The following tables were derived from those in Chas Stoddard's article "Microtonality and Scale Temperaments for Roland GS Synths" which fortunately at the sysex AND data level are COMPLETELY compatible with the Roland JV/XP synths. And at the data level they are also compatible with Yamaha's XG synth family. Although they can't be used in GM Mode directly, they can be used if sent BEFORE entering GM Mode. They are fully functional in Performance Mode.
The following formulas can be used to derive your own temperaments using ratios.
Using a given ratio, which we'll call R, to determine the Cents equivalent, use the formula:
Cents = LOG(R) * (1200/LOG(2)) ; where LOG(x) represents the common base ten logarithm of x.
Then to derive the JV/XP's Scale Tuning Offset from -64 thru 63 cents (which is the same range on the Roland GS family of synths), subtract Cents from the appropriate Equal Temperament Scale (based on the 12th roots of 2) Cent value, i.e. from the 12 semitone "equal" (logarithmic) values of 0, 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, and 1100 cents (based the 1200th roots of 2).
For example, assume that the ratio desired for the seventh semitone, the perfect fifth interval, is 3/2. Using the formula for Cents above gives a result of 702.0. Now subtract the E.T. 700 cent "equivalent" and the result of 2 is obtained as the Tuning Offset for G on the JV/XP.
To determine the data value for an appropriate sysex message, the Tuning Offset must have 64 added to it to convert its range from -64 thru 64 to 0 thru 127. That value in this case will equal 66 which must be converted to hexadecimal 42 for use in sysex.
Although the sysex messages bellow are based on GS Performance Part 1, of course, any Part may be used by using the appropiate JV/XP Parameter Address Map values which can be found in the Owner's Manuals, including the "alternate" address offsets starting at 00 00 10 00 for Part 1 in the System area.
For the info of any Yamaha XG synth owners, the parameter address map for XG Multi-Part 1 starts at 80 00 41. The 12 byte data is completely compatible. Only the "header" and checksum would need to be changed.
Also, transposition of these C Rooted tunings to another Root is easily made by left or right "cycling" of the Hex values in the Sysex messages (or Tuning Offsets) with "wrap around". For example, given:
F0 41 10 42 12 40 11 40 40 4A 44 4E 48 3E 48 42 4C 46 50 4A 17 F7
which is "rooted" in C, to transpose to D, cycle the data values to the right twice to produce:
F0 41 10 42 12 40 11 40 50 4A 40 4A 44 4E 48 3E 48 42 4C 46 17 F7
Note that the Checksum does NOT need to be changed.
Tuning Scale Name
1 Agricola's Pythag Monochord
2 Agricola's Monochord
3 Aron's 1/4th Comma
4 Artusi's Monochord
5 Barnes' V&Y variation
6 Bendeler's 1/3rd Comma
7 Benderler's 1/4 Comma
8 Colonna's Irregular Just
9 De Caus' Monochord
10 Dechales' 1/5th Comma
11 Dowland's Lute Tuning
12 Equal Temperament
13 Erlangen's Monochord
14 Euler's Monochord
15 Fogliano's Monochord
16 Galilei's Approximation
17 Gallimard's Modified Meantone
18 Ganassi's Monochord
19 Harmonic
20 Harrison's 3/10 Comma
21 Hawke's Modified 1/5th Comma
22 Keplar's Monochord
23 Kirnberger - 1/2 Comma
24 Leven's Monochord
25 Ling Lun
26 Malcom's Monochord
27 Marpurg's 1/3rd Comma
28 Marpurg's Monochord
29 Salinas' Meantone
30 Meantone - 2 sharp 5ths
31 Mercadier's 1/12-1/6 Comma
32 Mersenne's Improved Meantone 1
33 Mersenne's Improved Meantone 2
34 Mersenne's Approximation
35 Mersenne's Lute Tuning
36 Mersenne's Spinet Tuning 1
37 Mersenne's Spinet Tuning 2
38 Montvallon's Monochord
39 Nassarre's Equal Semitones
40 Neidhardt's 5th Circle 1/4 Comma
41 Neidhardt's 5th Circle 1/6 Comma
42 Neidhart's 3rd Circle
43 Neidhardt's Circular
44 Pure Major
45 Pure Minor
46 Pythagoras - Mean Semitones
47 Pythagorean
48 Rameau's Modified Meantone
49 Ramis' Monochord
50 Regularily Varied 5ths
51 Romieu's 1/7th Comma
52 Romieu's 1/8th Comma
53 Romieu's 1/9th Comma
54 Romieu's 1/10th Comma
55 Romieu's Monochord
56 Rossi's 2/9th Comma
57 Rousseau's Monochord
58 Salinas' 1/3rd Comma
59 Scheengaas' Variation
60 Schlick's (Theoretical)
61 Silberman's 1/6th Comma
62 Smith's 5/18th Comma
63 Stanhope's 1/3rd Comma
64 Strahle's Geometrical
65 Valotti & Young
66 Verheijen's 1/5th Comma
67 Von Wiesse's 1/2 Comma
68 Werckmeister 1 - 1/4 Comma
69 Werckmeister 4 - 1/4 Comma
70 Werckmeister 2 - 1/3rd Comma
71 Werckmeister - 1/7th Comma
72 Werckmeister 3
73 Young's 1/6th Comma
74 Zarlino's 2/7th Comma
75 Zazal
1 F0 41 10 42 12 40 11 40 40 4A 44 4E 48 3E 48 42 4C 46 50 4A 17 F7 2 F0 41 10 42 12 40 11 40 40 38 44 3C 48 3E 36 42 3A 46 3C 4A 73 F7 3 F0 41 10 42 12 40 11 40 40 28 39 4A 32 43 2B 3D 25 36 47 2F 56 F7 4 F0 41 10 42 12 40 11 40 40 3D 39 36 32 43 40 3D 3A 36 33 2F 3F F7 5 F0 41 10 42 12 40 11 40 40 3A 3C 2A 38 27 34 3C 36 3A 27 36 73 F7 6 F0 41 10 42 12 40 11 40 40 36 34 3A 38 3E 34 3A 38 36 3C 3A 43 F7 7 F0 41 10 42 12 40 11 40 40 3C 38 3A 3C 3E 3A 3C 3E 3A 3C 38 25 F7 8 F0 41 10 42 12 40 11 40 40 22 2E 33 32 3E 20 42 60 30 35 34 61 F7 9 F0 41 10 42 12 40 11 40 40 22 2E 26 32 3E 20 42 24 30 3C 34 23 F7 10 F0 41 10 42 12 40 11 40 40 31 3A 4C 3B 42 33 3C 48 39 49 36 0C F7 11 F0 41 10 42 12 40 11 40 40 48 44 30 34 3E 3D 42 4A 46 32 36 0A F7 12 F0 41 10 42 12 40 11 40 40 40 40 40 40 40 40 40 40 40 40 40 6F F7 13 F0 41 10 42 12 40 11 40 40 36 42 3A 32 3E 34 42 38 44 3C 34 2B F7 14 F0 41 10 42 12 40 11 40 40 22 44 26 32 3E 36 42 24 30 28 34 0B F7 15 F0 41 10 42 12 40 11 40 40 22 2E 50 32 3E 32 42 24 30 3C 34 67 F7 16 F0 41 10 42 12 40 11 40 40 43 3E 41 3C 3B 3A 39 38 37 36 35 29 F7 17 F0 41 10 42 12 40 11 40 40 30 39 3D 32 44 2E 3C 35 36 47 2F 48 F7 18 F0 41 10 42 12 40 11 40 40 34 2E 20 32 3E 3D 42 36 30 2F 34 75 F7 19 F0 41 10 42 12 40 11 40 40 45 44 3E 32 23 0F 42 68 46 21 34 3F F7 20 F0 41 10 42 12 40 11 40 40 21 37 4E 2E 44 25 3C 1C 33 49 31 6D F7 21 F0 41 10 42 12 40 11 40 40 2F 3B 43 36 42 32 3E 31 39 45 34 37 F7 22 F0 41 10 42 12 40 11 40 40 38 44 50 32 3E 36 42 3A 46 52 34 75 F7 23 F0 41 10 42 12 40 11 40 40 36 44 3A 32 3E 36 42 38 3B 3C 34 30 F7 24 F0 41 10 42 12 40 11 40 40 4C 5F 50 44 3E 3D 42 4E 61 3C 5D 6B F7 25 F0 41 10 42 12 40 11 40 40 4E 44 52 48 56 4C 42 50 46 54 4A 6B F7 26 F0 41 10 42 12 40 11 40 40 4C 44 50 32 3E 36 42 4E 30 3C 34 79 F7 27 F0 41 10 42 12 40 11 40 40 46 44 42 40 46 44 42 40 46 44 3C 51 F7 28 F0 41 10 42 12 40 11 40 40 22 44 50 32 3E 36 42 24 30 52 34 37 F7 29 F0 41 10 42 12 40 11 40 40 32 38 4C 30 44 2A 3C 23 34 48 2E 52 F7 30 F0 41 10 42 12 40 11 40 40 28 39 4A 32 43 2B 3D 39 36 47 2F 42 F7 31 F0 41 10 42 12 40 11 40 40 3A 3D 3C 3A 40 3A 3E 3A 3B 3E 3A 1D F7 32 F0 41 10 42 12 40 11 40 40 28 39 3F 32 43 2B 3D 25 36 41 2F 67 F7 33 F0 41 10 42 12 40 11 40 40 28 39 34 32 43 2B 3D 25 36 3C 2F 77 F7 34 F0 41 10 42 12 40 11 40 40 42 43 45 47 48 4A 4C 4E 4A 47 43 1E F7 35 F0 41 10 42 12 40 11 40 40 4C 2E 50 32 3E 4A 42 4E 30 52 34 65 F7 36 F0 41 10 42 12 40 11 40 40 4C 2E 50 32 3E 4A 42 4E 30 3C 34 7B F7 37 F0 41 10 42 12 40 11 40 40 22 44 26 32 3E 20 42 24 30 3C 34 0D F7 38 F0 41 10 42 12 40 11 40 40 38 44 50 32 3E 36 42 3A 30 3C 34 21 F7 39 F0 41 10 42 12 40 11 40 40 43 44 43 48 47 4C 4B 50 4F 54 47 05 F7 40 F0 41 10 42 12 40 11 40 40 3C 3E 40 3C 3E 40 3C 3E 40 3C 3E 07 F7 41 F0 41 10 42 12 40 11 40 40 42 44 3E 40 42 44 3E 40 42 44 3E 63 F7 42 F0 41 10 42 12 40 11 40 40 3C 3C 3C 3C 3E 3C 3E 3C 3A 40 3A 17 F7 43 F0 41 10 42 12 40 11 40 40 3A 3C 3C 38 3E 38 3E 3C 3A 3C 38 27 F7 44 F0 41 10 42 12 40 11 40 40 4C 44 50 30 3E 36 42 4E 30 3C 34 7B F7 45 F0 41 10 42 12 40 11 40 40 23 30 50 30 3E 36 42 4E 30 3C 34 38 F7 46 F0 41 10 42 12 40 11 40 40 42 44 46 48 3E 40 42 44 46 48 4A 3F F7 47 F0 41 10 42 12 40 11 40 40 51 44 41 48 3E 4C 42 4E 46 3E 4A 29 F7 48 F0 41 10 42 12 40 11 40 40 33 39 3E 32 43 31 3D 35 36 47 2F 41 F7 49 F0 41 10 42 12 40 11 40 40 38 2E 3A 32 3E 36 42 38 30 3C 34 4F F7 50 F0 41 10 42 12 40 11 40 40 38 3D 3D 38 40 37 3F 3A 3A 3F 37 25 F7 51 F0 41 10 42 12 40 11 40 40 38 3E 43 3C 41 39 3F 37 3D 42 3B 10 F7 52 F0 41 10 42 12 40 11 40 40 3B 3F 42 3D 41 3C 3F 38 3E 41 3D 06 F7 53 F0 41 10 42 12 40 11 40 40 3D 3F 41 3E 40 3E 40 3D 3F 41 3E 7B F7 54 F0 41 10 42 12 40 11 40 40 3F 40 41 3F 40 3F 40 3E 3F 40 3D 77 F7 55 F0 41 10 42 12 40 11 40 40 22 44 50 32 3E 36 42 24 30 3C 34 4D F7 56 F0 41 10 42 12 40 11 40 40 2B 3A 48 35 43 2E 3D 2A 38 46 31 46 F7 57 F0 41 10 42 12 40 11 40 40 22 44 50 32 3E 20 42 4E 30 12 34 63 F7 58 F0 41 10 42 12 40 11 40 40 1C 36 50 26 45 21 3B 16 30 4A 26 10 F7 59 F0 41 10 42 12 40 11 40 40 2B 3A 49 35 44 31 3E 4C 38 45 31 1F F7 60 F0 41 10 42 12 40 11 40 40 36 3C 42 38 42 36 3E 3C 3A 42 36 1F F7 61 F0 41 10 42 12 40 11 40 40 35 3D 45 3A 42 36 3E 33 3B 43 38 1F F7 62 F0 41 10 42 12 40 11 40 40 24 38 4C 30 44 28 3C 20 34 48 33 60 F7 63 F0 41 10 42 12 40 11 40 40 37 3D 3B 32 3E 35 42 39 38 3C 34 38 F7 64 F0 41 10 42 12 40 11 40 40 4B 53 59 5C 5D 5D 5B 58 53 4E 48 06 F7 65 F0 41 10 42 12 40 11 40 40 3A 3C 2A 38 27 34 3C 36 3A 27 36 73 F7 66 F0 41 10 42 12 40 11 40 40 2F 3B 47 36 42 32 3E 2D 39 45 34 37 F7 67 F0 41 10 42 12 40 11 40 40 42 44 46 48 3E 40 42 44 46 3C 4A 4B F7 68 F0 41 10 42 12 40 11 40 40 36 38 38 36 3E 34 3C 38 34 3C 38 45 F7 69 F0 41 10 42 12 40 11 40 40 3C 44 40 3C 44 40 42 38 40 42 3E 75 F7 70 F0 41 10 42 12 40 11 40 40 2E 3C 3A 38 3E 34 3A 32 36 44 32 49 F7 71 F0 41 10 42 12 40 11 40 40 37 32 3E 3B 3E 3B 3E 39 39 40 3D 27 F7 72 F0 41 10 42 12 40 11 40 40 3A 38 2A 36 27 34 3C 36 34 27 38 7D F7 73 F0 41 10 42 12 40 11 40 40 36 3C 3A 38 3E 34 3E 38 3A 3C 36 37 F7 74 F0 41 10 42 12 40 11 40 40 22 37 4D 32 44 26 3C 51 33 48 2A 3B F7 75 F0 41 10 42 12 40 11 40 40 72 40 40 0E 40 40 40 0E 40 40 0E 53 F7
C C# D D# E F F# G G# A A# B 1 0 10 4 14 8 -2 8 2 12 6 16 10 2 0 -8 4 -4 8 -2 -10 2 -6 6 -4 10 3 0 -24 -7 10 -14 3 -21 -3 -27 -10 7 -17 4 0 -3 -7 -10 -14 3 0 -3 -6 -10 -13 -17 5 0 -6 -4 -22 -8 -25 -12 -4 -10 -6 -25 -10 6 0 -10 -12 -6 -8 -2 -12 -6 -8 -10 -4 -6 7 0 -4 -8 -6 -4 -2 -6 -4 -2 -6 -4 -8 8 0 -30 -18 -13 -14 -2 -32 2 32 -16 -11 -12 9 0 -30 -18 -26 -14 -2 -32 2 -28 -16 -4 -12 10 0 -15 -6 12 -5 2 -13 -4 8 -7 9 -10 11 0 8 4 -16 -12 -2 -3 2 10 6 -14 -10 12 0 0 0 0 0 0 0 0 0 0 0 0 13 0 -10 2 -6 -14 -2 -12 2 -8 4 -4 -12 14 0 -30 4 -26 -14 -2 -10 2 -28 -16 -24 -12 15 0 -30 -18 16 -14 -2 -14 2 -28 -16 -4 -12 16 0 3 -2 1 -4 -5 -6 -7 -8 -9 -10 -11 17 0 -16 -7 -3 -14 4 -18 -4 -11 -10 7 -17 18 0 -12 -18 -32 -14 -2 -3 2 -10 -16 -17 -12 19 0 5 4 -2 -14 -29 -49 2 40 6 -31 -12 20 0 -31 -9 14 -18 4 -27 -4 -36 -13 9 -15 21 0 -17 -5 3 -10 2 -14 -2 -15 -7 5 -12 22 0 -8 4 16 -14 -2 -10 2 -6 6 18 -12 23 0 -10 4 -6 -14 -2 -10 2 -8 -5 -4 -12 24 0 12 31 16 4 -2 -3 2 14 33 -4 29 25 0 14 4 18 8 22 12 2 16 6 20 10 26 0 12 4 16 -14 -2 -10 2 14 -16 -4 -12 27 0 6 4 2 0 6 4 2 0 6 4 -4 28 0 -30 4 16 -14 -2 -10 2 -28 -16 18 -12 29 0 -14 -8 12 -16 4 -22 -4 -29 -12 8 -18 30 0 -24 -7 10 -14 3 -21 -3 -7 -10 7 -17 31 0 -6 -3 -4 -6 0 -6 -2 -6 -5 -2 -6 32 0 -24 -7 -1 -14 3 -21 -3 -27 -10 1 -17 33 0 -24 -7 -12 -14 3 -21 -3 -27 -10 -4 -17 34 0 2 3 5 7 8 10 12 14 10 7 3 35 0 12 -18 16 -14 -2 10 2 14 -16 18 -12 36 0 12 -18 16 -14 -2 10 2 14 -16 -4 -12 37 0 -30 4 -26 -14 -2 -32 2 -28 -16 -4 -12 38 0 -8 4 16 -14 -2 -10 2 -6 -16 -4 -12 39 0 3 4 3 8 7 12 11 16 15 20 7 40 0 -4 -2 0 -4 -2 0 -4 -2 0 -4 -2 41 0 2 4 -2 0 2 4 -2 0 2 4 -2 42 0 -4 -4 -4 -4 -2 -4 -2 -4 -6 0 -6 43 0 -6 -4 -4 -8 -2 -8 -2 -4 -6 -4 -8 44 0 12 4 16 -16 -2 -10 2 14 -16 -4 -12 45 0 -29 -16 16 -16 -2 -10 2 14 -16 -4 -12 46 0 2 4 6 8 -2 0 2 4 6 8 10 47 0 17 4 1 8 -2 12 2 14 6 -2 10 48 0 -13 -7 -2 -14 3 -15 -3 -11 -10 7 -17 49 0 -8 -18 -6 -14 -2 -10 2 -8 -16 -4 -12 50 0 -8 -3 -3 -8 0 -9 -1 -6 -6 -1 -9 51 0 -8 -2 3 -4 1 -7 -1 -9 -3 2 -5 52 0 -5 -1 2 -3 1 -4 -1 -8 -2 1 -3 53 0 -3 -1 1 -2 0 -2 0 -3 -1 1 -2 54 0 -1 0 1 -1 0 -1 0 -2 -1 0 -3 55 0 -30 4 16 -14 -2 -10 2 -28 -16 -4 -12 56 0 -21 -6 8 -11 3 -18 -3 -22 -8 6 -15 57 0 -30 4 16 -14 -2 -32 2 14 -16 -46 -12 58 0 -36 -10 16 -26 5 -31 -5 -42 -16 10 -26 59 0 -21 -6 9 -11 4 -15 -2 12 -8 5 -15 60 0 -10 -4 2 -8 2 -10 -2 -4 -6 2 -10 61 0 -11 -3 5 -6 2 -10 -2 -13 -5 3 -8 62 0 -28 -8 12 -16 4 -24 -4 -32 -12 8 -13 63 0 -9 -3 -5 -14 -2 -11 2 -7 -8 -4 -12 64 0 11 19 25 28 29 29 27 24 19 14 8 65 0 -6 -4 -22 -8 -25 -12 -4 -10 -6 -25 -10 66 0 -17 -5 7 -10 2 -14 -2 -19 -7 5 -12 67 0 2 4 6 8 -2 0 2 4 6 -4 10 68 0 -10 -8 -8 -10 -2 -12 -4 -8 -12 -4 -8 69 0 -4 4 0 -4 4 0 2 -8 0 2 -2 70 0 -18 -4 -6 -8 -2 -12 -6 -14 -10 4 -14 71 0 -9 -14 -2 -5 -2 -5 -2 -7 -7 0 -3 72 0 -6 -8 -22 -10 -25 -12 -4 -10 -12 -25 -8 73 0 -10 -4 -6 -8 -2 -12 -2 -8 -6 -4 -10 74 0 -30 -9 13 -14 4 -26 -4 17 -13 8 -22 75 0 50 0 0 -50 0 0 0 -50 0 0 -50
Benjamin Tubb
brtubb@cybertron.com
http://www.cybertron.com/~brtubb