13-limit: Difference between revisions

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== Edo approximation ==

[[Edo]]s which represent 13-limit intervals better (~~with~~ decreasing [[TE error]]): {{EDOs| 26, 27e, 29, 31, 41, 46, 53, 58, 72, 87, 103, 111, 121, 130, 183, 190, 198, 224, 270, 494 }} and so on.

[[Edo]]s which represent 13-limit intervals better ([[monotonicity limit]] ≥ 13 and decreasing [[TE error]]): {{EDOs| 15, 17c, 19, 26, 27e, 29, 31, 41, 46, 53, 58, 72, 87, 103, 111, 121, 130, 183, 190, 198, 224, 270, 494 }} and so on. For a more comprehensive list, see [[Sequence of equal temperaments by error]].

Here is a list of edos which tunes the 13-limit well relative to their size ({{nowrap|[[TE relative error]] < 5.5%}}): {{EDOs| 31, 41, 46, 53, 58, 72, 87, 94, 103, 111, 121, 130, 140, 152f, 159, 183, 190, 198, 212, 217, 224, 270, 282, 296, 301, 311, 320, 328, 342f, 354, 364, 369f, 373, 383, 400, 414, 422, 431, 441, 460, 472, 494 }}, and so on.

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== Music ==

~~; [https://youtube.com/@hojominori?si=gqJP3hzvup2YL0sz Hojo Minori]~~

* [https://youtu.be/xSIS2lobkTk?si=x-2-rESdZTZ9u_fy ''P`rismatic fut`URE] (2025)

; [[E8 Heterotic]]

* [https://~~youtu~~.be/cUR3MsI-mWM~~?si=-dIKc8d5kFln8H6T~~ ''Justification''] (2022)

* [https://www.youtube.com/watch?v=cUR3MsI-mWM ''Justification''] (2022)

; [[Francium]]

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* [http://sonic-arts.org/hill/10-passages-ji/10-passages-ji.htm ''Venusian Cataclysms'']{{dead link}} [http://sonic-arts.org/hill/10-passages-ji/02_hill_venusian-cataclysms.mp3 play]{{dead link}}

* [http://sonic-arts.org/hill/10-passages-ji/10-passages-ji.htm ''Chord Progression on the Harmonic Overtone Series'']{{dead link}} [http://sonic-arts.org/hill/10-passages-ji/06_hill_chord-progression-on-harmonic-series.mp3 play]{{dead link}}

; [https://youtube.com/@hojominori?si=gqJP3hzvup2YL0sz Hojo Minori]

* [https://www.youtube.com/watch?v=xSIS2lobkTk ''P`rismatic fut`URE''] (2025)

; [[Ben Johnston]]

@@ Line 9: / Line 9: @@
 == Edo approximation ==
-[[Edo]]s which represent 13-limit intervals better (with decreasing [[TE error]]): {{EDOs| 26, 27e, 29, 31, 41, 46, 53, 58, 72, 87, 103, 111, 121, 130, 183, 190, 198, 224, 270, 494 }} and so on.
+[[Edo]]s which represent 13-limit intervals better ([[monotonicity limit]] ≥ 13 and decreasing [[TE error]]): {{EDOs| 15, 17c, 19, 26, 27e, 29, 31, 41, 46, 53, 58, 72, 87, 103, 111, 121, 130, 183, 190, 198, 224, 270, 494 }} and so on. For a more comprehensive list, see [[Sequence of equal temperaments by error]].
 Here is a list of edos which tunes the 13-limit well relative to their size ({{nowrap|[[TE relative error]] < 5.5%}}): {{EDOs| 31, 41, 46, 53, 58, 72, 87, 94, 103, 111, 121, 130, 140, 152f, 159, 183, 190, 198, 212, 217, 224, 270, 282, 296, 301, 311, 320, 328, 342f, 354, 364, 369f, 373, 383, 400, 414, 422, 431, 441, 460, 472, 494 }}, and so on.
@@ Line 111: / Line 111: @@
 == Music ==
-; [https://youtube.com/@hojominori?si=gqJP3hzvup2YL0sz Hojo Minori]
-* [https://youtu.be/xSIS2lobkTk?si=x-2-rESdZTZ9u_fy ''P`rismatic fut`URE] (2025)
 ; [[E8 Heterotic]]
-* [https://youtu.be/cUR3MsI-mWM?si=-dIKc8d5kFln8H6T ''Justification''] (2022)
+* [https://www.youtube.com/watch?v=cUR3MsI-mWM ''Justification''] (2022)
 ; [[Francium]]
@@ Line 123: / Line 121: @@
 * [http://sonic-arts.org/hill/10-passages-ji/10-passages-ji.htm ''Venusian Cataclysms'']{{dead link}} [http://sonic-arts.org/hill/10-passages-ji/02_hill_venusian-cataclysms.mp3 play]{{dead link}}
 * [http://sonic-arts.org/hill/10-passages-ji/10-passages-ji.htm ''Chord Progression on the Harmonic Overtone Series'']{{dead link}} [http://sonic-arts.org/hill/10-passages-ji/06_hill_chord-progression-on-harmonic-series.mp3 play]{{dead link}}
+; [https://youtube.com/@hojominori?si=gqJP3hzvup2YL0sz Hojo Minori]
+* [https://www.youtube.com/watch?v=xSIS2lobkTk ''P`rismatic fut`URE''] (2025)
 ; [[Ben Johnston]]