23/18: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = vicesimotertial | | Name = vicesimotertial major third | ||
| Color name = 23o4, twetho 4th | | Color name = 23o4, twetho 4th | ||
| Sound = jid_23_18_pluck_adu_dr220.mp3 | | Sound = jid_23_18_pluck_adu_dr220.mp3 | ||
}} | }} | ||
'''23/18''' is a [[23-limit]] interval that is the [[mediant]] between [[9/7]] and [[14/11]], giving it a character that is somewhere between the gentle undecimal thirds and the more strident septimal supermajor ones. It is sharp of the [[81/64|Pythagorean major third]] by a vicesimoterial formal comma, [[736/729]]. | '''23/18''', the '''vicesimoterial major third''', is a [[23-limit]] interval that is the [[mediant]] between [[9/7]] and [[14/11]], giving it a character that is somewhere between the gentle undecimal thirds and the more strident septimal supermajor ones. It is sharp of the [[81/64|Pythagorean major third]] by a vicesimoterial formal comma, [[736/729]]. | ||
== Approximation == | == Approximation == | ||
This interval is decently represented by 6 steps of [[17edo]], and near perfectly by 29 steps of [[82edo]]. If used as a generator, it creates [[squares]] temperament. | This interval is decently represented by 6 steps of [[17edo]], and near perfectly by 29 steps of [[82edo]]. If used as a generator, it creates [[squares]] temperament. | ||
{{Interval edo approximation}} | |||
== See also == | == See also == | ||
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* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
[[Category:Third]] | [[Category:Third]] | ||
[[Category:Supermajor third]] | [[Category:Supermajor third]] | ||
Latest revision as of 19:25, 1 June 2026
| Interval information |
[sound info]
23/18, the vicesimoterial major third, is a 23-limit interval that is the mediant between 9/7 and 14/11, giving it a character that is somewhere between the gentle undecimal thirds and the more strident septimal supermajor ones. It is sharp of the Pythagorean major third by a vicesimoterial formal comma, 736/729.
Approximation
This interval is decently represented by 6 steps of 17edo, and near perfectly by 29 steps of 82edo. If used as a generator, it creates squares temperament.
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 3 | 1\3 | 400.00 | -24.36 | -6.09 |
| 14 | 5\14 | 428.57 | +4.21 | +4.91 |
| 17 | 6\17 | 423.53 | -0.83 | -1.18 |
| 20 | 7\20 | 420.00 | -4.36 | -7.27 |
| 28 | 10\28 | 428.57 | +4.21 | +9.82 |
| 31 | 11\31 | 425.81 | +1.44 | +3.73 |
| 34 | 12\34 | 423.53 | -0.83 | -2.37 |
| 37 | 13\37 | 421.62 | -2.74 | -8.46 |
| 45 | 16\45 | 426.67 | +2.30 | +8.63 |
| 48 | 17\48 | 425.00 | +0.64 | +2.54 |
| 51 | 18\51 | 423.53 | -0.83 | -3.55 |
| 54 | 19\54 | 422.22 | -2.14 | -9.64 |
| 62 | 22\62 | 425.81 | +1.44 | +7.45 |
| 65 | 23\65 | 424.62 | +0.25 | +1.36 |
| 68 | 24\68 | 423.53 | -0.83 | -4.73 |
| 79 | 28\79 | 425.32 | +0.95 | +6.27 |