Welcome mat
As you came on the site, you heard one of these clips, placed there to bid you welcome. We can’t tell you which one it was, because it was chosen at random. In any case, we thought that you might like to listen to some of the others and we made a list of them here for possible reference.

Where do they come from?
Some of them are examples which already appeared in various sections of the site, mostly from Harmonic Transformations, and have possibly been dressed up a little. Others are excerpts from complete works which make extensive use of a specific transformation or chord pattern.

Details
For each clip, you will find -
     (a) the title of the clip (click to hear)
     (b) the timing
     (c) details of form, orchestration, etc ... (click to see score)
     (d) the link to the technical structure involved
     (e) the origin of the clip.

Categories
These clips are divided into 3 categories -

A. Melody with Accompaniment
     This is probably the oldest and the most popular form of music.
     Folkloric music consists almost exclusively of melody,
          often (though not always) without accompaniment.
     Western classical music took a strong turn in this direction around 1750,
          and the romantic period thrived on it.

B. Polyphony
     Here, melody (or at least a melodic motif) passes from one voice to another.
          Canons, fugues, imitations, all belong to this category.
     Western classical music used polyphony extensively until about 1750,
          and it has not regained a comparable popularity since then.

C. Tapestry
     Background music, often of a repetitive nature,
          which one might compare to the design of fabric material.
     A fairly recent phenomernon, often found in film music,
          which would usually be considered design rather than art.

Juke Box

A1- Preludio Fresco- 26” - Violin with Bass and Rhythm -The Blues Chord
     From an original piece for solo violin,
          on the inverted 74 blues chord pattern, mounted on another inverted 74,
          and again mounted on another inverted 74.

A2- Reel Blue- 25” - Celtic Harp solo (original title - “Le maraudeur”) -The Blues Chord
     From an original piece in E major for diatonic accordion (or harmonica) in D major
     It is interesting to note that this clip (in C major) is written specifically for celtic harp
          and cannot be played on a concert double-action pedal harp.

A3- The last 5 (beg.)- 18” - Violin and Piano (original title - “Méditation élégiaque”) -Stretch Chords
     From an original piece (5’) which describes the last five minutes of a person’s life
     This piece is written with "stretch chords" all the way through.

A4- The Last 5 (end)- 20” From the same piece

A5- Pisa- 14” - A really irregular folktune for Violin and Piano
     From an original piece (5’), composed in a form ofRhythmic Transformations
          which produces a structure in Fibonacci numbers.
     The clip contains only the first 21 beats at the beginning.
          These 21 beats are divided in sections of 8-5-8, in turn subdivided in (3-2-3)-(2-3)-(3-2-3).
     You might enjoy following these divisions as you listen to the clip.

A6- Inverted Pisa- 14”
     The original piece is inchromatic minor(A minor) and contains a section inchromatic major(C major)
          which is heard here.

A7- Twinkle Limp 1- 15” -Twinkle, Twinkle, Little Starfor recorder and harp -Changing Meters
     The rhythmic transformation of ablation (with condensation) is applied to larger levels.
     The tune is presented complete, in its ABA form.
          In the A sections, an ablation forms ternary Level -10 and
          in the B section, an ablation forms ternary Level 0+1.
     The tune is walking on 3 legs all the way through.

A8- Twinkle Limp 1 Inversion- 15” - Indiatonic minor
     The same as the preceding clip,
          with both the melody and the harmony inverted.

A9- Twinkle Limp 2- 15” - A sequel, also for recorder and harp -Changing Meters
     The rhythmic transformation of ablation (with condensation) is applied to even larger levels.
     The tune is presented complete, in its ABA form.
          In the A sections, an ablation forms ternary Level 0+1 and
          in the B section, an ablation forms ternary Level +1+2.
     The tune is now stumbling on 3 legs.

A10- Twinkle Limp 2 Inversion- 15” - Indiatonic minor
     The same as the preceding clip,
          with both the melody and the harmony inverted.

A11- Birthday Limp 1- 13” -Happy Birthdayfor recorder and harp -Changing Meters
     The rhythmic transformation of ablation (with condensation) forms ternary Level 0+1,
          consisting of a bar of 6/8 followed by 2 bars of 3/4.
     The tune is walking on 3 legs all the way through as it was for "Twinkle Limp",
          all musical material is preserved by shortening the note-values.

A12- Birthday Limp 1 Inversion- 13” - Indiatonic minor
     The same as the preceding clip,
          with both the melody and the harmony inverted.

A13- Birthday Limp 2- 13” - A sequel, also for recorder and harp -Changing Meters
     The rhythmic transformation of ablation (with removal) forms ternary Level 0+1,
          consisting of 6 bars of 3/4 , instead of the original 8 bars.
     The tune is walking on 3 legs all the way through but, this time,
          musical material has been removed rather than shortening note-values.

A14- Birthday Limp 2 Inversion- 13” - Indiatonic minor
     The same as the preceding clip,
          with both the melody and the harmony inverted.

A15- Red River Limp 1- 20” -Red River Valley, for recorder and harp -Changing Meters
     The rhythmic transformation of ablation forms ternary Level -2-1,
          consisting of 8 bars of 3/4 , performed as 6/8,
               as is commonly done forDark Eyes,
          in theChromatic Minormode.

A16- Red River Limp 1 Inverson- 20” - In theChromatic Majormode
     The same as the preceding clip,
          with both the melody and the harmony inverted.

A17- Red River Limp 2- 17” - A sequel, also for recorder and harp -Changing Meters
     The rhythmic transformation of ablation forms Quinary Level -3-2-1,
          consisting of 8 bars of 5/8,
               with notes removed from the 6/8 version,
                    this one is all in eighth-notes.

A18- Red River Limp 2 Inverson- 17” - InChromatic Major
     The same as the preceding clip,
          with both the melody and the harmony inverted.

A19- Bonnie Circle- 32” -My Bonniefor clarinet and strings - on the Diatonic MajorCircle
     The original melody has been reconstructed in Fibonacci proportions
          a chorus composed of 8 bars (3+2+3),
                    reduced (by removal) from the original 16 bars of 2 choruses,
               on the chord pattern C7-F7-Bb - E7-Am - D7-G7-C,
          a verse composed of 5 bars (2+1+2)
                    reduced (by removal) from the original 8 bars of the verse,
               on the chord pattern B7-Em - A7 - D7-G(7), and
          a repeat of the chorus.

A20- Bonnie Circle Inverson- 32” - InDiatonic Minor
     The same as the preceding clip,
          with both the melody and the harmony inverted.

B1- Chopsticks- 20” - An unexpected 4-part canon -Diatonic Major
From a collection of English children’s songs, “TunesForTwo” Volume 1.
     This ubiquitous little piano piece (known in Russia as "Tati-Tati")
          is built on the DOMINANT/TONIC progression, all the way through (G7/C).
     In the first cell, we have the Orbit lines 0-0 and 3-2,
          and in the second cell, we have the Orbit lines 2-1 and 1-1,
               completing the 4-voice harmony (only the Fundamental Bass is missing).
     With this analysis, it is evident that the 2 cells can be played at the same time,
          preferably at different octaves, starting with the bass followed by the treble.

B2- Upside-down Chopsticks- 20” - An inverted version -Diatonic Minor
From the same collection of English children’s songs, “TunesForTwo” Volume 1.
     This inverted version is also built on the DOMINANT/TONIC progression, all the way through (Dm6/Am).
     In the first cell, we have the same Orbit lines 0-0 and 3-2,
          and in the second cell, we have the same Orbit lines 2-1 and 1-1,
     The voices are inverted, starting with the treble followed by the bass.

B3- Jacques & Pierrot- 24” - Quodlibet of the 2 most famous French songs -Rhythmic Levels
From a collection of French children’s songs, “2Voix1Mesure” Volume 1.
     The interest here lies in the different levels of the 2 songs.
     It would have been impossible to produce satisfactory polyphony between the two
          if "Frère Jacques" had not entered 2 notes ahead of "Au clair de la lune",
          in the form of a pick-up, because "Frère Jacques" is at a smaller rhythmic level.

B4- Little Bird- 22” - A 2-part canon by augmentation -Rhythmic Levels
     From a collection of French children’s songs, “2Voix1Mesure” Volume 4,
          original title "Ti zouazo" (in creole).
     This canon, like the "Jacques & Pierrot", also functions perfectly at 2 different levels,
          with 2 notes of the faster moving part acting as pick-up to the slower moving part.
     It also has the rare distinction of a repeat in the faster moving part.
     The canon takes place in 2 modes -
          first, in the diatonic minor mode and then in the diatonic major mode.

B5- Fanfare- 24” - 4-part canon for Brass with African drums -Chromaticism
     A combination of 3 forms ofChromaticism(Dominantization, Orbit 4, and Diminution),
          making all the voices completely chromatic (only semi-tones).

B6- Piano Slope- 22” - A constantly descending 4-part canon for Piano and Rhythm -
      Diminished Octaveson a DOMINANT-TONIC swing chord pattern.

B7- Chat- 30” - A quiet 4-way conversation -
     On alternating diminished seventh and augmented triadsonorities,
     melodic fragments, using Non-chordal Tones of the MEDIAN, pass from one voice to the other.

B8- Star Crossed- 30” - Two voices cross like stangers in the night -
     On the chord progression Bbm6/F/A7/Dm,
          the result ofMetamorphoses4 and 1 being applied to the same chord
               which is subsequentlydominantized,
     2 lines cross while 2 others complete the harmony in the middle register.

B9- Stop!- 30” - Increasingly violent clusters usingOrbit 4and Orbit 0 -
     the most violent cluster, at the end, consists of 3 consecutive semi-tones,
          certainly time to stop.

B10- Couples- 25” - A 4-part canon composed ofDiminished Octaves-
     each chord of the circle is presented in 2 different sonorities,
          each sonority consisting of a set of 2 diminished octaves.
     The 4 notes of each chord pair off in various semi-tone combinations
          provoking multiple sparks, guaranteed 2 per chord sonority.
     The very dissonant effect is slightly attenuated
          by the resolutions of the non-chordal tones of the COMMON TONE (Orbit 0).

B11- Supercouples- 25” - The same 4-part canon composed ofDiminished Octaves-
     each chord of the circle is now presented in 3 different sonorities,
          and left in its original dissonant state.

B12- Soft Supercouples- 25” - The same 4-part canon
     with the very dissonant effect slightly attenuated
          by the resolutions of the non-chordal tones of theCOMMON TONE(Orbit 0)
               as it was in Couples.

B13- Rain, Snow, and Hail- 32” - For harp, vibraphone, and marimba, based on Supercouples
     First, we hear Supercouples, a little faster than the original,
          with its complete 4-note chords,
               played on a harp.
     Then, we hear each chord broken up into 2 eighth-note parts of 2 notes each,
          with sonorities of diminished fifths, fourths, and major thirds,
               played on a vibraphone.
     Finally, we hear, once again, each chord broken up into 2 eighth-note parts of 2 notes each,
          this time uniquely with sonorities of semi-tones (diminished octaves),
               played on a marimba.
A lesson in arranging, exactly the same music each time, with completely different results.

B14- Push2 Circle Down- 30” - One of a series of canonic circles with variousNon-chordal Tones
     This 3-voice canon makes 3 flattening (descending)circles,
          the Fundamental Bass entering only on the last one.
     In the 3 canonic lines, we have (after theMetamorphosis 1)
          - an Orbit 0, which is tied to
          - an Orbit 1 (which substitutes for Orbit 3), in turn tied in to
          - a push2 (which replaces Orbit 2) and resolves to the next Orbit 10 a third higher,
               all of this withVoice-leading Athroughout.
     The push2 gives each chord a 2-5 sonority (occasionally 1-6 or 1-5)
          and the long 3-chord notes give the whole clip a quiet, placid feeling.

B15- Push2 Circle Down-b- 30” - A variaton of the preceding clip -
     The first bar has been removed,
          and shorter note-values give the clip a "Fanfare" feeling.

B16- Sus2 Circle Up- 30” - Almost, but not quite, an inversion of the preceding clip -
     - We have here 2 sharpening (ascending)circles(not 3).
     - The shorter note-values have a syncopated feeling.

B17- Cluster Circle Down- 30” - Using the push2 and the sus6 simultaneously
     We have here 2 flattening (descending)circles
     The push2 and sus6 produce4-note clustersof various sonorities (1-2-2, 2-1-2, 2-2-1, and one 2-2-2).
          which we hear on the fourth quarter-note of each chord
     At the very beginning of each chord, we hear a sus4 in the line which ends the bar on the push2.

B18- Cluster Circle Up- 30” - An inverted, simpler version of the preceding clip
     We have here 3 sharpening (ascending)circles
     The sus4 produces3-note clustersof various sonorities .
     There is only one note per chord and the clip has a quiet, relaxed feeling.

C1- Floating- 23” - 4-part canon of diminished seventh sounds (3-3-3) -
     Using the Chromaticim ofOrbit4is applied to the two dominant-shape chords
          of a swing with voice-leading A, producing a vague, almost atonal feeling.

C2- Buzzing- 20” - 3-part canon of diminished seventh sounds (3-3-3) -
     More tonally centered than the preceding clip,
     the action here is in the Orbit 0-0 line of theProcuration Bswing,
          with thepush+4andsus-2(which produce the diminished seventh sound)
               moving more and more rapidly.

C3- Cool- 24” - 4-part canon withs-2, s1(p+4, p5) (1-3-3) -
     Rather than enter the voices one at a time, they all enter together, but only on Orbit 0.
     Then Orbit 1 is added, then orbit 2, finally the sus-2/push+4 which completes the cool sound.
     The orbits disappear in the opposite order.

C4- Romp- 20” - A merry 4-part chase around the block (from C to Am and back 8 times) -
     The chase starts and ends with 2 voices (the central part has 4) and progresses through
          an unusual, enlarged swing which contains 2 successivemetamorphoses 4in each direction.

C5- Chromatic Romp- 20” - A chromatic version of the previous clip -
     A more quiet and calm romp.

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