30103edo: Difference between revisions
Jump to navigation
Jump to search
mNo edit summary |
m Misc. edits |
||
| Line 3: | Line 3: | ||
30103edo is consistent in the 11-odd-limit and is otherwise a strong 2.3.5.17 subgroup tuning. | 30103edo is consistent in the 11-odd-limit and is otherwise a strong 2.3.5.17 subgroup tuning. | ||
=== 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. | |||
=== Prime harmonics === | === Prime harmonics === | ||
{{harmonics in equal|30103}} | {{harmonics in equal|30103}} | ||
Revision as of 22:36, 7 July 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.
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) | |