45/38: Difference between revisions
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'''45/38''' is a [[19-limit]] interval, 292.7 [[cent]]s in size. In the [[Functional Just System]] and [[Helmholtz-Ellis notation]], it is an ''augmented second'', obtained by subtracting [[81/80]] and [[513/512]] to the [[19683/16384|Pythagorean augmented second]], but it may be called the '''Eratosthenes' minor third''' as it is flatter than the [[32/27|Pythagorean minor third]] by the ''password'' aka ''Eratosthenes' comma'' ([[1216/1215]]), an [[unnoticeable comma]] of about 1.4243 cents. | '''45/38''' is a [[19-limit]] interval, 292.7 [[cent]]s in size. In the [[Functional Just System]] and [[Helmholtz-Ellis notation]], it is an ''augmented second'', obtained by subtracting [[81/80]] and [[513/512]] to the [[19683/16384|Pythagorean augmented second]], but it may be called the '''Eratosthenes' minor third''' as it is flatter than the [[32/27|Pythagorean minor third]] by the ''password'' aka ''Eratosthenes' comma'' ([[1216/1215]]), an [[unnoticeable comma]] of about 1.4243 cents. | ||
== Approximation == | == Approximation == | ||
{{Interval edo approximation|45/38}} | |||
== See also == | == See also == | ||
* [[76/45]] – its [[octave complement]] | * [[76/45]] – its [[octave complement]] | ||
Latest revision as of 13:09, 3 November 2025
| Interval information |
45/38 is a 19-limit interval, 292.7 cents in size. In the Functional Just System and Helmholtz-Ellis notation, it is an augmented second, obtained by subtracting 81/80 and 513/512 to the Pythagorean augmented second, but it may be called the Eratosthenes' minor third as it is flatter than the Pythagorean minor third by the password aka Eratosthenes' comma (1216/1215), an unnoticeable comma of about 1.4243 cents.
Approximation
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 4 | 1\4 | 300.00 | +7.29 | +2.43 |
| 8 | 2\8 | 300.00 | +7.29 | +4.86 |
| 12 | 3\12 | 300.00 | +7.29 | +7.29 |
| 16 | 4\16 | 300.00 | +7.29 | +9.72 |
| 25 | 6\25 | 288.00 | -4.71 | -9.81 |
| 29 | 7\29 | 289.66 | -3.06 | -7.38 |
| 33 | 8\33 | 290.91 | -1.80 | -4.95 |
| 37 | 9\37 | 291.89 | -0.82 | -2.52 |
| 41 | 10\41 | 292.68 | -0.03 | -0.09 |
| 45 | 11\45 | 293.33 | +0.62 | +2.33 |
| 49 | 12\49 | 293.88 | +1.17 | +4.76 |
| 53 | 13\53 | 294.34 | +1.63 | +7.19 |
| 57 | 14\57 | 294.74 | +2.03 | +9.62 |
| 66 | 16\66 | 290.91 | -1.80 | -9.91 |
| 70 | 17\70 | 291.43 | -1.28 | -7.48 |
| 74 | 18\74 | 291.89 | -0.82 | -5.05 |
| 78 | 19\78 | 292.31 | -0.40 | -2.62 |