1789edo: Difference between revisions
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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. Addition of 29 and 31 harmonic intervals may also be suitable to spice up an otherwise monotonous scale. | 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. | ||
For its elaborate xenharmonicity, 1789edo has an essentially perfect [[9/8]], a very common interval. The associated comma is [5671 -3578⟩. | |||
== Tempered commas == | == Tempered commas == | ||
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!1789edo Steps | !1789edo Steps | ||
!Name | !Name | ||
|- | |||
|2.3 | |||
|Patent | |||
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|[5671 -3578⟩ | |||
|5.006 | |||
|7.464 | |||
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|- | |- | ||
|2.5 | |2.5 | ||