31/30: Difference between revisions
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| Sound = Ji-31-30-csound-foscil-220hz.mp3 | | Sound = Ji-31-30-csound-foscil-220hz.mp3 | ||
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'''31/30''' is the '''large tricesimoprimal quartertone''' measuring about 57{{cent}}. It differs from [[33/32]], the undecimal quartertone, by [[496/495]] (approx. 3.49{{cent}}). It differs from [[32/31]], another tricesimoprimal quartertone, by [[961/960]] (approx. 1.80{{cent}}); they together make [[16/15]]. | '''31/30''' is the '''large tricesimoprimal quartertone''' measuring about 57{{cent}}. It differs from [[33/32]], the undecimal quartertone, by [[496/495]] (approx. 3.49{{cent}}). It differs from [[32/31]], another tricesimoprimal quartertone, by [[961/960]] (approx. 1.80{{cent}}); they together make [[16/15]]. | ||
This interval is the 31st-partial chroma (31-limit formal comma) in [[Ben Johnston's notation]], denoted simply with the number "31", while its reciprocal is denoted as <span style="display: inline-block; transform: rotate(180deg)">31</span> (a turned 31). If the base note is C, then 31/16 is represented by C–B31. | This interval is the 31st-partial chroma (31-limit formal comma) in [[Ben Johnston's notation]], denoted simply with the number "31", while its reciprocal is denoted as <span style="display: inline-block; transform: rotate(180deg)">31</span> (a turned 31). If the base note is C, then 31/16 is represented by C–B31. | ||
{{ | == Approximation == | ||
{{Interval edo approximation}} | |||
== See also == | == See also == | ||
Latest revision as of 08:07, 6 October 2026
| Interval information |
reduced
[sound info]
31/30 is the large tricesimoprimal quartertone measuring about 57 ¢. It differs from 33/32, the undecimal quartertone, by 496/495 (approx. 3.49 ¢). It differs from 32/31, another tricesimoprimal quartertone, by 961/960 (approx. 1.80 ¢); they together make 16/15.
This interval is the 31st-partial chroma (31-limit formal comma) in Ben Johnston's notation, denoted simply with the number "31", while its reciprocal is denoted as 31 (a turned 31). If the base note is C, then 31/16 is represented by C–B31.
Approximation
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 2 | 0\2 | 0.00 | -56.77 | -9.46 |
| 20 | 1\20 | 60.00 | +3.23 | +5.39 |
| 21 | 1\21 | 57.14 | +0.38 | +0.66 |
| 22 | 1\22 | 54.55 | -2.22 | -4.07 |
| 23 | 1\23 | 52.17 | -4.59 | -8.80 |
| 41 | 2\41 | 58.54 | +1.77 | +6.05 |
| 42 | 2\42 | 57.14 | +0.38 | +1.32 |
| 43 | 2\43 | 55.81 | -0.95 | -3.41 |
| 44 | 2\44 | 54.55 | -2.22 | -8.15 |
| 62 | 3\62 | 58.06 | +1.30 | +6.70 |
| 63 | 3\63 | 57.14 | +0.38 | +1.97 |
| 64 | 3\64 | 56.25 | -0.52 | -2.76 |
| 65 | 3\65 | 55.38 | -1.38 | -7.49 |