12-Tone Scale Tuning Temperaments ================================= by Benjamin Tubb brtubb@cybertron.com 24 June 1997 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 setup for GS Performance Part 1 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 Roland JV/XP Scale Tuning Offset -64 to 63 cents 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