JULIAN RHODES' DREAM ORGANS
Although there are many small mutation divisions distributed throughout Liber Organum, this level is solely an harmonic-colouring resource. It is also an exploration of the possibilities of the harmonic series, and culminates in the division of a semitone into 16 parts.As the fractional harmonic series extends itself, here to x/255, it is apparent that a greater number of notes appear around B and B-flat than anywhere else in the octave. This point of new growth suggests a stellar nebula, a gas-cloud from which new stars form, and the level is so named.
Throughout this division, v. = very; 1-2 = half; 1-4 = one quarter; 1-8 = one eighth, etc.
NEBULA 128 1st 85 1/3 5th 64 1st 51 1/5 3rd 42 2/3 5th 36 4/7 7th flat 32 1st 28 4/9 2nd 24 4/5 3rd 23 3/11 4th 21 1/3 5th 19 9/13 6th 18 2/7 7th flat 17 1/15 7th 16 1st 15 1/17 2nd flat 14 2/9 2nd 13 1/19 3rd flat 12 4/5 3rd 12 4/21 3rd sharp 11 7/11 4th 11 3/20 4th sharp 10 2/3 5th 10 6/25 5th sharp 9 11/13 6th 9 13/27 6th sharp 9 1/7 7th flat 8 24/29 7th 1-2 flat 8 8/15 7th 8 16/31 1st flat 8 1st 7 25/33 1st sharp 7 9/17 2nd flat 7 11/35 2nd 1-2 flat 7 1/9 2nd 6 34/37 2nd sharp 6 14/19 3rd flat 6 22/39 3rd 1-2 flat 6 1/5 3rd 6 10/41 3rd sharp 6 2/21 4th flat 5 41/43 4th 1-2 flat 5 9/11 4th 5 31/45 4th 1-2 sharp 5 13/23 4th sharp 5 21/47 5th flat 5 1/3 5th 5 11/49 5th 1-2 sharp 5 3/25 5th sharp 5 1/51 6th flat 4 12/13 6th 4 44/53 6th 1-2 sharp 4 20/27 6th sharp 4 36/55 6th v.sharp 4 4/7 7th flat 4 28/57 7th 3-4 flat 4 12/29 7th 1-2 flat 4 20/59 7th 1-4 flat 4 4/15 7th 4 12/61 7th sharp 4 4/31 8th flat 4 4/63 8th 1-2 flat 4 8th 3 29/33 8th sharp 3 13/17 9th flat 3 23/35 9th 1-2 flat 3 5/9 9th 3 17/37 9th sharp 3 7/19 10th flat 3 11/39 10th 1-2 flat 3 1/5 10th 3 5/41 10th sharp 3 1/21 11th flat 2 42/43 11th 1-2 flat 2 10/11 11th 2 38/45 11th 1-2 sharp 2 18/23 11th sharp 2 34/47 12th flat 2 2/3 12th 2 30/49 12th 1-2 sharp 2 14/25 12th sharp 2 26/51 13th flat 2 6/13 13th 2 22/53 13th 1-2 sharp 2 10/27 13th sharp 2 2/7 14th flat 2 14/57 14th 3-4 flat 2 6/29 14th 1-2 flat 2 10/59 14th 1-4 flat 2 2/15 14th 2 6/61 14th sharp 2 2/31 15th flat 2 2/63 15th 1-2 flat 2 15th 1 63/65 15th 1-2 sharp 1 31/33 15th sharp 1 61/65 15th v. sharp 1 15/17 16th flat 1 59/69 16th 3-4 flat 1 29/35 16th 1-2 flat 1 57/71 16th 1-4 flat 1 7/9 16th 1 55/73 16th 1-2 sharp 1 27/37 16th sharp 1 53/75 16th v. sharp 1 13/19 17th flat 1 51/77 17th 3-4 flat 1 25/39 17th 1-2 flat 1 49/79 17th 1-4 flat 1 3/5 17th 1 47/81 17th 1-2 sharp 1 23/41 17th sharp 1 45/83 17th v. sharp 1 11/21 18th flat 1 43/85 18th 3-4 flat 1 21/43 18th 1-2 flat 1 41/87 18th 1-4 flat 1 5/11 18th 1 39/89 18th 1-4 sharp 1 19/45 18th 1-2 sharp 1 37/91 18th 3-4 sharp 1 9/23 18th sharp 1 35/93 19th v.flat 1 17/47 19th flat 1 33/95 19th 1-2 flat 1 1/3 19th 1 31/97 19th 1-4 sharp 1 15/49 19th 1-2 sharp 1 29/99 19th 3-4 sharp 1 7/25 19th sharp 1 27/101 20th v. flat 1 13/51 20th flat 1 25/103 20th 1-2 flat 1 3/13 20th 1 23/105 20th 1-4 sharp 1 11/53 20th 1-2 sharp 1 21/107 20th 3-4 sharp 1 5/27 20th sharp 1 19/109 20th sharper 1 9/55 20th v. sharp 1 17/111 21st v. flat 1 1/7 21st flat 1 15/113 21st 7-8 flat 1 7/57 21st 3-4 flat 1 13/115 21st 5-8 flat 1 3/29 21st 1-2 flat 1 11/117 21st 3-8 flat 1 5/59 21st 1-4 flat 1 9/119 21st 1-8 flat 1 1/15 21st 1 7/121 21st 1-2 sharp 1 3/61 21st sharp 1 5/123 21st v. sharp 1 1/31 22nd flat 1 3/125 22nd 3-4 flat 1 1/63 22nd 1-2 flat 1 1/127 22nd 1-4 flat 1 22nd 128/129 22nd 1-4 sharp 64/65 22nd 1-2 sharp 128/131 22nd 3-4 sharp 32/33 22nd sharp 128/133 22nd sharper 64/67 22nd v. sharp 128/135 23rd v. flat 16/17 23rd flat 128/137 23rd 7-8 flat 64/69 23rd 3-4 flat 128/139 23rd 5-8 flat 32/35 23rd 1-2 flat 128/141 23rd 3-8 flat 64/71 23rd 1-4 flat 128/143 23rd 1-8 flat 8/9 23rd 128/145 23rd 1-4 sharp 64/73 23rd 1-2 shaep 128/147 23rd 3-4 sharp 32/37 23rd sharp 128/149 23rd sharper 64/75 23rd v. sharp 128/151 24th v. flat 16/19 24th flat 128/153 24th 7-8 flat 64/77 24th 3-4 flat 128/155 24th 5-8 flat 32/39 24th 1-2 flat 128/157 24th 3-8 flat 64/79 24th 1-4 flat 128/159 24th 1-8 flat 4/5 24th 128/161 24th 1-4 sharp 64/81 24th 1-2 sharp 128/163 24th 3-4 sharp 32/41 24th sharp 128/165 24th sharper 64/83 24th v. sharp 128/167 25th v. flat 16/21 25th flat 118/169 25th 7-8 flat 64/85 25th 3-4 flat 128/171 25th 5-8 flat 32/43 25th 1-2 flat 128/173 25th 3-8 flat 64/87 25th 1-4 flat 128/175 25th 1-8 flat 8/11 25th 128/177 25th 1-8 sharp 64/89 25th 1-4 shaep 128/179 25th 3-8 shaep 32/45 25th 1-2 sharp 128/181 25th 5-8 sharp 66/91 25th 3-4 sharp 128/183 25th 7-8 sharp 16/23 25th sharp 128/185 25th v. sharp 64/93 26th v. flat 128/187 26th flatter 32/47 26th flat 128/189 26th 3-4 flat 64/95 26th 1-2 flat 128/191 26th 1-4 flat 2/3 26th 128/193 26th 1-8 sharp 64/97 26th 1-4 sharp 128/195 26th 3-8 sharp 32/49 26th 1-2 sharp 128/197 26th 5-8 sharp 64/99 26th 3-4 sharp 128/199 26th 7-8 sharp 16/25 26th sharp 128/201 26th v.sharp 64/101 27th v. flat 128/203 27th flatter 32/51 27th flat 128/205 27th 3-4 flat 64/103 27th 1-2 flat 128/207 27th 1-4 flat 8/13 27th 128/209 27th 1-8 sharp 64/105 27th 1-4 sharp 128/211 27th 3-8 sharp 32/53 27th 1-2 sharp 128/213 27th 5-8 sharp 64/107 27th 3-4 sharp 128/215 27th 7-8 sharp 16/27 27th sharp 128/217 27th sharper 64/109 27th and sharper 128/219 27th sharper still 32/55 27th v. sharp indeed 128/221 28th v. flat indeed 64/111 28th flatter still 128/223 28th flatter 4/7 28th flat 128/225 28th 15-16 flat 64/113 28th 7-8 flat 128/227 28th 13-16 flat 32/57 28th 3-4 flat 128/229 28th 11-16 flat 64/115 28th 5-8 flat 128/231 28th 9-16 flat 16/29 28th 1-2 flat 128/233 28th 7-16 flat 64/117 28th 3-8 flat 128/235 28th 5-16 flat 32/59 28th 1-4 flat 128/237 28th 3-16 flat 64/119 28th 1-8 flat 128/239 28th 1-16 flat 8/15 28th 128/241 28th 1-4 sharp 64/121 28th 1-2 sharp 128/243 28th 3-4 sharp 32/61 28th sharp 128/245 28th v. sharp 64/123 28th sharper 128/247 29th v. flat 16/31 29th flat 128/249 29th 7-8 flat 64/125 29th 3-4 flat 128/251 29th 5-6 flat 32/63 29th 1-2 flat 128/253 29th 3-8 flat 64/127 29th 1-4 flat 128/255 29th 1-8 flat 1/2 29th 8/17 30th flat 4/9 30th 8/19 31st flat 2/4 31st 8/21 31st sharp 9/11 32nd 8/23 32nd sharp 1/3 33rd 8/25 33rd sharp 4/13 34th 8/27 34th sharp 2/7 35th flat 8/29 35th sl. flat 4/15 35th 1/4 36th 2/9 37th 1/5 38th 2/11 39th 1/6 40th 2/13 41st 1/7 42nd flat 1/8 43rd 1/9 44th 1/10 45th 1/12 47th 1/14 49th flat 1/16 50th 1/20 52nd 1/24 54th 1/32 57th 1/48 61st 1/64 64th 1/128 71st
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