back to list

7-limit notation summary

🔗Herman Miller <hmiller@IO.COM>

2/20/2005 12:07:32 PM

Here's a similar list for the 7-limit temperaments. In addition to the ones mentioned in Paul's paper, I've added a few extra bonus temperaments at the end of the list. I haven't tried all the possible combinations of schisma accents with these, since most of them have at least a few accidental pairs that don't require them, but it's likely that I've missed a number of possibilities in the selection of Sagittal accidentals.

Blacksmith <<0, 5, 0, 8, 0, -14]] P = 239.18, G = 83.83
map: [<5, 8, 11, 14], <0, 0, 1, 0]]
MOS/DE: 5, *10++, 15++, 25
PN: (#C) D (bE) / ([E) ]E (F) / (#F) G (]G) / ([A) A (bB) / (B) [C (]C)
)||( [-3, -1, 2> +2 (71.52c)
/|) [2, 2, -1, -1> -1 (83.83c)

Dimisept <<4, 4, 4, -3, -5, -2]] P = 298.53, G = 101.46
map: [<4, 6, 9, 11], <0, 1, 1, 1]]
MOS/DE: 4, *8++, 12++, 20
PN: (#C) D (bE) / (E) F (#F) / (G) #G (A) / (bB) B (C)
./||\ [4, -1, -1> -2 (95.62c)
)||( [-3, -1, 2> +1 (101.46c)
|||( [-1, 1, 1, -1> +1 (101.46c)

Dominant <<1, 4, -2, 4, -6, -16]] P = 1195.23, G = 495.88
map: [<1, 2, 4, 2], <0, -1, -4, 2]]
MOS/DE: 1, 2++, 3+, 5++, *7+, 12++, 17, 29+
PN: B E A D G C F
/||\ [-11, 7> -7 (114.52c)

August <<3, 0, 6, -7, 1, 14]] P = 399.99, G = 107.31
map: [<3, 5, 7, 9], <0, -1, 0, -2]]
MOS/DE: 3, 6+, *9++, 12++, 21+
PN: #C D bE / F #F G / A bB B
|) [6, -2, 0, -1> +4 (29.25c)
||\ [-7, 3, 1> -3 (78.06c)

Pajara <<2, -4, -4, -11, -12, 2]] P = 598.45, G = 106.57
map: [<2, 3, 5, 6], <0, 1, -2, -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 (65.61c)
/|) [2, 2, -1, -1> +6 (40.95c)

Semaphore <<2, 8, 1, 8, -4, -20]] P = 1203.67, G = 252.48
map: [<1, 2, 4, 3], <0, -2, -8, -1]]
MOS/DE: 1, 2, 3+, 4++, *5++, 9, 14+, 19++, 24
PN: ([E #F [A B [D E [G) A [C D ]E G (]A C ]D F ]G bB ]C)
/|) [2, 2, -1, -1> +5 (58.73c)
|||) [-5, 5, 0, -1> -9 (135.01c)
)||( [-3, -1, 2> -14 (76.28c)

Meantone <<1, 4, 10, 4, 13, 12]] P = 1201.70, G = 504.13
map: [<1, 2, 4, 7], <0, -1, -4, -10]]
MOS/DE: 1, 2++, 3+, 5++, 7++, 12++, 19++, 31++
PN: B E A D G C F
)||( [-3, -1, 2> -7 (76.16c)
/|) [2, 2, -1, -1> +12 (41.12c)

Injera <<2, 8, 8, 8, 7, -4]] P = 600.89, G = 93.61
map: [<2, 3, 4, 5], <0, 1, 4, 4]]
MOS/DE: 2, 4, 6, *8, 10+, (*)12++, 14+, 26++
PN: (B C) #C D bE (E F) / (F #F) G #G A (bB B)
/|) [2, 2, -1, -1> -6 (39.23c)
./||\ [4, -1, -1> -5 (132.84c)

Negrisept <<4, -3, 2, -14, -8, 13]] P = 1203.19, G = 124.84
map: [<1, 2, 2, 3], <0, -4, 3, -2]]
MOS/DE: 1, 2, 3, 4, 5, 6, 7, 8+, *9++, 10++, 19++, 29++
PN: A [B [C #C D bE ]E ]F G
||\ [-7, 3, 1> -9 (79.61c)
|) [6, -2, 0, -1> +10 (45.23c)
/| [-4, 4, -1> -19 (34.38c)

Augene <<3, 0, -6, -7, -18, -14]] P = 399.02, G = 92.46
map: [<3, 5, 7, 8], <0, -1, 0, 2]]
MOS/DE: 3, 6, *9+, 12++, 15, 27+
PN: #C D bE / F #F G / A bB B
|||( [-1, 1, 1, -1> -3 (121.64c)
/| [-4, 4, -1> -4 (29.18c)

Keemun <<6, 5, 3, -6, -12, -7]] P = 1203.19, G = 317.83
map: [<1, 0, 1, 2], <0, 6, 5, 3]]
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 (68.15c)
|||( [-1, 1, 1, -1> +8 (136.30c)
./||\ [4, -1, -1> -11 (113.38c)
|) [6, -2, 0, -1> -15 (45.23c)
/| [-4, 4, -1> +19 (22.92c)
.)X( [1, -2, 1> -7 (181.10c)

Catler <<0, 0, 12, 0, 19, 28]] P = 99.81, G = 24.58
map: [<12, 19, 28, 33], <0, 0, 0, 1]]
MOS/DE: 12, 24
PN: D / bE / E / F / #F / G / #G / A / bB / B / C / #C
|) [6, -2, 0, -1> -1 (33.53c)

Hedgehog <<6, 10, 10, 2, -1, -5]] P = 598.45, G = 162.32
map: [<2, 4, 6, 7], <0, -3, -5, -5]]
MOS/DE: 2, 4+, 6++, *8++, 14+, 22++, 30
PN: ([B) ]C D [E (]F) / (]E) [G #G ]A ([C)
/|) [2, 2, -1, -1> +4 (50.82c)
|||( [-1, 1, 1, -1> -3 (111.5c)

Superpyth <<1, 9, -2, 12, -6, -30]] P = 1197.60, G = 489.43
map: [<1, 2, 6, 2], <0, -1, -9, 2]]
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)
/|) [2, 2, -1, -1> +5 (51.94c)
|||) [-5, 5, 0, -1> -7 (166.8c)
|||( [-1, 1, 1, -1> -12 (114.85c)
)||( [-3, -1, 2> -17 (62.91c)

Sensisept <<7, 9, 13, -2, 1, 5]] P = 1198.39, G = 443.16
map: [<1, -1, -1, -2], <0, 7, 9, 13]]
MOS/DE: 1, 2++, 3++, 5+, *8++, 11+, 19++, 27++
PN: (#G) ]C F ]A D [G B [E (#G)
/|) [2, 2, -1, -1> -8 (49.89c)
)||( [-3, -1, 2> +11 (81.21c)
/| [-4, 4, -1> +19 (31.32c)

Lemba <<6, -2, -2, -17, -20, 1]] P = 601.70, G = 230.87
map: [<2, 2, 5, 6], <0, 3, -1, -1]]
MOS/DE: 2, 4++, *6++, 10++, 16++, 26++
PN: (]A) [C D ]E ([G) / ([E) ]F #G [B (]C)
|||( [-1, 1, 1, -1> +3 (90.92c)
)||( [-3, -1, 2> -5 (49.03c)
/|) [2, 2, -1, -1> +8 (41.9c)

Porcupine <<3, 5, -6, 1, -18, -28]] P = 1196.91, G = 162.32
map: [<1, 2, 3, 2], <0, -3, -5, 6]]
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)
/|) [2, 2, -1, -1> -7 (60.68c)
./||\ [4, -1, -1> +8 (101.64c)

Flattone <<1, 4, -9, 4, -17, -32]] P = 1202.54, G = 507.14
map: [<1, 2, 4, -1], <0, -1, -4, 9]]
MOS/DE: 1, 2++, 3+, 5++, *7++, 12+, 19++, 26
PN: B E A D G C F
/|) [2, 2, -1, -1> -7 (57.64c)

Magic <<5, 1, 12, -10, 5, 25]] P = 1201.28, G = 380.80
map: [<1, 0, 2, -1], <0, 5, 1, 12]]
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
/|) [2, 2, -1, -1> -3 (58.89c)
|||) [-5, 5, 0, -1> +13 (145.24c)
||\ [-7, 3, 1> +16 (86.35c)
/| [-4, 4, -1> +19 (27.46c)
|) [6, -2, 0, -1> -22 (31.43c)

Doublewide <<8, 6, 6, -9, -13, -3]] P = 599.28, G = 272.31
map: [<2, 5, 6, 7], <0, -4, -3, -3]]
MOS/DE: 2, *4++, 6, 10, 14+, 18++, 22++
PN: (]C bE) #F [A [C D ]E ]G bB (#C [E) / ([G A) C ]D ]F #G [B [D E (G ]A)
/|) [2, 2, -1, -1> -2 (54.65)
|||( [-1, 1, 1, -1> -4 (109.3)
./||\ [4, -1, -1> +7 (108.36)

Nautilus <<6, 10, 3, 2, -12, -21]] P = 1202.66, G = 82.97
map: [<1, 2, 3, 3], <0, -6, -10, -3]]
MOS/DE: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13+, *14++, 15+, 29++
PN: (#G) A bB [B [C ]C #C D bE [E ]E ]F #F G (#G)
|||( [-1, 1, 1, -1> -13 (123.99c)
)||( [-3, -1, 2> -14 (41.01c)
/| [-4, 4, -1> -14 (41.01c)
|) [6, -2, 0, -1> +15 (41.96c)

Beatles <<2, -9, -4, -19, -12, 16]] P = 1197.10, G = 354.72
map: [<1, 1, 5, 4], <0, 2, -9, -4]]
MOS/DE: 1, 2+, 3++, 4+, *7++, 10++, 17+, 27++
PN: [E G [B D ]F A ]C
./||\ [4, -1, -1> +7 (88.83c)
/|) [2, 2, -1, -1> +17 (44.73c)

Liese <<3, 12, 11, 12, 9, -8]] P = 1202.62, G = 569.05
map: [<1, 3, 8, 8], <0, -3, -12, -11]]
MOS/DE: 1, 2++, 3, 5, 7, 9, 11, 13, 15+, 17++, *19++
PN: B ]E [B E ]A [E A ]D [A D ]G [D G ]C [G C ]F [C F
./||\ [4, -1, -1> +15 (117.36c)
/|) [2, 2, -1, -1> +17 (52.84c)
)||( [-3, -1, 2> -21 (76.22c)

Cynder<<3, 12, -1, 12, -10, -36]] P = 1201.70, G = 232.52
map: [<1, 1, 0, 3], <0, 3, 12, -1]]
MOS/DE: 1, 2, 3, 4+, *5++, 6, 11, 16, 21+, 26++, 31++
PN: A] C[ D E] G[
/|) [2, 2, -1, -1> -5 (50.21c)
|||( [-1, 1, 1, -1> +16 (126.36c)
)||( [-3, -1, 2> +21 (76.16c)

Orwell <<7, -3, 8, -21, -7, 27]] P = 1199.53, G = 271.49
map: [<1, 0, 3, 1], <0, 7, -3, 8]]
MOS/DE: 1, 2, 3+, 4++, 5+, *9++, 13+, 22++, 31++
PN: bE #F [A [C D ]E ]G bB #C
/|) [2, 2, -1, -1> +9 (44.38c)
)||( [-3, -1, 2> -13 (69.18c)
|) [6, -2, 0, -1> -22 (24.80c)
/| [-4, 4, -1> +31 (19.57c)
|( [10, -6, 1, -1> -53 (5.23c)

Garibaldi <<1, -8, -14, -15, -25, -10]] P = 1200.76, G = 498.12
map: [<1, 2, -1, -3], <0, -1, 8, 14]]
MOS/DE: 1, 2++, 3+, 5++, *7+, 12++, 17, 29+
PN: B E A D G C F
||\ [-7, 3, 1> +5 (89.08c)
/||\ [-11, 7> -7 (115.45c)
|) [6, -2, 0, -1> -12 (26.37c)
(|\ [-13, 5, 1, 1> +17 (62.7c)

Myna <<10, 9, 7, -9, -17, -9]] P = 1198.83, G = 309.89
map: [<1, -1, 0, 1], <0, 10, 9, 7]]
MOS/DE: 1, 2+, 3++, *4++, 7, 11, 15, 19, 23+, 27++, 31++
PN: (G#) B D F (G#)
/|) [2, 2, -1, -1> +4 (40.74c)
)||( [-3, -1, 2> +8 (81.48c)
|||( [-1, 1, 1, -1> +12 (122.23c)
./||\ [4, -1, -1> -19 (106.18c)
|) [6, -2, 0, -1> -27 (24.70c)
/| [-4, 4, -1> +31 (16.04c)

Miracle <<6, -7, -2, -25, -20, 15]] P = 1200.63, G = 116.72
map: [<1, 1, 3, 3], <0, 6, -7, -2]]
MOS/DE: 1, 2, 3, 4, 5, 6, 7, 8, 9+, *10++, 11, 21+, 31++
PN: (#G) ]A [B [C #C D bE ]E ]F [G (#G)
|) [6, -2, 0, -1> -10 (33.42c)
/|) [2, 2, -1, -1> +21 (49.87c)
/| [-4, 4, -1> +31 (16.45c)
|( [10, -6, 1, -1> -41 (16.98c)

Ennealimmal <<18, 27, 18, 1, -22, -34]] P = 133.34, G = 49.02
map: [<9, 15, 22, 26], <0, -2, -3, -2]]
MOS/DE: *9, 18++, 27++
PN: D / [E / ]E / #F / ]G / [A / bB / [C / ]C
/|) [2, 2, -1, -1> +1 (49.02c)

*********** bonus temperaments

Superpelog <<2, -6, 1, -14, -4, 19]] P = 1206.55, G = 260.76
map: [<1, 2, 1, 3], <0, -2, 6, -1]]
MOS/DE: 1, 2, 3+, 4++, 5++, *9++, 14++, 23+
PN: [E #F A [C D ]E G bB ]C
/|) [2, 2, -1, -1> -9 (66.26c)
|||( [-1, 1, 1, -1> +5 (97.25c)

Decimal <<4, 2, 2, -6, -8, -1]] P = 603.83, G = 250.61
map: [<2, 4, 5, 6], <0, -2, -1, -1]]
MOS/DE: 2, 4++, *6+, *10++, 14+, 24++
PN: (A) [C D ]E (G) / (bE) ]F #G [B (#C)
|||( [-1, 1, 1, -1> -2 (102.61c)
./||\ [4, -1, -1> +3 (148.01c)
|) [6, -2, 0, -1> +5 (45.4c)

Hexadecimal <<1, -3, 5, -7, 5, 20]] P = 1208.96, G = 530.16
map: [<1, 2, 1, 5], <0, -1, 3, -5]]
MOS/DE: 1, 2++, 3, 5+, *7++, 9++, 16++, 25
PN: bB [E [A D ]G ]C #F
)||( [-3, -1, 2> +7 (84.27c)

Valentine <<9, 5, -3, -13, -30, -21]] P = 1199.79, G = 77.83
map: [<1, 1, 2, 3], <0, 9, 5, -3]]
MOS/DE: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14+, *15++, 16+, 31++
PN: [A ]A bB B [C ]C #C D bE [E ]E F #F [G ]G
|) [6, -2, 0, -1> -15 (32.3c)
/|) [2, 2, -1, -1> +16 (45.54c)
/| [-4, 4, -1> +31 (13.24c)

Muggles <<5, 1, -7, -10, -25, -19]] P = 1203.15, G = 379.39
map: [<1, 0, 2, 5], <0, 5, 1, -7]]
MOS/DE: 1, 2+, 3++, 4, *7, 10, 13+, 16++, 19++
PN: (E ]G [C [E G B) ]D [G bB D #F ]A [D (F A ]C ]E [A C)
)||( [-3, -1, 2> -3 (64.97c)
|||( [-1, 1, 1, -1> +13 (119.52c)
/|) [2, 2, -1, -1> +16 (54.55c)

Superkleismic <<9, 10, -3, -5, -30, -35]] P = 1201.37, G = 322.37
map: [<1, 4, 5, 2], <0, -9, -10, 3]]
MOS/DE: 1, 2+, 3++, 4++, *7+, 11++, 15++, 26++
PN: (bB #C) ]E ]G B D F [A [C (bE #F)
/|) [2, 2, -1, -1> -11 (58.01c)
|) [6, -2, 0, -1> +15 (30.11c)
/| [-4, 4, -1> -26 (27.9c)

Hemiwürschmidt <<16, 2, 5, -34, -37, 6]] P = 1199.69, G = 193.82
map: [<1, -1, 2, 2], <0, 16, 2, 5]]
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 (36.76c)
)||( [-3, -1, 2> -12 (73.51c)
|||( [-1, 1, 1, -1> +13 (120.31c)
./||\ [4, -1, -1> -18 (110.27c)
/|) [2, 2, -1, -1> +25 (46.79c)