19/16: Difference between revisions
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'''19/16''' is a [[19-limit]] interval, 297.5 [[cent]]s in size, the '''otonal minor third''' or '''octave-reduced 19th harmonic''', which is extremely close to the minor third of [[12edo]] (300 cents). It is an ''undevicesimal | '''19/16''' is a [[19-limit]] interval, 297.5 [[cent]]s in size, the '''otonal minor third''' or '''octave-reduced 19th harmonic''', which is extremely close to the minor third of [[12edo]] (300 cents). It is an ''undevicesimal schisma'' aka ''Boethius' comma'' ([[513/512]]) above the [[32/27|Pythagorean minor third]]. | ||
== Approximation == | == Approximation == | ||
Revision as of 01:55, 3 May 2026
| Interval information |
octave-reduced 19th harmonic
reduced harmonic
[sound info]
19/16 is a 19-limit interval, 297.5 cents in size, the otonal minor third or octave-reduced 19th harmonic, which is extremely close to the minor third of 12edo (300 cents). It is an undevicesimal schisma aka Boethius' comma (513/512) above the Pythagorean minor third.
Approximation
19/16 is very accurately approximated by 121edo (30\121), although technically there is a slight difference, as that of 121edo is 0.007645 cents sharper.
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 4 | 1\4 | 300.00 | +2.49 | +0.83 |
| 8 | 2\8 | 300.00 | +2.49 | +1.66 |
| 12 | 3\12 | 300.00 | +2.49 | +2.49 |
| 16 | 4\16 | 300.00 | +2.49 | +3.32 |
| 20 | 5\20 | 300.00 | +2.49 | +4.14 |
| 24 | 6\24 | 300.00 | +2.49 | +4.97 |
| 28 | 7\28 | 300.00 | +2.49 | +5.80 |
| 32 | 8\32 | 300.00 | +2.49 | +6.63 |
| 36 | 9\36 | 300.00 | +2.49 | +7.46 |
| 40 | 10\40 | 300.00 | +2.49 | +8.29 |
| 44 | 11\44 | 300.00 | +2.49 | +9.12 |
| 48 | 12\48 | 300.00 | +2.49 | +9.95 |
| 73 | 18\73 | 295.89 | -1.62 | -9.87 |
| 77 | 19\77 | 296.10 | -1.41 | -9.04 |