Ed6: Difference between revisions

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== Introduction ==

The 6th harmonic is particularly wide as far as equivalences go. There are ~~3.855~~ hexataves in the human hearing range; imagine if that were the case with octaves. If one does indeed deal with hexatave equivalence, this fact shapes one's musical approach dramatically. Even so, the hexatave is one of the three particularly interesting composite harmonics whereof there are enough within the human hearing range to fill three periods of keyboard (the 10th, and to a lesser extent, the 12th share this property). Following this, the quintessential reason for using a hexatave based tuning is that it will split the difference between octave and tritave based tunings, which is a potentially very desirable thing for a tuning to do given the importance of these harmonics in the musics of much of the world (see [[44ed6]] and [[49ed6]]). However, this is not to say of ed6's not supporting this important 13 & 18 temperament that they can be dismissed out of hand as entirely worthless, for to do that would shut off all non-patent musical approaches to this equivalence. In fact, taking the ''n''-th root of 6 is itself an approach to finding temperaments like squares, tritonic, and sensi. This approach can of course be used indiscriminately.

The 6th harmonic is particularly wide as far as equivalences go. There are at most 4 hexataves in the [[human hearing range]]; imagine if that were the case with octaves. If one does indeed deal with hexatave equivalence, this fact shapes one's musical approach dramatically. Even so, the hexatave is one of the three particularly interesting composite harmonics whereof there are enough within the human hearing range to fill three periods of keyboard (the 10th, and to a lesser extent, the 12th share this property). Following this, the quintessential reason for using a hexatave based tuning is that it will split the difference between octave and tritave based tunings, which is a potentially very desirable thing for a tuning to do given the importance of these harmonics in the musics of much of the world (see [[44ed6]] and [[49ed6]]). However, this is not to say of ed6's not supporting this important 13 & 18 temperament that they can be dismissed out of hand as entirely worthless, for to do that would shut off all non-patent musical approaches to this equivalence. In fact, taking the ''n''-th root of 6 is itself an approach to finding temperaments like squares, tritonic, and sensi. This approach can of course be used indiscriminately.

Some equal divisions of the hexatave serve as generators for octave temperaments:

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 == Introduction ==
-The 6th harmonic is particularly wide as far as equivalences go. There are 3.855 hexataves in the human hearing range; imagine if that were the case with octaves. If one does indeed deal with hexatave equivalence, this fact shapes one's musical approach dramatically. Even so, the hexatave is one of the three particularly interesting composite harmonics whereof there are enough within the human hearing range to fill three periods of keyboard (the 10th, and to a lesser extent, the 12th share this property). Following this, the quintessential reason for using a hexatave based tuning is that it will split the difference between octave and tritave based tunings, which is a potentially very desirable thing for a tuning to do given the importance of these harmonics in the musics of much of the world (see [[44ed6]] and [[49ed6]]). However, this is not to say of ed6's not supporting this important 13 &amp; 18 temperament that they can be dismissed out of hand as entirely worthless, for to do that would shut off all non-patent musical approaches to this equivalence. In fact, taking the ''n''-th root of 6 is itself an approach to finding temperaments like squares, tritonic, and sensi. This approach can of course be used indiscriminately.
+The 6th harmonic is particularly wide as far as equivalences go. There are at most 4 hexataves in the [[human hearing range]]; imagine if that were the case with octaves. If one does indeed deal with hexatave equivalence, this fact shapes one's musical approach dramatically. Even so, the hexatave is one of the three particularly interesting composite harmonics whereof there are enough within the human hearing range to fill three periods of keyboard (the 10th, and to a lesser extent, the 12th share this property). Following this, the quintessential reason for using a hexatave based tuning is that it will split the difference between octave and tritave based tunings, which is a potentially very desirable thing for a tuning to do given the importance of these harmonics in the musics of much of the world (see [[44ed6]] and [[49ed6]]). However, this is not to say of ed6's not supporting this important 13 &amp; 18 temperament that they can be dismissed out of hand as entirely worthless, for to do that would shut off all non-patent musical approaches to this equivalence. In fact, taking the ''n''-th root of 6 is itself an approach to finding temperaments like squares, tritonic, and sensi. This approach can of course be used indiscriminately.
 Some equal divisions of the hexatave serve as generators for octave temperaments: