User:Eliora/5ed100: Difference between revisions
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Prime factorization
5 (prime)
Step size
1594.53 ¢
Octave
1\5ed100 (1594.53 ¢)
Twelfth
1\5ed100 (1594.53 ¢)
(semiconvergent)
Consistency limit
3
Distinct consistency limit
2
m Infobox ET added |
→Theory: Okay with MMTM banned I can do this now, because what is this |
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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. | 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 === | === 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. | 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. | If this is taken as a comma to be tempered, it results in 100 / 97.65625 = 1.024 = [[128/125]], the lesser diesis. | ||
== References == | == References == | ||
Revision as of 13:09, 30 May 2023
| ← 4ed100 | 5ed100 | 6ed100 → |
(semiconvergent)
5ed100, or the stellar magnitude tuning, 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).