5-limit: Difference between revisions
→Modern renderings: ''Maple Leaf Rag'' (1899) – rendered by Claudi Meneghin (2026): Add organ rendition |
→Modern renderings: Add Scott Joplin's ''Maple Leaf Rag'' (1899) – rendered by Claudi Meneghin for organ (2026-06-08, with detailed description of syntonic chroma adjustment in video description) |
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{{Wikipedia|Five-limit tuning}} | {{Wikipedia|Five-limit tuning}} | ||
[[File:Lattice 5lim.png|alt=The lattice is a grid with 60 degree triangles and intervals at the vertices. The center vertex is 1/1, moving right is multiplication by 3/2, up-right is multiplication by 5/4, and up-left is multiplication by 5/3. Everything is octave-reduced.|thumb|5-limit hexagonal lattice]] | [[File:Lattice 5lim.png|alt=The lattice is a grid with 60 degree triangles and intervals at the vertices. The center vertex is 1/1, moving right is multiplication by 3/2, up-right is multiplication by 5/4, and up-left is multiplication by 5/3. Everything is octave-reduced.|thumb|5-limit hexagonal lattice]] | ||
The '''5-limit''' consists of all [[just intonation]] intervals whose [[ratio|numerators and denominators]] are both products of the primes 2, 3, and 5 | The '''5-limit''' (a.k.a. ''ya'' in [[color notation]]) consists of all [[just intonation]] intervals whose [[ratio|numerators and denominators]] are both products of the primes 2, 3, and 5. The 5-limit is the third prime limit and is a superset of the [[3-limit]] and a subset of the [[7-limit]]. Some examples of 5-limit intervals are [[5/4]], [[6/5]], [[10/9]] and [[81/80]]. | ||
These things are contained by the 5-limit, but not the 3-limit: | These things are contained by the 5-limit, but not the 3-limit: | ||
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* [http://web.archive.org/web/20201127013240/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/5limit/The%20Ballad%20of%20Jed%20Clampett.mp3 ''The Ballad of Jed Clampett''] (unknown arranger) | * [http://web.archive.org/web/20201127013240/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/5limit/The%20Ballad%20of%20Jed%20Clampett.mp3 ''The Ballad of Jed Clampett''] (unknown arranger) | ||
; {{ | ; {{W|Scott Joplin}} | ||
* ''Maple Leaf Rag'' (1899) – rendered by [[Claudi Meneghin]] (2026) | * ''Maple Leaf Rag'' (1899) – rendered by [[Claudi Meneghin]] | ||
** [https://www.youtube.com/shorts/ | ** [https://www.youtube.com/shorts/N9psCtvbSQ8 harpsichord rendition] (2026-03-01) | ||
** [https://www.youtube.com/shorts/ | ** [https://www.youtube.com/shorts/N27o7IcOAJQ organ rendition (fragment) without swing] (2026-04-06) | ||
** [https://www.youtube.com/watch?v=MSuSe4NRvCM fortepiano rendition without swing] (2026-04-30) | |||
** harpsichord rendition [https://www.youtube.com/watch?v=95zyi0O7OE4 without swing] (2026-05-01) and [https://www.youtube.com/shorts/KuJzxepw6Ho with swing] (2026-05-02) | |||
** organ rendition with swing ([https://www.youtube.com/shorts/dKXbvsL_7xw 2026-05-18], [https://www.youtube.com/watch?v=L6qF9gxT7pA 2026-06-08]) and without swing ([https://www.youtube.com/watch?v=a9Sz2aGurzw 2026-05-25]), with detailed description of syntonic chroma adjustment in video descriptions | |||
=== 20th century === | === 20th century === | ||
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; [[Axoid Music]] | ; [[Axoid Music]] | ||
* [https://m.youtube.com/watch?v=D-5f11nR2BI ''Alien Harmonies - Pure Data Generative Microtonal Ambient Music''] (2022) | * [https://m.youtube.com/watch?v=D-5f11nR2BI ''Alien Harmonies - Pure Data Generative Microtonal Ambient Music''] (2022) | ||
; [[John Robert Bagby]] ([https://www.youtube.com/@SocraticSwansongs YouTube]) | |||
* [https://www.youtube.com/watch?v=F1vYmdaNHHE ''53 unequal divisions of the octave Just Intonation lumatone experiment''] (2024) – uses [https://sevish.com/scaleworkshop/?n=Harmonic+series+12+tone&l=29F28_3kF3h_pFo_3rF3k_gFf_rFp_m8Fk9_aF9_9F8_74F69_40F3h_23F1s_wFr_6F5_6rF5k_2sF29_5F4_29F1s_wFp_4iF3h_8wF6r_4F3_rFk_e8Faf_pFi_19Fw_1sF19_10Fp_afF74_14Fr_3F2_6rF4g_3hF29_pFg_3kF29_8F5_29F1e_b4F6r_5F3_rFg_3kF23_3hF20_69F3k_gF9_9F5_k9Fb4_1eFr_fF8_74F3r_1cFp_3hF1s_4gF29_2F1&version=2.4.1 this 53-tone subset] | |||
; [[William Copper]] ([http://www.williamcopper.com site 1] [http://www.hartenshield.com/william_copper.html site 2]{{dead link}}) | ; [[William Copper]] ([http://www.williamcopper.com site 1] [http://www.hartenshield.com/william_copper.html site 2]{{dead link}}) | ||