1789edo: Difference between revisions
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'''Table of selected intervals''' | '''Table of selected intervals''' | ||
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The "proper" Jacobin temperament in 1789edo, the maximum evenness scale that uses 822 as a generator, contains only 37 notes. The step sizes are 48 and 49, making them indistinguishable to human ear at this scale. This can be fixed by using divisors of 822 as a generaator, for example 137\1789 "6th root of 11/8" temperament having 222 notes. In addition, this can be re-interpreted by using 13/10 as a generator instead which produces a more vibrant 1205 out of 1789, and partitioning the resulting 13/5s in three around the octave. | The "proper" Jacobin temperament in 1789edo, the maximum evenness scale that uses 822 as a generator, contains only 37 notes. The step sizes are 48 and 49, making them indistinguishable to human ear at this scale. This can be fixed by using divisors of 822 as a generaator, for example 137\1789 "6th root of 11/8" temperament having 222 notes. In addition, this can be re-interpreted by using 13/10 as a generator instead which produces a more vibrant 1205 out of 1789, and partitioning the resulting 13/5s in three around the octave. | ||
Addition of 29 and 31 harmonic intervals may also be suitable to spice up an otherwise monotonous scale. | Addition of 29 and 31 harmonic intervals may also be suitable to spice up an otherwise monotonous scale. | ||
== Scales == | == Scales == | ||
Revision as of 20:18, 15 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
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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).
The "proper" Jacobin temperament in 1789edo, the maximum evenness scale that uses 822 as a generator, contains only 37 notes. The step sizes are 48 and 49, making them indistinguishable to human ear at this scale. This can be fixed by using divisors of 822 as a generaator, for example 137\1789 "6th root of 11/8" temperament having 222 notes. In addition, this can be re-interpreted by using 13/10 as a generator instead which produces a more vibrant 1205 out of 1789, and partitioning the resulting 13/5s in three around the octave.
Addition of 29 and 31 harmonic intervals may also be suitable to spice up an otherwise monotonous scale.
Scales
- Jacobin[37]
- Jacobin[74]
- Jacobin[111]
- Jacobin[222]
- Decimal[265]
- Decimal[1524]