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)^ | 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]] |