11/7: Difference between revisions
m Recategorize |
Rework; +"pentacircle minor sixth" and reasons; -"undecimal augmented fifth" (its octave complement isn't "undecimal diminished fourth" yet) |
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{{Infobox Interval | {{Infobox Interval | ||
| Name = undecimal minor sixth, | | Name = undecimal minor sixth, pentacircle minor sixth | ||
| Color name = 1or5, loru 5th | | Color name = 1or5, loru 5th | ||
| Sound = jid_11_7_pluck_adu_dr220.mp3 | | Sound = jid_11_7_pluck_adu_dr220.mp3 | ||
}} | }} | ||
In [[11-limit]] [[just intonation]], '''11/7''' is an '''undecimal minor sixth''', measuring about 782.5¢. It is the inversion of [[14/11]], the | In [[11-limit]] [[just intonation]], '''11/7''' is an '''undecimal minor sixth''', specifically the '''pentacircle minor sixth''', measuring about 782.5¢. It is the inversion of [[14/11]], the pentacircle major third, and represents the difference between the 7th and 11th harmonics of the [[harmonic series]]. | ||
In many notation systems (e.g. [[FJS]], [[HEJI]]), it is an imperfect fifth, as it is a [[3/2|perfect fifth (3/2)]] plus an instance of [[22/21]], which is a stack consisting of an [[33/32|undecimal quartertone (33/32)]] and a [[64/63|septimal comma (64/63)]], neither of which changes the [[scale|scale degree]] or [[interval quality|quality]]. However, it is only flat of the Pythagorean ([[3-limit]]) minor sixth of [[128/81]] (about 792.2¢) by a [[896/891|pentacircle comma (896/891)]], which makes it function more often as a minor sixth, hence the names. | |||
It is flat of the 5-limit minor sixth of [[8/5]] (about 813.7¢) by [[56/55]]. It is sharp of the 7-limit subminor sixth of [[14/9]] (about 764.9¢) by a mothwellsma, [[99/98]]. And finally, it is sharp of the classic augmented fifth of [[25/16]] (about 772.6¢) by a valinorsma, [[176/175]]. | |||
As 11/7 is 22/21 (about 80.5¢) above the perfect fifth, it can be resolved down by a step from 11/7 to 3/2. | |||
Following [[ | == Approximations by edos == | ||
Following [[edo]]s (up to 200) contain good approximations<ref>error magnitude below 7, both, absolute (in ¢) and relative (in r¢)</ref> of the interval 11/7. Errors are given by magnitude, the arrows in the table show if the edo representation is sharp (↑) or flat (↓). | |||
{| class="wikitable sortable right-1 center-2 right-3 right-4 center-5" | {| class="wikitable sortable right-1 center-2 right-3 right-4 center-5" | ||
|- | |- | ||
! [[ | ! [[Edo]] | ||
! class="unsortable" | deg\edo | ! class="unsortable" | deg\edo | ||
! Absolute <br> error ([[Cent|¢]]) | ! Absolute <br> error ([[Cent|¢]]) | ||
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== Proximity with π/2 == | == Proximity with π/2 == | ||
(11/7)/(π/2) = 22/7π is an [[unnoticeable comma]] of only | (11/7)/(π/2) = 22/7π is an [[unnoticeable comma]] of only 0.7 cents. | ||
== See also == | == See also == | ||