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Directory:Jon Awbrey/Papers/Riffs and Rotes (view source)
Revision as of 15:30, 22 January 2010
, 15:30, 22 January 2010→Selected Sequences
\text{p}_3^1
\text{p}_3^1
& = & \text{p}_{\text{p}_2^1}^1
& = & \text{p}_{\text{p}_2^1}^1
\\[10pt]
\\[12pt]
& = & \text{p}_{\text{p}_{\text{p}_1^1}^1}^1
& = & \text{p}_{\text{p}_{\text{p}_1^1}^1}^1
\end{array}</math>
\end{array}</math>
\text{p}_4^1
\text{p}_4^1
& = & \text{p}_{\text{p}_1^2}^1
& = & \text{p}_{\text{p}_1^2}^1
\\[10pt]
\\[12pt]
& = & \text{p}_{\text{p}_1^{\text{p}_1^1}}^1
& = & \text{p}_{\text{p}_1^{\text{p}_1^1}}^1
\end{array}</math>
\end{array}</math>
\text{p}_1^3
\text{p}_1^3
& = & \text{p}_1^{\text{p}_2^1}
& = & \text{p}_1^{\text{p}_2^1}
\\[10pt]
\\[12pt]
& = & \text{p}_1^{\text{p}_{\text{p}_1^1}^1}
& = & \text{p}_1^{\text{p}_{\text{p}_1^1}^1}
\end{array}</math>
\end{array}</math>
\text{p}_1^4
\text{p}_1^4
& = & \text{p}_1^{\text{p}_1^2}
& = & \text{p}_1^{\text{p}_1^2}
\\[10pt]
\\[12pt]
& = & \text{p}_1^{\text{p}_1^{\text{p}_1^1}}
& = & \text{p}_1^{\text{p}_1^{\text{p}_1^1}}
\end{array}</math>
\end{array}</math>
| [[Image:Riff 16 Big.jpg|65px]]
| [[Image:Riff 16 Big.jpg|65px]]
| [[Image:Rote 16 Big.jpg|90px]]
| [[Image:Rote 16 Big.jpg|90px]]
|}
|-
|
{| cellpadding="12" style="text-align:center; width:100%"
| width="10%" | <math>10\!</math>
| width="25%" |
<math>\begin{array}{lll}
\text{p}_1^1 \text{p}_3^1
& = & \text{p}_1^1 \text{p}_{\text{p}_2^1}^1
\\[12pt]
& = & \text{p}_1^1 \text{p}_{\text{p}_{\text{p}_1^1}^1}^1
\end{array}</math>
| width="15%" | <math>\text{p} \text{p}_{\text{p}_{\text{p}}}\!</math>
| width="25%" | [[Image:Riff 10 Big.jpg|90px]]
| width="25%" | [[Image:Rote 10 Big.jpg|80px]]
|-
| <math>11\!</math>
|
<math>\begin{array}{lll}
\text{p}_5^1
& = & \text{p}_{\text{p}_3^1}^1
\\[12pt]
& = & \text{p}_{\text{p}_{\text{p}_2^1}^1}^1
\\[12pt]
& = & \text{p}_{\text{p}_{\text{p}_{\text{p}_1^1}^1}^1}^1
\end{array}</math>
| <math>\text{p}_{\text{p}_{\text{p}_\text{p}}}\!</math>
| [[Image:Riff 11 Big.jpg|90px]]
| [[Image:Rote 11 Big.jpg|40px]]
|-
| <math>12\!</math>
|
<math>\begin{array}{lll}
\text{p}_1^2 \text{p}_2^1
& = & \text{p}_1^{\text{p}_1^1} \text{p}_{\text{p}_1^1}^1
\end{array}</math>
| <math>\text{p}^{\text{p}} \text{p}_{\text{p}}\!</math>
| [[Image:Riff 12 Big.jpg|65px]]
| [[Image:Rote 12 Big.jpg|105px]]
|-
| <math>13\!</math>
|
<math>\begin{array}{lll}
\text{p}_6^1
& = & \text{p}_{\text{p}_1^1 \text{p}_2^1}^1
\\[12pt]
& = & \text{p}_{\text{p}_1^1 \text{p}_{\text{p}_1^1}^1}^1
\end{array}</math>
| <math>\text{p}_{\text{p} \text{p}_{\text{p}}}\!</math>
| [[Image:Riff 13 Big.jpg|65px]]
| [[Image:Rote 13 Big.jpg|80px]]
|-
| <math>14\!</math>
|
<math>\begin{array}{lll}
\text{p}_1^1 \text{p}_4^1
& = & \text{p}_1^1 \text{p}_{\text{p}_1^2}^1
\\[12pt]
& = & \text{p}_1^1 \text{p}_{\text{p}_1^{\text{p}_1^1}}^1
\end{array}</math>
| <math>\text{p} \text{p}_{\text{p}^{\text{p}}}\!</math>
| [[Image:Riff 14 Big.jpg|90px]]
| [[Image:Rote 14 Big.jpg|105px]]
|-
| <math>17\!</math>
|
<math>\begin{array}{lll}
\text{p}_7^1
& = & \text{p}_{\text{p}_4^1}^1
\\[12pt]
& = & \text{p}_{\text{p}_{\text{p}_1^2}^1}^1
\\[12pt]
& = & \text{p}_{\text{p}_{\text{p}_1^{\text{p}_1^1}}^1}^1
\end{array}</math>
| <math>\text{p}_{\text{p}_{\text{p}^{\text{p}}}}\!</math>
| [[Image:Riff 17 Big.jpg|90px]]
| [[Image:Rote 17 Big.jpg|65px]]
|-
| <math>18\!</math>
|
<math>\begin{array}{lll}
\text{p}_1^1 \text{p}_2^2
& = & \text{p}_1^1 \text{p}_{\text{p}_1^1}^{\text{p}_1^1}
\end{array}</math>
| <math>\text{p} \text{p}_{\text{p}}^{\text{p}}\!</math>
| [[Image:Riff 18 Big.jpg|65px]]
| [[Image:Rote 18 Big.jpg|120px]]
|-
| <math>19\!</math>
|
<math>\begin{array}{lll}
\text{p}_8^1
& = & \text{p}_{\text{p}_1^3}^1
\\[12pt]
& = & \text{p}_{\text{p}_1^{\text{p}_2^1}}^1
\\[12pt]
& = & \text{p}_{\text{p}_1^{\text{p}_{\text{p}_1^1}^1}}^1
\end{array}</math>
| <math>\text{p}_{\text{p}^{\text{p}_{\text{p}}}}\!</math>
| [[Image:Riff 19 Big.jpg|90px]]
| [[Image:Rote 19 Big.jpg|65px]]
|-
| <math>23\!</math>
|
<math>\begin{array}{lll}
\text{p}_9^1
& = & \text{p}_{\text{p}_2^2}^1
\\[12pt]
& = & \text{p}_{\text{p}_{\text{p}_1^1}^{\text{p}_1^1}}^1
\end{array}</math>
| <math>\text{p}_{\text{p}_{\text{p}}^{\text{p}}}\!</math>
| [[Image:Riff 23 Big.jpg|65px]]
| [[Image:Rote 23 Big.jpg|80px]]
|-
| <math>25\!</math>
|
<math>\begin{array}{lll}
\text{p}_3^2
& = & \text{p}_{\text{p}_2^1}^{\text{p}_1^1}
\\[12pt]
& = & \text{p}_{\text{p}_{\text{p}_1^1}^1}^{\text{p}_1^1}
\end{array}</math>
| <math>\text{p}_{\text{p}_{\text{p}}}^{\text{p}}\!</math>
| [[Image:Riff 25 Big.jpg|65px]]
| [[Image:Rote 25 Big.jpg|80px]]
|-
| <math>27\!</math>
|
<math>\begin{array}{lll}
\text{p}_2^3
& = & \text{p}_{\text{p}_1^1}^{\text{p}_2^1}
\\[12pt]
& = & \text{p}_{\text{p}_1^1}^{\text{p}_{\text{p}_1^1}^1}
\end{array}</math>
| <math>\text{p}_{\text{p}}^{\text{p}_{\text{p}}}\!</math>
| [[Image:Riff 27 Big.jpg|65px]]
| [[Image:Rote 27 Big.jpg|80px]]
|-
| <math>32\!</math>
|
<math>\begin{array}{lll}
\text{p}_1^5
& = & \text{p}_1^{\text{p}_3^1}
\\[12pt]
& = & \text{p}_1^{\text{p}_{\text{p}_2^1}^1}
\\[12pt]
& = & \text{p}_1^{\text{p}_{\text{p}_{\text{p}_1^1}^1}^1}
\end{array}</math>
| <math>\text{p}^{\text{p}_{\text{p}_{\text{p}}}}\!</math>
| [[Image:Riff 32 Big.jpg|90px]]
| [[Image:Rote 32 Big.jpg|65px]]
|-
| <math>49\!</math>
|
<math>\begin{array}{lll}
\text{p}_4^2
& = & \text{p}_{\text{p}_1^2}^{\text{p}_1^1}
\\[12pt]
& = & \text{p}_{\text{p}_1^{\text{p}_1^1}}^{\text{p}_1^1}
\end{array}</math>
| <math>\text{p}_{\text{p}^{\text{p}}}^{\text{p}}\!</math>
| [[Image:Riff 49 Big.jpg|65px]]
| [[Image:Rote 49 Big.jpg|80px]]
|-
| <math>53\!</math>
|
<math>\begin{array}{lll}
\text{p}_{16}^1
& = & \text{p}_{\text{p}_1^4}^1
\\[12pt]
& = & \text{p}_{\text{p}_1^{\text{p}_1^2}}^1
\\[12pt]
& = & \text{p}_{\text{p}_1^{\text{p}_1^{\text{p}_1^1}}}^1
\end{array}</math>
| <math>\text{p}_{\text{p}^{\text{p}^{\text{p}}}}\!</math>
| [[Image:Riff 53 Big.jpg|90px]]
| [[Image:Rote 53 Big.jpg|90px]]
|-
| <math>64\!</math>
|
<math>\begin{array}{lll}
\text{p}_1^6
& = & \text{p}_1^{\text{p}_1^1 \text{p}_2^1}
\\[12pt]
& = & \text{p}_1^{\text{p}_1^1 \text{p}_{\text{p}_1^1}^1}
\end{array}</math>
| <math>\text{p}^{\text{p} \text{p}_{\text{p}}}\!</math>
| [[Image:Riff 64 Big.jpg|65px]]
| [[Image:Rote 64 Big.jpg|105px]]
|-
| <math>81\!</math>
|
<math>\begin{array}{lll}
\text{p}_2^4
& = & \text{p}_{\text{p}_1^1}^{\text{p}_1^2}
\\[12pt]
& = & \text{p}_{\text{p}_1^1}^{\text{p}_1^{\text{p}_1^1}}
\end{array}</math>
| <math>\text{p}_{\text{p}}^{\text{p}^{\text{p}}}\!</math>
| [[Image:Riff 81 Big.jpg|65px]]
| [[Image:Rote 81 Big.jpg|105px]]
|-
| <math>128\!</math>
|
<math>\begin{array}{lll}
\text{p}_1^7
& = & \text{p}_1^{\text{p}_4^1}
\\[12pt]
& = & \text{p}_1^{\text{p}_{\text{p}_1^2}^1}
\\[12pt]
& = & \text{p}_1^{\text{p}_{\text{p}_1^{\text{p}_1^1}}^1}
\end{array}</math>
| <math>\text{p}^{\text{p}_{\text{p}^{\text{p}}}}\!</math>
| [[Image:Riff 128 Big.jpg|90px]]
| [[Image:Rote 128 Big.jpg|90px]]
|-
| <math>256\!</math>
|
<math>\begin{array}{lll}
\text{p}_1^8
& = & \text{p}_1^{\text{p}_1^3}
\\[12pt]
& = & \text{p}_1^{\text{p}_1^{\text{p}_2^1}}
\\[12pt]
& = & \text{p}_1^{\text{p}_1^{\text{p}_{\text{p}_1^1}^1}}
\end{array}</math>
| <math>\text{p}^{\text{p}^{\text{p}_{\text{p}}}}\!</math>
| [[Image:Riff 256 Big.jpg|90px]]
| [[Image:Rote 256 Big.jpg|90px]]
|-
| <math>512\!</math>
|
<math>\begin{array}{lll}
\text{p}_1^9
& = & \text{p}_1^{\text{p}_2^2}
\\[12pt]
& = & \text{p}_1^{\text{p}_{\text{p}_1^1}^{\text{p}_1^1}}
\end{array}</math>
| <math>\text{p}^{\text{p}_{\text{p}}^{\text{p}}}\!</math>
| [[Image:Riff 512 Big.jpg|65px]]
| [[Image:Rote 512 Big.jpg|105px]]
|-
| <math>65536\!</math>
|
<math>\begin{array}{lll}
\text{p}_1^{16}
& = & \text{p}_1^{\text{p}_1^4}
\\[12pt]
& = & \text{p}_1^{\text{p}_1^{\text{p}_1^2}}
\\[12pt]
& = & \text{p}_1^{\text{p}_1^{\text{p}_1^{\text{p}_1^1}}}
\end{array}</math>
| <math>\text{p}^{\text{p}^{\text{p}^{\text{p}}}}\!</math>
| [[Image:Riff 65536 Big.jpg|90px]]
| [[Image:Rote 65536 Big.jpg|115px]]
|}
|}
|}
|}