22/13: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = tridecimal major sixth | | Name = tridecimal major sixth, major minthmic major sixth | ||
| Color name = 3u1o6, thulo 6th | | Color name = 3u1o6, thulo 6th | ||
| Sound = jid_22_13_pluck_adu_dr220.mp3 | | Sound = jid_22_13_pluck_adu_dr220.mp3 | ||
}} | }} | ||
'''22/13''', the '''tridecimal major sixth''', is a [[13-limit]] [[just intonation]] interval measuring about 910.8 [[cent]]s. It is the inverse of [[13/11]], the tridecimal minor third. It is sharp of the Pythagorean major sixth | '''22/13''', the '''tridecimal major sixth''' or '''major minthmic major sixth''', is a [[13-limit]] [[just intonation]] interval measuring about 910.8 [[cent]]s. It is the inverse of [[13/11]], the tridecimal minor third. It is sharp of the [[27/16|Pythagorean major sixth (27/16)]] by a [[352/351|major minthma (352/351)]]. | ||
== Approximation == | |||
This interval is well approximated by [[17edo|13\17]] (917.647 cents), and even better, by [[29edo|22\29]] (910.345 cents). | |||
{{Interval edo approximation|22/13}} | |||
== See also == | == See also == | ||
* [[13/11]] – its [[octave complement]] | * [[13/11]] – its [[octave complement]] | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
[[Category:Sixth]] | [[Category:Sixth]] | ||
[[Category:Major sixth]] | [[Category:Major sixth]] | ||
[[Category: | [[Category:Major minthmic]] | ||
Latest revision as of 13:13, 3 November 2025
| Interval information |
major minthmic major sixth
[sound info]
22/13, the tridecimal major sixth or major minthmic major sixth, is a 13-limit just intonation interval measuring about 910.8 cents. It is the inverse of 13/11, the tridecimal minor third. It is sharp of the Pythagorean major sixth (27/16) by a major minthma (352/351).
Approximation
This interval is well approximated by 13\17 (917.647 cents), and even better, by 22\29 (910.345 cents).
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 4 | 3\4 | 900.00 | -10.79 | -3.60 |
| 8 | 6\8 | 900.00 | -10.79 | -7.19 |
| 17 | 13\17 | 917.65 | +6.86 | +9.71 |
| 21 | 16\21 | 914.29 | +3.50 | +6.12 |
| 25 | 19\25 | 912.00 | +1.21 | +2.52 |
| 29 | 22\29 | 910.34 | -0.45 | -1.08 |
| 33 | 25\33 | 909.09 | -1.70 | -4.67 |
| 37 | 28\37 | 908.11 | -2.68 | -8.27 |
| 46 | 35\46 | 913.04 | +2.25 | +8.64 |
| 50 | 38\50 | 912.00 | +1.21 | +5.04 |
| 54 | 41\54 | 911.11 | +0.32 | +1.44 |
| 58 | 44\58 | 910.34 | -0.45 | -2.15 |
| 62 | 47\62 | 909.68 | -1.11 | -5.75 |
| 66 | 50\66 | 909.09 | -1.70 | -9.35 |
| 75 | 57\75 | 912.00 | +1.21 | +7.56 |
| 79 | 60\79 | 911.39 | +0.60 | +3.96 |