Non radical intervals with musical significance: Difference between revisions

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Musicians are typically interested in musical intervals that are rational (i.e. justly intoned ratios), or equal divisions of these intervals. However, not all intervals fit into this box.
Musicians are typically interested in musical intervals that are rational (i.e. justly intoned ratios), or equal divisions of these intervals. However, not all intervals fit into this box.


There are many non-radical intervals which have musical significance. By '''non-radical''' is meant a number that cannot be written in the form <math>(a/b)^{1/c}</math>, where <math>a</math>, <math>b</math> and <math>c</math> are integers. What follows is a list of musically significant non-radical intervals.
There are many non-radical intervals which have musical significance. By '''non-radical''' is meant a number that cannot be written in the form <math>(a/b)^c</math>, where <math>a</math> and <math>b</math> are integers and <math>c</math> is rational. What follows is a list of musically significant non-radical intervals.


{| class="wikitable"
{| class="wikitable"
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| | <math>e^{2\pi} \approx 535.4917</math>
| | <math>e^{2\pi} \approx 535.4917</math>
| | 10877.66
| | 10877.66
| |  
| | [[Zetave]]
| | The zeta function has units that are given as divisions of the interval <math>e^{2\pi}</math>.
| | The [[zeta]] function has units that are given as divisions of the interval <math>e^{2\pi}</math>.
|}
|}


[[Category:Lists of intervals]]
[[Category:Lists of intervals]]
[[Category:Math]]
[[Category:Math]]