19/15: Difference between revisions
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'''19/15''', the '''large undevicesimal major third''' is a [[19-limit]] interval, 409.2 [[cent]]s in size. In the [[Functional Just System]] and [[Helmholtz-Ellis notation]], it is a ''diminished fourth'', obtained by adding [[81/80]] and [[513/512]] to the [[8192/6561|Pythagorean diminished fourth]], but it may be called the '''Eratosthenes' major third''' as it is sharper than the [[81/64|Pythagorean major third]] by the ''password'' aka ''Eratosthenes' comma'' ([[1216/1215]]), an [[unnoticeable comma]] of about 1.4243 cents. | '''19/15''', the '''large undevicesimal major third''' is a [[19-limit]] interval, 409.2 [[cent]]s in size. In the [[Functional Just System]] and [[Helmholtz-Ellis notation]], it is a ''diminished fourth'', obtained by adding [[81/80]] and [[513/512]] to the [[8192/6561|Pythagorean diminished fourth]], but it may be called the '''Eratosthenes' major third''' as it is sharper than the [[81/64|Pythagorean major third]] by the ''password'' aka ''Eratosthenes' comma'' ([[1216/1215]]), an [[unnoticeable comma]] of about 1.4243 cents. | ||
== Approximation == | |||
{{Interval edo approximation|19/15}} | |||
== See also == | == See also == | ||
* [[30/19]] – its [[octave complement]] | * [[30/19]] – its [[octave complement]] | ||
Latest revision as of 13:07, 3 November 2025
| Interval information |
Eratosthenes' major third
[sound info]
19/15, the large undevicesimal major third is a 19-limit interval, 409.2 cents in size. In the Functional Just System and Helmholtz-Ellis notation, it is a diminished fourth, obtained by adding 81/80 and 513/512 to the Pythagorean diminished fourth, but it may be called the Eratosthenes' major third as it is sharper than the Pythagorean major 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 (%) |
|---|---|---|---|---|
| 3 | 1\3 | 400.00 | -9.24 | -2.31 |
| 6 | 2\6 | 400.00 | -9.24 | -4.62 |
| 9 | 3\9 | 400.00 | -9.24 | -6.93 |
| 12 | 4\12 | 400.00 | -9.24 | -9.24 |
| 32 | 11\32 | 412.50 | +3.26 | +8.68 |
| 35 | 12\35 | 411.43 | +2.18 | +6.37 |
| 38 | 13\38 | 410.53 | +1.28 | +4.06 |
| 41 | 14\41 | 409.76 | +0.51 | +1.75 |
| 44 | 15\44 | 409.09 | -0.15 | -0.56 |
| 47 | 16\47 | 408.51 | -0.73 | -2.87 |
| 50 | 17\50 | 408.00 | -1.24 | -5.18 |
| 53 | 18\53 | 407.55 | -1.70 | -7.50 |
| 56 | 19\56 | 407.14 | -2.10 | -9.81 |
| 76 | 26\76 | 410.53 | +1.28 | +8.12 |
| 79 | 27\79 | 410.13 | +0.88 | +5.81 |
See also
- 30/19 – its octave complement
- 45/38 – its fifth complement
- 24/19 – the small undevicesimal major third
- Gallery of just intervals