385/384: Difference between revisions

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The '''keenanisma''' is the [[11-limit]] comma '''385/384''' = {{Monzo| -7 -1 1 1 1 }} of 4.503 [[cent]]s. Tempering it out leads to a temperament of the 11-limit rank four [[Keenanismic family]].

{{Infobox Interval

| Icon =

| Ratio = 385/384

| Monzo = -7 -1 1 1 1

| Cents = 4.5026

| Name = keenanisma

| Color name =

| FJS name = P1<sup>5, 7, 11</sup>

| Sound =

}}

The '''keenanisma''' is the [[11-limit]] [[comma]] '''385/384''' = {{Monzo| -7 -1 1 1 1 }} of 4.503 [[cent]]s. Tempering it out leads to a temperament of the 11-limit rank four [[Keenanismic family]].

The keenanisma equates [[48/35]] with [[11/8]] and [[35/24]] with [[16/11]]; these are [[7-limit]] intervals of low complexity, lying across from 1/1 in the hexanies 8/7-6/5-48/35-8/5-12/7-2 and 7/6-5/4-35/24-5/3-7/4-2. Hence keenanismic tempering allows the hexany to be viewed as containing some 11-limit harmony. The hexany is a fundamental construct in the 3D lattice of [[The_Seven_Limit_Symmetrical_Lattices|7-limit pitch classes]], the "deep holes" of the lattice as opposed to the "holes" represented by major and minor tetrads, and in terms of the [[The_Seven_Limit_Symmetrical_Lattices|cubic lattice of 7-limit tetrads]], the otonal tetrad with root 11 (or 11/8) is represented by [-2 0 0]: 1-6/5-48/35-12/7-2. In terms of 7-limit chord relationships, this complexity is as low as possible for an 11-limit projection comma, equaling the [0 1 -1] of 56/55 and less than the other alternatives. Since keenanismic temperament is also quite accurate, this singles it out as being of special interest.

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[[File:keenanismic tetrads in 31edo sym.png]]

== See also ==

* [[Keenanismic chords]]

* [[Keenanismic family]]

* [[Comma]]

* [[List of superparticular intervals]]

[[Category:11-limit]]

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[[Category:Comma]]

[[Category:Keenanismic]]

[[Category:Superparticular]]

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-The '''keenanisma''' is the [[11-limit]] comma '''385/384''' = {{Monzo| -7 -1 1 1 1 }} of 4.503 [[cent]]s. Tempering it out leads to a temperament of the 11-limit rank four [[Keenanismic family]].
+{{Infobox Interval
+| Icon =
+| Ratio = 385/384
+| Monzo = -7 -1 1 1 1
+| Cents = 4.5026
+| Name = keenanisma
+| Color name =
+| FJS name = P1<sup>5, 7, 11</sup>
+| Sound =
+}}
+The '''keenanisma''' is the [[11-limit]] [[comma]] '''385/384''' = {{Monzo| -7 -1 1 1 1 }} of 4.503 [[cent]]s. Tempering it out leads to a temperament of the 11-limit rank four [[Keenanismic family]].
 The keenanisma equates [[48/35]] with [[11/8]] and [[35/24]] with [[16/11]]; these are [[7-limit]] intervals of low complexity, lying across from 1/1 in the hexanies 8/7-6/5-48/35-8/5-12/7-2 and 7/6-5/4-35/24-5/3-7/4-2. Hence keenanismic tempering allows the hexany to be viewed as containing some 11-limit harmony. The hexany is a fundamental construct in the 3D lattice of [[The_Seven_Limit_Symmetrical_Lattices|7-limit pitch classes]], the "deep holes" of the lattice as opposed to the "holes" represented by major and minor tetrads, and in terms of the [[The_Seven_Limit_Symmetrical_Lattices|cubic lattice of 7-limit tetrads]], the otonal tetrad with root 11 (or 11/8) is represented by [-2 0 0]: 1-6/5-48/35-12/7-2. In terms of 7-limit chord relationships, this complexity is as low as possible for an 11-limit projection comma, equaling the [0 1 -1] of 56/55 and less than the other alternatives. Since keenanismic temperament is also quite accurate, this singles it out as being of special interest.
@@ Line 8: / Line 19: @@
 [[File:keenanismic tetrads in 31edo sym.png]]
+== See also ==
+* [[Keenanismic chords]]
+* [[Keenanismic family]]
+* [[Comma]]
+* [[List of superparticular intervals]]
 [[Category:11-limit]]
@@ Line 13: / Line 30: @@
 [[Category:Comma]]
 [[Category:Keenanismic]]
+[[Category:Superparticular]]