Harmonic Analysis
Ordered Factorizations
How many ordered ways does a number factor — and what does that count say about it, from aliquot balance to Ray Tomes' mainline harmonics.
Ordered Factorizations
Harmonic Scale Exploration — All Numbers 1–360
| N ▲ | H | log10[H]/log10[N] | K | RT Mainline | Aliquot Type | Ratio H:N | n2 | n3 | n5 | n7 | n11 | n13 | n17 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 2 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 3 | - | - | - | - | - | 0 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 4 | - | - | - | - | - | 2 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 5 | - | - | - | - | - | 0 | 0 | 1 | 0 | 0 | 0 | 0 | |
| 6 | - | - | - | - | - | 1 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 7 | - | - | - | - | - | 0 | 0 | 0 | 1 | 0 | 0 | 0 | |
| 8 | - | - | - | - | - | 3 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 9 | - | - | - | - | - | 0 | 2 | 0 | 0 | 0 | 0 | 0 | |
| 10 | - | - | - | - | - | 1 | 0 | 1 | 0 | 0 | 0 | 0 | |
| 11 | - | - | - | - | - | 0 | 0 | 0 | 0 | 1 | 0 | 0 | |
| 12 | - | - | - | Mainline | - | - | 2 | 1 | 0 | 0 | 0 | 0 | 0 |
| 13 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 1 | 0 | |
| 14 | - | - | - | - | - | 1 | 0 | 0 | 1 | 0 | 0 | 0 | |
| 15 | - | - | - | - | - | 0 | 1 | 1 | 0 | 0 | 0 | 0 | |
| 16 | - | - | - | - | - | 4 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 17 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 1 | |
| 18 | - | - | - | - | - | 1 | 2 | 0 | 0 | 0 | 0 | 0 | |
| 19 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 20 | - | - | - | - | - | 2 | 0 | 1 | 0 | 0 | 0 | 0 | |
| 21 | - | - | - | - | - | 0 | 1 | 0 | 1 | 0 | 0 | 0 | |
| 22 | - | - | - | - | - | 1 | 0 | 0 | 0 | 1 | 0 | 0 | |
| 23 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 24 | - | - | - | Mainline | - | - | 3 | 1 | 0 | 0 | 0 | 0 | 0 |
| 25 | - | - | - | - | - | 0 | 0 | 2 | 0 | 0 | 0 | 0 | |
| 26 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 1 | 0 | |
| 27 | - | - | - | - | - | 0 | 3 | 0 | 0 | 0 | 0 | 0 | |
| 28 | - | - | - | - | - | 2 | 0 | 0 | 1 | 0 | 0 | 0 | |
| 29 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 30 | - | - | - | - | - | 1 | 1 | 1 | 0 | 0 | 0 | 0 | |
| 31 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 32 | - | - | - | - | - | 5 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 33 | - | - | - | - | - | 0 | 1 | 0 | 0 | 1 | 0 | 0 | |
| 34 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 0 | 1 | |
| 35 | - | - | - | - | - | 0 | 0 | 1 | 1 | 0 | 0 | 0 | |
| 36 | - | - | - | Mainline | - | - | 2 | 2 | 0 | 0 | 0 | 0 | 0 |
| 37 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 38 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 39 | - | - | - | - | - | 0 | 1 | 0 | 0 | 0 | 1 | 0 | |
| 40 | - | - | - | - | - | 3 | 0 | 1 | 0 | 0 | 0 | 0 | |
| 41 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 42 | - | - | - | - | - | 1 | 1 | 0 | 1 | 0 | 0 | 0 | |
| 43 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 44 | - | - | - | - | - | 2 | 0 | 0 | 0 | 1 | 0 | 0 | |
| 45 | - | - | - | - | - | 0 | 2 | 1 | 0 | 0 | 0 | 0 | |
| 46 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 47 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 48 | - | - | - | Mainline | - | - | 4 | 1 | 0 | 0 | 0 | 0 | 0 |
| 49 | - | - | - | - | - | 0 | 0 | 0 | 2 | 0 | 0 | 0 | |
| 50 | - | - | - | - | - | 1 | 0 | 2 | 0 | 0 | 0 | 0 | |
| 51 | - | - | - | - | - | 0 | 1 | 0 | 0 | 0 | 0 | 1 | |
| 52 | - | - | - | - | - | 2 | 0 | 0 | 0 | 0 | 1 | 0 | |
| 53 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 54 | - | - | - | - | - | 1 | 3 | 0 | 0 | 0 | 0 | 0 | |
| 55 | - | - | - | - | - | 0 | 0 | 1 | 0 | 1 | 0 | 0 | |
| 56 | - | - | - | - | - | 3 | 0 | 0 | 1 | 0 | 0 | 0 | |
| 57 | - | - | - | - | - | 0 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 58 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 59 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 60 | - | - | - | - | - | 2 | 1 | 1 | 0 | 0 | 0 | 0 | |
| 61 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 62 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 63 | - | - | - | - | - | 0 | 2 | 0 | 1 | 0 | 0 | 0 | |
| 64 | - | - | - | - | - | 6 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 65 | - | - | - | - | - | 0 | 0 | 1 | 0 | 0 | 1 | 0 | |
| 66 | - | - | - | - | - | 1 | 1 | 0 | 0 | 1 | 0 | 0 | |
| 67 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 68 | - | - | - | - | - | 2 | 0 | 0 | 0 | 0 | 0 | 1 | |
| 69 | - | - | - | - | - | 0 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 70 | - | - | - | - | - | 1 | 0 | 1 | 1 | 0 | 0 | 0 | |
| 71 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 72 | - | - | - | Mainline | - | - | 3 | 2 | 0 | 0 | 0 | 0 | 0 |
| 73 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 74 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 75 | - | - | - | - | - | 0 | 1 | 2 | 0 | 0 | 0 | 0 | |
| 76 | - | - | - | - | - | 2 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 77 | - | - | - | - | - | 0 | 0 | 0 | 1 | 1 | 0 | 0 | |
| 78 | - | - | - | - | - | 1 | 1 | 0 | 0 | 0 | 1 | 0 | |
| 79 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 80 | - | - | - | - | - | 4 | 0 | 1 | 0 | 0 | 0 | 0 | |
| 81 | - | - | - | - | - | 0 | 4 | 0 | 0 | 0 | 0 | 0 | |
| 82 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 83 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 84 | - | - | - | - | - | 2 | 1 | 0 | 1 | 0 | 0 | 0 | |
| 85 | - | - | - | - | - | 0 | 0 | 1 | 0 | 0 | 0 | 1 | |
| 86 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 87 | - | - | - | - | - | 0 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 88 | - | - | - | - | - | 3 | 0 | 0 | 0 | 1 | 0 | 0 | |
| 89 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 90 | - | - | - | - | - | 1 | 2 | 1 | 0 | 0 | 0 | 0 | |
| 91 | - | - | - | - | - | 0 | 0 | 0 | 1 | 0 | 1 | 0 | |
| 92 | - | - | - | - | - | 2 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 93 | - | - | - | - | - | 0 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 94 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 95 | - | - | - | - | - | 0 | 0 | 1 | 0 | 0 | 0 | 0 | |
| 96 | - | - | - | Mainline | - | - | 5 | 1 | 0 | 0 | 0 | 0 | 0 |
| 97 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 98 | - | - | - | - | - | 1 | 0 | 0 | 2 | 0 | 0 | 0 | |
| 99 | - | - | - | - | - | 0 | 2 | 0 | 0 | 1 | 0 | 0 | |
| 100 | - | - | - | - | - | 2 | 0 | 2 | 0 | 0 | 0 | 0 | |
| 101 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 102 | - | - | - | - | - | 1 | 1 | 0 | 0 | 0 | 0 | 1 | |
| 103 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 104 | - | - | - | - | - | 3 | 0 | 0 | 0 | 0 | 1 | 0 | |
| 105 | - | - | - | - | - | 0 | 1 | 1 | 1 | 0 | 0 | 0 | |
| 106 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 107 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 108 | - | - | - | - | - | 2 | 3 | 0 | 0 | 0 | 0 | 0 | |
| 109 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 110 | - | - | - | - | - | 1 | 0 | 1 | 0 | 1 | 0 | 0 | |
| 111 | - | - | - | - | - | 0 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 112 | - | - | - | - | - | 4 | 0 | 0 | 1 | 0 | 0 | 0 | |
| 113 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 114 | - | - | - | - | - | 1 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 115 | - | - | - | - | - | 0 | 0 | 1 | 0 | 0 | 0 | 0 | |
| 116 | - | - | - | - | - | 2 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 117 | - | - | - | - | - | 0 | 2 | 0 | 0 | 0 | 1 | 0 | |
| 118 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 119 | - | - | - | - | - | 0 | 0 | 0 | 1 | 0 | 0 | 1 | |
| 120 | - | - | - | - | - | 3 | 1 | 1 | 0 | 0 | 0 | 0 | |
| 121 | - | - | - | - | - | 0 | 0 | 0 | 0 | 2 | 0 | 0 | |
| 122 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 123 | - | - | - | - | - | 0 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 124 | - | - | - | - | - | 2 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 125 | - | - | - | - | - | 0 | 0 | 3 | 0 | 0 | 0 | 0 | |
| 126 | - | - | - | - | - | 1 | 2 | 0 | 1 | 0 | 0 | 0 | |
| 127 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 128 | - | - | - | - | - | 7 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 129 | - | - | - | - | - | 0 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 130 | - | - | - | - | - | 1 | 0 | 1 | 0 | 0 | 1 | 0 | |
| 131 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 132 | - | - | - | - | - | 2 | 1 | 0 | 0 | 1 | 0 | 0 | |
| 133 | - | - | - | - | - | 0 | 0 | 0 | 1 | 0 | 0 | 0 | |
| 134 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 135 | - | - | - | - | - | 0 | 3 | 1 | 0 | 0 | 0 | 0 | |
| 136 | - | - | - | - | - | 3 | 0 | 0 | 0 | 0 | 0 | 1 | |
| 137 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 138 | - | - | - | - | - | 1 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 139 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 140 | - | - | - | - | - | 2 | 0 | 1 | 1 | 0 | 0 | 0 | |
| 141 | - | - | - | - | - | 0 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 142 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 143 | - | - | - | - | - | 0 | 0 | 0 | 0 | 1 | 1 | 0 | |
| 144 | - | - | - | Mainline | - | - | 4 | 2 | 0 | 0 | 0 | 0 | 0 |
| 145 | - | - | - | - | - | 0 | 0 | 1 | 0 | 0 | 0 | 0 | |
| 146 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 147 | - | - | - | - | - | 0 | 1 | 0 | 2 | 0 | 0 | 0 | |
| 148 | - | - | - | - | - | 2 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 149 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 150 | - | - | - | - | - | 1 | 1 | 2 | 0 | 0 | 0 | 0 | |
| 151 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 152 | - | - | - | - | - | 3 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 153 | - | - | - | - | - | 0 | 2 | 0 | 0 | 0 | 0 | 1 | |
| 154 | - | - | - | - | - | 1 | 0 | 0 | 1 | 1 | 0 | 0 | |
| 155 | - | - | - | - | - | 0 | 0 | 1 | 0 | 0 | 0 | 0 | |
| 156 | - | - | - | - | - | 2 | 1 | 0 | 0 | 0 | 1 | 0 | |
| 157 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 158 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 159 | - | - | - | - | - | 0 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 160 | - | - | - | - | - | 5 | 0 | 1 | 0 | 0 | 0 | 0 | |
| 161 | - | - | - | - | - | 0 | 0 | 0 | 1 | 0 | 0 | 0 | |
| 162 | - | - | - | - | - | 1 | 4 | 0 | 0 | 0 | 0 | 0 | |
| 163 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 164 | - | - | - | - | - | 2 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 165 | - | - | - | - | - | 0 | 1 | 1 | 0 | 1 | 0 | 0 | |
| 166 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 167 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 168 | - | - | - | - | - | 3 | 1 | 0 | 1 | 0 | 0 | 0 | |
| 169 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 2 | 0 | |
| 170 | - | - | - | - | - | 1 | 0 | 1 | 0 | 0 | 0 | 1 | |
| 171 | - | - | - | - | - | 0 | 2 | 0 | 0 | 0 | 0 | 0 | |
| 172 | - | - | - | - | - | 2 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 173 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 174 | - | - | - | - | - | 1 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 175 | - | - | - | - | - | 0 | 0 | 2 | 1 | 0 | 0 | 0 | |
| 176 | - | - | - | - | - | 4 | 0 | 0 | 0 | 1 | 0 | 0 | |
| 177 | - | - | - | - | - | 0 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 178 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 179 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 180 | - | - | - | - | - | 2 | 2 | 1 | 0 | 0 | 0 | 0 | |
| 181 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 182 | - | - | - | - | - | 1 | 0 | 0 | 1 | 0 | 1 | 0 | |
| 183 | - | - | - | - | - | 0 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 184 | - | - | - | - | - | 3 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 185 | - | - | - | - | - | 0 | 0 | 1 | 0 | 0 | 0 | 0 | |
| 186 | - | - | - | - | - | 1 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 187 | - | - | - | - | - | 0 | 0 | 0 | 0 | 1 | 0 | 1 | |
| 188 | - | - | - | - | - | 2 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 189 | - | - | - | - | - | 0 | 3 | 0 | 1 | 0 | 0 | 0 | |
| 190 | - | - | - | - | - | 1 | 0 | 1 | 0 | 0 | 0 | 0 | |
| 191 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 192 | - | - | - | - | - | 6 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 193 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 194 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 195 | - | - | - | - | - | 0 | 1 | 1 | 0 | 0 | 1 | 0 | |
| 196 | - | - | - | - | - | 2 | 0 | 0 | 2 | 0 | 0 | 0 | |
| 197 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 198 | - | - | - | - | - | 1 | 2 | 0 | 0 | 1 | 0 | 0 | |
| 199 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 200 | - | - | - | - | - | 3 | 0 | 2 | 0 | 0 | 0 | 0 | |
| 201 | - | - | - | - | - | 0 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 202 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 203 | - | - | - | - | - | 0 | 0 | 0 | 1 | 0 | 0 | 0 | |
| 204 | - | - | - | - | - | 2 | 1 | 0 | 0 | 0 | 0 | 1 | |
| 205 | - | - | - | - | - | 0 | 0 | 1 | 0 | 0 | 0 | 0 | |
| 206 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 207 | - | - | - | - | - | 0 | 2 | 0 | 0 | 0 | 0 | 0 | |
| 208 | - | - | - | - | - | 4 | 0 | 0 | 0 | 0 | 1 | 0 | |
| 209 | - | - | - | - | - | 0 | 0 | 0 | 0 | 1 | 0 | 0 | |
| 210 | - | - | - | - | - | 1 | 1 | 1 | 1 | 0 | 0 | 0 | |
| 211 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 212 | - | - | - | - | - | 2 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 213 | - | - | - | - | - | 0 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 214 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 215 | - | - | - | - | - | 0 | 0 | 1 | 0 | 0 | 0 | 0 | |
| 216 | - | - | - | - | - | 3 | 3 | 0 | 0 | 0 | 0 | 0 | |
| 217 | - | - | - | - | - | 0 | 0 | 0 | 1 | 0 | 0 | 0 | |
| 218 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 219 | - | - | - | - | - | 0 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 220 | - | - | - | - | - | 2 | 0 | 1 | 0 | 1 | 0 | 0 | |
| 221 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 1 | 1 | |
| 222 | - | - | - | - | - | 1 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 223 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 224 | - | - | - | - | - | 5 | 0 | 0 | 1 | 0 | 0 | 0 | |
| 225 | - | - | - | - | - | 0 | 2 | 2 | 0 | 0 | 0 | 0 | |
| 226 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 227 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 228 | - | - | - | - | - | 2 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 229 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 230 | - | - | - | - | - | 1 | 0 | 1 | 0 | 0 | 0 | 0 | |
| 231 | - | - | - | - | - | 0 | 1 | 0 | 1 | 1 | 0 | 0 | |
| 232 | - | - | - | - | - | 3 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 233 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 234 | - | - | - | - | - | 1 | 2 | 0 | 0 | 0 | 1 | 0 | |
| 235 | - | - | - | - | - | 0 | 0 | 1 | 0 | 0 | 0 | 0 | |
| 236 | - | - | - | - | - | 2 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 237 | - | - | - | - | - | 0 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 238 | - | - | - | - | - | 1 | 0 | 0 | 1 | 0 | 0 | 1 | |
| 239 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 240 | - | - | - | - | - | 4 | 1 | 1 | 0 | 0 | 0 | 0 | |
| 241 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 242 | - | - | - | - | - | 1 | 0 | 0 | 0 | 2 | 0 | 0 | |
| 243 | - | - | - | - | - | 0 | 5 | 0 | 0 | 0 | 0 | 0 | |
| 244 | - | - | - | - | - | 2 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 245 | - | - | - | - | - | 0 | 0 | 1 | 2 | 0 | 0 | 0 | |
| 246 | - | - | - | - | - | 1 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 247 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 1 | 0 | |
| 248 | - | - | - | - | - | 3 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 249 | - | - | - | - | - | 0 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 250 | - | - | - | - | - | 1 | 0 | 3 | 0 | 0 | 0 | 0 | |
| 251 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 252 | - | - | - | - | - | 2 | 2 | 0 | 1 | 0 | 0 | 0 | |
| 253 | - | - | - | - | - | 0 | 0 | 0 | 0 | 1 | 0 | 0 | |
| 254 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 255 | - | - | - | - | - | 0 | 1 | 1 | 0 | 0 | 0 | 1 | |
| 256 | - | - | - | - | - | 8 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 257 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 258 | - | - | - | - | - | 1 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 259 | - | - | - | - | - | 0 | 0 | 0 | 1 | 0 | 0 | 0 | |
| 260 | - | - | - | - | - | 2 | 0 | 1 | 0 | 0 | 1 | 0 | |
| 261 | - | - | - | - | - | 0 | 2 | 0 | 0 | 0 | 0 | 0 | |
| 262 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 263 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 264 | - | - | - | - | - | 3 | 1 | 0 | 0 | 1 | 0 | 0 | |
| 265 | - | - | - | - | - | 0 | 0 | 1 | 0 | 0 | 0 | 0 | |
| 266 | - | - | - | - | - | 1 | 0 | 0 | 1 | 0 | 0 | 0 | |
| 267 | - | - | - | - | - | 0 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 268 | - | - | - | - | - | 2 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 269 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 270 | - | - | - | - | - | 1 | 3 | 1 | 0 | 0 | 0 | 0 | |
| 271 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 272 | - | - | - | - | - | 4 | 0 | 0 | 0 | 0 | 0 | 1 | |
| 273 | - | - | - | - | - | 0 | 1 | 0 | 1 | 0 | 1 | 0 | |
| 274 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 275 | - | - | - | - | - | 0 | 0 | 2 | 0 | 1 | 0 | 0 | |
| 276 | - | - | - | - | - | 2 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 277 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 278 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 279 | - | - | - | - | - | 0 | 2 | 0 | 0 | 0 | 0 | 0 | |
| 280 | - | - | - | - | - | 3 | 0 | 1 | 1 | 0 | 0 | 0 | |
| 281 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 282 | - | - | - | - | - | 1 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 283 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 284 | - | - | - | - | - | 2 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 285 | - | - | - | - | - | 0 | 1 | 1 | 0 | 0 | 0 | 0 | |
| 286 | - | - | - | - | - | 1 | 0 | 0 | 0 | 1 | 1 | 0 | |
| 287 | - | - | - | - | - | 0 | 0 | 0 | 1 | 0 | 0 | 0 | |
| 288 | - | - | - | Mainline | - | - | 5 | 2 | 0 | 0 | 0 | 0 | 0 |
| 289 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 2 | |
| 290 | - | - | - | - | - | 1 | 0 | 1 | 0 | 0 | 0 | 0 | |
| 291 | - | - | - | - | - | 0 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 292 | - | - | - | - | - | 2 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 293 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 294 | - | - | - | - | - | 1 | 1 | 0 | 2 | 0 | 0 | 0 | |
| 295 | - | - | - | - | - | 0 | 0 | 1 | 0 | 0 | 0 | 0 | |
| 296 | - | - | - | - | - | 3 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 297 | - | - | - | - | - | 0 | 3 | 0 | 0 | 1 | 0 | 0 | |
| 298 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 299 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 1 | 0 | |
| 300 | - | - | - | - | - | 2 | 1 | 2 | 0 | 0 | 0 | 0 | |
| 301 | - | - | - | - | - | 0 | 0 | 0 | 1 | 0 | 0 | 0 | |
| 302 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 303 | - | - | - | - | - | 0 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 304 | - | - | - | - | - | 4 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 305 | - | - | - | - | - | 0 | 0 | 1 | 0 | 0 | 0 | 0 | |
| 306 | - | - | - | - | - | 1 | 2 | 0 | 0 | 0 | 0 | 1 | |
| 307 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 308 | - | - | - | - | - | 2 | 0 | 0 | 1 | 1 | 0 | 0 | |
| 309 | - | - | - | - | - | 0 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 310 | - | - | - | - | - | 1 | 0 | 1 | 0 | 0 | 0 | 0 | |
| 311 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 312 | - | - | - | - | - | 3 | 1 | 0 | 0 | 0 | 1 | 0 | |
| 313 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 314 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 315 | - | - | - | - | - | 0 | 2 | 1 | 1 | 0 | 0 | 0 | |
| 316 | - | - | - | - | - | 2 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 317 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 318 | - | - | - | - | - | 1 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 319 | - | - | - | - | - | 0 | 0 | 0 | 0 | 1 | 0 | 0 | |
| 320 | - | - | - | - | - | 6 | 0 | 1 | 0 | 0 | 0 | 0 | |
| 321 | - | - | - | - | - | 0 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 322 | - | - | - | - | - | 1 | 0 | 0 | 1 | 0 | 0 | 0 | |
| 323 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 1 | |
| 324 | - | - | - | - | - | 2 | 4 | 0 | 0 | 0 | 0 | 0 | |
| 325 | - | - | - | - | - | 0 | 0 | 2 | 0 | 0 | 1 | 0 | |
| 326 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 327 | - | - | - | - | - | 0 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 328 | - | - | - | - | - | 3 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 329 | - | - | - | - | - | 0 | 0 | 0 | 1 | 0 | 0 | 0 | |
| 330 | - | - | - | - | - | 1 | 1 | 1 | 0 | 1 | 0 | 0 | |
| 331 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 332 | - | - | - | - | - | 2 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 333 | - | - | - | - | - | 0 | 2 | 0 | 0 | 0 | 0 | 0 | |
| 334 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 335 | - | - | - | - | - | 0 | 0 | 1 | 0 | 0 | 0 | 0 | |
| 336 | - | - | - | - | - | 4 | 1 | 0 | 1 | 0 | 0 | 0 | |
| 337 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 338 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 2 | 0 | |
| 339 | - | - | - | - | - | 0 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 340 | - | - | - | - | - | 2 | 0 | 1 | 0 | 0 | 0 | 1 | |
| 341 | - | - | - | - | - | 0 | 0 | 0 | 0 | 1 | 0 | 0 | |
| 342 | - | - | - | - | - | 1 | 2 | 0 | 0 | 0 | 0 | 0 | |
| 343 | - | - | - | - | - | 0 | 0 | 0 | 3 | 0 | 0 | 0 | |
| 344 | - | - | - | - | - | 3 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 345 | - | - | - | - | - | 0 | 1 | 1 | 0 | 0 | 0 | 0 | |
| 346 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 347 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 348 | - | - | - | - | - | 2 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 349 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 350 | - | - | - | - | - | 1 | 0 | 2 | 1 | 0 | 0 | 0 | |
| 351 | - | - | - | - | - | 0 | 3 | 0 | 0 | 0 | 1 | 0 | |
| 352 | - | - | - | - | - | 5 | 0 | 0 | 0 | 1 | 0 | 0 | |
| 353 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 354 | - | - | - | - | - | 1 | 1 | 0 | 0 | 0 | 0 | 0 | |
| 355 | - | - | - | - | - | 0 | 0 | 1 | 0 | 0 | 0 | 0 | |
| 356 | - | - | - | - | - | 2 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 357 | - | - | - | - | - | 0 | 1 | 0 | 1 | 0 | 0 | 1 | |
| 358 | - | - | - | - | - | 1 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 359 | - | - | - | - | - | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 360 | - | - | - | - | - | 3 | 2 | 1 | 0 | 0 | 0 | 0 |
Range up to 2^
Harmonic Scale Exploration (Bonus)
| N | H | log10[H]/log10[N] | K | RT Mainline | Aliquot Type | Ratio H:N | Just Intonation Scale | n2 | n3 | n5 | n7 | n11 | n13 | n17 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 24 | - | - | - | Mainline | - | - | Fundamental (1/1) | 3 | 1 | 0 | 0 | 0 | 0 | 0 |
| 27 | - | - | - | - | - | Major Second (9/8) | 0 | 3 | 0 | 0 | 0 | 0 | 0 | |
| 30 | - | - | - | - | - | Major Third (5/4) | 1 | 1 | 1 | 0 | 0 | 0 | 0 | |
| 32 | - | - | - | - | - | Perfect Fourth (4/3) | 5 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 36 | - | - | - | Mainline | - | - | Perfect Fifth (3/2) | 2 | 2 | 0 | 0 | 0 | 0 | 0 |
| 40 | - | - | - | - | - | Major Sixth (5/3) | 3 | 0 | 1 | 0 | 0 | 0 | 0 | |
| 45 | - | - | - | - | - | Major Seventh (15/8) | 0 | 2 | 1 | 0 | 0 | 0 | 0 | |
| 48 | - | - | - | Mainline | - | - | Octave (2/1) | 4 | 1 | 0 | 0 | 0 | 0 | 0 |
| 72 | - | - | - | Mainline | - | - | Perfect Fifth (Octave) (3/1) | 3 | 2 | 0 | 0 | 0 | 0 | 0 |
| 96 | - | - | - | Mainline | - | - | Double Octave (4/1) | 5 | 1 | 0 | 0 | 0 | 0 | 0 |
| 144 | - | - | - | Mainline | - | - | Mainline (Ray Tomes) (6/1) | 4 | 2 | 0 | 0 | 0 | 0 | 0 |
| 34560 | - | - | - | Mainline | - | - | Mainline Base (1440/1) | 8 | 3 | 1 | 0 | 0 | 0 | 0 |
- H(n)
- The "harmonic sum" — the count of all ordered factorizations of n (ways to write n as an ordered product of integers ≥ 2, plus 1 for n itself). The central quantity of this analysis.
- Aliquot Type
- Whether H(n) is less than n (Deficient), equal to n (Balanced), or greater than n (Abundant). Abundant numbers are the most harmonically rich.
- log10[H] / log10[N]
- Logarithmic growth rate of H(n) relative to n. Values > 1 indicate superlinear harmonic growth; highly composite numbers score highest.
- Ratio H:N
- H(n) / n — a direct measure of harmonic density. Higher values mean more factorization paths per unit.
- RT Mainline
- Flags numbers identified by Ray Tomes as "mainline harmonics" — numbers like 12, 24, 144, 1440, 34560 that appear most strongly in natural cycles.
- K
- Number of distinct prime factors (ω function). Higher K means more ways to factor, generally correlating with larger H(n).
- n2, n3, n5, n7, n11, n13, n17
- Exponents of each small prime in the factorization of n (e.g. n=12 → n2=2, n3=1). Numbers built from small primes have the highest harmonic scores.
- Just Intonation Scale / Ratio
- The musical interval name and frequency ratio (e.g. 3/2 = Perfect Fifth). Shows which harmonic numbers correspond to natural musical tuning.
- N
- The integer being analysed.
Note: The idea that certain harmonic numbers (products of small primes like 2, 3, 5, 7...) are privileged in nature and form a "mainline" of harmonics was encountered in Ray Tomes' Theory of Harmonics. Tomes argues that the universe develops cycles and structures whose wavelengths are related by these highly composite harmonic numbers, appearing in physics, music, and cosmology alike.