30103edo: Difference between revisions
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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. | ||
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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 | Any integer [[Gallery of arithmetic pitch sequences#APS of jots|arithmetic pitch sequence of ''n'' jots]] is technically a subset of 30103edo, since it is every ''n''th step of 30103edo. | ||
=== Prime harmonics === | === Prime harmonics === | ||
Latest revision as of 19:14, 13 April 2025
| ← 30102edo | 30103edo | 30104edo → |
30103 equal divisions of the octave (abbreviated 30103edo or 30103ed2), also called 30103-tone equal temperament (30103tet) or 30103 equal temperament (30103et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 30103 equal parts of about 0.0399 ¢ each. Each step represents a frequency ratio of 21/30103, or the 30103rd root of 2.
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 30103edo, since it is every nth step of 30103edo.
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) | |