1789edo: Difference between revisions
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===Temperaments=== | ===Temperaments=== | ||
Since 1789edo contains the 2.5 subgroup, it can be used for the finite decimal temperament - that is, where all the interval targets in just intonation are expressed as terminating decimals. For example, [[5/4]], [[25/16]], [[128/125]], [[32/25]], 625/512, etc. This rings particularly true for the French attempts to decimalize a lot more things than we are used to today. | Since 1789edo contains the 2.5 subgroup, it can be used for the finite decimal temperament - that is, where all the interval targets in just intonation are expressed as terminating decimals. For example, [[5/4]], [[25/16]], [[128/125]], [[32/25]], 625/512, etc. This rings particularly true for the French attempts to decimalize a lot more things than we are used to today. | ||
Revision as of 12:40, 4 November 2021
1789 EDO divides the octave into equal steps of 0.67 cents each. It is the 278th prime edo. Perhaps the most notable fact about 1789edo, is the fact that it tempers out the jacobin comma (6656/6655), which is quite appropriate for edo's number. Although there are temperaments which are better suited for tempering this comma, 1789edo is unique in that it's number is the hallmark year of the French Revolution, thus making the temperance of the Jacobin comma on topic.
Theory
Script error: No such module "primes_in_edo".
1789edo can be adapted for use with the 2.5.11.13.29.31 subgroup.
Table of selected intervals
| Step | Name | JI Approximation or Monzo |
|---|---|---|
| 0 | Unison | 1/1 exact |
| 25 | 28-thirds comma | [65 -28] |
| 61 | Lesser diesis | 128/125 |
| 576 | Major third | 5/4 |
| 677 | Jacobin naiadic | 13/10 |
| 822 | Jacobin superfourth | 11/8 |
| 1789 | Octave | 2/1 exact |
Temperaments
Since 1789edo contains the 2.5 subgroup, it can be used for the finite decimal temperament - that is, where all the interval targets in just intonation are expressed as terminating decimals. For example, 5/4, 25/16, 128/125, 32/25, 625/512, etc. This rings particularly true for the French attempts to decimalize a lot more things than we are used to today.
This property of 1789edo is amplified by poor approximation of 3 and 7, allowing for cognitive separation of the intervals (or whatever is left of it at such small step size).