User:Eliora/5ed100
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This page presents a novelty topic.
It may contain ideas which are less likely to find practical applications in music, or numbers or structures that are arbitrary or exceedingly small, large, or complex. Novelty topics are often developed by a single person or a small group. As such, this page may also contain idiosyncratic terms, notation, or conceptual frameworks. |
| ← 4ed100 | 5ed100 | 6ed100 → |
(semiconvergent)
5ed100, the stellar magnitude tuning or 5 equal divisions of the double decave, is an equal-step tuning with each pitch being about 2.512 times larger than the other, the number known as the Pogson's ratio.
Theory
The tuning is pretty meaningless as far as pitches go, since there's only 7-8 steps of it in the entire human hearing range, but it has a real life equivalence to astronomy - each step of it is known as the Pogson's ratio and it has an application of being the factor which sets two stars being 1 magnitude apart. This means subdividing it makes a meaningful major tenth of 1594.525 cents.
Tempered commas
Astronomers might sometimes round 2.512 to 2.5, which leads to confusion with the other 2.5 - that is the logarithm multiplier required for base-10 logarithm conversion, with the formula being involved 2.5 log10(m1 - m2). The factor of 2.5 is simply coincidentally close enough to the 5th root of 100.
If this is taken as a comma to be tempered, it results in 100 / 97.65625 = 1.024 = 128/125, the lesser diesis.
References
- Wikipedia Contributors, Magnitude (astronomy).