Harmony / Transformations / Metamorphoses / Individual / No. 1




Metamorphosis 1 is usually presented closed, in the last form.
     The chord changes:
          - its direction;
          - the swing to which it belongs
               (1 fifth away - with the metamorphosed chord in the interior position);
          - but not its position in the series of fifths
               (the chord keeps the sameFRAME);
          - the note which acts asOrbit 3(theMOTRIX);
               (from the sixth to the seventh, or from the seventh to the sixth);
          -Orbit 0andOrbit 1replace each other,
               the note which wasOrbit 0becomesOrbit 1(indicated01) and
               the note which wasOrbit 1becomesOrbit 0(indicated10).

The Voice-leading-C Circle

If we apply Metamorphosis 1 to each of a succession of chords, they will all progress in the same direction, with the same kind ofMOTRIXand eventually, after 7 chords, return to the original chord, producing what we call a "circle", with an exchange ofOrbit 0andOrbit 1on each chord. This is the circle which we saw in themajor modeand which we can now analyse and understand far better with the concept of Metamorphosis.

4modes06
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The Voice-leading for this Natural Canon circle is3-2,2-3, with01-10and10-01-
      3-2and01-10both descend in parallel motion, and
      2-3and10-01both remain in place.
           10-01is the realCOMMON TONE, but
           2-3is a deceptive common tone which is not even in tune inJust Intonation.
The Primary Notes have been colored according to the last form of the chord
     because theCOMMON TONEmust always be next to theMOTRIX
          The Fundamental Bass is evidently included.

Exchange of Orbits 0 and 1
Do not be surprised to see theCOMMON TONEof one chord (really10)
on the same note as thePROPER TONEof the next chord (really01).

New Options
The Voice-leading of these circles becomes clear with this orbit analysis
and this process enables us to apply other Voice-leading for circles,
not just the banalVoice-leading Cwhich we have here,
withOrbit 2procuringOrbit 3,2-3.

The Voice-leading-A Circle

WithVoice-leading A, the result is far more interesting and musically attractive.
     Line 1 (all fifths),
               the result of the Orbit line1-0(in this case01-01) remaining in the same voice,
          is usually omitted, being incompatible with Line 3, the Fundamental Bass (all roots).
     Line 2 is a Natural 3-part Canon composed of the Orbit chain3-2-10,
          which can be performed alone or with either of the other 2 lines (1 or 3).

harm2402
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The inversion ofOrbit 1andOrbit 0
     might confuse the identification of the Voice-leading:
The Voice-leading itself is clearly Voice-leading A with procuration0-3.
     However, we are not dealing with an ordinaryOrbit 0
          but with an originalOrbit 1which was transformed into anOrbit 0(10),
               more precisely, with procuration10-3.
The final result is quite similar to that which we had in the Swing
     withVoice-leading Band no Metamorphosis
          (a 3-part canon and an added different line).

The Voice-leading-B Circle

With Voice-leading B, the process is more delicate
     due to the difficulty of producing the required "V"-shape in the procuration ofOrbit 3.
Two solutions are possible -

harm2403
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Make the jump of a sixth fromOrbit 01A up toOrbit 3F (in the Soprano voice),
     feasible for one progression but difficult (not impossible) to repeat indefinitely, or

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Insert aSubstitution of Incompleteness 10(3)
     possibly followed byOrbit 3itself (C, B, first chord in the Tenor voice),
          which eliminates the need for the "V"-shape in the procuration ofOrbit 3
               because everything now moves by step (between neighboring notes).
We have here a Natural Canon Orbit line10 - 01 - 10(3)-3 - 2which flows through the four voices,
     quite similar to the Voice-leading-C Swing, but affecting 4 voices instead of only 2.

Once again, the inversion ofOrbit 1andOrbit 0
     might confuse the identification of the Voice-leading.
The Voice-leading itself is clearly Voice-leading B with procuration1-3.
     However, we are not dealing with an ordinaryOrbit 1
          but with an originalOrbit 0which was transformed into anOrbit 1(01))
               more precisely, with procuration01-3.
The final result is quite similar to that which we had in the Swing
     with Voice-leading A and no Metamorphoses (a 4-part canon).

Attack the next two Metamorphoses are your own risk.
The safest thing is to come back later when Metamorphoses 1 and 4 will be well digested.


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