29-limit: Difference between revisions
+rank, lattice representation, relation to odd limits and harmonic/subharmonic modes |
No edit summary |
||
| (10 intermediate revisions by 5 users not shown) | |||
| Line 6: | Line 6: | ||
These things are contained by the 29-limit, but not the 23-limit: | These things are contained by the 29-limit, but not the 23-limit: | ||
* The [[29-odd-limit]]; | * The [[29-odd-limit]]; | ||
* Mode 15 of the harmonic or subharmonic series. | * Mode 15 of the harmonic or subharmonic series. | ||
The 29-limit intervals of the 2.3.29 subgroup are [[submajor and supraminor]], with [[29/27]] being a supraminor second, [[32/29]] a submajor second, [[29/24]] a supraminor third, and [[36/29]] a submajor third, with their [[octave complement]]s classified accordingly. While supraminor and submajor intervals occur in lower limits, such as [[14/13]], [[11/10]], and [[17/14]], these combine multiple primes higher than 3, unlike the 29-limit ones. The [[29/1|29th harmonic]] is thus quite simple to classify by [[5L 2s|diatonic]] classification, and has a characteristic [[interval quality]] like harmonics [[5/1|5]], [[7/1|7]], etc. Primes [[17/1|17]] and [[23/1|23]] are not so friendly in terms of interval categorization, and may be considered discordant to the fundamental, being a semitone and a tritone when [[octave reduced]] respectively. Thus many people wish to exclude them, leading to the [[2.3.5.7.11.13.19.29 subgroup]]. | |||
However, the 29-limit approaches the point where [[consonance]] stops being registered, and intervals become very close to each other, such as [[29/28]] only being wider than [[30/29]] by [[841/840]], a comma of 2.06{{c}}. This difference is [[JND|unnoticeable]] melodically, and very difficult to hear harmonically. | |||
== Edo approximations == | == Edo approximations == | ||
[[282edo]] is the smallest edo that is [[consistent]] to the [[29-odd-limit]]. [[1323edo]] is the smallest edo that is [[distinctly consistent]] to the 29-odd-limit. | [[282edo]] is the smallest edo that is [[consistent]] to the [[29-odd-limit]]. [[1323edo]] is the smallest edo that is [[distinctly consistent]] to the 29-odd-limit. The intervals [[29/16]] and [[32/29]] are very accurately approximated by [[7edo]] (1\7 for 32/29, 6\7 for 29/16). | ||
Edos with increasingly better approximations of the 29-limit ([[monotonicity limit]] ≥ 29 and decreasing [[TE error]]): {{EDOs| 72, 77, 99ef, 118, 121i, 130, 140, 152fgj, 159, 183, 217, 243e, 270, 282, 311, 422, 472, 494h, 525, 535, 540, 554e, 566gj, 571, 581, 581j, 624j, 653, 692i, 718, 742i, 814, 882, 908, 954hj, 1106, 1282, 1308, 1323, 1395, 1578 }}, etc. For a more comprehensive list, see [[Sequence of equal temperaments by error]]. | |||
{{Note| [[Wart notation]] is used to specify the [[val]] chosen for the edo. In the above list, "99ef" means taking the second closest approximations of harmonics 11 and 13. }} | |||
== Music == | == Music == | ||
; [[Gordon Wery]] | |||
* [https://www.youtube.com/watch?v=VinHNxf1CAg ''lucky lopside''] (2025) | |||
; [[Domin]] | |||
* [https://www.youtube.com/watch?v=3kVJ4aFj0wY ''Ixnge Uotbnatsz (2.3.7.13.29 JI)''] (2026) | |||
* [https://www.youtube.com/watch?v=r43wGByQXlg ''Ixnge Blulg (2.3.7.13.29 JI)''] (2025) | |||
* [https://www.youtube.com/watch?v=pgpQQnfrfXs ''Ixnge Euiia (2.3.7.13.29 JI) (dark ambient)''] (2025) | |||
* [https://www.youtube.com/watch?v=g5yi9nYUHiU ''Exngo Onkha (2.3.7.13.29 JI)''] (2025) | |||
* [https://www.youtube.com/watch?v=_8UNYagV-TI ''Ixnge Bnga (2.3.7.13.29 JI)''] (2025) | |||
* [https://www.youtube.com/watch?v=aoIkVeBkYTQ ''Angagn Yeein (2.3.7.13.29 JI)''] (2025) | |||
* [https://www.youtube.com/watch?v=-Q0sY4gHBSA ''Exngo Rhkue (2.3.7.13.29 JI)''] (2025) | |||
* [https://www.youtube.com/watch?v=6rsoSUyaIbA ''Oxnga Cryxs (2.3.7.13.29 JI)''] (2025) | |||
* [https://www.youtube.com/watch?v=G6NDUBrBhgc ''Angagn Dgaa (2.3.7.13.29 JI)''] (2025) | |||
* [https://www.youtube.com/watch?v=papYRvAUGGU ''Exngo Auerkt (2.3.7.13.29 JI)''] (2025) | |||
* [https://www.youtube.com/watch?v=cCCJ5DZLvFw ''Angagn Rgar (2.3.7.13.29 JI)''] (2025) | |||
* [https://www.youtube.com/watch?v=udqAU6yXU9c ''Ixnge Ioikra (2.3.7.13.29 JI)''] (2025) | |||
* [https://www.youtube.com/watch?v=sEQ744soAsg ''Ixnge Sauej (2.3.7.13.29 JI)''] (2025) | |||
* [https://www.youtube.com/watch?v=FR6_FWtRS6c ''Oxnga Otrahn (2.3.7.13.29 JI)''] (2025) | |||
* [https://www.youtube.com/watch?v=Dl4LTKeOvxk ''Angagn Ehji (2.3.7.13.29 JI)''] (2025) | |||
* [https://www.youtube.com/watch?v=n2jU3wE0qQs ''Angagn Leish (2.3.7.13.29 JI)''] (2025) | |||
* [https://www.youtube.com/watch?v=kSn5EPCiTpk ''Angagn Aazx (2.3.7.13.29 JI)''] (2025) | |||
* [https://www.youtube.com/watch?v=c-OvHwWsN1o ''Angagn Ount (2.3.7.13.29 JI)''] (2025) | |||
* [https://www.youtube.com/watch?v=AIpeXF9Y2eo ''Axngo Zilt (2.3.7.13.29 JI)''] (2025) | |||
* [https://www.youtube.com/watch?v=l2AbFDG46NE ''Oxnga Żdżarg (2.3.7.13.29 JI)''] (2025) | |||
* [https://www.youtube.com/watch?v=MPNcubgnb7g ''Exngo Akkaya (2.3.7.13.29 JI)''] (2025) | |||
* [https://www.youtube.com/watch?v=Uek49JwDuQo ''Oxnga Shkarr (2.3.7.13.29 JI)''] (2025) | |||
* [https://www.youtube.com/watch?v=K7zxsA-XpHs ''Axngo Knett (2.3.7.13.29 JI)''] (2025) | |||
* [https://www.youtube.com/watch?v=mI6rRBqmVSs ''Axngo Ndge (2.3.7.13.29 JI)''] (2026) | |||
; [[Francium]] | |||
* [https://www.youtube.com/watch?v=PwvKS0RhTgs ''Spring Your Miracle''] (2026) | |||
; [[Randy Wells]] | ; [[Randy Wells]] | ||
* [https://www.youtube.com/watch?v=4RsACF6s-5U ''Cloud Aliens''] (2021) | * [https://www.youtube.com/watch?v=4RsACF6s-5U ''Cloud Aliens''] (2021) | ||
[[Category:29-limit| ]] <!-- main article --> | [[Category:29-limit| ]] <!-- main article --> | ||