Notes on 7-limit temperament notation, part 2

This message starts where the previous one left off, at augene.

Augene
12&15, 12&27, 15&27, 15&42, 27&42
[<3, 5, 7, 8], <0, -1, 0, 2]>
TOP P = 399.020013, G = 90.593035
TOP-RMS P = 398.751606, G = 90.459945

-3 -2 -1 0 +1 +2 +3
0 D E!!/ E\! F
+1 D||\ E F/| F||\ G A!!/ A\!
+2 G/| G||\ A B!!/ B\! C D!!/
+3 B C/| C||\ D

/| [-4, 4, -1> (+1, -4)
||\ [-7, 3, 1> (+1, -3)

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Keemun
4&15, 4&19, 15&19
[<1, 0, 1, 2], <0, 6, 5, 3]>
TOP P = 1203.187309, G = 317.834461
TOP-RMS P = 1202.645814, G = 317.170481

08 F 17 A!!/ 26 C)!!( 01
01 D|) 10 F)||( 19 A\! 28 C 03 E!!/ 12 G)!!( 21
21 A|) 30 C)||( 05 E\! 14 G 23 B!!/ 32 D)!!( 07 F!)
07 E|) 16 G)||( 25 B\! 00 D 09 F/| 18 A)!!( 27 C!)
27 B|) 02 D)||( 11 F||\ 20 A 29 C/| 04 E)!!( 13 G!)
13 22 A)||( 31 C||\ 06 E 15 G/| 24 B)!!( 33 D!)
33 08 E)||( 17 G||\ 26 B

/| [-4, 4, -1> (-5, +19)
|) [6, -2, 0, -1> (+4, -15)
)||( [-3, -1, 2> (-1, +4)
||\ [-7, 3, 1> (-6, +23)

See yesterday's message on keemun vs. hanson notation for explanation.

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Catler
12&26
[<12, 19, 28, 34], <0, 0, 0, -1]>
TOP P = 99.806172, G = 24.583958 (e.g.)
TOP-RMS P = 99.870029, G = 26.755075

-1 0 +1
D!) D D|)
D(|\ E!!/ E(!/
E!) E E|)
E(|\ F F|)
F(|\ F||\ G(!/
G!) G G|)
G(|\ G||\ A(!/
A!) A A|)
A(|\ B!!/ B(!/
B!) B B|)
C!) C C|)
C(|\ C||\ D(!/
D!) D D|)

|) [6, -2, 0, -1> (+0, +1)
(|\ [-13, 5, 1, 1> (+1, -1)
||\ [-7, 3, 1> (+1, +0)

|) + (|\ = ||\

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Hedgehog
[<2, 4, 6, 7], <0, -3, -5, -5]>
TOP P = 598.4467109, G = 162.3159606
TOP-RMS P = 599.619018, G = 164.247626

B
C||\
D)||(
E
07 F||\ 18 B/|)
10 G)||( 21 D\!)
13 A 02 E!!!(
16 B)!!( 05 E/|)
19 C)||( 08 G\!)
00 D 11 G|||(
03 E)!!( 14 A/|)
06 F)||( 17 C\!)
09 G 20 C|||(
12 A)!!( 01 D/|)
15 B!!/ 04 F\!)
C
D)!!(
E!!/
F

/|) [2, 2, -1, -1> (-1, +4)
)||( [-3, -1, 2> (+2, -7)
|||( [-1, 1, 1, -1> (+1, -3)
||\ [-7, 3, 1> (+4, -14)

/|) + )||( = |||(

Another option:

.(|\ [2, -3, 0, 1> (-1, +4)
)/|\ [-3, 4, 1, -2> (+2, -7)
|||( [-1, 1, 1, -1> (+1, -3)
||\ [-7, 3, 1> (+4, -14)

.(|\ + )/|\ = |||(

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Superpyth
5&22, 5&27, 22&27, 22&49, 27&49
[<1, 2, 6, 2], <0, -1, -9, 2]>
TOP P = 1197.596121, G = 489.427183
TOP-RMS P = 1197.067108, G = 488.512092

10 E'(| 30 A'(| 01 D'(| 21 G'(| 41 C'(| 12 F'(| 32 A)||(
03 D)||( 23 G)||( 43 C)||( 14 F)||( 34 B'!!) 05 E'!!) 25 A'!!)
45 D'!!) 16 G'!!) 36 B\!) 07 E\!) 27 A\!) 47 D\!) 18 G\!)
38 B 09 E 29 A 00 D 20 G 40 C 11 F
31 A/|) 02 D/|) 22 G/|) 42 C/|) 13 F/|) 33 A.||) 04 D.||)
24 G.||) 44 C.||) 15 F.||) 35 B)!!( 06 E)!!( 26 A)!!( 46 D)!!(
17 G)!!( 37 B.(! 08 E.(! 28 A.(! 48 D.(! 19 G.(! 39 C.(!

'(| [1, 0, 2, -2> (+9, -22)
~|) [-4, -1, 0, 2> (-2, +5) alt.
/|) [2, 2, -1, -1> (-2, +5) pref.
)||( [-3, -1, 2> (+7, -17)
.||) [-2, 1, -1, 1> (-4, +10)
|||( [-1, 1, 1 -1> (+5, -12)

'(| + ~|) = )||(
'(| + .||) = |||(
~|) + /|) = .||)
/|) + )||( = |||(

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Sensisept
19&27, 19&46, 27&46, 27&73, 46&73
[<1, -1, -1, -2], <0, 7, 9, 13]>
TOP P = 1198.389531, G = 443.160293
TOP-RMS P = 1199.713890, G = 443.276999

23 A!!/ 40 C/|) 11 F 28 A|) 45 D\! 16 G)!!(
33 B\\! 04 E!!/ 21 G/|) 38 C 09 E|) 26 A\! 43 D)!!(
14 F)||( 31 B!!/ 02 D/|) 19 G 36 B|) 07 E\! 24 A)!!(
41 C)||( 12 F/| 29 A/|) 00 D 17 G\!) 34 B\! 05 E)!!(
22 G)||( 39 C/| 10 F!) 27 A 44 D\!) 15 F||\ 32 B)!!(
03 D)||( 20 G/| 37 C!) 08 E 25 A\!) 42 C||\ 13 F//|
30 A)||( 01 D/| 18 G!) 35 B 06 E\!) 23 G||\

|) [6, -2, 0, -1> (+10, -27)
/| [-4, 4, -1> (-7, +19)
/|) [2, 2, -1, -1> (+3, -8)
//| [-8, 8, -2> (-14, +38)
)||( [-3, -1, 2> (-4, +11)
||\ [-7, 3, 1> (-11, +30)

|) + /| = /|)
|) + //| != )||(
/| + /| = //|
/| + /|) != )||(
/| + )||( = ||\
/|) + //| != ||\

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Lemba
10&16, 10&26, 16&26
[<2, 2, 5, 6], <0, 3, -1, -1]>
TOP P = 601.700493, G = 230.874926
TOP-RMS P = 601.479448, G = 232.661024

F

22 C 09 F.||)
01 D|) 14 A\!)
06 F!) 19 B\!
11 G 24 C.||)
16 A|) 03 E\!)
21 C!) 08 F/|)
00 D 13 G.||)
05 E|) 18 B\!)
10 G!) 23 C/|)
15 A 02 E'!!)
20 B|) 07 F/|
25 D!) 12 G/|)
04 E 17 B'!!)

B

/| [-4, 4, -1> (-5, +13)
|) [6, -2, 0, -1> (+2, -5) pref.
~|) [-4, -1, 0, 2> (+2, -5) alt.
/|) [2, 2, -1, -1> (-3, +8)
.||) [-2, 1, -1, 1> (-1, +3)

/| + |) = /|)
~|) + /|) = .||)

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Porcupine
15&22, 15&37, 22&37, 22&59, 37&59
[<1, 2, 3, 2], <0, -3, -5, 6]>
TOP P = 1196.905960, G = 162.317661
TOP-RMS P = 1197.839112, G = 162.586787

21 A~!) 26 A||\
31 B/|) 36 D~!) 04 D||\
09 E/|) 14 G~!) 19 G||\
24 A/|) 29 B 34 C||\
02 D/|) 07 E 12 F||\
17 G/|) 22 A 27 B\!)
32 C/|) 00 D 05 E\!)
10 F/|) 15 G 20 A\!)
25 B!!/ 30 C 35 D\!)
03 E!!/ 08 F 13 G\!)
18 A!!/ 23 A~|) 28 C\!)
33 D!!/ 01 D~|) 06 F\!)
11 G!!/ 16 G~|)

~|) [-4, -1, 0, 2> (-2, +15)
/|) [2, 2, -1, -1> (+1, -7)
.||) [-2, 1, -1, 1> (-1, +8)
||\ [-7, 3, 1> (+2, -14)

~|) + /|) = .||)

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Flattone
19&26, 19&45, 26&45
[<1, 2, 4, -1], <0, -1, -4, 9]>
TOP P = 1202.536419, G = 507.137966
TOP-RMS P = 1203.645752, G = 507.758889

13 A'!!) 24 D'!!) 09 G'!!)
20 B/|) 05 E/|) 16 A/|) 01 D/|) 12 G/|) 23 C/|) 08 F/|)
19 B 04 E 15 A 00 D 11 G 22 C 07 F
18 B\!) 03 E\!) 14 A\!) 25 D\!) 10 G\!) 21 C\!) 06 F\!)
17 A.||) 02 D.||) 13 G.||)

~|) [-4, -1, 0, 2> (-8, +19)
/|) [2, 2, -1, -1> (+3, -7)
.||) [-2, 1, -1, 1> (-5, +12)

~|) + /|) = .||)

It's interesting how many of these have ~|) + /|) = .||) . Considering how frequently .||) comes up, I might as well adopt )/|| and use it for .||) from here on (at least for anything less than 19-limit temperaments).