5-limit notation summary

Here are my notes on notation ideas for the 5-limit temperaments mentioned in Paul's paper. I give the temperament name, the wedgie for identification, the TOP period and generator size in cents, the 5-limit tuning map, a list of its MOS/DE scales up to 31 steps, suggested pseudo-nominal notations, and a list of appropriate 5-limit Sagittal accidentals for each. In the MOS/DE list, I've added one + to indicate scales that are slightly improper but not too badly, and ++ for proper scales. The MOS/DE scale marked with * is the one picked by Dave's formula. This is all assuming that I've crunched all the numbers correctly. The selection of Sagittal accidentals can also be a little bit subjective at times; there isn't always one best possibility.

Father <<1, -1, -4]] P = 1185.87, G = 447.39
map: [<1, 2, 2], <0, -1, 1]]
MOS/DE: 1+, 2++, 3++, 5++, *8++, 13, 21, 29
PN: (#G ]C) F ]A D [G B ([E #G)
./||| [0, 3, -2> -5 (134.81c)
.)X( [1, -2, 1> +3 (156.29c)
/|) [1, -5, 3> +8 (21.48c)

Bug <<2, 3, 0]] P = 1200.00, G = 260.26
map: [<1, 2, 3], <0, -2, -3]]
MOS/DE: 1, 2, 3+, 4++, 5++, *9++, 14++, 23++
PN: ([E #F) A [C D ]E G (bB ]C)
./||\ [4, -1, -1> +5 (101.28c)
||\ [-7, 3, 1> -9 (57.69c)
)||( [-3, -1, 2> -4 (158.97c)

Dicot <<2, 1, -3]] P = 1207.66, G = 353.22
map: [<1, 1, 2], <0, 2, 1]]
MOS/DE: 1, 2+, 3++, 4+, *7++, 10+, 17++, 24++
PN: [E G [B D ]F A ]C
.||\ [8, -5, 0> -10 (90.8c)
.X\ [-3, 2, 0> +4 (205.21c)
||\ [-7, 3, 1> +7 (57.21c)

Meantone <<1, 4, 4]] P = 1201.70, G = 504.13
map: [<1, 2, 4], <0, -1, -4]]
MOS/DE: 1+, 2++, 3+, 5++, *7++, 12++, 19++, 31++
PN: B E A D G C F
)||( [-3, -1, 2> -7 (76.16c)
||\ [-7, 3, 1> -7 (76.16c)
/||\ [-11, 7, 0> -7 (76.16c)
.//| [7, 0, -3> +12 (41.12c)
./||\ [4, -1, -1> +5 (117.27c)

Augmented <<3, 0, -7]] P = 399.02, G = 93.15
map: [<3, 5, 7], <0, -1, 0]]
MOS/DE: 3, 6, *9+, 12++, 15, 27+
PN: #C D bE / F #F G / A bB B
||\ [-7, 3, 1> -3 (119.58c)
/| [-4, 4, -1> -4 (26.44c)

Mavila <<1, -3, -7]] P = 1206.55, G = 521.52
map: [<1, 2, 1], <0, -1, 3]]
MOS/DE: 1+, 2++, 3, 5+, *7++, 9, 16, 23
PN: [B [E A D G ]C ]F
)||( [-3, -1, 2> +7 (31.00c)
./||| [0, 3, -2> -9 (132.51c)
.)X( [1, -2, 1> +5 (194.5c)

Porcupine <<3, 5, 1]] P = 1196.91, G = 162.32
map: [<1, 2, 3], <0, -3, -5]]
MOS/DE: 1, 2, 3, 4, 5, 6+, *7++, 8+, 15++, 22++
PN: A [B ]C D [E ]F G
)||( [-3, -1, 2> -7 (60.68c)
.//| [16, -13, 2> +15 (40.95c)
./||\ [4, -1, -1> +8 (101.64c)

Blackwood <<0, 5, 8]] P = 238.87, G = 158.78
map: [<5, 8, 11], <0, 0, 1]]
MOS/DE: *5++, 10++, 15++, 25
PN: D / ]E / G / A / [C
)||( [-3, -1, 2> +2 (78.69c)
||\ [-7, 3, 1> +1 (158.78c)

Dimipent <<4, 4, -3]] P = 299.16, G = 101.67
map: [<4, 6, 9], <0, 1, 1]]
MOS/DE: 4+, *8++, 12++, 20
PN: (#C) D (bE) / (E) F (#F) / (G) #G (A) / (bB) B (C)
)||( [-3, -1, 2> +1 (101.67c)
./||\ [4, -1, -1> -2 (95.82c)
/|) [1, -5, 3> -2 (95.82c)

Srutal <<2, -4, -11]] P = 599.56, G = 104.70
map: [<2, 3, 5], <0, 1, -2]]
MOS/DE: 2, 4, 6, *8+, 10++, 12++, 22+
PN: C #C D bE E / #F G #G A bB
)||( [-3, -1, 2> -5 (76.06c)
/| [-4, 4, -1> +6 (28.64c)

Magic <<5, 1, -10]] P = 1201.28, G = 380.80
map: [<1, 0, 2], <0, 5, 1]]
MOS/DE: 1, 2+, 3++, 4, *7, 10, 13, 16+, 19++, 22+
PN: (E ]G [C bE G B) ]D [G bB D #F ]A [D (F A #C ]E [A C)
||\ [-7, 3, 1> +16 (86.35c)
/| [-4, 4, -1> +19 (27.46c)
)||( [-3, -1, 2> -3 (58.89c)
./||| [0, 3, -2> +13 (145.24c)
.X\ [-3, 2> +10 (204.13c)

Ripple <<5, 8, 1]] P = 1203.32, G = 101.99
map: [<1, 2, 3], <0, -5, -8]]
MOS/DE: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10+, 11++, *12++, 23
PN: (#G) A bB B C #C D bE E F #F G (#G)
)||( [-3, -1, 2> -11 (81.41c)
./||\ [4, -1, -1> +13 (122.58c)
.(|\ [3, 4, -4> +12 (20.59)
||\ [-7, 3, 1> -23 (60.82c)

Hanson <<6, 5, -6]] P = 1200.29, G = 317.07
map: [<1, 0, 1], <0, 6, 5]]
MOS/DE: 1, 2+, 3++, 4++, *7, 11+, 15++, 19++
PN: (E G bB [D) ]E ]G B D F [A [C (]D #F A C)
)||( [-3, -1, 2> +4 (67.99c)
/|) [1, -5, 3> -15 (45.12c)
/| [-4, 4, -1> +19 (22.86c)
.)X( [1, -2, 1> -7 (181.10c)
./||\ [4, -1, -1> -11 (113.11c)

Negripent <<4, -3, -14]] P = 1201.82, G = 126.15
map: [<1, 2, 2], <0, -4, 3]]
MOS/DE: 1, 2, 3, 4, 5, 6, 7, 8+, *9++, 10++, 19++, 29
PN: (]G) A bB [C ]C D [E ]E #F G ([A)
)||( [-3, -1, 2> +10 (59.63c)
||\ [-7, 3, 1> -9 (66.52c)

Tetracot <<4, 9, 5]] P = 1199.03, G = 176.11
map: [<1, 1, 1], <0, 4, 9]]
MOS/DE: 1, 2, 3, 4, 5+, 6++, *7++, 13, 20, 27+
PN: [A [B C D E ]F ]G
/| [-4, 4, -1> +7 (33.77c)

Superpyth <<1, 9, 12]] P = 1197.60, G = 489.43
map: [<1, 2, 6], <0, -1, -9]]
MOS/DE: 1+, 2++, 3+, *5++, 7, 12, 17+, 22++, 27
PN: (B [E [A [D [G [C) E A D G C (]E ]A ]D ]G ]C F)
||\ [-7, 3, 1> -12 (114.85c)
)||( [-3, -1, 2> -17 (62.91c)
.)X( [1, -2, 1> -7 (166.80c)
.||\ [8, -5> +5 (51.94c)

Helmholtz <<1, -8, -15]] 1200.07, G = 498.28
map: [<1, 2, -1], <0, -1, 8]]
MOS/DE: 1+, 2++, 3+, 5++, *7+, 12++, 17, 29
PN: (#G #C #F) B E A D G C F (bB bE #G)
||\ [-7, 3, 1> +5 (91.26c)
/||\ [-11, 7> -7 (112.25c)
/| [-4, 4, -1> -12 (20.98c)
)||( [-3, -1, 2> +17 (70.28c)

Sensipent <<7, 9, -2]] P = 1199.59, G = 442.98
map: [<1, -1, -1], <0, 7, 9]]
MOS/DE: 1+, 2++, 3++, 5+, *8++, 11+, 19++, 27+
PN: ([A) ]C F ]A D [G B [E (]G)
/|) [1, -5, 3> -8 (54.89c)
)||( [-3, -1, 2> +11 (74.48c)
/| [-4, 4, -1> +19 (19.59c)

Passion <<5, -4, -18]] P = 1198.31, G = 98.40
map: [<1, 2, 2], <0, -5, 4]]
MOS/DE: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11+, *12++, 13, 25
PN: (#G) A bB B C #C D bE E F #F G (#G)
)||( [-3, -1, 2> +13 (80.89c)
||\ [-7, 3, 1> -11 (115.91c)
.//| [7, 0, -3> -12 (17.51c)

Würschmidt <<8, 1, -17]] P = 1199.69, G = 387.64
map: [<1, -1, 2], <0, 8, 1]]
MOS/DE: 1, 2+, *3++, 4, 7, 10, 13, 16, 19, 22, 25, 28+, 31++
PN: E *[C [E ]G *bE G B *[G [B ]D *bB D #F *[D ]F ]A *F A #C *[A ]C ]E *C
.//| [7, 0, -3> -3 (36.76c)
)||( [-3, -1, 2> -6 (73.51c)
./||\ [4, -1, -1> -9 (110.27c)
.)X( [1, -2, 1> -15 (183.79c)
.X\ [-3, 2> +16 (203.86c)
./||| [0, 3, -2> +22 (130.34c)
||\ [-7, 3, 1> +25 (93.59c)
.(|\ [3, 4, -4> +28 (56.83c)
/| [-4, 4, -1> +31 (20.07c)

Compton <<0, 12, 19]] P = 100.05, G = 15.13
map: [<12, 19, 28], <0, 0, -1]]
MOS/DE: *12, 24
PN: D / bE / E / F / #F / G / #G / A / bB / B / C / #C
/| [-4, 4, -1> +1 (15.13)

Amity <<5, 13, 9]] P = 1199.85, G = 339.47
map: [<1, 3, 6], <0, -5, -13]]
MOS/DE: 1, 2+, 3++, 4++, *7++, 11, 18, 25
PN: E G [B D ]F A C
/| [-4, 4, -1> -7 (23.4c)

Orson <<7, -3, -21]] P = 1200.24, G = 271.65
map: [<1, 0, 3], <0, 7, -3]]
MOS/DE: 1, 2, 3+, 4++, 5+, *9++, 13+, 22++, 31++
PN: bE #F [A [C D ]E ]G bB #C
./||\ [4, -1, -1> -4 (113.62c)
.//| [7, 0, -3> +9 (44.40c)
)||( [-3, -1, 2> -13 (69.22c)
||\ [-7, 3, 1> +18 (88.81c)
/| [-4, 4, -1> +31 (19.59c)

Vishnu <<14, 6, -23]] P = 599.97, G = 71.15
map: [<2, 4, 5], <0, -7, -3]]
MOS/DE: 2, 4, 6, 8, 10, 12, 14+, *16++, 18+
PN: (B) C ]C [D D ]D [E E (F) / (F) #F [G ]G #G [A ]A bB (B)
)||( [-3, -1, 2> +1 (71.15c)
.//| [7, 0, -3> +9 (40.34c)

Luna <<15, -2, -38]] P = 1199.98, G = 193.20
map: [<1, 4, 2], <0, -15, 2]]
MOS/DE: 1, 2, 3, 4, 5+, *6++, 7, 13, 19+, 25++, 31++
PN: (#G) bB C D E #F (#G)
.//| [7, 0, -3> -6 (40.8c)
./||\ [4, -1, -1> +13 (111.59c)
)||( [-3, -1, 2> +19 (70.78c)