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Sankyo20

tremblay_Inversus.doc

ذدà،±ل>‏ے fh‏ےےےeےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےےى¥ء9 ً؟ bjbj‎د‎د.Fں¥ں¥ ےےےےےےl$¾¾¾¾عœ$ع0>‚‚‚‚‚‚‚‚Y0[0[0[0[0[0[0$2 84B0‚‚‚‚‚0p ‚‚”0p p p ‚‚‚Y0p ‚Y0p ¶p &%Q'‌'‚vpêBœ{جآ$ڑ¾‚i'‌'¼ھ00ع0q',z4‚îz4‌'p $$ظMusical theory of diatonic Inversus Playing a melody the “right” way is called “Rectus”, playing it by inverting the notes vertically around a pivotal point is called “Inversus”. Analyzing the Inversus process used by W.A. Mozart, I infer the following rule: To stay in the same key when going “inversus”, a diatonic scale is pivoting around its third degree. That note being the central note of the I chord, that chord stays identical when inverted, while the IV and V chords are always interchanged. Example in the C major scale: Rectus BCDEFGAInversusAGFEDCB E is the third note of the scale (C, D, E, F, G, A, B). Chord I (C major): C-E-G inverts to G-E-C (mirror position of the same C chord). Chord IV (F major): F-A-C inverts to D-B-G (mirror position of G major V chord) Chord V (G major): G-B-D inverts to C-A- F (mirror position of F major IV chord) Applying that rule to a mechanical instrument, we have two cases: The instrument has an odd number of notes. Inverting the band (or book), the pivoting point falls on the central note. Ex.: With the Sankyo 15k, note C8 stays identical, in unison: 123456789101112131415RectusC DEFGABCDEFGABCInversusCBAGFEDCBAGFEDC C is the central note of the A minor chord (A-C-E = E-A-C). So we are inverting the scale based on that chord: A minor aeolian modal scale. The V chord E minor (E-G-B) is permuting with the IV chord D minor (A-F-D, mirror position of D-F-A). Ex.:California dream: CalDrmIn.mid 2. The instrument has an even number of notes. Inverting the band, the pivoting point falls between two notes. With the Sankyo 20k, between E10 and F11: 1234567891011121314151617181920Rectus CDEFGABCDEFGABCDEFGAInversus AGFEDCBAGFEDCBAGFEDC The whole central octave becomes the pivoting point, and B is the actual pivoting note one octave apart: B7 inverts to B14. B being the central note of the G major chord (G-B-D = D-B-G), we are inverting the scale based on that chord: G major mixolydian modal scale. With that F natural (not F#) the V chord is D minor (D-F-A), inverting to the IV chord C major (G-E-C, alternate position of C-E-G). Ex.:Forlorne: Forlorin.mid How to invert the important C major key With an odd numbered notes instrument, the pivot note must be E, so the C major chord will stay the same when inverted: C-E-G = G-E-C. Imagine the Sankyo 20 noter as being an odd numbered 21 noter. Adding a virtual note (V) in the lower margin (M), E10 becomes the center note, the “hinge”: M1234567891011121314151617181920Rectus VCDEFGABCDEFGABCDEFGA Inversus AGFEDCBAGFEDCBAGFEDC E is the central note of the C major chord. So we are inverting the scale based on that chord: C major scale. (The inverted band moves down the width of a track, since its upper margin has been diminished, as explained in the main text). In rectus, all 20 notes play normally. In inversus, a hole in virtual V will activate the highest A. So we don’t loose any notes. Ex.: BrunoInv.mid If we slide the inverted scale in the other direction, note F11 becomes the center, and we get a scale in D minor, dorian mode, [D-F-A= A-F-D): 1234567891011121314151617181920MRectus CDEFGABCDEFGABCDEFGAV Inversus AGFEDCBAGF E DCBAGFEDC Ex.: Scarborough Fair (ScarboIn.mid) and So What? (SoWhatIn.mid) Arranging in inversus is challenging, especially with preexisting melodies. The permutation of chords V and IV is delicate. I consider the chords as incomplete 4-notes (Dm7=G7, CM7=C6, F6=G7, Em7=FM7…). I imagine the accompaniment as an inverted melody on its own. Since the treble notes are heard more distinctly than the bass notes in a music box, the accompaniment is less clearly perceived than the treble melody. My MIDI examples are just studies to illustrate the inversus, not polished arrangements. 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