30/19: Difference between revisions
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'''30/19''', the '''small undevicesimal minor sixth''' is a [[19-limit]] interval, 790.8 [[cent]]s in size. In the [[Functional Just System]] and [[Helmholtz-Ellis notation]], it is an ''augmented fifth'', obtained by subtracting [[81/80]] and [[513/512]] from the [[6561/4096|Pythagorean augmented fifth]], but it may be called the '''Eratosthenes' minor sixth''' as it is flatter than the [[128/81|Pythagorean minor sixth]] by the ''password'' aka ''Eratosthenes' comma'' ([[1216/1215]]), an [[unnoticeable comma]] of about 1.4243 cents. | '''30/19''', the '''small undevicesimal minor sixth''' is a [[19-limit]] interval, 790.8 [[cent]]s in size. In the [[Functional Just System]] and [[Helmholtz-Ellis notation]], it is an ''augmented fifth'', obtained by subtracting [[81/80]] and [[513/512]] from the [[6561/4096|Pythagorean augmented fifth]], but it may be called the '''Eratosthenes' minor sixth''' as it is flatter than the [[128/81|Pythagorean minor sixth]] by the ''password'' aka ''Eratosthenes' comma'' ([[1216/1215]]), an [[unnoticeable comma]] of about 1.4243 cents. | ||
== Approximation == | |||
{{Interval_Edo_Approximation | 30/19}} | |||
== See also == | == See also == | ||
* [[19/15]] – its [[octave complement]] | * [[19/15]] – its [[octave complement]] | ||
Revision as of 07:37, 3 November 2025
| Interval information |
Eratosthenes' minor sixth
[sound info]
30/19, the small undevicesimal minor sixth is a 19-limit interval, 790.8 cents in size. In the Functional Just System and Helmholtz-Ellis notation, it is an augmented fifth, obtained by subtracting 81/80 and 513/512 from the Pythagorean augmented fifth, but it may be called the Eratosthenes' minor sixth as it is flatter than the Pythagorean minor sixth 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 (%) |
|---|---|---|---|---|
| 3 | 2\3 | 800.00 | +9.24 | +2.31 |
| 6 | 4\6 | 800.00 | +9.24 | +4.62 |
| 9 | 6\9 | 800.00 | +9.24 | +6.93 |
| 12 | 8\12 | 800.00 | +9.24 | +9.24 |
| 32 | 21\32 | 787.50 | -3.26 | -8.68 |
| 35 | 23\35 | 788.57 | -2.18 | -6.37 |
| 38 | 25\38 | 789.47 | -1.28 | -4.06 |
| 41 | 27\41 | 790.24 | -0.51 | -1.75 |
| 44 | 29\44 | 790.91 | +0.15 | +0.56 |
| 47 | 31\47 | 791.49 | +0.73 | +2.87 |
| 50 | 33\50 | 792.00 | +1.24 | +5.18 |
| 53 | 35\53 | 792.45 | +1.70 | +7.50 |
| 56 | 37\56 | 792.86 | +2.10 | +9.81 |
| 76 | 50\76 | 789.47 | -1.28 | -8.12 |
| 79 | 52\79 | 789.87 | -0.88 | -5.81 |
See also
- 19/15 – its octave complement
- 19/12 – the large undevicesimal minor sixth
- Gallery of just intervals