Harmonotonic tuning: Difference between revisions

Line 244:

! colspan="2" rowspan="2" |monotonic tuning

! colspan="9" |frequency

!

! colspan="9" |pitch

!

! colspan="9" |length

|-

! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8 !! 9 !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8 !! 9 !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8 ~~!! 9~~

! (0) !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8

! !! (0) !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8

|-

! style="background-color: #00DB00;" |

! 4-ODO = 4th overtone mode = 4-ADO

| 1/1 || 5/4 || 3/2 || 7/4 || 2/1 || 5/2 || 3/1 || 7/2 || 4/1 || 0.00 || 0.32 || 0.58 || 0.81 || 1.00 || 1.32 || 1.58 || 1.81 || 2.00 || 1/1 || 4/5 || 2/3 || 4/7 || 1/2 || 2/5 || 1/3 || 2/7 || 1/4

| (4/4) || 5/4 || 6/4 || 7/4 || 8/4 || ''5/2'' || ''3/1'' || ''7/2'' || ''4/1''

!

| 0.00 || 0.32 || 0.58 || 0.81 || 1.00 || ''1.32'' || ''1.58'' || ''1.81'' || ''2.00''

!

| 1/1 || 4/5 || 2/3 || 4/7 || 1/2 || ''2/5'' || ''1/3'' || ''2/7'' || ''1/4''

|-

! style="background-color: #34A853;" |

! 4-EDO = rank-1 temperament w/ generator 300¢ = APS⁴√2 ≈ APS1.189

| ~~1.00~~ || ~~1.19~~ || ~~1.41~~ || ~~1.68~~ || ~~2.00~~ || 2.38 || 2.83 || 3.36 || 4~~.00 |~~| 0.00 || 0.25 || 0.50 || 0.75 || 1.00 || 1.25 || 1.50 || 1.75 || 2.00 || 1.00 || 0.84 || 0.71 || 0.59 || 0.50 || 0.42 || 0.35 || 0.30 || 0.25

| (2⁰⸍⁴) || 2¹⸍⁴ || 2²⸍⁴ || 2³⸍⁴ || 2⁴⸍⁴ || ''2.38'' || ''2.83'' || ''3.36'' || ''4''

!

| 0.00 || 0.25 || 0.50 || 0.75 || 1.00 || ''1.25'' || ''1.50'' || ''1.75'' || ''2.00''

!

| 1.00 || 0.84 || 0.71 || 0.59 || 0.50 || ''0.42'' || ''0.35'' || ''0.30'' || ''0.25''

|-

! style="background-color: #45818E;" |

! 4-UDO = 4th undertone mode

| 1/1 || 8/7 || 4/3 || 8/5 || 2/1 || 16/7 || 8/3 || 16/5 || 4/1 || 0.00 || 0.19 || 0.42 || 0.68 || 1.00 || 1.19 || 1.42 || 1.68 || 2.00 || 1/1 || 7/8 || 3/4 || 5/8 || 1/2 || 7/16 || 3/8 || 5/16 || 1/4

| (8/8) || 8/7 || 8/6 || 8/5 || 8/4 || ''16/7'' || ''8/3'' || ''16/5'' || ''4/1''

!

| 0.00 || 0.19 || 0.42 || 0.68 || 1.00 || ''1.19'' || ''1.42'' || ''1.68'' || ''2.00''

!

| 1/1 || 7/8 || 3/4 || 5/8 || 1/2 || ''7/16'' || ''3/8'' || ''5/16'' || ''1/4''

|-

! style="background-color: #B4A7D6;" |

! 4-EFDφ

| 1~~.00~~ || 1.15 || 1.31 || 1.46 || ~~1.62~~ || 1.87 || 2.12 || 2.37 || 2.62 || 0.00 || 0.21 || 0.39 || 0.55 || 0.69 || 0.90 || 1.08 || 1.24 || 1.39 || 1.00 || 0.87 || 0.76 || 0.68 || 0.62 || 0.54 || 0.47 || 0.42 || 0.38

| (1) || 1.15 || 1.31 || 1.46 || φ || ''1.87'' || ''2.12'' || ''2.37'' || ''2.62''

!

| 0.00 || 0.21 || 0.39 || 0.55 || 0.69 || ''0.90'' || ''1.08'' || ''1.24'' || ''1.39''

!

| 1.00 || 0.87 || 0.76 || 0.68 || 0.62 || ''0.54'' || ''0.47'' || ''0.42'' || ''0.38''

|-

! style="background-color: #674EA7;" |

! 4-ELDφ

| 1~~.00~~ || 1.11 || 1.24 || 1.40 || ~~1.62~~ || 1.79 || 2.00 || 2.27 || 2.62 || 0.00 || 0.14 || 0.31 || 0.49 || 0.69 || 0.84 || 1.00 || 1.18 || 1.39 || 1.00 || 0.90 || 0.81 || 0.71 || 0.62 || 0.56 || 0.50 || 0.44 || 0.38

| (1) || 1.11 || 1.24 || 1.40 || φ || ''1.79'' || ''2.00'' || ''2.27'' || ''2.62''

!

| 0.00 || 0.14 || 0.31 || 0.49 || 0.69 || ''0.84'' || ''1.00'' || ''1.18'' || ''1.39''

!

| 1.00 || 0.90 || 0.81 || 0.71 || 0.62 || ''0.56'' || ''0.50'' || ''0.44'' || ''0.38''

|-

! style="background-color: #D2EB00;" |

! overtone series segment = 9-OS = 9-OD9

| 1/1 || 2/1 || 3/1 || 4/1 || 5/1 || 6/1 || 7/1 || 8/1 || 9/1 || 0.00 || 1.00 || 1.58 || 2.00 || 2.32 || 2.58 || 2.81 || 3.00 || 3.17 || 1/1 || 1/2 || 1/3 || 1/4 || 1/5 || 1/6 || 1/7 || 1/8 || 1/9

| (1/1) || 2/1 || 3/1 || 4/1 || 5/1 || 6/1 || 7/1 || 8/1 || 9/1

!

| 0.00 || 1.00 || 1.58 || 2.00 || 2.32 || 2.58 || 2.81 || 3.00 || 3.17

!

| 1/1 || 1/2 || 1/3 || 1/4 || 1/5 || 1/6 || 1/7 || 1/8 || 1/9

|-

! style="background-color: #A1A200;" |

! undertone series segment = 9-US = 9-UD9 = 9-EDL

| 1/1 || 9/8 || 9/7 || 3/2 || 9/5 || 9/4 || 3/1 || 9/2 || 9/1 || 0.00 || 0.17 || 0.36 || 0.58 || 0.85 || 1.17 || 1.58 || 2.17 || 3.17 || 1/1 || 8/9 || 7/9 || 2/3 || 5/9 || 4/9 || 1/3 || 2/9 || 1/9

| (9/9) || 9/8 || 9/7 || 9/6 || 9/5 || 9/4 || 9/3 || 9/2 || 9/1

!

| 0.00 || 0.17 || 0.36 || 0.58 || 0.85 || 1.17 || 1.58 || 2.17 || 3.17

!

| 1/1 || 8/9 || 7/9 || 2/3 || 5/9 || 4/9 || 1/3 || 2/9 || 1/9

|-

! style="background-color: #FF7700;" |

! 9-OS(3/4)

| 1/1 || 7/4 || 5/2 || 13/4 || 4/1 || 19/4 || 11/2 || 25/4 || 7/~~1 |~~| 0.00 || 0.81 || 1.32 || 1.70 || 2.00 || 2.25 || 2.46 || 2.64 || 2.81 || 1/1 || 4/7 || 2/5 || 4/13 || 1/4 || 4/19 || 2/11 || 4/25 || 1/7

| (4/4) || 7/4 || 10/4 || 13/4 || 16/4 || 19/4 || 22/4 || 25/4 || 28/4

!

| 0.00 || 0.81 || 1.32 || 1.70 || 2.00 || 2.25 || 2.46 || 2.64 || 2.81

!

| 1/1 || 4/7 || 2/5 || 4/13 || 1/4 || 4/19 || 2/11 || 4/25 || 1/7

|-

! style="background-color: #C95E00;" |

! 9-US(3/4)

| 1/1 || 28/25 || 14/11 || 28/19 || 7/4 || 28/13 || 14/5 || 4/1 || 7/~~1 |~~| 0.00 || 0.16 || 0.35 || 0.56 || 0.81 || 1.11 || 1.49 || 2.00 || 2.81 || 1/1 || 25/28 || 11/14 || 19/28 || 4/7 || 13/28 || 5/14 || 1/4 || 1/7

| (28/28) || 28/25 || 28/22 || 28/19 || 28/16 || 28/13 || 28/10 || 28/7 || 28/4

!

| 0.00 || 0.16 || 0.35 || 0.56 || 0.81 || 1.11 || 1.49 || 2.00 || 2.81

!

| 1/1 || 25/28 || 11/14 || 19/28 || 4/7 || 13/28 || 5/14 || 1/4 || 1/7

|-

! style="background-color: #FFC000;" |

! (1/⁴√2)-shifted overtone series segment = 9-AFS(1/⁴√2)

| 1~~.00~~ || 1.84 || 2.68 || 3.52 || 4.36 || 5.20 || 6.05 || 6.89 || 7.73 || 0.00 || 0.88 || 1.42 || 1.82 || 2.13 || 2.38 || 2.60 || 2.78 || 2.95 || 1.00 || 0.54 || 0.37 || 0.28 || 0.23 || 0.19 || 0.17 || 0.15 || 0.13

| (1) || 1.84 || 2.68 || 3.52 || 4.36 || 5.20 || 6.05 || 6.89 || 7.73

!

| 0.00 || 0.88 || 1.42 || 1.82 || 2.13 || 2.38 || 2.60 || 2.78 || 2.95

!

| 1.00 || 0.54 || 0.37 || 0.28 || 0.23 || 0.19 || 0.17 || 0.15 || 0.13

|-

! style="background-color: #C59500;" |

! (1/⁴√2)-shifted undertone series segment = 9-ALS(1/⁴√2)

| 1~~.00~~ || 1.12 || 1.28 || 1.48 || 1.77 || 2.19 || 2.88 || 4.20 || 7.73 || 0.00 || 0.17 || 0.35 || 0.57 || 0.82 || 1.13 || 1.53 || 2.07 || 2.95 || 1.00 || 0.89 || 0.78 || 0.67 || 0.56 || 0.46 || 0.35 || 0.24 || 0.13

| (1) || 1.12 || 1.28 || 1.48 || 1.77 || 2.19 || 2.88 || 4.20 || 7.73

!

| 0.00 || 0.17 || 0.35 || 0.57 || 0.82 || 1.13 || 1.53 || 2.07 || 2.95

!

| 1.00 || 0.89 || 0.78 || 0.67 || 0.56 || 0.46 || 0.35 || 0.24 || 0.13

|-

! style="background-color: #00CFA9;" |

! AS5/4 = 1D JI lattice of 5/4 = 5/4 chain

| 1/1 || 5/4 || 25/16 || ~~125~~/64 || ~~625~~/~~256~~ || ~~3125~~/~~1024~~ || ~~15625~~/~~4096~~ || ~~78125~~/~~16384~~ || ~~390625~~/~~65536 |~~| 0.00 || 0.32 || 0.64 || 0.97 || 1.29 || 1.61 || 1.93 || 2.25 || 2.58 || 1/1 || 4/5 || 16/25 || 64/125 || 256/625 || 1024/3125 || 4096/15625 || 16384/78125 || 65536/390625

| (5⁰/4⁰) || 5¹/4¹ || 5²/4² || 5³/4³ || 5⁴/4⁴ || 5⁵/4⁵ || 5⁶/4⁶ || 5⁷/4⁷ || 5⁸/4⁸

!

| 0.00 || 0.32 || 0.64 || 0.97 || 1.29 || 1.61 || 1.93 || 2.25 || 2.58

!

| 1/1 || 4/5 || 16/25 || 64/125 || 256/625 || 1024/3125 || 4096/15625 || 16384/78125 || 65536/390625

|-

! style="background-color: #F4CCCC;" |

! 9 pitches of 1/2-powharmonic series = harmonic series compressed by 1/2

| ~~1.00~~ || ~~1.41~~ || ~~1.73~~ || ~~2.00~~ || ~~2.24 |~~| ~~2.45~~ || ~~2.65~~ || ~~2.83~~ || ~~3.00~~ || 0.00 || 0.50 || 0.79 || 1.00 || 1.16 || 1.29 || 1.40 || 1.50 || 1.58 || 1.00 || 0.71 || 0.58 || 0.50 || 0.45 || 0.41 || 0.38 || 0.35 || 0.33

| √1 || √2 || √3 || √4 || √5 || √6 || √7 || √8 || √9

!

| 0.00 || 0.50 || 0.79 || 1.00 || 1.16 || 1.29 || 1.40 || 1.50 || 1.58

!

| 1.00 || 0.71 || 0.58 || 0.50 || 0.45 || 0.41 || 0.38 || 0.35 || 0.33

|-

! style="background-color: #E06666;" |

! 9 pitches of 1/2-subpowharmonic = subharmonic series compressed by 1/2

| 1~~.00~~ || 1.06 || 1.13 || 1.22 || 1.34 || 1.50 || 1.73 || 2.12 || 3~~.00 |~~| 0.00 || 0.08 || 0.18 || 0.29 || 0.42 || 0.58 || 0.79 || 1.08 || 1.58 || 1.00 || 0.94 || 0.88 || 0.82 || 0.75 || 0.67 || 0.58 || 0.47 || 0.33

| (1) || 1.06 || 1.13 || 1.22 || 1.34 || 1.50 || 1.73 || 2.12 || 3

!

| 0.00 || 0.08 || 0.18 || 0.29 || 0.42 || 0.58 || 0.79 || 1.08 || 1.58

!

| 1.00 || 0.94 || 0.88 || 0.82 || 0.75 || 0.67 || 0.58 || 0.47 || 0.33

|-

! style="background-color: #00B6FF;" |

! 9 pitches of 2-logharmonic series

| 1~~.00~~ || 1.58 || 2.00 || 2.32 || 2.58 || 2.81 || 3.00 || 3.17 || 3.32 || 0.00 || 0.66 || 1.00 || 1.22 || 1.37 || 1.49 || 1.58 || 1.66 || 1.73 || 1.00 || 0.63 || 0.50 || 0.43 || 0.39 || 0.36 || 0.33 || 0.32 || 0.30

| (1) || 1.58 || 2.00 || 2.32 || 2.58 || 2.81 || 3.00 || 3.17 || 3.32

!

| 0.00 || 0.66 || 1.00 || 1.22 || 1.37 || 1.49 || 1.58 || 1.66 || 1.73

!

| 1.00 || 0.63 || 0.50 || 0.43 || 0.39 || 0.36 || 0.33 || 0.32 || 0.30

|-

! style="background-color: #006D99;" |

! 9 pitches of 2-sublogharmonic series

| 1~~.00~~ || 1.05 || 1.11 || 1.18 || 1.29 || 1.43 || 1.66 || 2.10 || 3.32 || 0.00 || 0.07 || 0.15 || 0.24 || 0.36 || 0.52 || 0.73 || 1.07 || 1.73 || 1.00 || 0.95 || 0.90 || 0.85 || 0.78 || 0.70 || 0.60 || 0.48 || 0.30

| (1) || 1.05 || 1.11 || 1.18 || 1.29 || 1.43 || 1.66 || 2.10 || 3.32

!

| 0.00 || 0.07 || 0.15 || 0.24 || 0.36 || 0.52 || 0.73 || 1.07 || 1.73

!

| 1.00 || 0.95 || 0.90 || 0.85 || 0.78 || 0.70 || 0.60 || 0.48 || 0.30

|}

@@ Line 244: / Line 244: @@
 ! colspan="2" rowspan="2" |monotonic tuning
 ! colspan="9" |frequency
+!
 ! colspan="9" |pitch
+!
 ! colspan="9" |length
 |-
-! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8 !! 9 !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8 !! 9 !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8 !! 9
+! (0) !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8
+! !! (0) !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8
+! !! (0) !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8
 |-
 ! style="background-color: #00DB00;" |
 ! 4-ODO = 4th overtone mode = 4-ADO
-| 1/1 || 5/4 || 3/2 || 7/4 || 2/1 || 5/2 || 3/1 || 7/2 || 4/1 || 0.00 || 0.32 || 0.58 || 0.81 || 1.00 || 1.32 || 1.58 || 1.81 || 2.00 || 1/1 || 4/5 || 2/3 || 4/7 || 1/2 || 2/5 || 1/3 || 2/7 || 1/4
+| (4/4) || 5/4 || 6/4 || 7/4 || 8/4 || ''5/2'' || ''3/1'' || ''7/2'' || ''4/1''
+!
+| 0.00 || 0.32 || 0.58 || 0.81 || 1.00 || ''1.32'' || ''1.58'' || ''1.81'' || ''2.00''
+!
+| 1/1 || 4/5 || 2/3 || 4/7 || 1/2 || ''2/5'' || ''1/3'' || ''2/7'' || ''1/4''
 |-
 ! style="background-color: #34A853;" |
 ! 4-EDO = rank-1 temperament w/ generator 300¢ = APS⁴√2 ≈ APS1.189
-| 1.00 || 1.19 || 1.41 || 1.68 || 2.00 || 2.38 || 2.83 || 3.36 || 4.00 || 0.00 || 0.25 || 0.50 || 0.75 || 1.00 || 1.25 || 1.50 || 1.75 || 2.00 || 1.00 || 0.84 || 0.71 || 0.59 || 0.50 || 0.42 || 0.35 || 0.30 || 0.25
+| (2⁰⸍⁴) || 2¹⸍⁴ || 2²⸍⁴ || 2³⸍⁴ || 2⁴⸍⁴ || ''2.38'' || ''2.83'' || ''3.36'' || ''4''
+!
+| 0.00 || 0.25 || 0.50 || 0.75 || 1.00 || ''1.25'' || ''1.50'' || ''1.75'' || ''2.00''
+!
+| 1.00 || 0.84 || 0.71 || 0.59 || 0.50 || ''0.42'' || ''0.35'' || ''0.30'' || ''0.25''
 |-
 ! style="background-color: #45818E;" |
 ! 4-UDO = 4th undertone mode
-| 1/1 || 8/7 || 4/3 || 8/5 || 2/1 || 16/7 || 8/3 || 16/5 || 4/1 || 0.00 || 0.19 || 0.42 || 0.68 || 1.00 || 1.19 || 1.42 || 1.68 || 2.00 || 1/1 || 7/8 || 3/4 || 5/8 || 1/2 || 7/16 || 3/8 || 5/16 || 1/4
+| (8/8) || 8/7 || 8/6 || 8/5 || 8/4 || ''16/7'' || ''8/3'' || ''16/5'' || ''4/1''
+!
+| 0.00 || 0.19 || 0.42 || 0.68 || 1.00 || ''1.19'' || ''1.42'' || ''1.68'' || ''2.00''
+!
+| 1/1 || 7/8 || 3/4 || 5/8 || 1/2 || ''7/16'' || ''3/8'' || ''5/16'' || ''1/4''
 |-
 ! style="background-color: #B4A7D6;" |
 ! 4-EFDφ
-| 1.00 || 1.15 || 1.31 || 1.46 || 1.62 || 1.87 || 2.12 || 2.37 || 2.62 || 0.00 || 0.21 || 0.39 || 0.55 || 0.69 || 0.90 || 1.08 || 1.24 || 1.39 || 1.00 || 0.87 || 0.76 || 0.68 || 0.62 || 0.54 || 0.47 || 0.42 || 0.38
+| (1) || 1.15 || 1.31 || 1.46 || φ || ''1.87'' || ''2.12'' || ''2.37'' || ''2.62''
+!
+| 0.00 || 0.21 || 0.39 || 0.55 || 0.69 || ''0.90'' || ''1.08'' || ''1.24'' || ''1.39''
+!
+| 1.00 || 0.87 || 0.76 || 0.68 || 0.62 || ''0.54'' || ''0.47'' || ''0.42'' || ''0.38''
 |-
 ! style="background-color: #674EA7;" |
 ! 4-ELDφ
-| 1.00 || 1.11 || 1.24 || 1.40 || 1.62 || 1.79 || 2.00 || 2.27 || 2.62 || 0.00 || 0.14 || 0.31 || 0.49 || 0.69 || 0.84 || 1.00 || 1.18 || 1.39 || 1.00 || 0.90 || 0.81 || 0.71 || 0.62 || 0.56 || 0.50 || 0.44 || 0.38
+| (1) || 1.11 || 1.24 || 1.40 || φ || ''1.79'' || ''2.00'' || ''2.27'' || ''2.62''
+!
+| 0.00 || 0.14 || 0.31 || 0.49 || 0.69 || ''0.84'' || ''1.00'' || ''1.18'' || ''1.39''
+!
+| 1.00 || 0.90 || 0.81 || 0.71 || 0.62 || ''0.56'' || ''0.50'' || ''0.44'' || ''0.38''
 |-
 ! style="background-color: #D2EB00;" |
 ! overtone series segment = 9-OS = 9-OD9
-| 1/1 || 2/1 || 3/1 || 4/1 || 5/1 || 6/1 || 7/1 || 8/1 || 9/1 || 0.00 || 1.00 || 1.58 || 2.00 || 2.32 || 2.58 || 2.81 || 3.00 || 3.17 || 1/1 || 1/2 || 1/3 || 1/4 || 1/5 || 1/6 || 1/7 || 1/8 || 1/9
+| (1/1) || 2/1 || 3/1 || 4/1 || 5/1 || 6/1 || 7/1 || 8/1 || 9/1
+!
+| 0.00 || 1.00 || 1.58 || 2.00 || 2.32 || 2.58 || 2.81 || 3.00 || 3.17
+!
+| 1/1 || 1/2 || 1/3 || 1/4 || 1/5 || 1/6 || 1/7 || 1/8 || 1/9
 |-
 ! style="background-color: #A1A200;" |
 ! undertone series segment = 9-US = 9-UD9 = 9-EDL
-| 1/1 || 9/8 || 9/7 || 3/2 || 9/5 || 9/4 || 3/1 || 9/2 || 9/1 || 0.00 || 0.17 || 0.36 || 0.58 || 0.85 || 1.17 || 1.58 || 2.17 || 3.17 || 1/1 || 8/9 || 7/9 || 2/3 || 5/9 || 4/9 || 1/3 || 2/9 || 1/9
+| (9/9) || 9/8 || 9/7 || 9/6 || 9/5 || 9/4 || 9/3 || 9/2 || 9/1
+!
+| 0.00 || 0.17 || 0.36 || 0.58 || 0.85 || 1.17 || 1.58 || 2.17 || 3.17
+!
+| 1/1 || 8/9 || 7/9 || 2/3 || 5/9 || 4/9 || 1/3 || 2/9 || 1/9
 |-
 ! style="background-color: #FF7700;" |
 ! 9-OS(3/4)
-| 1/1 || 7/4 || 5/2 || 13/4 || 4/1 || 19/4 || 11/2 || 25/4 || 7/1 || 0.00 || 0.81 || 1.32 || 1.70 || 2.00 || 2.25 || 2.46 || 2.64 || 2.81 || 1/1 || 4/7 || 2/5 || 4/13 || 1/4 || 4/19 || 2/11 || 4/25 || 1/7
+| (4/4) || 7/4 || 10/4 || 13/4 || 16/4 || 19/4 || 22/4 || 25/4 || 28/4
+!
+| 0.00 || 0.81 || 1.32 || 1.70 || 2.00 || 2.25 || 2.46 || 2.64 || 2.81
+!
+| 1/1 || 4/7 || 2/5 || 4/13 || 1/4 || 4/19 || 2/11 || 4/25 || 1/7
 |-
 ! style="background-color: #C95E00;" |
 ! 9-US(3/4)
-| 1/1 || 28/25 || 14/11 || 28/19 || 7/4 || 28/13 || 14/5 || 4/1 || 7/1 || 0.00 || 0.16 || 0.35 || 0.56 || 0.81 || 1.11 || 1.49 || 2.00 || 2.81 || 1/1 || 25/28 || 11/14 || 19/28 || 4/7 || 13/28 || 5/14 || 1/4 || 1/7
+| (28/28) || 28/25 || 28/22 || 28/19 || 28/16 || 28/13 || 28/10 || 28/7 || 28/4
+!
+| 0.00 || 0.16 || 0.35 || 0.56 || 0.81 || 1.11 || 1.49 || 2.00 || 2.81
+!
+| 1/1 || 25/28 || 11/14 || 19/28 || 4/7 || 13/28 || 5/14 || 1/4 || 1/7
 |-
 ! style="background-color: #FFC000;" |
 ! (1/⁴√2)-shifted overtone series segment = 9-AFS(1/⁴√2)
-| 1.00 || 1.84 || 2.68 || 3.52 || 4.36 || 5.20 || 6.05 || 6.89 || 7.73 || 0.00 || 0.88 || 1.42 || 1.82 || 2.13 || 2.38 || 2.60 || 2.78 || 2.95 || 1.00 || 0.54 || 0.37 || 0.28 || 0.23 || 0.19 || 0.17 || 0.15 || 0.13
+| (1) || 1.84 || 2.68 || 3.52 || 4.36 || 5.20 || 6.05 || 6.89 || 7.73
+!
+| 0.00 || 0.88 || 1.42 || 1.82 || 2.13 || 2.38 || 2.60 || 2.78 || 2.95
+!
+| 1.00 || 0.54 || 0.37 || 0.28 || 0.23 || 0.19 || 0.17 || 0.15 || 0.13
 |-
 ! style="background-color: #C59500;" |
 ! (1/⁴√2)-shifted undertone series segment = 9-ALS(1/⁴√2)
-| 1.00 || 1.12 || 1.28 || 1.48 || 1.77 || 2.19 || 2.88 || 4.20 || 7.73 || 0.00 || 0.17 || 0.35 || 0.57 || 0.82 || 1.13 || 1.53 || 2.07 || 2.95 || 1.00 || 0.89 || 0.78 || 0.67 || 0.56 || 0.46 || 0.35 || 0.24 || 0.13
+| (1) || 1.12 || 1.28 || 1.48 || 1.77 || 2.19 || 2.88 || 4.20 || 7.73
+!
+| 0.00 || 0.17 || 0.35 || 0.57 || 0.82 || 1.13 || 1.53 || 2.07 || 2.95
+!
+| 1.00 || 0.89 || 0.78 || 0.67 || 0.56 || 0.46 || 0.35 || 0.24 || 0.13
 |-
 ! style="background-color: #00CFA9;" |
 ! AS5/4 = 1D JI lattice of 5/4 = 5/4 chain
-| 1/1 || 5/4 || 25/16 || 125/64 || 625/256 || 3125/1024 || 15625/4096 || 78125/16384 || 390625/65536 || 0.00 || 0.32 || 0.64 || 0.97 || 1.29 || 1.61 || 1.93 || 2.25 || 2.58 || 1/1 || 4/5 || 16/25 || 64/125 || 256/625 || 1024/3125 || 4096/15625 || 16384/78125 || 65536/390625
+| (5⁰/4⁰) || 5¹/4¹ || 5²/4² || 5³/4³ || 5⁴/4⁴ || 5⁵/4⁵ || 5⁶/4⁶ || 5⁷/4⁷ || 5⁸/4⁸
+!
+| 0.00 || 0.32 || 0.64 || 0.97 || 1.29 || 1.61 || 1.93 || 2.25 || 2.58
+!
+| 1/1 || 4/5 || 16/25 || 64/125 || 256/625 || 1024/3125 || 4096/15625 || 16384/78125 || 65536/390625
 |-
 ! style="background-color: #F4CCCC;" |
 ! 9 pitches of 1/2-powharmonic series = harmonic series compressed by 1/2
-| 1.00 || 1.41 || 1.73 || 2.00 || 2.24 || 2.45 || 2.65 || 2.83 || 3.00 || 0.00 || 0.50 || 0.79 || 1.00 || 1.16 || 1.29 || 1.40 || 1.50 || 1.58 || 1.00 || 0.71 || 0.58 || 0.50 || 0.45 || 0.41 || 0.38 || 0.35 || 0.33
+| √1 || √2 || √3 || √4 || √5 || √6 || √7 || √8 || √9
+!
+| 0.00 || 0.50 || 0.79 || 1.00 || 1.16 || 1.29 || 1.40 || 1.50 || 1.58
+!
+| 1.00 || 0.71 || 0.58 || 0.50 || 0.45 || 0.41 || 0.38 || 0.35 || 0.33
 |-
 ! style="background-color: #E06666;" |
 ! 9 pitches of 1/2-subpowharmonic = subharmonic series compressed by 1/2
-| 1.00 || 1.06 || 1.13 || 1.22 || 1.34 || 1.50 || 1.73 || 2.12 || 3.00 || 0.00 || 0.08 || 0.18 || 0.29 || 0.42 || 0.58 || 0.79 || 1.08 || 1.58 || 1.00 || 0.94 || 0.88 || 0.82 || 0.75 || 0.67 || 0.58 || 0.47 || 0.33
+| (1) || 1.06 || 1.13 || 1.22 || 1.34 || 1.50 || 1.73 || 2.12 || 3
+!
+| 0.00 || 0.08 || 0.18 || 0.29 || 0.42 || 0.58 || 0.79 || 1.08 || 1.58
+!
+| 1.00 || 0.94 || 0.88 || 0.82 || 0.75 || 0.67 || 0.58 || 0.47 || 0.33
 |-
 ! style="background-color: #00B6FF;" |
 ! 9 pitches of 2-logharmonic series
-| 1.00 || 1.58 || 2.00 || 2.32 || 2.58 || 2.81 || 3.00 || 3.17 || 3.32 || 0.00 || 0.66 || 1.00 || 1.22 || 1.37 || 1.49 || 1.58 || 1.66 || 1.73 || 1.00 || 0.63 || 0.50 || 0.43 || 0.39 || 0.36 || 0.33 || 0.32 || 0.30
+| (1) || 1.58 || 2.00 || 2.32 || 2.58 || 2.81 || 3.00 || 3.17 || 3.32
+!
+| 0.00 || 0.66 || 1.00 || 1.22 || 1.37 || 1.49 || 1.58 || 1.66 || 1.73
+!
+| 1.00 || 0.63 || 0.50 || 0.43 || 0.39 || 0.36 || 0.33 || 0.32 || 0.30
 |-
 ! style="background-color: #006D99;" |
 ! 9 pitches of 2-sublogharmonic series
-| 1.00 || 1.05 || 1.11 || 1.18 || 1.29 || 1.43 || 1.66 || 2.10 || 3.32 || 0.00 || 0.07 || 0.15 || 0.24 || 0.36 || 0.52 || 0.73 || 1.07 || 1.73 || 1.00 || 0.95 || 0.90 || 0.85 || 0.78 || 0.70 || 0.60 || 0.48 || 0.30
+| (1) || 1.05 || 1.11 || 1.18 || 1.29 || 1.43 || 1.66 || 2.10 || 3.32
+!
+| 0.00 || 0.07 || 0.15 || 0.24 || 0.36 || 0.52 || 0.73 || 1.07 || 1.73
+!
+| 1.00 || 0.95 || 0.90 || 0.85 || 0.78 || 0.70 || 0.60 || 0.48 || 0.30
 |}