30103edo: Difference between revisions
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=== As an interval size measure === | === As an interval size measure === | ||
Since logarithm of 2 in base 10 is equal to 0.30102999..., one step of 30103edo comes exceptionally close to being one step of an otherwise perfectly decimal tuning system, [[100000ed10]], similar to heptameride being one step of [[301edo]] and savart being one step of [[1000ed10]]. It was named '''jot''' by Augustus de Morgan in 1864. | Since logarithm of 2 in base 10 is equal to 0.30102999..., one step of 30103edo comes exceptionally close to being one step of an otherwise perfectly decimal tuning system, [[100000ed10]], similar to heptameride being one step of [[301edo]] and savart being one step of [[1000ed10]]. It was named '''jot''' by Augustus de Morgan in 1864. | ||
Any integer [[Gallery of arithmetic pitch sequences#APS of jots|arithmetic pitch sequence of ''n'' jots]] is technically a subset of 30130edo, since it is every ''n''th step of 30130edo. | |||
=== Prime harmonics === | === Prime harmonics === | ||
Revision as of 03:31, 13 December 2024
| ← 30102edo | 30103edo | 30104edo → |
30103edo is consistent in the 11-odd-limit and is otherwise a strong 2.3.5.17 subgroup tuning.
As an interval size measure
Since logarithm of 2 in base 10 is equal to 0.30102999..., one step of 30103edo comes exceptionally close to being one step of an otherwise perfectly decimal tuning system, 100000ed10, similar to heptameride being one step of 301edo and savart being one step of 1000ed10. It was named jot by Augustus de Morgan in 1864.
Any integer arithmetic pitch sequence of n jots is technically a subset of 30130edo, since it is every nth step of 30130edo.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | -0.0050 | -0.0001 | +0.0078 | -0.0108 | -0.0134 | +0.0042 | -0.0144 | +0.0085 | +0.0079 | -0.0068 |
| Relative (%) | +0.0 | -12.6 | -0.1 | +19.5 | -27.0 | -33.7 | +10.6 | -36.2 | +21.4 | +19.8 | -17.2 | |
| Steps (reduced) |
30103 (0) |
47712 (17609) |
69897 (9691) |
84510 (24304) |
104139 (13830) |
111394 (21085) |
123045 (2633) |
127875 (7463) |
136173 (15761) |
146240 (25828) |
149136 (28724) | |