing its harmonic origins.
          In a generative theory, one does not harmonize a melody,
     one seeks the Chord Pattern whose Voice-leading Lines produced the Melody, and
          the Melo-lines Table, presented in the Preface,
               will enable us to retrace the Chord Pattern which generated the Melody.

Observation of the Entities
A simple matter, since Entities have been clearly defined in each of Melody's components -
     Melo-rhythm, Melo-harmony, and Melo-lines.
          The more variety in the size (length) of these Entities, the better.

Observation of the Symmetries
Also, a fairly simple matter.
     Here, moderation is the ideal -
          avoiding scarcity and excess as much as possible.

Twinkle, Twinkle, Little Star

Analysis of the Melo-rhythm

Beware ! You might very well find the song looking like this -

analtwinkle01

The first thing to do is to verify the "grammar" and "spelling" of this example.
     The best way is to forget it completely and start all over.
          How ? Back to the footsies !
Singing the song with the footsies at all the levels will remind us -
     that Level 0 is at 0 + 2 (no pick-up and 2 notes in the first Off-beat) and
     that bar-lines at Level 0 will occur just before the Right Foot strikes,
          (the first bar-line will be just before the third note of the song).
All the bar-lines of the original copy are misplaced.
     Remember that the Cells of Level 0 always have a Bar-line in their center
          between the Off-beat and the Beat.
You might also want to check, and review, the Graphics and the Melo-rhythmic boxes of this song.

Now concerning the disposition of the staff-lines, which should not be of any arbitrary length -
     Place the right number of cells (no more, no less) on each staff-line, the same number on each line.

analtwinkle02

Note -
     1. There are 4 cells in each of the 3 staff-lines.
     2. The first and third staff-lines are what are called "A" sections, Entities in the three components.
          The second staff-line is what is called a "B" section, the "Bridge" of this song,
               which is not an Entity in the Melo-harmony (ending on a DOMINANT chord).
     The complete song has what is called an "ABA" form
          which is an "AABA" with the first "A" removed.
The bar-lines -
     at Level -1, the bar-lines are dashed,
     at Level 0, the bar-lines are solid (single),
     at Level +1, the bar-lines are double,
     at Level +2, the bar-line is triple (end of the second staff-line),
     at Level +3, the bar-line is quadruple (end of the first staff-line),
     at Level +4, the bar-line is quintuple (a heavy line, end of the third staff-line).
Note the bar-lines of the first staff-line -
     single, dashed, double, dashed, single, dashed, quadruple,
          the last bar-line is NOT triple as one would expect.
               That would have happened in the first staff-line (had it remained in the song).
We now have a reliable rhythmical analysis of the song.

Analysis of the Melo-harmony

analtwinkle03

The A sections
1. In the Melody, we will start with the last cell (end of the third staff-line), in which the notes are D / C.
     In the table, we see that the notes D / C
          are the line Orbit 1 to Orbit 1
          in the Chord PatternM4, DOMINANT / TONIC.
     When this Chord Pattern is opened (on the bottom harmonic staff), it will become M34 at Level +1
          with a long DOMINANT chord which will occupy the space of the
               fourth, fifth, sixth, and seventh chords of the top harmonic staff.

analtwinkle04

2. In the Melody, we will now look at the center of the pattern, the second cell, in which the notes are A / G.
     In the table, we see that the notes A / G
          are the line Orbit 2 to Orbit 1
          in the Chord Pattern M6, COUNTER / TONIC.
     We now have a TONIC as fourth chord (on the top harmonic staff),
          and the M34 becomes an M54 at Level +1
               with a TONIC tenant chord on the first half of the DOMINANT chord (on the bottom harmonic staff).

analtwinkle05

3. In the Melody, we will now look at the two remaining cells -
     In the first cell, in which the notes are C / G, we evidently have
          the Chord Pattern M5, TONIC / TONIC
               both notes Orbit 1 (on account of the Metamorphosis 1 at the bar-line).
     However, in the third cell, in which the notes are F / E, we could find in the table either -
          the line Orbit 3 to Orbit 2,
               in the Chord Pattern M4, DOMINANT / TONIC, or
          the line Orbit 1 to Orbit 2,
               in the Chord Pattern M6, COUNTER / TONIC.

analtwinkle06

4. We are clearly dealing with the consequent of the Harmony (the last two cells),
     and we must find a "consequent-oriented" solution in the table.
          The notes F / E are placed farther right (on the "consequent" side)
               in the M6, COUNTER / TONIC pattern than in the M4 pattern.
     The complete Chord Pattern is thus -
          M5664, TONIC / TONIC \ COUNTER / TONIC \ COUNTER / TONIC \ DOMINANT / TONIC.
We now have all the information we need to place the Orbit colors on the musical text of the "A" sections.

analtwinkle07

The B section
1. In the Melody, we will start with the last cell (end of the second staff-line), in which the notes are E / D,
     In the table, we see that the notes E / D
          are the line Orbit 2 to Orbit 1
          in the Chord Pattern M3, TONIC / DOMINANT.
2. The same will apply to the second cell, in the center, in which the notes in the Melody are also E / D,
     because the Bridge consists of two identical 2-cell sections.

analtwinkle08

3. Because, being parts of a Bridge, they are both "antecedent-oriented",
          the first and third cells will also be Chord Pattern M3, TONIC / DOMINANT
     with the Orbit 0 to Orbit 3 line, (on the left in the table),
          producing the line Orbit 0 to Orbit 3, and Orbit 2 to Orbit 1 in each of the 2 sections,
               which we saw in the Voice-leading A Swing.

analtwinkle09

Complete Analysis
All the Rhythmical analysis is in the bar-lines and disposition,
     all the Harmonic analysis is on the Harmonic Staves, and
          the Voice-leading is in the Orbit colors.

Observation of the Entities

In the A sections
In the Melo-rhythm, we have two identical 2-cell entities 2x (H1F H1M).
In the Melo-harmony, we have one 4-cell entity M5664.
In the Melo-lines, we have two 2-cell entities
          Orbit 1 to Orbit 1, Orbit 2 to Orbit 1, and
          Orbit 1 to Orbit 2, Orbit 1 to Orbit 1.
     A reasonable variety, with the Melo-harmonic entity longer than those of the two other components.

In the B section
In the Melo-rhythm, again we have the two same 2-cell entities 2x (H1F H1M).
In the Melo-harmony, we have no true entities because we have no strong M4 pattern.
     however, we do have four identical, weak M3 patterns.
In the Melo-lines, we have two identical 2-cell entities
          2x (Orbit 0 to Orbit 3, Orbit 2 to Orbit 1)
     Here again, a reasonable variety.

Observation of the Symmetries

In the A sections
In the Melo-rhythm, the exact symmetry between the two 2-cell entities is not in itself excessive.
In the Melo-harmony, there is no appreciable symmetry within its single 4-cell entity
     only the repeat in the second "A" at the end, which is very welcome.
In the Melo-lines, there is no appreciable contour, melodic symmetry between the 2-cell entities.

In the B section
In the Melo-rhythm, having exactly the same entities (H1F H1M) as in the "A" sections is truly excessive
          six times in all, without the slightest variation.
     The French version (Ah, vous dirai-je, maman) has Feminine Rhymes
               on the second and fourth cells of the Bridge
          which relieve the excessive repetition of the H1F H1M pattern.
     We might consider suggestions of improvement when we are ready for Analysis.
In the Melo-harmony, the repeat of the M3 pattern is hardly excessive, being a weak progression.
In the Melo-lines, the orbit chain 0-3-2-1 lends itself to rich, polyphonic treatment, with its natural canon.

Between the A and B sections
The symmetry here is truly remarkable, between the last half of the "A" section and the Bridge.
     The repeat of the notes F-F / E-E \ D-D / C, in the last half of the "A" section,
           a diatonic second higher as G-G / F-F \ E-E / D, in the Bridge,
               creates considerable unity between the "A" and "B" sections.
          A process which should certainly be used more often.

If you already know how Generation works, you might like to see it for this song.

Polly, Put The Kettle On

Analysis of the Melo-rhythm

This song is usually well-written with Level -1 bars of 2/4 or 2/2 time.
     You can confirm this by singing it and relying on the footsies ! to find Level 0
          with no pick-up and 4 notes in the first Off-beat (the first bar of Level -1).
You might also want to check, and review, the Graphics and the Melo-rhythmic boxes of this song.

analpolly01

This 2-line disposition is very useful to spot the Symmetry of the Masculine and Feminine Rhymes.
     There are 2 cells in each of the 2 staff-lines.
The bar-lines -
     at Level -1 (at the center of each staff-line), the bar-lines are dashed,
     at Level 0 (at the beginning of each staff-line), the bar-lines are solid (single),
     at Level +1 (at the end of the first staff-line), the bar-line is double,
     at Level +2 (at the end of the second staff-line), the bar-line is triple,
We now have a reliable rhythmical analysis of the song.

Analysis of the Melo-harmony

This song is a little more complicated. We will maintain the same order of the steps.

analpolly02

1. We start with the very last cell (at the end of the second staff-line) -
     In the Melody, we find the notes B / C (surrounding the bar-line).
     In the table, we see that the notes B / C
          are the Orbit 2 to Orbit 1 line
               in the M4 Chord Pattern, DOMINANT / TONIC.
                    (See "5." for analysis of the other notes in this cell.)
2. Next we look at the second cell (in the center of the song, at the end of the first staff-line) -
     In the Melody, we find the notes C / B (surrounding the bar-line)
     In the table, we see that the notes C / B
          are the Orbit 1 to Orbit 2 line
               in the M3 Chord Pattern, TONIC / DOMINANT,
     but we also find the note D (with a non-chordal tone E) in the Off-beat of the cell
          which lead us to believe that the ANTE-1 (probably dominantized) is involved,
          and that we are dealing with the Orbit 3 to Orbit 2 line
               in the M1 Chord Pattern, ANTE-1 / DOMINANT.
3. Next we look at the first cell (at the beginning of the first staff-line) -
     In the Melody, we find the notes G / E, C ,
          the M5 Chord Pattern, TONIC / TONIC.
               (there are no Orbit Voice-leading lines when we remain on the same chord).
     The A and F are evidently Non-chordal Tones and
          the E is, in all probability, a double Non-chordal Tone of the C.
4. Finally, the third cell (at the beginning of the second staff-line) -
     is identical to the first cell,
          the M5 Chord Pattern, TONIC / TONIC.
5. On the Off-beat of the fourth cell, we also find the note A which indicates an ANTE-1 tenant chord,
     in which the note A is Orbit 1 substituting for Orbit 3,
          resolving to the note B Orbit 2 of the DOMINANT.
     In such a case, it is recommended to have another tenant chord (an ANTE-2)
          at the end of the Beat of the previous (third) cell.
     It might seem surprising to see this bar (E, C, C, E) all on Orbit 1,
          the E is, as we already know, a double Non-chordal Tone of the C, on the chord of C, and
          the following C is also a double Non-chordal Tone of the E, on the chord of Am.
We now have all the information we need to place the Orbit colors on the musical text of the song.

analpolly03

Observation of the Entities

In the Melo-rhythm, we have one 4-cell entity K2F= K2F= K2F= pK1M.
In the Melo-harmony, we have one 4-cell entity M5154.
In the Melo-lines, we have four 1-cell entities,
     a reasonable variety.

Observation of the Symmetries

In the Melo-rhythm, there is -
     exact symmetry between the first three cells 3x (K2F=),
          which makes the abrupt change of the fourth cell imperative (pK1M).
In the Melo-harmony, there is exact symmetry between the first and thid cells M5154.
In the Melo-lines, there is exact melodic symmetry in the first three cells.
     The symmetry is almost excessive in the Melo-rhythm and Melo-lines.

If you already know how Generation works, you might like to see it for this song.

Red River Valley

Analysis of the Melo-rhythm

Beware of these old "folk-songs" ! We have seen this one written with very small bars, at Level -2.
     You are far better to sing it and rely on the footsies to find Level 0
          with 2 notes pick-up and 6 notes in the first Off-beat (the first bar of Level -1).
Write your own version, with bars of Whole note at Level -1.
You might also want to check, and review, the Graphics and the Melo-rhythmic boxes of this song.

analredriver01

This 2-line disposition is very useful to spot the Symmetry of the Masculine and Feminine Rhymes.
     There are 2 cells in each of the 2 staff-lines.
The bar-lines -
     at Level -1, the bar-lines are dashed,
     at Level 0 (at the center of each staff-line), the bar-lines are solid (single),
     at Level +1 (at the end of the first staff-line), the bar-line is double,
     at Level +2 (at the end of the second staff-line), the bar-line is triple,
We now have a reliable rhythmical analysis of the song.

Analysis of the Melo-harmony

This is a simple song to analyse harmonically. The important thing is to remember the order of the steps.

analredriver02

1. We start with the very last cell (at the end of the second staff-line) -
     In the Melody, we find the notes D / C (surrounding the bar-line).
     In the table, we see that the notes D / C
          are the Orbit 1 to Orbit 1 line
               in the M4 Chord Pattern, DOMINANT / TONIC.
                    (See "5." for analysis of the other notes in this cell.)
2. Next we look at the second cell (in the center of the song, at the end of the first staff-line) -
     In the Melody, we find the notes E / D (surrounding the bar-line)
     In the table, we see that the notes E / D
          are the Orbit 2 to Orbit 1 line
               in the M3 Chord Pattern, TONIC / DOMINANT,
     but we also find the note C in the Off-beat of the cell
          which is the Orbit 1 to Orbit 1 line
     and the note G in the Off-beat of the cell
          which is the Orbit 0 to Orbit 1 line.
     This second cell has three orbits on the Off-beat, (Orbit 1, Orbit 2, and Orbit 0)
          all resolving to Orbit 1 on the Beat.
3. Next we look at the first cell (at the beginning of the first staff-line) -
     In the Melody, we find the notes E / C (surrounding the bar-line),
          the M5 Chord Pattern, TONIC / TONIC.
               (there are no Orbit Voice-leading lines when we remain on the same chord).
     The Ds are evidently Non-chordal Tones.
4. Finally, we look at the third cell (at the beginning of the second staff-line) -
     In the Melody, we find the notes E / F (surrounding the bar-line).
          discounting the note G, of course, which is an obvious Non-chordal Tone of F.
     In the table, we see that the notes E / F
          are the Orbit 2 to Orbit 1 line
               in the M7 Chord Pattern, TONIC / COUNTER,
     but we also find the note C in the Off-beat of the cell
          which is the Orbit 0 to Orbit 1 line.
     This third cell has two orbits on the Off-beat, (Orbit 2 and Orbit 0)
          both resolving to Orbit 1 on the Beat.
5. The TONIC tenant chord on the Off-beat of the fourth cell
          (in which the note C is Orbit 1, and the note B a Non-chordal Tone)
     is not absolutely necessary, and the DOMINANT chord could occupy the whole Off-beat,
          in which case the note B would be Orbit 2,
               also resolving to Orbit 1,
          (and the note C would be a Non-chordal Tone).
     With the Metamorphosis 1 on the TONIC tenant and the Non-chordal tones,
          the whole bar has been colored as Orbit 1.
We now have all the information we need to place the Orbit colors on the musical text of the song.

analredriver03

Complete Analysis
All the rhythmical analysis is in the bar-lines and disposition,
     all the Harmonic analysis is on the Harmonic Staves, and
          the Voice-leading is in the Orbit colors.

Observation of the Entities

In the Melo-rhythm, we have two identical 2-cell entities 2x (p2H3F-- p2H3M).
In the Melo-harmony, we have one 4-cell entity M5374.
In the Melo-lines, we have four 1-cell entities
     Orbit 2 to Orbit 1, on the M5 (the same chord),
     Orbit 2 to Orbit 1, on the M3,
     Orbit 2 to Orbit 1, on the M7, and
     Orbit 1 to Orbit 1, on the M4.
          The first cell could very well be considered as only Orbit 1,
               with the note E a double Non-chordal Tone (ss3) of the C.
The maximum possible variety,
     with the Melo-harmonic entity longer than those of the two other components.

Observation of the Symmetries

In the Melo-rhythm, there is -
     not only exact symmetry between the two 2-cell entities 2x (p2H3F-- p2H3M),
     but Off-beat symmetry between the four cells p2H3,
          rich, but hardly excessive.
In the Melo-harmony, there is no appreciable symmetry within its single 4-cell entity M5374.
In the Melo-lines, there is no appreciable contour, melodic symmetry between the four 1-cell entities.
     The symmetry is mostly in the Melo-rhythm.

If you already know how Generation works, you might like to see it for this song.

Rock-A-Bye, Baby

Analysis of the Melo-rhythm

This song is usually written in 6/8 time, starting on the first beat with the bar-lines misplaced, but
          we will immediately pass to a well-written version with Level -1 bars of 3/4 time.
     You can confirm this by singing it and relying on the footsies ! to find Level 0
          which is at 0 + 3 (with no pick-up and 3 notes in the first Off-beat).
You might also want to check, and review, the Graphics and the Melo-rhythmic boxes of this song.

analrock01

This disposition is useful to spot the Symmetry between the two lines.
     There are 4 cells in each of the 2 staff-lines, eight cells in all.
The bar-lines -
     at Level -1, the bar-lines are dashed,
     at Level 0, the bar-lines are solid (single),
     at Level +1, (in the middle of each staff-line), the bar-lines are double,
     at Level +2 (at the end of the first staff-line), the bar-line is triple,
     at Level +3 (at the end of the second staff-line), the bar-line is quadruple.
We now have a reliable rhythmical analysis of the song.

Analysis of the Melo-harmony

This one will not be as easy as the others and patience will be required.

analrock02

1. We start with the eighth and last cell (at the end of the second staff-line) -
     In the Melody, we find the notes B / C (surrounding the bar-line).
     In the table, we see that the notes B / C
          are the Orbit 2 to Orbit 1 line
               in the M4 Chord Pattern, DOMINANT / TONIC
     but we also find the note D
          which is Orbit 1 also resolving to Orbit 1,
     as well as the note A which is p2 of B.
          We have two Melo-lines Orbit 1 and Orbit 2
               both resolving to Orbit 1.
          A Tenant Chord might be advisable here as we will later see (in 9.).
2. Next we look at the fourth cell (in the center of the song, at the end of the first staff-line) -
     In the Melody, we find the notes A / G (surrounding the bar-line).
     In the table, we see that the notes A / G
          are the Orbit 2 to Orbit 1 line
               in the M6 Chord Pattern, COUNTER / TONIC.
     This is where we must be wary because there is little chance of this being a valid choice.
          We will therefore move on and return to this fourth cell later (in 7.).
3. Let's look at the second cell (in the middle of the first staff-line) -
     In the Melody, we find the notes C / B (surrounding the bar-line),
     In the table, we see that the notes C / B
          are the Orbit 1 to Orbit 2 line
               in the M3 Chord Pattern, TONIC / DOMINANT,
     but we also find the notes E and G in the Off-beat of the cell
          which are pp3 and Orbit 0 itself,
               resolving to Orbit 2 on the Beat.
          Here we have two Melo-lines Orbit 0 and Orbit 1
               both resolving to Orbit 2.
4. The first cell is completely on notes of the Tonic chord (E, G, E / D, C, with the D s2 of the C)
               evidently the M5 Chord Pattern, TONIC / TONIC.
5. The fifth cell is identical to the first, pattern M5 with the same Melo-lines,
     and the sixth cell is identical to the second, pattern M3.
6. The third cell is completely on notes of the DOMINANT chord (F, G, F / E, D, with the E s6 of the D),
               evidently the M2 Chord Pattern, DOMINANT / DOMINANT.
7. We are now in a position to re-evaluate the fourth cell which cannot be M6 as we suspected,
     and must be M4 DOMINANT / TONIC,
          regardless of the notes we find in the melody which strongly suggest M6.
               Much more will be said of this (possibly excessive) use of Non-chordal Tones in Analysis.
8. And, finally, for the seventh cell, we find the notes F / E (surrounding the bar-line).
     In this specific rhytmic position, just before the final DOMINANT / TONIC of the eighth cell,
          it is preferable to have the "cadential 64 chord" (TONIC, with Bass G) preceded by the COUNTER.
     But we also have the notes G and C in the Off-beat,
          in this rhythmic position, clearly a "normal" TONIC chord.
9. Now back to the last cell,.
          in which an ANTE-1 tenant chord (possibly dominantized) will precede the DOMINANT.
     A lot of tenant chords in the last two cells, the perfect place to put them, at the end of the song.
The complete pattern is thus M5324 5364
     TONIC / TONIC \ TONIC / DOMINANT \ DOMINANT / DOMINANT \ DOMINANT / TONIC
     TONIC / TONIC \ TONIC / DOMINANT \ (TONIC) - COUNTER / TONIC \ (ANTE-1) - DOMINANT / TONIC.
          C / C \ C6 / G \ G / G7 \ G7 / C \ C / C \ C6 / G-G/7 \ C/E-F6 / C/G \ D7-G7 / C
               The most complex pattern in this group of seven songs, with several tenant chords.
We now have all the information we need to place the Orbit colors on the musical text of the song.

analrock03

Observation of the Entities

In the Melo-rhythm, we have four identical 2-cell entities 4x (K2F+ K2M).
     with a welcome added pick-up between the last two entities,
          which acts as fusion between these two entities, producing a MI-MI-MA.
In the Melo-harmony, we have two similar 4-cell entities M5324 and M5364.
In the Melo-lines, we have one 8-cell entity -
     the fourth cell ends on Orbit 0 and the eighth cell ends on Orbit 1.
Three different sizes of Entities - a top score !.

Observation of the Symmetries

In the Melo-rhythm, there is -
     exact symmetry between the four 2-cell entities (two per staff-line),
          plus a bonus pick-up between the last two entities.
     However, the fusions are not constant where they should be -
          The Beat of the first cell has a Feminine Rhyme, while
               the Beat of the fifth cell has a Masculine Rhyme with a Pick-up, and
          the Beat of the third cell has a Masculine Rhyme with a Pick-up, while
               the Beat of the fifth cell has a Feminine Rhyme.
In the Melo-harmony, there is a repeat of the same pattern in aA and aC both M53,
     the cAM24 and cCM64, being different,
          the best place to present a change.
In the Melo-lines, there is an exact repeat of aA and aC, but
     cA and cC are quite different.
All in all, despite some irregularities, a fairly good score.

If you already know how Generation works, you might like to see it for this song.

Oh Where, Oh Where, Is My Little Dog Gone?

Analysis of the Melo-rhythm

This song is usually well-written with Level -1 bars of 6/8 time.
     You can confirm this by singing it and relying on the footsies ! to find Level 0
          which is at 1 + 5 (with 1 note pick-up and 5 notes in the first Off-beat).
You might also want to check, and review, the Graphics and the Melo-rhythmic boxes of this song.

analwhere01

This disposition is useful to spot the Symmetry between the two lines.
     There are 2 cells in each of the 2 staff-lines.
The bar-lines -
     at Level -1, the bar-lines are dashed,
     at Level 0, the bar-lines are solid (single),
     at Level +1 (at the end of the first staff-line), the bar-line is double,
     at Level +2 (at the end of the second staff-line), the bar-line is triple,
We now have a reliable rhythmical analysis of the song.

Analysis of the Melo-harmony

No big problem here if we follow the order of the steps.

analwhere02

1. We start with the fourth and last cell (at the end of the second staff-line) -
     In the Melody, we find the notes D / C (surrounding the bar-line).
     In the table, we see that the notes D / C
          are the Orbit 1 to Orbit 1 line
               in the M4 Chord Pattern, DOMINANT / TONIC
     but we also find the notes A and G in the Off-beat of the cell
          which are the s2 and Orbit 0 itself also resolving to Orbit 1,
     as well as the notes F and E which are ss7 and s6 of D.
          We have two Melo-lines Orbit 0 and Orbit 1
               both resolving to Orbit 1.
2. Next we look at the second cell (in the center of the song, at the end of the first staff-line) -
     In the Melody, we find the notes D / G (surrounding the bar-line)
          which are the Orbit 1 to Orbit 0 line
               in the M4 Chord Pattern, DOMINANT / TONIC
                    even if this orbit combination does not appear in the table
                         because it is not a resolution (only a Primary Note option).
     This might seem like no more than a hunch, but it is confirmed by the fact
          that only the last note (the Beat) of this cell is different from what we found in the fourth cell.
     These two cells obviously have the same Melo-harmony Pattern.
          This will be further confirmed by the pattern of the other two cells.
          Here again we have two Melo-lines Orbit 0 and Orbit 1
               this time resolving to Orbit 0.
3. Next we look at the first cell (at the beginning of the first staff-line) -
     In the Melody, we find the notes C / D (surrounding the bar-line),
     In the table, we see that the notes C / D
          are the Orbit 1 to Orbit 1 line
               in the M3 Chord Pattern, TONIC / DOMINANT,
     but we also find the notes G and E in the Off-beat of the cell
          which are Orbit 0 and Orbit 2,
               both resolving to Orbit 1 on the Beat.
          Here we have three Melo-lines Orbit 0, Orbit 2, and Orbit 1
               all resolving to Orbit 1.
4. Finally, we look at the third cell (at the beginning of the second staff-line) -
     which is identical to the first cell with the same M3 Chord Pattern, TONIC / DOMINANT.
The complete pattern is thus M3434
     TONIC / DOMINANT \ DOMINANT / TONIC \ TONIC / DOMINANT \ DOMINANT / TONIC.
We now have all the information we need to place the Orbit colors on the musical text of the song.

analwhere03

Observation of the Entities

In the Melo-rhythm, we have two almost identical 2-cell entities 2x (pK3F pK3M).
In the Melo-harmony, we have two identical 2-cell entities M3434.
In the Melo-lines, we have one 4-cell entity -
     Orbit 1 to Orbit 1, Orbit 1 to Orbit 0, and
     Orbit 1 to Orbit 1, Orbit 1 to Orbit 1.
The Melo-lines are different from the other two.

Observation of the Symmetries

In the Melo-rhythm, there is -
     almost exact symmetry between the two 2-cell entities (the two staff-lines),
          except for the process of fusion where,
               the first cell has Eight noteEight noteEight noteQuarter note as Feminine Rhyme on the Beat, and
               the third cell has Quarter noteEight noteQuarter note in the corresponding position.
          The 2-note pick-up before the third cell is not only justified but advantageous,
               making the Masculine Rhyme of the second cell shorter than that of the fourth cell.
In the Melo-harmony, there is a repeat of the same pattern M3434.
In the Melo-lines, there is an almost exact repeat of the two lines, except for the last note.
All in all, par for the course.

If you already know how Generation works, you might like to see it for this song.

Happy Birthday

Analysis of the Melo-rhythm

This song is usually well-written with Level -1 bars of 3/4 time.
     You can confirm this by singing it and relying on the footsies ! to find Level 0
          with 2 notes pick-up and 3 notes in the first Off-beat (the first bar of Level -1).
You might also want to check, and review, the Graphics and the Melo-rhythmic boxes of this song.

analbirthday01

This 2-line disposition is very useful to spot the MI-MI-MA structure of the song.
     There are 2 cells in each of the 2 staff-lines.
The bar-lines -
     at Level -1, the bar-lines are dashed,
     at Level 0 (at the center of each staff-line), the bar-lines are solid (single),
     at Level +1 (at the end of the first staff-line), the bar-line is double,
     at Level +2 (at the end of the second staff-line), the bar-line is triple,
We now have a reliable rhythmical analysis of the song.

Analysis of the Melo-harmony

This is a simple song to analyse harmonically. The important thing is to remember the order of the steps.

analbirthday02

1. We start with the very last cell (at the end of the second staff-line) -
     In the Melody, we find the notes D / C (surrounding the bar-line).
     In the table, we see that the notes D / C
          are the Orbit 1 to Orbit 1 line
               in the M4 Chord Pattern, DOMINANT / TONIC
                    (See "5." for analysis of the other notes in this cell.)
2. Next we look at the second cell (in the center of the song, at the end of the first staff-line) -
     In the Melody, once again we find the notes D / C (surrounding the bar-line)
     In the table, we see that the notes D / C
          are once again the Orbit 1 to Orbit 1 line
               in the M4 Chord Pattern, DOMINANT / TONIC,
     but we also find the notes A and G in the Off-beat of the cell
          which are the sus2 and Orbit 0 itself.
     This second cell has two orbits on the Off-beat, (Orbit 0, and Orbit 1)
          both resolving to Orbit 1 on the Beat.
     With two M4 Chord Patterns, we know that we have two Melo-harmonic Entities in this song.
3. Next we look at the first cell (at the beginning of the first staff-line) -
     In the Melody, we find the notes C / B (surrounding the bar-line),
     In the table, we see that the notes C / B
          are the Orbit 1 to Orbit 2 line
               in the M3 Chord Pattern, TONIC / DOMINANT,
     but we also find the notes A and G in the Off-beat of the cell
          which are the sus2 and Orbit 0 itself (as in the second cell).
     This first cell has two orbits on the Off-beat, (Orbit 0, and Orbit 1)
          both resolving to Orbit 2 on the Beat.
4. Finally, we look at the third cell (at the beginning of the second staff-line) -
     In the Melody, we find the notes C / B-A (surrounding the bar-line).
     In the table, we see that the notes B / A
          are the Orbit 3 to Orbit 2 line
               in the M7 Chord Pattern, TONIC / COUNTER.
          Observe, in the melody, that the note C (Orbit 0) is a substitution of the note B (Orbit 3),
               and that the note B is a sus4 of the note A (Orbit 2).
     But we also find the note G in the Off-beat of the cell
          which is the Orbit 1 to Orbit 1 line (resolving to the note F at the end of the Beat),
     as well as the note E in the Off-beat of the cell
          which is the Orbit 2 to Orbit 1 line (also resolving to the note F).
     This third cell has three orbits on the Off-beat -
          Orbit 1 and Orbit 2, which resolve to Orbit 1 on the Beat, as well as
          Orbit 0 which resolves to Orbit 2 on the Beat, substituting for Orbit 3.
5. The TONIC tenant chord on the Off-beat of the fourth cell
          is absolutely necessary here, and the DOMINANT chord only occupies the end of the Off-beat.
     In this TONIC tenant chord we find
          the note E, which is the Orbit 2 to Orbit 1 line, and
          the note C, which is the Orbit 1 to Orbit 1 line,
               from the TONIC to the DOMINANT (see the M3 Chord Pattern in the table).
We now have all the information we need to place the Orbit colors on the musical text of the song.

analbirthday03

Observation of the Entities

In the Melo-rhythm, we have a MI-MI-MA, composed of -
     two identical 1-cell entities 2x (p2K2M), and
     one 2-cell entity p2K2F p2K2M)
In the Melo-harmony, we have two 2-cell entities M34 and M74.
In the Melo-lines, we have two 2-cell entities -
     Orbit 1 to Orbit 2, Orbit 1 to Orbit 1 on the M34, and
     Orbit 0 to Orbit 2, Orbit 1 to Orbit 1 on the M74,
There is relatively little variety here,
     only the Melo-rhythmic MI-MI-MA, slightly different from the others, with its divided first half.
For all intents and purposes, we have a 2-piece pasting.

Observation of the Symmetries

In the Melo-rhythm, there is -
     not only exact symmetry between the two 1-cell entities (in the first staff-line), 2x (p2H2M)
     but also Off-beat symmetry between the four cells, all p2H2,
          rich, but hardly excessive.
In the Melo-harmony, there is a pasting of two patterns M34 and M74,
     no veritable symmetry.
In the Melo-lines, there is contour symmetry between the two 1-cell entities (in the first staff-line).
All in all, we find a reasonable quantity of symmetry in this song,
     in the Melo-rhythm and in the Melo-line contours.

If you already know how Generation works, you might like to see it for this song.

Down in The Valley

We have found two versions of this song. They both have the same Melo-rhythm and the same Melo-harmony, but not the same Melo-lines. The version presented here is different from the one presented in Rhythm-Transformations (used in the Kurt Weill opera), and has been chosen because the Melo-lines lead more directly to the Melo-harmony.

Analysis of the Melo-rhythm

Beware ! We found the song looking like this -

analvalley01

The bars are evidently too short and the staff-lines are not properly disposed.
     Go back to the footsies to establish Level 0
          which is at 3 + 5 (3 notes pick-up and 5 notes in the first Off-beat).
You might also want to check, and review, the Graphics and the Melo-rhythmic boxes of this song.

Place the right number of cells (no more, no less) on each staff-line, the same number on each line.

analvalley02

This disposition, with 1 cell in each of the 2 staff-lines, clearly shows the Symmetry between the two lines.
The bar-lines -
     at Level -1, the bar-lines are dashed,
     at Level 0 (at the end of the first staff-line), the bar-line is solid (single),
     at Level +1 (at the end of the second staff-line), the bar-line is double.
We now have a reliable rhythmical analysis of the song.

Note that there is a considerable change in note-values -
     we have substituted Sixteenth noteSixteenth noteSixteenth note for Quarter noteQuarter noteQuarter note start because the bars are so much longer.

Analysis of the Melo-harmony

This version of the song is easy to analyse harmonically, and there are only 2 cells.

analvalley03

1. We start with the last, second cell (at the end of the second staff-line) -
     In the Melody, we find the notes D / C (surrounding the bar-line).
     In the table, we see that the notes D / C
          are the Orbit 1 to Orbit 1 line
               in the M4 Chord Pattern, DOMINANT / TONIC,
     but we also find the note B in the Off-beat of the cell
          which is Orbit 2 also resolving to Orbit 1,
               the note F is a ss7 of D and the note C is a p4 of D.
     This second cell has two orbits on the Off-beat, (Orbit 2 and Orbit 1)
          both resolving to Orbit 1 on the Beat.
2. Next we look at the first cell (in the center of the song, at the end of the first staff-line) -
     In the Melody, we find the notes C / D (surrounding the bar-line)
     In the table, we see that the notes C / D
          are the Orbit 1 to Orbit 1 line
               in the M3 Chord Pattern, TONIC / DOMINANT,
     but we also find the note E on the Off-beat of the cell
          which is Orbit 2 also resolving to Orbit 1,
               the note D is a s2 of C.
     This first cell has two orbits on the Off-beat, (Orbit 2 and Orbit 1)
          both resolving to Orbit 1 on the Beat.
We now have all the information we need to place the Orbit colors on the musical text of the song.

analvalley04

Observation of the Entities

In the Melo-rhythm, we have 2 identical split cells, each fused together
          2x (p2F=p2M)2x (Sixteenth noteSixteenth noteSixteenth note \ Eight note. Eight note. ' Sixteenth noteSixteenth noteSixteenth note / Quarter note. ' )
     two identical 1-cell entities.
In the Melo-harmony, we have one 2-cell entity M34.
In the Melo-lines, we have two similar 1-cell entities -
     Orbit 2 and Orbit 1 to Orbit 1.
The Melo-harmony is different from the 2 others.

Observation of the Symmetries

In the Melo-rhythm, there is -
     not only exact symmetry between the two 1-cell entities (the two staff-lines), 2x (p2F=p2M)
     but exact symmetry between the four pick-ups, all Sixteenth noteSixteenth noteSixteenth note,
          rich, but hardly excessive.
In the Melo-harmony, there is only one pattern M34,
     with the inverse symmetry of its generation.
In the Melo-lines, there is contour symmetry between the Off-beats (with pick-up) of the two cells,
     and inverse symmetry between the Beats (with pick-up) of the two cells,
          the result of Melo-line symmetry (Orbit 2 and Orbit 1 to Orbit 1)
               and inverse Melo-harmony.
There is far more Symmetry here than there was in the first version of this song.

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