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A133269
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Groups of 4 numbers describing a sequence of Major 7th chords by assigning numbers 1 to 12 to an octave.
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4
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1, 5, 8, 12, 5, 9, 12, 4, 8, 12, 3, 7, 12, 4, 7, 11, 5, 9, 12, 4, 9, 1, 4, 8, 12, 4, 7, 11, 4, 8, 11, 3, 8, 12, 3, 7, 12, 4, 7, 11, 3, 7, 10, 2, 7, 11, 2, 6, 12, 4, 7, 11, 4, 8, 11, 3, 7, 11, 2, 6, 11, 3, 6, 10, 5, 9, 12, 4, 9, 1, 4, 8, 12, 4, 7, 11, 4, 8, 11, 3, 9, 1, 4, 8, 1, 5, 8, 12, 4, 8, 11, 3, 8
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| A major 7th chord has intervals of 4, 7 and 11 half tones above the base tone.
Starting from base tones at C, C#, D, D#, E, F etc and wrapping around the tones higher than an octave 13->1, 14->2 etc,
and assigning numbers 1 to 12 to the half tones within the octave,
the chords (4 tones each) are represented as 1->{1, 5, 8, 12}, 2-> {2, 6, 9, 1}, 3-> {3, 7, 10, 2}, 4-> {4, 8, 11, 3},
5-> {5, 9, 12, 4}, 6-> {6, 10, 1, 5}, 7-> {7, 11, 2, 6}, 8-> {8, 12, 3, 7},
9-> {9, 1, 4, 8}, 10-> {10, 2, 5, 9}, 11-> {11, 3, 6, 10}, 12-> {12, 4, 7, 11}.
The sequence starts with the chord at base 1, defining a(1) - a(4), and then appends
iteratively in groups of 4 the chords at base a(k), k=2,3,4,.. to the sequence.
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LINKS
| Mel Bey, manuscript book.
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EXAMPLE
| The starting chord is (1,5,8,12). a(2)=5 means to append (5,9,12,4), the chord at 5. a(3)=8 means to append (8,12,3,7).
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MATHEMATICA
| Clear[s, p] s[i_] = {i, If[i + 4 > 12, i - 8, i + 4], If[i + 7 > 12, i - 5, i + 7], If[i + 11 > 12, i - 1, i + 11]}; t[a_] := Flatten[s /@ a]; p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]]; p[4]
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CROSSREFS
| Sequence in context: A154486 A162612 A133522 * A076635 A116602 A079896
Adjacent sequences: A133266 A133267 A133268 * A133270 A133271 A133272
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KEYWORD
| nonn,less,easy
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Oct 16 2007
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EXTENSIONS
| Comments inserted for clarification - The Assoc. Eds. of the OEIS - Aug 29 2010
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