12,080
edits
Changes
+ Miscellaneous Examples (Reduction 8:1)
==Animations==
===Riffs 1 to 60===
{| align="center"
| [[Image:Animation Riff 60 x 0.16.gif]]
|}
===Rotes 1 to 60===
{| align="center"
| [[Image:Animation Rote 60 x 0.16.gif]]
|}
==Image Gallery==
===Reduction 6:1===
====Cacti====
{| align="center" border="1" cellpadding="20" style="text-align:center; width:90%"
|-
| width="50%" | '''Image'''
| width="50%" | '''Scale'''
|-
| [[Image:Rooted Node Big.jpg|20px]] || 117 px <br> ↓ <br> 20 px
|-
| [[Image:Rooted Edge Big.jpg|20px]] || 117 px <br> ↓ <br> 20 px
|}
====Riffs====
{| align="center" border="1" cellpadding="20" style="text-align:center; width:90%"
|-
| width="15%" | '''Integer'''
| width="70%" | '''Riff'''
| width="15%" | '''Scale'''
|-
| 1 || ||
|-
| 2 || [[Image:Riff 2 Big.jpg|20px]] || 117 px <br> ↓ <br> 20 px
|-
| 3 || [[Image:Riff 3 Big.jpg|40px]] || 240 px <br> ↓ <br> 40 px
|-
| 4 || [[Image:Riff 4 Big.jpg|40px]] || 233 px <br> ↓ <br> 40 px
|-
| 5 || [[Image:Riff 5 Big.jpg|65px]] || 384 px <br> ↓ <br> 65 px
|-
| 6 || [[Image:Riff 6 Big.jpg|65px]] || 384 px <br> ↓ <br> 65 px
|-
| 7 || [[Image:Riff 7 Big.jpg|65px]] || 377 px <br> ↓ <br> 65 px
|-
| 8 || [[Image:Riff 8 Big.jpg|65px]] || 384 px <br> ↓ <br> 65 px
|-
| 9 || [[Image:Riff 9 Big.jpg|40px]] || 240 px <br> ↓ <br> 40 px
|-
| 10 || [[Image:Riff 10 Big.jpg|90px]] || 528 px <br> ↓ <br> 90 px
|-
| 11 || [[Image:Riff 11 Big.jpg|90px]] || 528 px <br> ↓ <br> 90 px
|-
| 12 || [[Image:Riff 12 Big.jpg|65px]] || 384 px <br> ↓ <br> 65 px
|-
| 13 || [[Image:Riff 13 Big.jpg|65px]] || 384 px <br> ↓ <br> 65 px
|-
| 14 || [[Image:Riff 14 Big.jpg|90px]] || 521 px <br> ↓ <br> 90 px
|-
| 15 || [[Image:Riff 15 Big.jpg|90px]] || 528 px <br> ↓ <br> 90 px
|-
| 16 || [[Image:Riff 16 Big.jpg|65px]] || 377 px <br> ↓ <br> 65 px
|-
| 17 || [[Image:Riff 17 Big.jpg|90px]] || 521 px <br> ↓ <br> 90 px
|-
| 18 || [[Image:Riff 18 Big.jpg|65px]] || 384 px <br> ↓ <br> 65 px
|-
| 19 || [[Image:Riff 19 Big.jpg|90px]] || 528 px <br> ↓ <br> 90 px
|-
| 20 || [[Image:Riff 20 Big.jpg|90px]] || 528 px <br> ↓ <br> 90 px
|-
| 21 || [[Image:Riff 21 Big.jpg|90px]] || 521 px <br> ↓ <br> 90 px
|-
| 22 || [[Image:Riff 22 Big.jpg|115px]] || 672 px <br> ↓ <br> 115 px
|-
| 23 || [[Image:Riff 23 Big.jpg|65px]] || 384 px <br> ↓ <br> 65 px
|-
| 24 || [[Image:Riff 24 Big.jpg|115px]] || 672 px <br> ↓ <br> 115 px
|-
| 25 || [[Image:Riff 25 Big.jpg|65px]] || 384 px <br> ↓ <br> 65 px
|-
| 26 || [[Image:Riff 26 Big.jpg|90px]] || 528 px <br> ↓ <br> 90 px
|-
| 27 || [[Image:Riff 27 Big.jpg|65px]] || 384 px <br> ↓ <br> 65 px
|-
| 28 || [[Image:Riff 28 Big.jpg|90px]] || 521 px <br> ↓ <br> 90 px
|-
| 29 || [[Image:Riff 29 Big.jpg|90px]] || 528 px <br> ↓ <br> 90 px
|-
| 30 || [[Image:Riff 30 Big.jpg|115px]] || 672 px <br> ↓ <br> 115 px
|-
| 31 || [[Image:Riff 31 Big.jpg|115px]] || 672 px <br> ↓ <br> 115 px
|-
| 32 || [[Image:Riff 32 Big.jpg|90px]] || 528 px <br> ↓ <br> 90 px
|-
| 33 || [[Image:Riff 33 Big.jpg|115px]] || 672 px <br> ↓ <br> 115 px
|-
| 34 || [[Image:Riff 34 Big.jpg|115px]] || 665 px <br> ↓ <br> 115 px
|-
| 35 || [[Image:Riff 35 Big.jpg|90px]] || 521 px <br> ↓ <br> 90 px
|-
| 36 || [[Image:Riff 36 Big.jpg|65px]] || 384 px <br> ↓ <br> 65 px
|-
| 37 || [[Image:Riff 37 Big.jpg|65px]] || 384 px <br> ↓ <br> 65 px
|-
| 38 || [[Image:Riff 38 Big.jpg|115px]] || 672 px <br> ↓ <br> 115 px
|-
| 39 || [[Image:Riff 39 Big.jpg|115px]] || 672 px <br> ↓ <br> 115 px
|-
| 40 || [[Image:Riff 40 Big.jpg|135px]] || 816 px <br> ↓ <br> 135 px
|-
| 41 || [[Image:Riff 41 Big.jpg|90px]] || 528 px <br> ↓ <br> 90 px
|-
| 42 || [[Image:Riff 42 Big.jpg|115px]] || 665 px <br> ↓ <br> 115 px
|-
| 43 || [[Image:Riff 43 Big.jpg|90px]] || 521 px <br> ↓ <br> 90 px
|-
| 44 || [[Image:Riff 44 Big.jpg|115px]] || 672 px <br> ↓ <br> 115 px
|-
| 45 || [[Image:Riff 45 Big.jpg|90px]] || 528 px <br> ↓ <br> 90 px
|-
| 46 || [[Image:Riff 46 Big.jpg|90px]] || 528 px <br> ↓ <br> 90 px
|-
| 47 || [[Image:Riff 47 Big.jpg|90px]] || 528 px <br> ↓ <br> 90 px
|-
| 48 || [[Image:Riff 48 Big.jpg|65px]] || 384 px <br> ↓ <br> 65 px
|-
| 49 || [[Image:Riff 49 Big.jpg|65px]] || 377 px <br> ↓ <br> 65 px
|-
| 50 || [[Image:Riff 50 Big.jpg|90px]] || 528 px <br> ↓ <br> 90 px
|-
| 51 || [[Image:Riff 51 Big.jpg|115px]] || 665 px <br> ↓ <br> 115 px
|-
| 52 || [[Image:Riff 52 Big.jpg|90px]] || 528 px <br> ↓ <br> 90 px
|-
| 53 || [[Image:Riff 53 Big.jpg|90px]] || 521 px <br> ↓ <br> 90 px
|-
| 54 || [[Image:Riff 54 Big.jpg|90px]] || 528 px <br> ↓ <br> 90 px
|-
| 55 || [[Image:Riff 55 Big.jpg|115px]] || 672 px <br> ↓ <br> 115 px
|-
| 56 || [[Image:Riff 56 Big.jpg|135px]] || 809 px <br> ↓ <br> 135 px
|-
| 57 || [[Image:Riff 57 Big.jpg|115px]] || 672 px <br> ↓ <br> 115 px
|-
| 58 || [[Image:Riff 58 Big.jpg|115px]] || 672 px <br> ↓ <br> 115 px
|-
| 59 || [[Image:Riff 59 Big.jpg|115px]] || 665 px <br> ↓ <br> 115 px
|-
| 60 || [[Image:Riff 60 Big.jpg|115px]] || 672 px <br> ↓ <br> 115 px
|-
| 64 || [[Image:Riff 64 Big.jpg|65px]] || 384 px <br> ↓ <br> 65 px
|-
| 81 || [[Image:Riff 81 Big.jpg|65px]] || 377 px <br> ↓ <br> 65 px
|-
| 105 || [[Image:Riff 105 Big.jpg|115px]] || 665 px <br> ↓ <br> 115 px
|-
| 128 || [[Image:Riff 128 Big.jpg|90px]] || 521 px <br> ↓ <br> 90 px
|-
| 165 || [[Image:Riff 165 Big.jpg|135px]] || 816 px <br> ↓ <br> 135 px
|-
| 256 || [[Image:Riff 256 Big.jpg|90px]] || 528 px <br> ↓ <br> 90 px
|-
| 512 || [[Image:Riff 512 Big.jpg|65px]] || 384 px <br> ↓ <br> 65 px
|-
| 2010 || [[Image:Riff 2010 Big.jpg|185px]] || 1104 px <br> ↓ <br> 185 px
|-
| 2500 || [[Image:Riff 2500 Big.jpg|90px]] || 528 px <br> ↓ <br> 90 px
|-
| 65536 || [[Image:Riff 65536 Big.jpg|90px]] || 521 px <br> ↓ <br> 90 px
|-
| 802701 || [[Image:Riff 802701 Big.jpg|210px]] || 1248 px <br> ↓ <br> 210 px
|-
| 123456789 || [[Image:Riff 123456789 Big.jpg|220px]] || 1296 px <br> ↓ <br> 220 px
|}
====Rotes====
{| align="center" border="1" cellpadding="20" style="text-align:center; width:90%"
|-
| width="15%" | '''Integer'''
| width="70%" | '''Rote'''
| width="15%" | '''Scale'''
|-
| 1 || [[Image:Rote 1 Big.jpg|20px]] || 117 px <br> ↓ <br> 20 px
|-
| 2 || [[Image:Rote 2 Big.jpg|40px]] || 233 px <br> ↓ <br> 40 px
|-
| 3 || [[Image:Rote 3 Big.jpg|40px]] || 233 px <br> ↓ <br> 40 px
|-
| 4 || [[Image:Rote 4 Big.jpg|65px]] || 377 px <br> ↓ <br> 65 px
|-
| 5 || [[Image:Rote 5 Big.jpg|40px]] || 233 px <br> ↓ <br> 40 px
|-
| 6 || [[Image:Rote 6 Big.jpg|80px]] || 473 px <br> ↓ <br> 80 px
|-
| 7 || [[Image:Rote 7 Big.jpg|65px]] || 377 px <br> ↓ <br> 65 px
|-
| 8 || [[Image:Rote 8 Big.jpg|65px]] || 377 px <br> ↓ <br> 65 px
|-
| 9 || [[Image:Rote 9 Big.jpg|80px]] || 473 px <br> ↓ <br> 80 px
|-
| 10 || [[Image:Rote 10 Big.jpg|80px]] || 473 px <br> ↓ <br> 80 px
|-
| 11 || [[Image:Rote 11 Big.jpg|40px]] || 233 px <br> ↓ <br> 40 px
|-
| 12 || [[Image:Rote 12 Big.jpg|105px]] || 617 px <br> ↓ <br> 105 px
|-
| 13 || [[Image:Rote 13 Big.jpg|80px]] || 473 px <br> ↓ <br> 80 px
|-
| 14 || [[Image:Rote 14 Big.jpg|105px]] || 617 px <br> ↓ <br> 105 px
|-
| 15 || [[Image:Rote 15 Big.jpg|80px]] || 473 px <br> ↓ <br> 80 px
|-
| 16 || [[Image:Rote 16 Big.jpg|90px]] || 521 px <br> ↓ <br> 90 px
|-
| 17 || [[Image:Rote 17 Big.jpg|65px]] || 377 px <br> ↓ <br> 65 px
|-
| 18 || [[Image:Rote 18 Big.jpg|120px]] || 713 px <br> ↓ <br> 120 px
|-
| 19 || [[Image:Rote 19 Big.jpg|65px]] || 377 px <br> ↓ <br> 65 px
|-
| 20 || [[Image:Rote 20 Big.jpg|105px]] || 617 px <br> ↓ <br> 105 px
|-
| 21 || [[Image:Rote 21 Big.jpg|105px]] || 617 px <br> ↓ <br> 105 px
|-
| 22 || [[Image:Rote 22 Big.jpg|80px]] || 473 px <br> ↓ <br> 80 px
|-
| 23 || [[Image:Rote 23 Big.jpg|80px]] || 473 px <br> ↓ <br> 80 px
|-
| 24 || [[Image:Rote 24 Big.jpg|105px]] || 617 px <br> ↓ <br> 105 px
|-
| 25 || [[Image:Rote 25 Big.jpg|80px]] || 473 px <br> ↓ <br> 80 px
|-
| 26 || [[Image:Rote 26 Big.jpg|120px]] || 713 px <br> ↓ <br> 120 px
|-
| 27 || [[Image:Rote 27 Big.jpg|80px]] || 473 px <br> ↓ <br> 80 px
|-
| 28 || [[Image:Rote 28 Big.jpg|130px]] || 761 px <br> ↓ <br> 130 px
|-
| 29 || [[Image:Rote 29 Big.jpg|80px]] || 473 px <br> ↓ <br> 80 px
|-
| 30 || [[Image:Rote 30 Big.jpg|120px]] || 713 px <br> ↓ <br> 120 px
|-
| 31 || [[Image:Rote 31 Big.jpg|40px]] || 233 px <br> ↓ <br> 40 px
|-
| 32 || [[Image:Rote 32 Big.jpg|65px]] || 377 px <br> ↓ <br> 65 px
|-
| 33 || [[Image:Rote 33 Big.jpg|80px]] || 473 px <br> ↓ <br> 80 px
|-
| 34 || [[Image:Rote 34 Big.jpg|105px]] || 617 px <br> ↓ <br> 105 px
|-
| 35 || [[Image:Rote 35 Big.jpg|105px]] || 617 px <br> ↓ <br> 105 px
|-
| 36 || [[Image:Rote 36 Big.jpg|145px]] || 857 px <br> ↓ <br> 145 px
|-
| 37 || [[Image:Rote 37 Big.jpg|105px]] || 617 px <br> ↓ <br> 105 px
|-
| 38 || [[Image:Rote 38 Big.jpg|105px]] || 617 px <br> ↓ <br> 105 px
|-
| 39 || [[Image:Rote 39 Big.jpg|120px]] || 713 px <br> ↓ <br> 120 px
|-
| 40 || [[Image:Rote 40 Big.jpg|105px]] || 617 px <br> ↓ <br> 105 px
|-
| 41 || [[Image:Rote 41 Big.jpg|80px]] || 473 px <br> ↓ <br> 80 px
|-
| 42 || [[Image:Rote 42 Big.jpg|145px]] || 857 px <br> ↓ <br> 145 px
|-
| 43 || [[Image:Rote 43 Big.jpg|105px]] || 617 px <br> ↓ <br> 105 px
|-
| 44 || [[Image:Rote 44 Big.jpg|105px]] || 617 px <br> ↓ <br> 105 px
|-
| 45 || [[Image:Rote 45 Big.jpg|120px]] || 713 px <br> ↓ <br> 120 px
|-
| 46 || [[Image:Rote 46 Big.jpg|120px]] || 713 px <br> ↓ <br> 120 px
|-
| 47 || [[Image:Rote 47 Big.jpg|80px]] || 473 px <br> ↓ <br> 80 px
|-
| 48 || [[Image:Rote 48 Big.jpg|105px]] || 617 px <br> ↓ <br> 105 px
|-
| 49 || [[Image:Rote 49 Big.jpg|80px]] || 473 px <br> ↓ <br> 80 px
|-
| 50 || [[Image:Rote 50 Big.jpg|120px]] || 713 px <br> ↓ <br> 120 px
|-
| 51 || [[Image:Rote 51 Big.jpg|105px]] || 617 px <br> ↓ <br> 105 px
|-
| 52 || [[Image:Rote 52 Big.jpg|145px]] || 857 px <br> ↓ <br> 145 px
|-
| 53 || [[Image:Rote 53 Big.jpg|90px]] || 521 px <br> ↓ <br> 90 px
|-
| 54 || [[Image:Rote 54 Big.jpg|120px]] || 713 px <br> ↓ <br> 120 px
|-
| 55 || [[Image:Rote 55 Big.jpg|80px]] || 473 px <br> ↓ <br> 80 px
|-
| 56 || [[Image:Rote 56 Big.jpg|130px]] || 761 px <br> ↓ <br> 130 px
|-
| 57 || [[Image:Rote 57 Big.jpg|105px]] || 617 px <br> ↓ <br> 105 px
|-
| 58 || [[Image:Rote 58 Big.jpg|120px]] || 713 px <br> ↓ <br> 120 px
|-
| 59 || [[Image:Rote 59 Big.jpg|65px]] || 377 px <br> ↓ <br> 65 px
|-
| 60 || [[Image:Rote 60 Big.jpg|155px]] || 905 px <br> ↓ <br> 155 px
|-
| 64 || [[Image:Rote 64 Big.jpg|105px]] || 617 px <br> ↓ <br> 105 px
|-
| 81 || [[Image:Rote 81 Big.jpg|105px]] || 617 px <br> ↓ <br> 105 px
|-
| 105 || [[Image:Rote 105 Big.jpg|145px]] || 857 px <br> ↓ <br> 145 px
|-
| 128 || [[Image:Rote 128 Big.jpg|90px]] || 521 px <br> ↓ <br> 90 px
|-
| 165 || [[Image:Rote 165 Big.jpg|120px]] || 713 px <br> ↓ <br> 120 px
|-
| 256 || [[Image:Rote 256 Big.jpg|90px]] || 521 px <br> ↓ <br> 90 px
|-
| 512 || [[Image:Rote 512 Big.jpg|105px]] || 617 px <br> ↓ <br> 105 px
|-
| 2010 || [[Image:Rote 2010 Big.jpg|190px]] || 1145 px <br> ↓ <br> 190 px
|-
| 2500 || [[Image:Rote 2500 Big.jpg|170px]] || 1001 px <br> ↓ <br> 170 px
|-
| 65536 || [[Image:Rote 65536 Big.jpg|115px]] || 665 px <br> ↓ <br> 115 px
|-
| 802701 || [[Image:Rote 802701 Big.jpg|330px]] || 1961 px <br> ↓ <br> 330 px
|-
| 123456789 || [[Image:Rote 123456789 Big.jpg|345px]] || 2048 px <br> ↓ <br> 345 px
|}
===Reduction 10:1===
====Cacti====
{| align="center" border="1" cellpadding="20" style="text-align:center; width:90%"
|-
| width="50%" | '''Image'''
| width="50%" | '''Scale'''
|-
| [[Image:Rooted Node Big.jpg|12px]] || 117 px <br> ↓ <br> 12 px
|-
| [[Image:Rooted Edge Big.jpg|12px]] || 117 px <br> ↓ <br> 12 px
|}
====Riffs====
{| align="center" border="1" cellpadding="20" style="text-align:center; width:90%"
|-
| width="15%" | '''Integer'''
| width="70%" | '''Riff'''
| width="15%" | '''Scale'''
|-
| 1 || ||
|-
| 2 || [[Image:Riff 2 Big.jpg|12px]] || 117 px <br> ↓ <br> 12 px
|-
| 3 || [[Image:Riff 3 Big.jpg|24px]] || 240 px <br> ↓ <br> 24 px
|-
| 4 || [[Image:Riff 4 Big.jpg|24px]] || 233 px <br> ↓ <br> 24 px
|-
| 5 || [[Image:Riff 5 Big.jpg|38px]] || 384 px <br> ↓ <br> 38 px
|-
| 6 || [[Image:Riff 6 Big.jpg|38px]] || 384 px <br> ↓ <br> 38 px
|-
| 7 || [[Image:Riff 7 Big.jpg|38px]] || 377 px <br> ↓ <br> 38 px
|-
| 8 || [[Image:Riff 8 Big.jpg|38px]] || 384 px <br> ↓ <br> 38 px
|-
| 9 || [[Image:Riff 9 Big.jpg|24px]] || 240 px <br> ↓ <br> 24 px
|-
| 10 || [[Image:Riff 10 Big.jpg|54px]] || 528 px <br> ↓ <br> 54 px
|-
| 11 || [[Image:Riff 11 Big.jpg|54px]] || 528 px <br> ↓ <br> 54 px
|-
| 12 || [[Image:Riff 12 Big.jpg|38px]] || 384 px <br> ↓ <br> 38 px
|-
| 13 || [[Image:Riff 13 Big.jpg|38px]] || 384 px <br> ↓ <br> 38 px
|-
| 14 || [[Image:Riff 14 Big.jpg|54px]] || 521 px <br> ↓ <br> 54 px
|-
| 15 || [[Image:Riff 15 Big.jpg|54px]] || 528 px <br> ↓ <br> 54 px
|-
| 16 || [[Image:Riff 16 Big.jpg|38px]] || 377 px <br> ↓ <br> 38 px
|-
| 17 || [[Image:Riff 17 Big.jpg|54px]] || 521 px <br> ↓ <br> 54 px
|-
| 18 || [[Image:Riff 18 Big.jpg|38px]] || 384 px <br> ↓ <br> 38 px
|-
| 19 || [[Image:Riff 19 Big.jpg|54px]] || 528 px <br> ↓ <br> 54 px
|-
| 20 || [[Image:Riff 20 Big.jpg|54px]] || 528 px <br> ↓ <br> 54 px
|-
| 21 || [[Image:Riff 21 Big.jpg|54px]] || 521 px <br> ↓ <br> 54 px
|-
| 22 || [[Image:Riff 22 Big.jpg|68px]] || 672 px <br> ↓ <br> 68 px
|-
| 23 || [[Image:Riff 23 Big.jpg|38px]] || 384 px <br> ↓ <br> 38 px
|-
| 24 || [[Image:Riff 24 Big.jpg|68px]] || 672 px <br> ↓ <br> 68 px
|-
| 25 || [[Image:Riff 25 Big.jpg|38px]] || 384 px <br> ↓ <br> 38 px
|-
| 26 || [[Image:Riff 26 Big.jpg|54px]] || 528 px <br> ↓ <br> 54 px
|-
| 27 || [[Image:Riff 27 Big.jpg|38px]] || 384 px <br> ↓ <br> 38 px
|-
| 28 || [[Image:Riff 28 Big.jpg|54px]] || 521 px <br> ↓ <br> 54 px
|-
| 29 || [[Image:Riff 29 Big.jpg|54px]] || 528 px <br> ↓ <br> 54 px
|-
| 30 || [[Image:Riff 30 Big.jpg|68px]] || 672 px <br> ↓ <br> 68 px
|-
| 31 || [[Image:Riff 31 Big.jpg|68px]] || 672 px <br> ↓ <br> 68 px
|-
| 32 || [[Image:Riff 32 Big.jpg|54px]] || 528 px <br> ↓ <br> 54 px
|-
| 33 || [[Image:Riff 33 Big.jpg|68px]] || 672 px <br> ↓ <br> 68 px
|-
| 34 || [[Image:Riff 34 Big.jpg|68px]] || 665 px <br> ↓ <br> 68 px
|-
| 35 || [[Image:Riff 35 Big.jpg|54px]] || 521 px <br> ↓ <br> 54 px
|-
| 36 || [[Image:Riff 36 Big.jpg|38px]] || 384 px <br> ↓ <br> 38 px
|-
| 37 || [[Image:Riff 37 Big.jpg|38px]] || 384 px <br> ↓ <br> 38 px
|-
| 38 || [[Image:Riff 38 Big.jpg|68px]] || 672 px <br> ↓ <br> 68 px
|-
| 39 || [[Image:Riff 39 Big.jpg|68px]] || 672 px <br> ↓ <br> 68 px
|-
| 40 || [[Image:Riff 40 Big.jpg|82px]] || 816 px <br> ↓ <br> 82 px
|-
| 41 || [[Image:Riff 41 Big.jpg|54px]] || 528 px <br> ↓ <br> 54 px
|-
| 42 || [[Image:Riff 42 Big.jpg|68px]] || 665 px <br> ↓ <br> 68 px
|-
| 43 || [[Image:Riff 43 Big.jpg|54px]] || 521 px <br> ↓ <br> 54 px
|-
| 44 || [[Image:Riff 44 Big.jpg|68px]] || 672 px <br> ↓ <br> 68 px
|-
| 45 || [[Image:Riff 45 Big.jpg|54px]] || 528 px <br> ↓ <br> 54 px
|-
| 46 || [[Image:Riff 46 Big.jpg|54px]] || 528 px <br> ↓ <br> 54 px
|-
| 47 || [[Image:Riff 47 Big.jpg|54px]] || 528 px <br> ↓ <br> 54 px
|-
| 48 || [[Image:Riff 48 Big.jpg|38px]] || 384 px <br> ↓ <br> 38 px
|-
| 49 || [[Image:Riff 49 Big.jpg|38px]] || 377 px <br> ↓ <br> 38 px
|-
| 50 || [[Image:Riff 50 Big.jpg|54px]] || 528 px <br> ↓ <br> 54 px
|-
| 51 || [[Image:Riff 51 Big.jpg|68px]] || 665 px <br> ↓ <br> 68 px
|-
| 52 || [[Image:Riff 52 Big.jpg|54px]] || 528 px <br> ↓ <br> 54 px
|-
| 53 || [[Image:Riff 53 Big.jpg|54px]] || 521 px <br> ↓ <br> 54 px
|-
| 54 || [[Image:Riff 54 Big.jpg|54px]] || 528 px <br> ↓ <br> 54 px
|-
| 55 || [[Image:Riff 55 Big.jpg|68px]] || 672 px <br> ↓ <br> 68 px
|-
| 56 || [[Image:Riff 56 Big.jpg|82px]] || 809 px <br> ↓ <br> 82 px
|-
| 57 || [[Image:Riff 57 Big.jpg|68px]] || 672 px <br> ↓ <br> 68 px
|-
| 58 || [[Image:Riff 58 Big.jpg|68px]] || 672 px <br> ↓ <br> 68 px
|-
| 59 || [[Image:Riff 59 Big.jpg|68px]] || 665 px <br> ↓ <br> 68 px
|-
| 60 || [[Image:Riff 60 Big.jpg|68px]] || 672 px <br> ↓ <br> 68 px
|-
| 64 || [[Image:Riff 64 Big.jpg|38px]] || 384 px <br> ↓ <br> 38 px
|-
| 81 || [[Image:Riff 81 Big.jpg|38px]] || 377 px <br> ↓ <br> 38 px
|-
| 105 || [[Image:Riff 105 Big.jpg|68px]] || 665 px <br> ↓ <br> 68 px
|-
| 128 || [[Image:Riff 128 Big.jpg|54px]] || 521 px <br> ↓ <br> 54 px
|-
| 165 || [[Image:Riff 165 Big.jpg|82px]] || 816 px <br> ↓ <br> 82 px
|-
| 256 || [[Image:Riff 256 Big.jpg|54px]] || 528 px <br> ↓ <br> 54 px
|-
| 512 || [[Image:Riff 512 Big.jpg|38px]] || 384 px <br> ↓ <br> 38 px
|-
| 2010 || [[Image:Riff 2010 Big.jpg|110px]] || 1104 px <br> ↓ <br> 110 px
|-
| 2500 || [[Image:Riff 2500 Big.jpg|54px]] || 528 px <br> ↓ <br> 54 px
|-
| 65536 || [[Image:Riff 65536 Big.jpg|54px]] || 521 px <br> ↓ <br> 54 px
|-
| 802701 || [[Image:Riff 802701 Big.jpg|125px]] || 1248 px <br> ↓ <br> 125 px
|-
| 123456789 || [[Image:Riff 123456789 Big.jpg|130px]] || 1296 px <br> ↓ <br> 130 px
|}
====Rotes====
{| align="center" border="1" cellpadding="20" style="text-align:center; width:90%"
|-
| width="15%" | '''Integer'''
| width="70%" | '''Rote'''
| width="15%" | '''Scale'''
|-
| 1 || [[Image:Rote 1 Big.jpg|12px]] || 117 px <br> ↓ <br> 12 px
|-
| 2 || [[Image:Rote 2 Big.jpg|24px]] || 233 px <br> ↓ <br> 24 px
|-
| 3 || [[Image:Rote 3 Big.jpg|24px]] || 233 px <br> ↓ <br> 24 px
|-
| 4 || [[Image:Rote 4 Big.jpg|38px]] || 377 px <br> ↓ <br> 38 px
|-
| 5 || [[Image:Rote 5 Big.jpg|24px]] || 233 px <br> ↓ <br> 24 px
|-
| 6 || [[Image:Rote 6 Big.jpg|48px]] || 473 px <br> ↓ <br> 48 px
|-
| 7 || [[Image:Rote 7 Big.jpg|38px]] || 377 px <br> ↓ <br> 38 px
|-
| 8 || [[Image:Rote 8 Big.jpg|38px]] || 377 px <br> ↓ <br> 38 px
|-
| 9 || [[Image:Rote 9 Big.jpg|48px]] || 473 px <br> ↓ <br> 48 px
|-
| 10 || [[Image:Rote 10 Big.jpg|48px]] || 473 px <br> ↓ <br> 48 px
|-
| 11 || [[Image:Rote 11 Big.jpg|24px]] || 233 px <br> ↓ <br> 24 px
|-
| 12 || [[Image:Rote 12 Big.jpg|62px]] || 617 px <br> ↓ <br> 62 px
|-
| 13 || [[Image:Rote 13 Big.jpg|48px]] || 473 px <br> ↓ <br> 48 px
|-
| 14 || [[Image:Rote 14 Big.jpg|62px]] || 617 px <br> ↓ <br> 62 px
|-
| 15 || [[Image:Rote 15 Big.jpg|48px]] || 473 px <br> ↓ <br> 48 px
|-
| 16 || [[Image:Rote 16 Big.jpg|54px]] || 521 px <br> ↓ <br> 54 px
|-
| 17 || [[Image:Rote 17 Big.jpg|38px]] || 377 px <br> ↓ <br> 38 px
|-
| 18 || [[Image:Rote 18 Big.jpg|72px]] || 713 px <br> ↓ <br> 72 px
|-
| 19 || [[Image:Rote 19 Big.jpg|38px]] || 377 px <br> ↓ <br> 38 px
|-
| 20 || [[Image:Rote 20 Big.jpg|62px]] || 617 px <br> ↓ <br> 62 px
|-
| 21 || [[Image:Rote 21 Big.jpg|62px]] || 617 px <br> ↓ <br> 62 px
|-
| 22 || [[Image:Rote 22 Big.jpg|48px]] || 473 px <br> ↓ <br> 48 px
|-
| 23 || [[Image:Rote 23 Big.jpg|48px]] || 473 px <br> ↓ <br> 48 px
|-
| 24 || [[Image:Rote 24 Big.jpg|62px]] || 617 px <br> ↓ <br> 62 px
|-
| 25 || [[Image:Rote 25 Big.jpg|48px]] || 473 px <br> ↓ <br> 48 px
|-
| 26 || [[Image:Rote 26 Big.jpg|72px]] || 713 px <br> ↓ <br> 72 px
|-
| 27 || [[Image:Rote 27 Big.jpg|48px]] || 473 px <br> ↓ <br> 48 px
|-
| 28 || [[Image:Rote 28 Big.jpg|76px]] || 761 px <br> ↓ <br> 76 px
|-
| 29 || [[Image:Rote 29 Big.jpg|48px]] || 473 px <br> ↓ <br> 48 px
|-
| 30 || [[Image:Rote 30 Big.jpg|72px]] || 713 px <br> ↓ <br> 72 px
|-
| 31 || [[Image:Rote 31 Big.jpg|24px]] || 233 px <br> ↓ <br> 24 px
|-
| 32 || [[Image:Rote 32 Big.jpg|38px]] || 377 px <br> ↓ <br> 38 px
|-
| 33 || [[Image:Rote 33 Big.jpg|48px]] || 473 px <br> ↓ <br> 48 px
|-
| 34 || [[Image:Rote 34 Big.jpg|62px]] || 617 px <br> ↓ <br> 62 px
|-
| 35 || [[Image:Rote 35 Big.jpg|62px]] || 617 px <br> ↓ <br> 62 px
|-
| 36 || [[Image:Rote 36 Big.jpg|86px]] || 857 px <br> ↓ <br> 86 px
|-
| 37 || [[Image:Rote 37 Big.jpg|62px]] || 617 px <br> ↓ <br> 62 px
|-
| 38 || [[Image:Rote 38 Big.jpg|62px]] || 617 px <br> ↓ <br> 62 px
|-
| 39 || [[Image:Rote 39 Big.jpg|72px]] || 713 px <br> ↓ <br> 72 px
|-
| 40 || [[Image:Rote 40 Big.jpg|62px]] || 617 px <br> ↓ <br> 62 px
|-
| 41 || [[Image:Rote 41 Big.jpg|48px]] || 473 px <br> ↓ <br> 48 px
|-
| 42 || [[Image:Rote 42 Big.jpg|86px]] || 857 px <br> ↓ <br> 86 px
|-
| 43 || [[Image:Rote 43 Big.jpg|62px]] || 617 px <br> ↓ <br> 62 px
|-
| 44 || [[Image:Rote 44 Big.jpg|62px]] || 617 px <br> ↓ <br> 62 px
|-
| 45 || [[Image:Rote 45 Big.jpg|72px]] || 713 px <br> ↓ <br> 72 px
|-
| 46 || [[Image:Rote 46 Big.jpg|72px]] || 713 px <br> ↓ <br> 72 px
|-
| 47 || [[Image:Rote 47 Big.jpg|48px]] || 473 px <br> ↓ <br> 48 px
|-
| 48 || [[Image:Rote 48 Big.jpg|62px]] || 617 px <br> ↓ <br> 62 px
|-
| 49 || [[Image:Rote 49 Big.jpg|48px]] || 473 px <br> ↓ <br> 48 px
|-
| 50 || [[Image:Rote 50 Big.jpg|72px]] || 713 px <br> ↓ <br> 72 px
|-
| 51 || [[Image:Rote 51 Big.jpg|62px]] || 617 px <br> ↓ <br> 62 px
|-
| 52 || [[Image:Rote 52 Big.jpg|86px]] || 857 px <br> ↓ <br> 86 px
|-
| 53 || [[Image:Rote 53 Big.jpg|54px]] || 521 px <br> ↓ <br> 54 px
|-
| 54 || [[Image:Rote 54 Big.jpg|72px]] || 713 px <br> ↓ <br> 72 px
|-
| 55 || [[Image:Rote 55 Big.jpg|48px]] || 473 px <br> ↓ <br> 48 px
|-
| 56 || [[Image:Rote 56 Big.jpg|76px]] || 761 px <br> ↓ <br> 76 px
|-
| 57 || [[Image:Rote 57 Big.jpg|62px]] || 617 px <br> ↓ <br> 62 px
|-
| 58 || [[Image:Rote 58 Big.jpg|72px]] || 713 px <br> ↓ <br> 72 px
|-
| 59 || [[Image:Rote 59 Big.jpg|38px]] || 377 px <br> ↓ <br> 38 px
|-
| 60 || [[Image:Rote 60 Big.jpg|90px]] || 905 px <br> ↓ <br> 90 px
|-
| 64 || [[Image:Rote 64 Big.jpg|62px]] || 617 px <br> ↓ <br> 62 px
|-
| 81 || [[Image:Rote 81 Big.jpg|62px]] || 617 px <br> ↓ <br> 62 px
|-
| 105 || [[Image:Rote 105 Big.jpg|86px]] || 857 px <br> ↓ <br> 86 px
|-
| 128 || [[Image:Rote 128 Big.jpg|54px]] || 521 px <br> ↓ <br> 54 px
|-
| 165 || [[Image:Rote 165 Big.jpg|72px]] || 713 px <br> ↓ <br> 72 px
|-
| 256 || [[Image:Rote 256 Big.jpg|54px]] || 521 px <br> ↓ <br> 54 px
|-
| 512 || [[Image:Rote 512 Big.jpg|62px]] || 617 px <br> ↓ <br> 62 px
|-
| 2010 || [[Image:Rote 2010 Big.jpg|115px]] || 1145 px <br> ↓ <br> 115 px
|-
| 2500 || [[Image:Rote 2500 Big.jpg|100px]] || 1001 px <br> ↓ <br> 100 px
|-
| 65536 || [[Image:Rote 65536 Big.jpg|68px]] || 665 px <br> ↓ <br> 68 px
|-
| 802701 || [[Image:Rote 802701 Big.jpg|196px]] || 1961 px <br> ↓ <br> 196 px
|-
| 123456789 || [[Image:Rote 123456789 Big.jpg|205px]] || 2048 px <br> ↓ <br> 205 px
|}
==Riffs in Numerical Order==
{| align="center" border="1" cellpadding="10"
|+ style="height:25px" | <math>\text{Riffs in Numerical Order}\!</math>
| valign="bottom" |
<p> </p><br>
<p><math>1\!</math></p><br>
<p><math>\begin{array}{l} \varnothing \\ 1 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 2 Big.jpg|20px]]</p><br>
<p><math>\text{p}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!1 \\ 2 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 3 Big.jpg|40px]]</p><br>
<p><math>\text{p}_\text{p}\!</math></p><br>
<p><math>\begin{array}{l} 2\!:\!1 \\ 3 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 4 Big.jpg|40px]]</p><br>
<p><math>\text{p}^\text{p}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!2 \\ 4 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 5 Big.jpg|65px]]</p><br>
<p><math>\text{p}_{\text{p}_\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 3\!:\!1 \\ 5 \end{array}</math></p>
|-
| valign="bottom" |
<p>[[Image:Riff 6 Big.jpg|65px]]</p><br>
<p><math>\text{p} \text{p}_\text{p}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!1 ~~ 2\!:\!1 \\ 6 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 7 Big.jpg|65px]]</p><br>
<p><math>\text{p}_{\text{p}^\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 4\!:\!1 \\ 7 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 8 Big.jpg|65px]]</p><br>
<p><math>\text{p}^{\text{p}_\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!3 \\ 8 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 9 Big.jpg|40px]]</p><br>
<p><math>\text{p}_\text{p}^\text{p}\!</math></p><br>
<p><math>\begin{array}{l} 2\!:\!2 \\ 9 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 10 Big.jpg|90px]]</p><br>
<p><math>\text{p} \text{p}_{\text{p}_\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!1 ~~ 3\!:\!1 \\ 10 \end{array}</math></p>
|-
| valign="bottom" |
<p>[[Image:Riff 11 Big.jpg|90px]]</p><br>
<p><math>\text{p}_{\text{p}_{\text{p}_\text{p}}}\!</math></p><br>
<p><math>\begin{array}{l} 5\!:\!1 \\ 11 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 12 Big.jpg|65px]]</p><br>
<p><math>\text{p}^\text{p} \text{p}_\text{p}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!2 ~~ 2\!:\!1 \\ 12 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 13 Big.jpg|65px]]</p><br>
<p><math>\text{p}_{\text{p} \text{p}_\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 6\!:\!1 \\ 13 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 14 Big.jpg|90px]]</p><br>
<p><math>\text{p} \text{p}_{\text{p}^\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!1 ~~ 4\!:\!1 \\ 14 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 15 Big.jpg|90px]]</p><br>
<p><math>\text{p}_\text{p} \text{p}_{\text{p}_\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 2\!:\!1 ~~ 3\!:\!1 \\ 15 \end{array}</math></p>
|-
| valign="bottom" |
<p>[[Image:Riff 16 Big.jpg|65px]]</p><br>
<p><math>\text{p}^{\text{p}^\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!4 \\ 16 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 17 Big.jpg|90px]]</p><br>
<p><math>\text{p}_{\text{p}_{\text{p}^\text{p}}}\!</math></p><br>
<p><math>\begin{array}{l} 7\!:\!1 \\ 17 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 18 Big.jpg|65px]]</p><br>
<p><math>\text{p} \text{p}_\text{p}^\text{p}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!1 ~~ 2\!:\!2 \\ 18 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 19 Big.jpg|90px]]</p><br>
<p><math>\text{p}_{\text{p}^{\text{p}_\text{p}}}\!</math></p><br>
<p><math>\begin{array}{l} 8\!:\!1 \\ 19 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 20 Big.jpg|90px]]</p><br>
<p><math>\text{p}^\text{p} \text{p}_{\text{p}_\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!2 ~~ 3\!:\!1 \\ 20 \end{array}</math></p>
|-
| valign="bottom" |
<p>[[Image:Riff 21 Big.jpg|90px]]</p><br>
<p><math>\text{p}_\text{p} \text{p}_{\text{p}^\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 2\!:\!1 ~~ 4\!:\!1 \\ 21 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 22 Big.jpg|115px]]</p><br>
<p><math>\text{p} \text{p}_{\text{p}_{\text{p}_\text{p}}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!1 ~~ 5\!:\!1 \\ 22 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 23 Big.jpg|65px]]</p><br>
<p><math>\text{p}_{\text{p}_\text{p}^\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 9\!:\!1 \\ 23 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 24 Big.jpg|115px]]</p><br>
<p><math>\text{p}^{\text{p}_\text{p}} \text{p}_\text{p}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!3 ~~ 2\!:\!1 \\ 24 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 25 Big.jpg|65px]]</p><br>
<p><math>\text{p}_{\text{p}_\text{p}}^\text{p}\!</math></p><br>
<p><math>\begin{array}{l} 3\!:\!2 \\ 25 \end{array}</math></p>
|-
| valign="bottom" |
<p>[[Image:Riff 26 Big.jpg|90px]]</p><br>
<p><math>\text{p} \text{p}_{\text{p} \text{p}_\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!1 ~~ 6\!:\!1 \\ 26 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 27 Big.jpg|65px]]</p><br>
<p><math>\text{p}_\text{p}^{\text{p}_\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 2\!:\!3 \\ 27 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 28 Big.jpg|90px]]</p><br>
<p><math>\text{p}^\text{p} \text{p}_{\text{p}^\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!2 ~~ 4\!:\!1 \\ 28 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 29 Big.jpg|90px]]</p><br>
<p><math>\text{p}_{\text{p} \text{p}_{\text{p}_\text{p}}}\!</math></p><br>
<p><math>\begin{array}{l} 10\!:\!1 \\ 29 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 30 Big.jpg|115px]]</p><br>
<p><math>\text{p} \text{p}_\text{p} \text{p}_{\text{p}_\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!1 ~~ 2\!:\!1 ~~ 3\!:\!1 \\ 30 \end{array}</math></p>
|-
| valign="bottom" |
<p>[[Image:Riff 31 Big.jpg|115px]]</p><br>
<p><math>\text{p}_{\text{p}_{\text{p}_{\text{p}_\text{p}}}}\!</math></p><br>
<p><math>\begin{array}{l} 11\!:\!1 \\ 31 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 32 Big.jpg|90px]]</p><br>
<p><math>\text{p}^{\text{p}_{\text{p}_\text{p}}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!5 \\ 32 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 33 Big.jpg|115px]]</p><br>
<p><math>\text{p}_\text{p} \text{p}_{\text{p}_{\text{p}_\text{p}}}\!</math></p><br>
<p><math>\begin{array}{l} 2\!:\!1 ~~ 5\!:\!1 \\ 33 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 34 Big.jpg|115px]]</p><br>
<p><math>\text{p} \text{p}_{\text{p}_{\text{p}^\text{p}}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!1 ~~ 7\!:\!1 \\ 34 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 35 Big.jpg|90px]]</p><br>
<p><math>\text{p}_{\text{p}_\text{p}} \text{p}_{\text{p}^\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 3\!:\!1 ~~ 4\!:\!1 \\ 35 \end{array}</math></p>
|-
| valign="bottom" |
<p>[[Image:Riff 36 Big.jpg|65px]]</p><br>
<p><math>\text{p}^\text{p} \text{p}_\text{p}^\text{p}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!2 ~~ 2\!:\!2 \\ 36 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 37 Big.jpg|65px]]</p><br>
<p><math>\text{p}_{\text{p}^\text{p} \text{p}_\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 12\!:\!1 \\ 37 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 38 Big.jpg|115px]]</p><br>
<p><math>\text{p} \text{p}_{\text{p}^{\text{p}_\text{p}}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!1 ~~ 8\!:\!1 \\ 38 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 39 Big.jpg|115px]]</p><br>
<p><math>\text{p}_\text{p} \text{p}_{\text{p} \text{p}_\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 2\!:\!1 ~~ 6\!:\!1 \\ 39 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 40 Big.jpg|135px]]</p><br>
<p><math>\text{p}^{\text{p}_\text{p}} \text{p}_{\text{p}_\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!3 ~~ 3\!:\!1 \\ 40 \end{array}</math></p>
|-
| valign="bottom" |
<p>[[Image:Riff 41 Big.jpg|90px]]</p><br>
<p><math>\text{p}_{\text{p}_{\text{p} \text{p}_\text{p}}}\!</math></p><br>
<p><math>\begin{array}{l} 13\!:\!1 \\ 41 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 42 Big.jpg|115px]]</p><br>
<p><math>\text{p} \text{p}_\text{p} \text{p}_{\text{p}^\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!1 ~~ 2\!:\!1 ~~ 4\!:\!1 \\ 42 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 43 Big.jpg|90px]]</p><br>
<p><math>\text{p}_{\text{p} \text{p}_{\text{p}^\text{p}}}\!</math></p><br>
<p><math>\begin{array}{l} 14\!:\!1 \\ 43 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 44 Big.jpg|115px]]</p><br>
<p><math>\text{p}^\text{p} \text{p}_{\text{p}_{\text{p}_\text{p}}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!2 ~~ 5\!:\!1 \\ 44 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 45 Big.jpg|90px]]</p><br>
<p><math>\text{p}_\text{p}^\text{p} \text{p}_{\text{p}_\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 2\!:\!2 ~~ 3\!:\!1 \\ 45 \end{array}</math></p>
|-
| valign="bottom" |
<p>[[Image:Riff 46 Big.jpg|90px]]</p><br>
<p><math>\text{p} \text{p}_{\text{p}_\text{p}^\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!1 ~~ 9\!:\!1 \\ 46 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 47 Big.jpg|90px]]</p><br>
<p><math>\text{p}_{\text{p}_\text{p} \text{p}_{\text{p}_\text{p}}}\!</math></p><br>
<p><math>\begin{array}{l} 15\!:\!1 \\ 47 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 48 Big.jpg|65px]]</p><br>
<p><math>\text{p}^{\text{p}^\text{p}} \text{p}_\text{p}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!4 ~~ 2\!:\!1 \\ 48 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 49 Big.jpg|65px]]</p><br>
<p><math>\text{p}_{\text{p}^\text{p}}^\text{p}\!</math></p><br>
<p><math>\begin{array}{l} 4\!:\!2 \\ 49 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 50 Big.jpg|90px]]</p><br>
<p><math>\text{p} \text{p}_{\text{p}_\text{p}}^\text{p}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!1 ~~ 3\!:\!2 \\ 50 \end{array}</math></p>
|-
| valign="bottom" |
<p>[[Image:Riff 51 Big.jpg|115px]]</p><br>
<p><math>\text{p}_\text{p} \text{p}_{\text{p}_{\text{p}^\text{p}}}\!</math></p><br>
<p><math>\begin{array}{l} 2\!:\!1 ~~ 7\!:\!1 \\ 51 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 52 Big.jpg|90px]]</p><br>
<p><math>\text{p}^\text{p} \text{p}_{\text{p} \text{p}_\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!2 ~~ 6\!:\!1 \\ 52 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 53 Big.jpg|90px]]</p><br>
<p><math>\text{p}_{\text{p}^{\text{p}^\text{p}}}\!</math></p><br>
<p><math>\begin{array}{l} 16\!:\!1 \\ 53 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 54 Big.jpg|90px]]</p><br>
<p><math>\text{p} \text{p}_\text{p}^{\text{p}_\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!1 ~~ 2\!:\!3 \\ 54 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 55 Big.jpg|115px]]</p><br>
<p><math>\text{p}_{\text{p}_\text{p}} \text{p}_{\text{p}_{\text{p}_\text{p}}}\!</math></p><br>
<p><math>\begin{array}{l} 3\!:\!1 ~~ 5\!:\!1 \\ 55 \end{array}</math></p>
|-
| valign="bottom" |
<p>[[Image:Riff 56 Big.jpg|135px]]</p><br>
<p><math>\text{p}^{\text{p}_\text{p}} \text{p}_{\text{p}^\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!3 ~~ 4\!:\!1 \\ 56 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 57 Big.jpg|115px]]</p><br>
<p><math>\text{p}_\text{p} \text{p}_{\text{p}^{\text{p}_\text{p}}}\!</math></p><br>
<p><math>\begin{array}{l} 2\!:\!1 ~~ 8\!:\!1 \\ 57 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 58 Big.jpg|115px]]</p><br>
<p><math>\text{p} \text{p}_{\text{p} \text{p}_{\text{p}_\text{p}}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!1 ~~ 10\!:\!1 \\ 58 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 59 Big.jpg|115px]]</p><br>
<p><math>\text{p}_{\text{p}_{\text{p}_{\text{p}^\text{p}}}}\!</math></p><br>
<p><math>\begin{array}{l} 17\!:\!1 \\ 59 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Riff 60 Big.jpg|115px]]</p><br>
<p><math>\text{p}^\text{p} \text{p}_\text{p} \text{p}_{\text{p}_\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!2 ~~ 2\!:\!1 ~~ 3\!:\!1 \\ 60 \end{array}</math></p>
|}
==Rotes in Numerical Order==
{| align="center" border="1" cellpadding="6"
| valign="bottom" |
<p>[[Image:Rote 1 Big.jpg|20px]]</p><br>
<p><math>1\!</math></p><br>
<p><math>\begin{array}{l} \varnothing \\ 1 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 2 Big.jpg|40px]]</p><br>
<p><math>\text{p}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!1 \\ 2 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 3 Big.jpg|40px]]</p><br>
<p><math>\text{p}_\text{p}\!</math></p><br>
<p><math>\begin{array}{l} 2\!:\!1 \\ 3 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 4 Big.jpg|65px]]</p><br>
<p><math>\text{p}^\text{p}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!2 \\ 4 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 5 Big.jpg|40px]]</p><br>
<p><math>\text{p}_{\text{p}_\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 3\!:\!1 \\ 5 \end{array}</math></p>
|-
| valign="bottom" |
<p>[[Image:Rote 6 Big.jpg|80px]]</p><br>
<p><math>\text{p} \text{p}_\text{p}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!1 ~~ 2\!:\!1 \\ 6 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 7 Big.jpg|65px]]</p><br>
<p><math>\text{p}_{\text{p}^\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 4\!:\!1 \\ 7 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 8 Big.jpg|65px]]</p><br>
<p><math>\text{p}^{\text{p}_\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!3 \\ 8 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 9 Big.jpg|80px]]</p><br>
<p><math>\text{p}_\text{p}^\text{p}\!</math></p><br>
<p><math>\begin{array}{l} 2\!:\!2 \\ 9 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 10 Big.jpg|80px]]</p><br>
<p><math>\text{p} \text{p}_{\text{p}_\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!1 ~~ 3\!:\!1 \\ 10 \end{array}</math></p>
|-
| valign="bottom" |
<p>[[Image:Rote 11 Big.jpg|40px]]</p><br>
<p><math>\text{p}_{\text{p}_{\text{p}_\text{p}}}\!</math></p><br>
<p><math>\begin{array}{l} 5\!:\!1 \\ 11 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 12 Big.jpg|105px]]</p><br>
<p><math>\text{p}^\text{p} \text{p}_\text{p}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!2 ~~ 2\!:\!1 \\ 12 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 13 Big.jpg|80px]]</p><br>
<p><math>\text{p}_{\text{p} \text{p}_\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 6\!:\!1 \\ 13 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 14 Big.jpg|105px]]</p><br>
<p><math>\text{p} \text{p}_{\text{p}^\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!1 ~~ 4\!:\!1 \\ 14 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 15 Big.jpg|80px]]</p><br>
<p><math>\text{p}_\text{p} \text{p}_{\text{p}_\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 2\!:\!1 ~~ 3\!:\!1 \\ 15 \end{array}</math></p>
|-
| valign="bottom" |
<p>[[Image:Rote 16 Big.jpg|90px]]</p><br>
<p><math>\text{p}^{\text{p}^\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!4 \\ 16 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 17 Big.jpg|65px]]</p><br>
<p><math>\text{p}_{\text{p}_{\text{p}^\text{p}}}\!</math></p><br>
<p><math>\begin{array}{l} 7\!:\!1 \\ 17 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 18 Big.jpg|120px]]</p><br>
<p><math>\text{p} \text{p}_\text{p}^\text{p}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!1 ~~ 2\!:\!2 \\ 18 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 19 Big.jpg|65px]]</p><br>
<p><math>\text{p}_{\text{p}^{\text{p}_\text{p}}}\!</math></p><br>
<p><math>\begin{array}{l} 8\!:\!1 \\ 19 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 20 Big.jpg|105px]]</p><br>
<p><math>\text{p}^\text{p} \text{p}_{\text{p}_\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!2 ~~ 3\!:\!1 \\ 20 \end{array}</math></p>
|-
| valign="bottom" |
<p>[[Image:Rote 21 Big.jpg|105px]]</p><br>
<p><math>\text{p}_\text{p} \text{p}_{\text{p}^\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 2\!:\!1 ~~ 4\!:\!1 \\ 21 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 22 Big.jpg|80px]]</p><br>
<p><math>\text{p} \text{p}_{\text{p}_{\text{p}_\text{p}}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!1 ~~ 5\!:\!1 \\ 22 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 23 Big.jpg|80px]]</p><br>
<p><math>\text{p}_{\text{p}_\text{p}^\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 9\!:\!1 \\ 23 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 24 Big.jpg|105px]]</p><br>
<p><math>\text{p}^{\text{p}_\text{p}} \text{p}_\text{p}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!3 ~~ 2\!:\!1 \\ 24 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 25 Big.jpg|80px]]</p><br>
<p><math>\text{p}_{\text{p}_\text{p}}^\text{p}\!</math></p><br>
<p><math>\begin{array}{l} 3\!:\!2 \\ 25 \end{array}</math></p>
|-
| valign="bottom" |
<p>[[Image:Rote 26 Big.jpg|120px]]</p><br>
<p><math>\text{p} \text{p}_{\text{p} \text{p}_\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!1 ~~ 6\!:\!1 \\ 26 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 27 Big.jpg|80px]]</p><br>
<p><math>\text{p}_\text{p}^{\text{p}_\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 2\!:\!3 \\ 27 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 28 Big.jpg|130px]]</p><br>
<p><math>\text{p}^\text{p} \text{p}_{\text{p}^\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!2 ~~ 4\!:\!1 \\ 28 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 29 Big.jpg|80px]]</p><br>
<p><math>\text{p}_{\text{p} \text{p}_{\text{p}_\text{p}}}\!</math></p><br>
<p><math>\begin{array}{l} 10\!:\!1 \\ 29 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 30 Big.jpg|120px]]</p><br>
<p><math>\text{p} \text{p}_\text{p} \text{p}_{\text{p}_\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!1 ~~ 2\!:\!1 ~~ 3\!:\!1 \\ 30 \end{array}</math></p>
|-
| valign="bottom" |
<p>[[Image:Rote 31 Big.jpg|40px]]</p><br>
<p><math>\text{p}_{\text{p}_{\text{p}_{\text{p}_\text{p}}}}\!</math></p><br>
<p><math>\begin{array}{l} 11\!:\!1 \\ 31 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 32 Big.jpg|65px]]</p><br>
<p><math>\text{p}^{\text{p}_{\text{p}_\text{p}}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!5 \\ 32 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 33 Big.jpg|80px]]</p><br>
<p><math>\text{p}_\text{p} \text{p}_{\text{p}_{\text{p}_\text{p}}}\!</math></p><br>
<p><math>\begin{array}{l} 2\!:\!1 ~~ 5\!:\!1 \\ 33 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 34 Big.jpg|105px]]</p><br>
<p><math>\text{p} \text{p}_{\text{p}_{\text{p}^\text{p}}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!1 ~~ 7\!:\!1 \\ 34 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 35 Big.jpg|105px]]</p><br>
<p><math>\text{p}_{\text{p}_\text{p}} \text{p}_{\text{p}^\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 3\!:\!1 ~~ 4\!:\!1 \\ 35 \end{array}</math></p>
|-
| valign="bottom" |
<p>[[Image:Rote 36 Big.jpg|145px]]</p><br>
<p><math>\text{p}^\text{p} \text{p}_\text{p}^\text{p}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!2 ~~ 2\!:\!2 \\ 36 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 37 Big.jpg|105px]]</p><br>
<p><math>\text{p}_{\text{p}^\text{p} \text{p}_\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 12\!:\!1 \\ 37 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 38 Big.jpg|105px]]</p><br>
<p><math>\text{p} \text{p}_{\text{p}^{\text{p}_\text{p}}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!1 ~~ 8\!:\!1 \\ 38 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 39 Big.jpg|120px]]</p><br>
<p><math>\text{p}_\text{p} \text{p}_{\text{p} \text{p}_\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 2\!:\!1 ~~ 6\!:\!1 \\ 39 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 40 Big.jpg|105px]]</p><br>
<p><math>\text{p}^{\text{p}_\text{p}} \text{p}_{\text{p}_\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!3 ~~ 3\!:\!1 \\ 40 \end{array}</math></p>
|-
| valign="bottom" |
<p>[[Image:Rote 41 Big.jpg|80px]]</p><br>
<p><math>\text{p}_{\text{p}_{\text{p} \text{p}_\text{p}}}\!</math></p><br>
<p><math>\begin{array}{l} 13\!:\!1 \\ 41 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 42 Big.jpg|145px]]</p><br>
<p><math>\text{p} \text{p}_\text{p} \text{p}_{\text{p}^\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!1 ~~ 2\!:\!1 ~~ 4\!:\!1 \\ 42 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 43 Big.jpg|105px]]</p><br>
<p><math>\text{p}_{\text{p} \text{p}_{\text{p}^\text{p}}}\!</math></p><br>
<p><math>\begin{array}{l} 14\!:\!1 \\ 43 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 44 Big.jpg|105px]]</p><br>
<p><math>\text{p}^\text{p} \text{p}_{\text{p}_{\text{p}_\text{p}}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!2 ~~ 5\!:\!1 \\ 44 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 45 Big.jpg|120px]]</p><br>
<p><math>\text{p}_\text{p}^\text{p} \text{p}_{\text{p}_\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 2\!:\!2 ~~ 3\!:\!1 \\ 45 \end{array}</math></p>
|-
| valign="bottom" |
<p>[[Image:Rote 46 Big.jpg|120px]]</p><br>
<p><math>\text{p} \text{p}_{\text{p}_\text{p}^\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!1 ~~ 9\!:\!1 \\ 46 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 47 Big.jpg|80px]]</p><br>
<p><math>\text{p}_{\text{p}_\text{p} \text{p}_{\text{p}_\text{p}}}\!</math></p><br>
<p><math>\begin{array}{l} 15\!:\!1 \\ 47 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 48 Big.jpg|105px]]</p><br>
<p><math>\text{p}^{\text{p}^\text{p}} \text{p}_\text{p}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!4 ~~ 2\!:\!1 \\ 48 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 49 Big.jpg|80px]]</p><br>
<p><math>\text{p}_{\text{p}^\text{p}}^\text{p}\!</math></p><br>
<p><math>\begin{array}{l} 4\!:\!2 \\ 49 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 50 Big.jpg|120px]]</p><br>
<p><math>\text{p} \text{p}_{\text{p}_\text{p}}^\text{p}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!1 ~~ 3\!:\!2 \\ 50 \end{array}</math></p>
|-
| valign="bottom" |
<p>[[Image:Rote 51 Big.jpg|105px]]</p><br>
<p><math>\text{p}_\text{p} \text{p}_{\text{p}_{\text{p}^\text{p}}}\!</math></p><br>
<p><math>\begin{array}{l} 2\!:\!1 ~~ 7\!:\!1 \\ 51 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 52 Big.jpg|145px]]</p><br>
<p><math>\text{p}^\text{p} \text{p}_{\text{p} \text{p}_\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!2 ~~ 6\!:\!1 \\ 52 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 53 Big.jpg|90px]]</p><br>
<p><math>\text{p}_{\text{p}^{\text{p}^\text{p}}}\!</math></p><br>
<p><math>\begin{array}{l} 16\!:\!1 \\ 53 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 54 Big.jpg|120px]]</p><br>
<p><math>\text{p} \text{p}_\text{p}^{\text{p}_\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!1 ~~ 2\!:\!3 \\ 54 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 55 Big.jpg|80px]]</p><br>
<p><math>\text{p}_{\text{p}_\text{p}} \text{p}_{\text{p}_{\text{p}_\text{p}}}\!</math></p><br>
<p><math>\begin{array}{l} 3\!:\!1 ~~ 5\!:\!1 \\ 55 \end{array}</math></p>
|-
| valign="bottom" |
<p>[[Image:Rote 56 Big.jpg|130px]]</p><br>
<p><math>\text{p}^{\text{p}_\text{p}} \text{p}_{\text{p}^\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!3 ~~ 4\!:\!1 \\ 56 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 57 Big.jpg|105px]]</p><br>
<p><math>\text{p}_\text{p} \text{p}_{\text{p}^{\text{p}_\text{p}}}\!</math></p><br>
<p><math>\begin{array}{l} 2\!:\!1 ~~ 8\!:\!1 \\ 57 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 58 Big.jpg|120px]]</p><br>
<p><math>\text{p} \text{p}_{\text{p} \text{p}_{\text{p}_\text{p}}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!1 ~~ 10\!:\!1 \\ 58 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 59 Big.jpg|65px]]</p><br>
<p><math>\text{p}_{\text{p}_{\text{p}_{\text{p}^\text{p}}}}\!</math></p><br>
<p><math>\begin{array}{l} 17\!:\!1 \\ 59 \end{array}</math></p>
| valign="bottom" |
<p>[[Image:Rote 60 Big.jpg|155px]]</p><br>
<p><math>\text{p}^\text{p} \text{p}_\text{p} \text{p}_{\text{p}_\text{p}}\!</math></p><br>
<p><math>\begin{array}{l} 1\!:\!2 ~~ 2\!:\!1 ~~ 3\!:\!1 \\ 60 \end{array}</math></p>
|}
==Miscellaneous Examples (Reduction 8:1)==
{| align="center" border="1" width="96%"
|+ style="height:24px" | <math>\text{Integers, Riffs, Rotes}\!</math>
|- style="height:50px; background:#f0f0ff"
|
{| cellpadding="12" style="background:#f0f0ff; text-align:center; width:100%"
| width="10%" | <math>\text{Integer}\!</math>
| width="45%" | <math>\text{Riff}\!</math>
| width="45%" | <math>\text{Rote}\!</math>
|}
|-
|
{| cellpadding="12" style="text-align:center; width:100%"
| width="10%" | <math>1\!</math>
| width="45%" |
| width="45%" | [[Image:Rote 1 Big.jpg|15px]]
|-
| <math>2\!</math>
| [[Image:Riff 2 Big.jpg|15px]]
| [[Image:Rote 2 Big.jpg|30px]]
|-
| <math>3\!</math>
| [[Image:Riff 3 Big.jpg|30px]]
| [[Image:Rote 3 Big.jpg|30px]]
|-
| <math>4\!</math>
| [[Image:Riff 4 Big.jpg|30px]]
| [[Image:Rote 4 Big.jpg|48px]]
|-
| <math>2010\!</math>
| [[Image:Riff 2010 Big.jpg|138px]]
| [[Image:Rote 2010 Big.jpg|144px]]
|-
| <math>2011\!</math>
| [[Image:Riff 2011 Big.jpg|84px]]
| [[Image:Rote 2011 Big.jpg|120px]]
|-
| <math>2500\!</math>
| [[Image:Riff 2500 Big.jpg|66px]]
| [[Image:Rote 2500 Big.jpg|125px]]
|-
| <math>802701\!</math>
| [[Image:Riff 802701 Big.jpg|156px]]
| [[Image:Rote 802701 Big.jpg|245px]]
|-
| <math>123456789\!</math>
| [[Image:Riff 123456789 Big.jpg|162px]]
| [[Image:Rote 123456789 Big.jpg|256px]]
|}
|}
==Cactus Graphs==
==Cactus Graphs==
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; text-align:center; width:90%"
===Hi Res===
<br>
{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:90%"
|-
|-
| height="100px" | [[Image:Cactus Node Big Fat.jpg|20px]]
| height="100px" | [[Image:Rooted Node Big.jpg|20px]]
| 117px → 20px
| 117 px → 20 px
|-
|-
| height="100px" | [[Image:Cactus Spike Big Fat.jpg|20px]]
| height="100px" | [[Image:Rooted Edge Big.jpg|20px]]
| 117px → 20px
| 117 px → 20 px
|-
|-
| height="100px" | [[Image:Cactus A Big.jpg|20px]]
| height="100px" | [[Image:Cactus A Big.jpg|20px]]
| ---px → 20px
| 117 px → 20 px
|-
|-
| height="120px" | [[Image:Cactus (A) Big.jpg|20px]]
| height="120px" | [[Image:Cactus (A) Big.jpg|20px]]
| ---px → 20px
| 117 px → 20 px
|-
|-
| height="100px" | [[Image:Cactus ABC Big.jpg|50px]]
| height="100px" | [[Image:Cactus ABC Big.jpg|50px]]
| ---px → 50px
| 290 px → 50 px
|-
|-
| height="160px" | [[Image:Cactus ((A)(B)(C)) Big.jpg|70px]]
| height="160px" | [[Image:Cactus ((A)(B)(C)) Big.jpg|65px]]
| ---px → 70px
| 386 px → 65 px
|-
| height="120px" | [[Image:Cactus (A)B Big.jpg|35px]]
| 204 px → 35 px
|-
|-
| height="120px" | [[Image:Cactus (A(B)) Big.jpg|60px]]
| height="120px" | [[Image:Cactus (A(B)) Big.jpg|60px]]
| ---px → 60px
| 348 px → 60 px
|-
|-
| height="120px" | [[Image:Cactus (A,B) Big.jpg|70px]]
| height="120px" | [[Image:Cactus (A,B) Big.jpg|65px]]
| ---px → 70px
| 386 px → 65 px
|-
|-
| height="160px" | [[Image:Cactus ((A,B)) Big.jpg|70px]]
| height="160px" | [[Image:Cactus ((A,B)) Big.jpg|65px]]
| ---px → 70px
| 386 px → 65 px
|-
|-
| height="120px" | [[Image:Cactus (A,B,C) Big.jpg|70px]]
| height="120px" | [[Image:Cactus (A,B,C) Big.jpg|65px]]
| ---px → 70px
| 386 px → 65 px
|-
|-
| height="160px" | [[Image:Cactus ((A),(B),(C)) Big.jpg|70px]]
| height="160px" | [[Image:Cactus ((A),(B),(C)) Big.jpg|65px]]
| ---px → 70px
| 386 px → 65 px
|-
|-
| height="160px" | [[Image:Cactus ((A,B,C)) Big.jpg|70px]]
| height="160px" | [[Image:Cactus ((A,B,C)) Big.jpg|65px]]
| ---px → 70px
| 386 px → 65 px
|-
|-
| height="200px" | [[Image:Cactus (((A),(B),(C))) Big.jpg|70px]]
| height="200px" | [[Image:Cactus (((A),(B),(C))) Big.jpg|65px]]
| ---px → 70px
| 386 px → 65 px
|-
|-
| height="160px" | [[Image:Cactus (A,(B),(C)) Big.jpg|70px]]
| height="160px" | [[Image:Cactus (A,(B),(C)) Big.jpg|65px]]
| ---px → 70px
| 386 px → 65 px
|-
|-
| height="200px" | [[Image:Cactus (((A),B,C)) Big.jpg|70px]]
| height="200px" | [[Image:Cactus (((A),B,C)) Big.jpg|65px]]
| ---px → 70px
| 386 px → 65 px
|-
|-
| height="160px" | [[Image:Cactus (A,(B,C)) Big.jpg|90px]]
| height="160px" | [[Image:Cactus (A,(B,C)) Big.jpg|90px]]
| ---px → 90px
| 530 px → 90 px
|-
| height="160px" | [[Image:Cactus (X,(A),(B),(C)) Big.jpg|90px]]
| 530 px → 90 px
|}
|}
<br>
===Lo Res===
<br>
{| align="center" cellpadding="8"
| [[Image:Cactus Graph Node Connective.jpg]]
|-
| [[Image:Cactus Graph Lobe Connective.jpg]]
|-
| [[Image:Cactus Graph Lobe Rule.jpg]]
|-
| [[Image:Cactus Graph Spike Rule.jpg]]
|}
<br>
==Differential Logic==
==Differential Logic==
\operatorname{d}p ~ \operatorname{d}q
\operatorname{d}p ~ \operatorname{d}q
\end{array}</math>
\end{array}</math>
|}
==Propositional Equation Reasoning Systems==
===Analysis of contingent propositions===
{| align="center" cellpadding="8"
| [[Image:Logical Graph (P (Q)) (P (R)).jpg|500px]] || (26)
|}
{| align="center" cellpadding="8" style="text-align:center"
| [[Image:Venn Diagram (P (Q)) (P (R)).jpg|500px]] || (27)
|-
| <math>\text{Venn Diagram for}~ \texttt{(} p \texttt{~(} q \texttt{))~(} p \texttt{~(} r \texttt{))}</math>
|}
{| align="center" cellpadding="8" style="text-align:center"
| [[Image:Venn Diagram (P (Q R)).jpg|500px]] || (28)
|-
| <math>\text{Venn Diagram for}~ \texttt{(} p \texttt{~(} q ~ r \texttt{))}</math>
|}
{| align="center" cellpadding="8"
| [[Image:Logical Graph (P (Q)) (P (R)) = (P (Q R)).jpg|500px]] || (29)
|}
====Equation 1 : Proof 1====
{| align="center" cellpadding="8"
| [[Image:Logical Graph (P (Q)) (P (R)) = (P (Q R)) Proof 1.jpg|500px]]
| (30)
|}
====Equation 1 : Proof 2====
=====Single Image Version=====
{| align="center" cellpadding="8"
| [[Image:Logical Graph (P (Q)) (P (R)) = (P (Q R)) Proof 2a Alt.jpg|500px]]
| (31)
|}
=====Serial Image Version=====
{| align="center" cellpadding="8"
|
{| align="center" cellpadding="0" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black; text-align:center"
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 2-1-0.jpg|500px]]
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 2-1-1.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Cast P.jpg|500px]]
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 2-1-2.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Domination.jpg|500px]]
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 2-1-3.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Cancellation.jpg|500px]]
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 2-1-4.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Cast Q.jpg|500px]]
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 2-1-5.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Cancellation.jpg|500px]]
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 2-1-6.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Domination.jpg|500px]]
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 2-1-7.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Cast R.jpg|500px]]
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 2-1-8.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Cancellation.jpg|500px]]
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 2-1-9.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- DNF.jpg|500px]]
|}
| (31)
|}
{| align="center" cellpadding="8"
|
{| align="center" cellpadding="0" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black; text-align:center"
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 2-2-0.jpg|500px]]
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 2-2-1.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Cast P.jpg|500px]]
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 2-2-2.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Domination.jpg|500px]]
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 2-2-3.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Cancellation.jpg|500px]]
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 2-2-4.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Cast Q.jpg|500px]]
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 2-2-5.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Domination.jpg|500px]]
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 2-2-6.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Cancellation.jpg|500px]]
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 2-2-7.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Cast R.jpg|500px]]
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 2-2-8.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Cancellation.jpg|500px]]
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 2-2-9.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- DNF.jpg|500px]]
|}
| (33)
|}
====Equation 1 : Proof 3====
{|
|
* '''Variant 1'''
# start
# cast p
# dom
# can
# empty
# can
# cast q
# dom
# can
# dom
# spike
# can
# cast r
# can
# empty
# spike
# can
|
* '''Variant 2'''
# start
# cast p
# dom
# can
# empty
# can
# cast q
# can
# dom
# can
# spike
# can
# cast r
# can
# empty
# spike
# can
|}
=====Variant 1=====
{| align="center" cellpadding="8" style="text-align:center; width:90%"
|
<pre>
o-----------------------------------------------------------o
| Equation E_1. Proof 3. |
o-----------------------------------------------------------o
| 1 |
| q o o r q o r |
| | | | |
| p o o p p o |
| \ / | |
| o---------o |
| \ / |
| \ / |
| \ / |
| \ / |
| o |
| | |
| | |
| | |
| | |
| @ |
| |
o==================================< CAST "p" >=============o
| 2 |
| q r q r q r qr |
| o o o o o o o o o |
| | | | |/ |/ |/ |
| o o o o o o |
| \ / | \ / | |
| o-------o o-------o |
| \ / \ / |
| \ / \ / |
| \ / \ / |
| o o |
| | | |
| | | |
| | | |
| p o---------------o---o p |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| @ |
| |
o==================================< Domination >===========o
| 3 |
| q r q r |
| o o o o o o |
| | | | / / / |
| o o o o o o |
| \ / | \ / | |
| o-------o o-------o |
| \ / \ / |
| \ / \ / |
| \ / \ / |
| o o |
| | | |
| | | |
| | | |
| p o---------------o---o p |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| @ |
| |
o==================================< Cancellation >=========o
| 4 |
| q r q r |
| o o o |
| | | | |
| o o o |
| \ / | |
| o-------o o-------o |
| \ / \ / |
| \ / \ / |
| \ / \ / |
| o o |
| | | |
| | | |
| | | |
| p o---------------o---o p |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| @ |
| |
o==================================< Emptiness >============o
| 5 |
| q r q r |
| o o o |
| | | | |
| o o o |
| \ / | |
| o-------o o |
| \ / | |
| \ / | |
| \ / | |
| o o |
| | | |
| | | |
| | | |
| p o---------------o---o p |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| @ |
| |
o==================================< Cancellation >=========o
| 6 |
| q r q r |
| o o o |
| | | | |
| o o o |
| \ / | |
| o-------o |
| \ / |
| \ / |
| \ / |
| o |
| | |
| | |
| | |
| p o---------------o---o p |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| @ |
| |
o==================================< CAST "q" >=============o
| 7 |
| o o |
| r r | r | |
| o o o o o o r |
| | | | | | | |
| o o o o o o |
| \ / | \ / | |
| o-------o o-------o |
| \ / \ / |
| \ / \ / |
| \ / \ / |
| o o |
| | | |
| | | |
| | | |
| q o---------------o---o q |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| p o-------o---o p |
| \ / |
| \ / |
| \ / |
| @ |
| |
o==================================< Domination >===========o
| 8 |
| o o |
| r r | r | |
| o o o o o o |
| | | | | | | |
| o o o o o o |
| \ / | \ / | |
| o-------o o-------o |
| \ / \ / |
| \ / \ / |
| \ / \ / |
| o o |
| | | |
| | | |
| | | |
| q o---------------o---o q |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| p o-------o---o p |
| \ / |
| \ / |
| \ / |
| @ |
| |
o==================================< Cancellation >=========o
| 9 |
| r r r |
| o o o |
| | | | |
| o o o o o |
| / | \ / | |
| o-------o o-------o |
| \ / \ / |
| \ / \ / |
| \ / \ / |
| o o |
| | | |
| | | |
| | | |
| q o---------------o---o q |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| p o-------o---o p |
| \ / |
| \ / |
| \ / |
| @ |
| |
o==================================< Domination >===========o
| 10 |
| r r |
| o o |
| | | |
| o o o o |
| / | \ | |
| o-------o o-------o |
| \ / \ / |
| \ / \ / |
| \ / \ / |
| o o |
| | | |
| | | |
| | | |
| q o---------------o---o q |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| p o-------o---o p |
| \ / |
| \ / |
| \ / |
| @ |
| |
o==================================< Spike >================o
| 11 |
| r r |
| o o |
| | | |
| o o |
| / | |
| o-------o o |
| \ / | |
| \ / | |
| \ / | |
| o o |
| | | |
| | | |
| | | |
| q o---------------o---o q |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| p o-------o---o p |
| \ / |
| \ / |
| \ / |
| @ |
| |
o==================================< Cancellation >=========o
| 12 |
| r r |
| o o |
| | | |
| o o |
| / | |
| o-------o |
| \ / |
| \ / |
| \ / |
| o |
| | |
| | |
| | |
| q o---------------o---o q |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| p o-------o---o p |
| \ / |
| \ / |
| \ / |
| @ |
| |
o==================================< CAST "r" >=============o
| 13 |
| o o |
| | | |
| o o o o |
| | | | | |
| o o o o |
| / | / | |
| o-------o o-------o |
| \ / \ / |
| \ / \ / |
| \ / \ / |
| o o |
| | | |
| | | |
| | | |
| r o---------------o---o r |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| q o-------o---o q |
| \ / |
| \ / |
| \ / |
| p o-------o---o p |
| \ / |
| \ / |
| \ / |
| @ |
| |
o==================================< Cancellation >=========o
| 14 |
| o o |
| / | |
| o-------o o-------o |
| \ / \ / |
| \ / \ / |
| \ / \ / |
| o o |
| | | |
| | | |
| | | |
| r o---------------o---o r |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| q o-------o---o q |
| \ / |
| \ / |
| \ / |
| p o-------o---o p |
| \ / |
| \ / |
| \ / |
| @ |
| |
o==================================< Emptiness & Spike >====o
| 15 |
| o o 16 |
| | | |
| | | |
| | | |
| o o |
| | | |
| | | |
| | | |
| r o---------------o---o r |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| q o-------o---o q |
| \ / |
| \ / |
| \ / |
| p o-------o---o p |
| \ / |
| \ / |
| \ / |
| @ |
| |
o==================================< Cancellation >=========o
| 17 |
| r o-------o---o r |
| \ / |
| \ / |
| \ / |
| q o-------o---o q |
| \ / |
| \ / |
| \ / |
| p o-------o---o p |
| \ / |
| \ / |
| \ / |
| @ |
| |
o==================================< QED >==================o
</pre>
| (40)
|}
=====Variant 2=====
{| align="center" cellpadding="8"
|
{| align="center" cellpadding="0" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black; text-align:center"
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 3-00.jpg|500px]]
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 3-01.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Cast P.jpg|500px]]
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 3-02.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Domination.jpg|500px]]
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 3-03.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Cancellation.jpg|500px]]
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 3-04.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Emptiness.jpg|500px]]
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 3-05.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Cancellation.jpg|500px]]
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 3-06.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Cast Q.jpg|500px]]
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 3-07.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Cancellation.jpg|500px]]
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 3-08.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Domination.jpg|500px]]
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 3-09.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Cancellation.jpg|500px]]
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 3-10.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Spike.jpg|500px]]
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 3-11.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Cancellation.jpg|500px]]
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 3-12.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Cast R.jpg|500px]]
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 3-13.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Cancellation.jpg|500px]]
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 3-14.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Emptiness.jpg|500px]]
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 3-15.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Spike.jpg|500px]]
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 3-16.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Cancellation.jpg|500px]]
|-
| [[Image:Proof (P (Q)) (P (R)) = (P (Q R)) 3-17.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- QED.jpg|500px]]
|}
| (40)
|}
===Praeclarum Theorema : Proof by CAST===
{| align="center" cellpadding="8"
|
{| align="center" cellpadding="0" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black; text-align:center"
|-
| [[Image:Proof Praeclarum Theorema CAST 00.jpg|500px]]
|-
| [[Image:Proof Praeclarum Theorema CAST 01.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Cast A.jpg|500px]]
|-
| [[Image:Proof Praeclarum Theorema CAST 02.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Domination.jpg|500px]]
|-
| [[Image:Proof Praeclarum Theorema CAST 03.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Cancellation.jpg|500px]]
|-
| [[Image:Proof Praeclarum Theorema CAST 04.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Domination.jpg|500px]]
|-
| [[Image:Proof Praeclarum Theorema CAST 05.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Cancellation.jpg|500px]]
|-
| [[Image:Proof Praeclarum Theorema CAST 06.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Cast D.jpg|500px]]
|-
| [[Image:Proof Praeclarum Theorema CAST 07.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Domination.jpg|500px]]
|-
| [[Image:Proof Praeclarum Theorema CAST 08.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Cancellation.jpg|500px]]
|-
| [[Image:Proof Praeclarum Theorema CAST 09.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Domination.jpg|500px]]
|-
| [[Image:Proof Praeclarum Theorema CAST 10.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Cancellation.jpg|500px]]
|-
| [[Image:Proof Praeclarum Theorema CAST 11.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Cast B.jpg|500px]]
|-
| [[Image:Proof Praeclarum Theorema CAST 12.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Cancellation.jpg|500px]]
|-
| [[Image:Proof Praeclarum Theorema CAST 13.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Domination.jpg|500px]]
|-
| [[Image:Proof Praeclarum Theorema CAST 14.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Cancellation.jpg|500px]]
|-
| [[Image:Proof Praeclarum Theorema CAST 15.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Cast C.jpg|500px]]
|-
| [[Image:Proof Praeclarum Theorema CAST 16.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Cancellation.jpg|500px]]
|-
| [[Image:Proof Praeclarum Theorema CAST 17.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- Cancellation.jpg|500px]]
|-
| [[Image:Proof Praeclarum Theorema CAST 18.jpg|500px]]
|-
| [[Image:Equational Inference Bar -- QED.jpg|500px]]
|}
| (23)
|}
|}