12/11: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Wikispaces>FREEZE
No edit summary
Xenwolf (talk | contribs)
autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops
8,705 edits
switched to infobox interval; simplified links
Line 1: Line 1:
'''12/11'''
{{Infobox Interval
|2 1 0 0 -1>
| Icon =
| Ratio = 12/11
| Monzo = 2 1 0 0 -1
| Cents = 150.63706
| Name = undecimal neutral second
| Sound = jid_12_11_pluck_adu_dr220.mp3
}}


150.63706 cents
The (lesser) neutral second is a strangely exotic interval found between the 11th and 12th partials of the harmonic series. In Just Intonation it is represented by the [[superparticular]] ratio 12/11, and is about 150.6 [[cent|cents]] large. One step of [[8edo|8edo]] is an excellent approximation of the just neutral second, and eight of them exceed the octave by the comma (12/11)^8/2 = {{Monzo|15 8 0 0 -8}}. It follows that EDOs which are multiples of 8, such as [[16edo]] and [[24edo]], will also represent this interval well.


[[File:jid_12_11_pluck_adu_dr220.mp3]] [[:File:jid_12_11_pluck_adu_dr220.mp3|sound sample]]
'''12/11''' differs from the larger undecimal neutral second 11/10 (~165 cents) by 121/120 (~14.4 cents). Temperaments which conflate the two (thus tempering out 121/120) include [[15edo]], [[22edo]], [[31edo]], [[orwell]], [[porcupine]], [[mohajira]] and [[valentine]].


The (lesser) neutral second is a strangely exotic interval found between the 11th and 12th partials of the harmonic series. In Just Intonation it is represented by the [[superparticular|superparticular]] ratio 12/11, and is about 150.6 [[cent|cents]] large. One step of [[8edo|8edo]] is an excellent approximation of the just neutral second, and eight of them exceed the octave by the comma (12/11)^8/2 = |15 8 0 0 -8>. It follows that EDOs which are multiples of 8, such as [[16edo|16edo]] and [[24edo|24edo]], will also represent this interval well.
12/11 differs from the larger undecimal neutral second 11/10 (~165 cents) by 121/120 (~14.4 cents). Temperaments which conflate the two (thus tempering out 121/120) include [[15edo|15edo]], [[22edo|22edo]], [[31edo|31edo]], [[Orwell|orwell]], [[Porcupine|porcupine]], [[Mohajira|mohajira]] and [[Valentine|valentine]].
[[Category:11-limit]]
[[Category:11-limit]]
[[Category:interval]]
[[Category:interval]]

Revision as of 22:54, 11 October 2018

Interval information
Ratio 12/11
Factorization 22 × 3 × 11-1
Monzo [2 1 0 0 -1⟩
Size in cents 150.6371¢
Name undecimal neutral second
FJS name [math]\displaystyle{ \text{M2}_{11} }[/math]
Special properties superparticular,
reduced
Tenney height (log2 nd) 7.04439
Weil height (log2 max(n, d)) 7.16993
Wilson height (sopfr(nd)) 18

[sound info]
Open this interval in xen-calc

The (lesser) neutral second is a strangely exotic interval found between the 11th and 12th partials of the harmonic series. In Just Intonation it is represented by the superparticular ratio 12/11, and is about 150.6 cents large. One step of 8edo is an excellent approximation of the just neutral second, and eight of them exceed the octave by the comma (12/11)^8/2 = [15 8 0 0 -8⟩. It follows that EDOs which are multiples of 8, such as 16edo and 24edo, will also represent this interval well.

12/11 differs from the larger undecimal neutral second 11/10 (~165 cents) by 121/120 (~14.4 cents). Temperaments which conflate the two (thus tempering out 121/120) include 15edo, 22edo, 31edo, orwell, porcupine, mohajira and valentine.

Retrieved from "https://en.xen.wiki/index.php?title=12/11&oldid=36590"