Ripple family: Difference between revisions
apply changes discussed and leave notes about the change to avoid any theoretical confusion that might take place |
m fix subheader levels to what i think is the current standard(?) |
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[[Badness]] (Dirichlet): 3.259 | [[Badness]] (Dirichlet): 3.259 | ||
== Septimal ripple == | |||
{{ See also | Dual-fifth temperaments }} | {{ See also | Dual-fifth temperaments }} | ||
Septimal ripple interprets the generator as a very flat ~15/14, so that 3 and 5 are flat and 7 is sharp; of these, 3 is the most damaged, but is also the simplest, so is still viable as an approximation. Due to the sharp 7 and flatter 3, ~21/16 can be fairly in-tune, acting as the alternate fourth in a dual-fourth interpretation, so that the inconsistent but more accurate ~16/9 is reached as ~21/16 * ~4/3 = ~7/4, though this assumes you are putting the most damage on 3 as to get larger primes more in tune. This has another advantage, specific to the 11-limit: this accurate but inconsistent ~9/8 (which is usually just to slightly sharp) can find the neutral third ~11/9 with reasonable accuracy. | Septimal ripple interprets the generator as a very flat ~15/14, so that 3 and 5 are flat and 7 is sharp; of these, 3 is the most damaged, but is also the simplest, so is still viable as an approximation. Due to the sharp 7 and flatter 3, ~21/16 can be fairly in-tune, acting as the alternate fourth in a dual-fourth interpretation, so that the inconsistent but more accurate ~16/9 is reached as ~21/16 * ~4/3 = ~7/4, though this assumes you are putting the most damage on 3 as to get larger primes more in tune. This has another advantage, specific to the 11-limit: this accurate but inconsistent ~9/8 (which is usually just to slightly sharp) can find the neutral third ~11/9 with reasonable accuracy. | ||
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[[Badness]] (Dirichlet): 1.521 | [[Badness]] (Dirichlet): 1.521 | ||
=== 11-limit === | |||
A notable [[patent val]] tuning of 11-limit ripple not appearing in the optimal ET sequence is [[47edo]]. | A notable [[patent val]] tuning of 11-limit ripple not appearing in the optimal ET sequence is [[47edo]]. | ||