List of 3-limit factorizations: Difference between revisions
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This list includes prime factorizations and [[monzo]]s of all numbers from 1 to | This list includes prime factorizations and [[monzo]]s of all numbers from 1 to 9999999 (10<sup>7</sup>-1) which are divisible by 3, and not divisible by any larger [[prime number]]. | ||
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| 995328 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 12 5 }} | | 995328 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 12 5 }} | ||
|- | |||
| 1062882 || 2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 1 12 }} | |||
|- | |||
| 1119744 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 9 7 }} | |||
|- | |||
| 1179648 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 || {{Monzo| 17 2 }} | |||
|- | |||
| 1259712 || 2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 6 9 }} | |||
|- | |||
| 1327104 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3 || {{Monzo| 14 4 }} | |||
|- | |||
| 1417176 || 2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 3 11 }} | |||
|- | |||
| 1492992 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 11 6 }} | |||
|- | |||
| 1572864 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3 || {{Monzo| 19 1 }} | |||
|- | |||
| 1594323 || 3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 0 13 }} | |||
|- | |||
| 1679616 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 8 8 }} | |||
|- | |||
| 1769472 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3 || {{Monzo| 16 3 }} | |||
|- | |||
| 1889568 || 2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 5 10 }} | |||
|- | |||
| 1990656 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 13 5 }} | |||
|- | |||
| 2125764 || 2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 2 12 }} | |||
|- | |||
| 2239488 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 10 7 }} | |||
|- | |||
| 2359296 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 || {{Monzo| 18 2 }} | |||
|- | |||
| 2519424 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 7 9 }} | |||
|- | |||
| 2654208 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3 || {{Monzo| 15 4 }} | |||
|- | |||
| 2834352 || 2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 4 11 }} | |||
|- | |||
| 2985984 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 12 6 }} | |||
|- | |||
| 3145728 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3 || {{Monzo| 20 1 }} | |||
|- | |||
| 3188646 || 2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 1 13 }} | |||
|- | |||
| 3359232 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 9 8 }} | |||
|- | |||
| 3538944 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3 || {{Monzo| 17 3 }} | |||
|- | |||
| 3779136 || 2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 6 10 }} | |||
|- | |||
| 3981312 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 14 5 }} | |||
|- | |||
| 4251528 || 2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 3 12 }} | |||
|- | |||
| 4478976 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 11 7 }} | |||
|- | |||
| 4718592 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 || {{Monzo| 19 2 }} | |||
|- | |||
| 4782969 || 3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 0 14 }} | |||
|- | |||
| 5038848 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 8 9 }} | |||
|- | |||
| 5308416 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3 || {{Monzo| 16 4 }} | |||
|- | |||
| 5668704 || 2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 5 11 }} | |||
|- | |||
| 5971968 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 13 6 }} | |||
|- | |||
| 6291456 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3 || {{Monzo| 21 1 }} | |||
|- | |||
| 6377292 || 2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 2 13 }} | |||
|- | |||
| 6718464 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 10 8 }} | |||
|- | |||
| 7077888 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3 || {{Monzo| 18 3 }} | |||
|- | |||
| 7558272 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 7 10 }} | |||
|- | |||
| 7962624 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 15 5 }} | |||
|- | |||
| 8503056 || 2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 4 12 }} | |||
|- | |||
| 8957952 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 12 7 }} | |||
|- | |||
| 9437184 || 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 || {{Monzo| 20 2 }} | |||
|- | |||
| 9565938 || 2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 || {{Monzo| 1 14 }} | |||
|} | |} | ||
{{todo|inline=1|clarify|improve synopsis|comment=Explain the musical uses for this table in the introduction.}} | |||
{{todo|inline=1|link|comment=Link to this table from relevant pages, and add a see also at the end to give readers somewhere to go next.}} | |||
[[Category:3-limit]] | |||
[[Category:Math]] | |||
[[Category:Lists]] | |||
Latest revision as of 06:46, 21 December 2024
This list includes prime factorizations and monzos of all numbers from 1 to 9999999 (107-1) which are divisible by 3, and not divisible by any larger prime number.
| integer | factorization | monzo |
|---|---|---|
| 3 | 3 | [0 1⟩ |
| 6 | 2⋅3 | [1 1⟩ |
| 9 | 3⋅3 | [0 2⟩ |
| 12 | 2⋅2⋅3 | [2 1⟩ |
| 18 | 2⋅3⋅3 | [1 2⟩ |
| 24 | 2⋅2⋅2⋅3 | [3 1⟩ |
| 27 | 3⋅3⋅3 | [0 3⟩ |
| 36 | 2⋅2⋅3⋅3 | [2 2⟩ |
| 48 | 2⋅2⋅2⋅2⋅3 | [4 1⟩ |
| 54 | 2⋅3⋅3⋅3 | [1 3⟩ |
| 72 | 2⋅2⋅2⋅3⋅3 | [3 2⟩ |
| 81 | 3⋅3⋅3⋅3 | [0 4⟩ |
| 96 | 2⋅2⋅2⋅2⋅2⋅3 | [5 1⟩ |
| 108 | 2⋅2⋅3⋅3⋅3 | [2 3⟩ |
| 144 | 2⋅2⋅2⋅2⋅3⋅3 | [4 2⟩ |
| 162 | 2⋅3⋅3⋅3⋅3 | [1 4⟩ |
| 192 | 2⋅2⋅2⋅2⋅2⋅2⋅3 | [6 1⟩ |
| 216 | 2⋅2⋅2⋅3⋅3⋅3 | [3 3⟩ |
| 243 | 3⋅3⋅3⋅3⋅3 | [0 5⟩ |
| 288 | 2⋅2⋅2⋅2⋅2⋅3⋅3 | [5 2⟩ |
| 324 | 2⋅2⋅3⋅3⋅3⋅3 | [2 4⟩ |
| 384 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅3 | [7 1⟩ |
| 432 | 2⋅2⋅2⋅2⋅3⋅3⋅3 | [4 3⟩ |
| 486 | 2⋅3⋅3⋅3⋅3⋅3 | [1 5⟩ |
| 576 | 2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 | [6 2⟩ |
| 648 | 2⋅2⋅2⋅3⋅3⋅3⋅3 | [3 4⟩ |
| 729 | 3⋅3⋅3⋅3⋅3⋅3 | [0 6⟩ |
| 768 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3 | [8 1⟩ |
| 864 | 2⋅2⋅2⋅2⋅2⋅3⋅3⋅3 | [5 3⟩ |
| 972 | 2⋅2⋅3⋅3⋅3⋅3⋅3 | [2 5⟩ |
| 1152 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 | [7 2⟩ |
| 1296 | 2⋅2⋅2⋅2⋅3⋅3⋅3⋅3 | [4 4⟩ |
| 1458 | 2⋅3⋅3⋅3⋅3⋅3⋅3 | [1 6⟩ |
| 1536 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3 | [9 1⟩ |
| 1728 | 2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3 | [6 3⟩ |
| 1944 | 2⋅2⋅2⋅3⋅3⋅3⋅3⋅3 | [3 5⟩ |
| 2187 | 3⋅3⋅3⋅3⋅3⋅3⋅3 | [0 7⟩ |
| 2304 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 | [8 2⟩ |
| 2592 | 2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3 | [5 4⟩ |
| 2916 | 2⋅2⋅3⋅3⋅3⋅3⋅3⋅3 | [2 6⟩ |
| 3072 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3 | [10 1⟩ |
| 3456 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3 | [7 3⟩ |
| 3888 | 2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3 | [4 5⟩ |
| 4374 | 2⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [1 7⟩ |
| 4608 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 | [9 2⟩ |
| 5184 | 2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3 | [6 4⟩ |
| 5832 | 2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3 | [3 6⟩ |
| 6144 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3 | [11 1⟩ |
| 6561 | 3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [0 8⟩ |
| 6912 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3 | [8 3⟩ |
| 7776 | 2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3 | [5 5⟩ |
| 8748 | 2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [2 7⟩ |
| 9216 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 | [10 2⟩ |
| 10368 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3 | [7 4⟩ |
| 11664 | 2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3 | [4 6⟩ |
| 12288 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3 | [12 1⟩ |
| 13122 | 2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [1 8⟩ |
| 13824 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3 | [9 3⟩ |
| 15552 | 2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3 | [6 5⟩ |
| 17496 | 2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [3 7⟩ |
| 18432 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 | [11 2⟩ |
| 19683 | 3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [0 9⟩ |
| 20736 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3 | [8 4⟩ |
| 23328 | 2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3 | [5 6⟩ |
| 24576 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3 | [13 1⟩ |
| 26244 | 2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [2 8⟩ |
| 27648 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3 | [10 3⟩ |
| 31104 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3 | [7 5⟩ |
| 34992 | 2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [4 7⟩ |
| 36864 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 | [12 2⟩ |
| 39366 | 2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [1 9⟩ |
| 41472 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3 | [9 4⟩ |
| 46656 | 2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3 | [6 6⟩ |
| 49152 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3 | [14 1⟩ |
| 52488 | 2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [3 8⟩ |
| 55296 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3 | [11 3⟩ |
| 59049 | 3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [0 10⟩ |
| 62208 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3 | [8 5⟩ |
| 69984 | 2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [5 7⟩ |
| 73728 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 | [13 2⟩ |
| 78732 | 2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [2 9⟩ |
| 82944 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3 | [10 4⟩ |
| 93312 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3 | [7 6⟩ |
| 98304 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3 | [15 1⟩ |
| 104976 | 2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [4 8⟩ |
| 110592 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3 | [12 3⟩ |
| 118098 | 2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [1 10⟩ |
| 124416 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3 | [9 5⟩ |
| 139968 | 2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [6 7⟩ |
| 147456 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 | [14 2⟩ |
| 157464 | 2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [3 9⟩ |
| 165888 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3 | [11 4⟩ |
| 177147 | 3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [0 11⟩ |
| 186624 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3 | [8 6⟩ |
| 196608 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3 | [16 1⟩ |
| 209952 | 2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [5 8⟩ |
| 221184 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3 | [13 3⟩ |
| 236196 | 2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [2 10⟩ |
| 248832 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3 | [10 5⟩ |
| 279936 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [7 7⟩ |
| 294912 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 | [15 2⟩ |
| 314928 | 2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [4 9⟩ |
| 331776 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3 | [12 4⟩ |
| 354294 | 2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [1 11⟩ |
| 373248 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3 | [9 6⟩ |
| 393216 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3 | [17 1⟩ |
| 419904 | 2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [6 8⟩ |
| 442368 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3 | [14 3⟩ |
| 472392 | 2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [3 10⟩ |
| 497664 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3 | [11 5⟩ |
| 531441 | 3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [0 12⟩ |
| 559872 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [8 7⟩ |
| 589824 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 | [16 2⟩ |
| 629856 | 2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [5 9⟩ |
| 663552 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3 | [13 4⟩ |
| 708588 | 2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [2 11⟩ |
| 746496 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3 | [10 6⟩ |
| 786432 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3 | [18 1⟩ |
| 839808 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [7 8⟩ |
| 884736 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3 | [15 3⟩ |
| 944784 | 2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [4 10⟩ |
| 995328 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3 | [12 5⟩ |
| 1062882 | 2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [1 12⟩ |
| 1119744 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [9 7⟩ |
| 1179648 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 | [17 2⟩ |
| 1259712 | 2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [6 9⟩ |
| 1327104 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3 | [14 4⟩ |
| 1417176 | 2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [3 11⟩ |
| 1492992 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3 | [11 6⟩ |
| 1572864 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3 | [19 1⟩ |
| 1594323 | 3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [0 13⟩ |
| 1679616 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [8 8⟩ |
| 1769472 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3 | [16 3⟩ |
| 1889568 | 2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [5 10⟩ |
| 1990656 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3 | [13 5⟩ |
| 2125764 | 2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [2 12⟩ |
| 2239488 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [10 7⟩ |
| 2359296 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 | [18 2⟩ |
| 2519424 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [7 9⟩ |
| 2654208 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3 | [15 4⟩ |
| 2834352 | 2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [4 11⟩ |
| 2985984 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3 | [12 6⟩ |
| 3145728 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3 | [20 1⟩ |
| 3188646 | 2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [1 13⟩ |
| 3359232 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [9 8⟩ |
| 3538944 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3 | [17 3⟩ |
| 3779136 | 2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [6 10⟩ |
| 3981312 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3 | [14 5⟩ |
| 4251528 | 2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [3 12⟩ |
| 4478976 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [11 7⟩ |
| 4718592 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 | [19 2⟩ |
| 4782969 | 3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [0 14⟩ |
| 5038848 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [8 9⟩ |
| 5308416 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3 | [16 4⟩ |
| 5668704 | 2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [5 11⟩ |
| 5971968 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3 | [13 6⟩ |
| 6291456 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3 | [21 1⟩ |
| 6377292 | 2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [2 13⟩ |
| 6718464 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [10 8⟩ |
| 7077888 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3 | [18 3⟩ |
| 7558272 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [7 10⟩ |
| 7962624 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3 | [15 5⟩ |
| 8503056 | 2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [4 12⟩ |
| 8957952 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [12 7⟩ |
| 9437184 | 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅3⋅3 | [20 2⟩ |
| 9565938 | 2⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3⋅3 | [1 14⟩ |
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Todo: clarify , improve synopsis Explain the musical uses for this table in the introduction. |
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Todo: link Link to this table from relevant pages, and add a see also at the end to give readers somewhere to go next. |