28:36:42:49 - Revision history

Pailiaq at 04:33, 26 May 2026

2026-05-26T04:33:43Z

← Older revision		Revision as of 04:33, 26 May 2026
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	On the dominant, this chord is [[3/2]]–[[27/14]]–[[9/4]]–[[21/8]] above the tonic, which is [[octave equivalence\|octave-equivalent]] to [[28/27\|27/28]]–[[9/8]]–[[21/16]]–3/2. This chord resolves to [[4:5:6]] on the tonic by leading the 27/28 up by [[28/27]] to [[1/1]], and the 21/16 down by [[21/20]] to 5/4. 28/27 is often considered a better interval for voice leading than [[16/15]] due to its size of 62.96 [[cent]]s, which is much closer to the optimum of around 70 cents<ref>Secor, George. "The 17-tone puzzle — and the Neo-medieval Key That Unlocks It" Xenharmonikôn 18, 2006. http://anaphoria.com/Secor17puzzle.pdf</ref> than 16/15, which is 111.73 cents.		On the dominant, this chord is [[3/2]]–[[27/14]]–[[9/4]]–[[21/8]] above the tonic, which is [[octave equivalence\|octave-equivalent]] to [[28/27\|27/28]]–[[9/8]]–[[21/16]]–3/2. This chord resolves to [[4:5:6]] on the tonic by leading the 27/28 up by [[28/27]] to [[1/1]], and the 21/16 down by [[21/20]] to 5/4. 28/27 is often considered a better interval for voice leading than [[16/15]] due to its size of 62.96 [[cent]]s, which is much closer to the optimum of around 70 cents<ref>Secor, George. "The 17-tone puzzle — and the Neo-medieval Key That Unlocks It" Xenharmonikôn 18, 2006. http://anaphoria.com/Secor17puzzle.pdf</ref> than 16/15, which is 111.73 cents.

			{{chord edo approximation}}

	== See also ==		== See also ==

Overthink: better word

2026-03-12T04:05:25Z

better word

← Older revision		Revision as of 04:05, 12 March 2026
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	This chord occurs on the V of the [[5L 2s\|diatonic]] scale in [[superpyth]] temperament. Note that the [[tritone]] represents [[15/11]] in undecimal superpyth, which reduces it to a [[15-odd-limit]] [[swetismic chords\|swetismic]] [[essentially tempered chord]].		This chord occurs on the V of the [[5L 2s\|diatonic]] scale in [[superpyth]] temperament. Note that the [[tritone]] represents [[15/11]] in undecimal superpyth, which reduces it to a [[15-odd-limit]] [[swetismic chords\|swetismic]] [[essentially tempered chord]].

	On the dominant, this chord is [[3/2]]–[[27/14]]–[[9/4]]–[[21/8]] above the tonic, which is [[octave equivalence\|octave-equivalent]] to [[28/27\|27/28]]–[[9/8]]–[[21/16]]–3/2. This chord resolves to [[4:5:6]] on the tonic by ~~inflecting~~ the 27/28 up by [[28/27]] to [[1/1]], and the 21/16 down by [[21/20]] to 5/4. 28/27 is often considered a better interval for voice leading than [[16/15]] due to its size of 62.96 [[cent]]s, which is much closer to the optimum of around 70 cents<ref>Secor, George. "The 17-tone puzzle — and the Neo-medieval Key That Unlocks It" Xenharmonikôn 18, 2006. http://anaphoria.com/Secor17puzzle.pdf</ref> than 16/15, which is 111.73 cents.		On the dominant, this chord is [[3/2]]–[[27/14]]–[[9/4]]–[[21/8]] above the tonic, which is [[octave equivalence\|octave-equivalent]] to [[28/27\|27/28]]–[[9/8]]–[[21/16]]–3/2. This chord resolves to [[4:5:6]] on the tonic by leading the 27/28 up by [[28/27]] to [[1/1]], and the 21/16 down by [[21/20]] to 5/4. 28/27 is often considered a better interval for voice leading than [[16/15]] due to its size of 62.96 [[cent]]s, which is much closer to the optimum of around 70 cents<ref>Secor, George. "The 17-tone puzzle — and the Neo-medieval Key That Unlocks It" Xenharmonikôn 18, 2006. http://anaphoria.com/Secor17puzzle.pdf</ref> than 16/15, which is 111.73 cents.

	== See also ==		== See also ==

TallKite at 00:08, 11 March 2026

2026-03-11T00:08:58Z

← Older revision		Revision as of 00:08, 11 March 2026
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	{{Infobox chord\|ColorName = r,z7 ~~or ru-zo7~~}}		{{Infobox chord\|ColorName = ru zo-7 or r,z7}}
	'''28:36:42:49''' is a septimal [[dominant seventh chord]]. This chord is similar to the harmonic seventh chord [[4:5:6:7]], except the major third is inflected up by [[36/35]] from [[5/4]] to [[9/7]]. This makes it stand out from the rest of the chord, and the [[49/36]] interval between the 9/7 and the [[7/4]] acts as a dissonance. This is in contrast to the [[5-limit]] [[20:25:30:36]] dominant seventh chord, which has the seventh inflected up by 36/35 from [[7/4]] to [[9/5]] compared to 4:5:6:7.		'''28:36:42:49''' is a septimal [[dominant seventh chord]]. This chord is similar to the harmonic seventh chord [[4:5:6:7]], except the major third is inflected up by [[36/35]] from [[5/4]] to [[9/7]]. This makes it stand out from the rest of the chord, and the [[49/36]] interval between the 9/7 and the [[7/4]] acts as a dissonance. This is in contrast to the [[5-limit]] [[20:25:30:36]] dominant seventh chord, which has the seventh inflected up by 36/35 from [[7/4]] to [[9/5]] compared to 4:5:6:7.

TallKite at 23:28, 10 March 2026

2026-03-10T23:28:00Z

← Older revision		Revision as of 23:28, 10 March 2026
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	{{Infobox chord\|ColorName = ~~rz7~~ or ru-zo7}}		{{Infobox chord\|ColorName = r,z7 or ru-zo7}}
	'''28:36:42:49''' is a septimal [[dominant seventh chord]]. This chord is similar to the harmonic seventh chord [[4:5:6:7]], except the major third is inflected up by [[36/35]] from [[5/4]] to [[9/7]]. This makes it stand out from the rest of the chord, and the [[49/36]] interval between the 9/7 and the [[7/4]] acts as a dissonance. This is in contrast to the [[5-limit]] [[20:25:30:36]] dominant seventh chord, which has the seventh inflected up by 36/35 from [[7/4]] to [[9/5]] compared to 4:5:6:7.		'''28:36:42:49''' is a septimal [[dominant seventh chord]]. This chord is similar to the harmonic seventh chord [[4:5:6:7]], except the major third is inflected up by [[36/35]] from [[5/4]] to [[9/7]]. This makes it stand out from the rest of the chord, and the [[49/36]] interval between the 9/7 and the [[7/4]] acts as a dissonance. This is in contrast to the [[5-limit]] [[20:25:30:36]] dominant seventh chord, which has the seventh inflected up by 36/35 from [[7/4]] to [[9/5]] compared to 4:5:6:7.

Overthink: note 49/36 acts as a dissonance rather than the 9/7 note itself

2026-01-29T05:50:16Z

note 49/36 acts as a dissonance rather than the 9/7 note itself

← Older revision		Revision as of 05:50, 29 January 2026
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	{{Infobox chord\|ColorName = rz7 or ru-zo7}}		{{Infobox chord\|ColorName = rz7 or ru-zo7}}
	'''28:36:42:49''' is a septimal [[dominant seventh chord]]. This chord is similar to the harmonic seventh chord [[4:5:6:7]], except the major third is inflected up by [[36/35]] from [[5/4]] to [[9/7]]. This makes it stand out ~~as a dissonance~~ from the rest of the chord. This is in contrast to the [[5-limit]] [[20:25:30:36]] dominant seventh chord, which has the seventh inflected up by 36/35 from [[7/4]] to [[9/5]] compared to 4:5:6:7.		'''28:36:42:49''' is a septimal [[dominant seventh chord]]. This chord is similar to the harmonic seventh chord [[4:5:6:7]], except the major third is inflected up by [[36/35]] from [[5/4]] to [[9/7]]. This makes it stand out from the rest of the chord, and the [[49/36]] interval between the 9/7 and the [[7/4]] acts as a dissonance. This is in contrast to the [[5-limit]] [[20:25:30:36]] dominant seventh chord, which has the seventh inflected up by 36/35 from [[7/4]] to [[9/5]] compared to 4:5:6:7.

	This chord occurs on the V of the [[5L 2s\|diatonic]] scale in [[superpyth]] temperament. Note that the ~~[[49/36]]~~ [[tritone]] represents [[15/11]] in undecimal superpyth, which reduces it to a [[15-odd-limit]] [[swetismic chords\|swetismic]] [[essentially tempered chord]].		This chord occurs on the V of the [[5L 2s\|diatonic]] scale in [[superpyth]] temperament. Note that the [[tritone]] represents [[15/11]] in undecimal superpyth, which reduces it to a [[15-odd-limit]] [[swetismic chords\|swetismic]] [[essentially tempered chord]].

	On the dominant, this chord is [[3/2]]–[[27/14]]–[[9/4]]–[[21/8]] above the tonic, which is [[octave equivalence\|octave-equivalent]] to [[28/27\|27/28]]–[[9/8]]–[[21/16]]–3/2. This chord resolves to [[4:5:6]] on the tonic by inflecting the 27/28 up by [[28/27]] to [[1/1]], and the 21/16 down by [[21/20]] to 5/4. 28/27 is often considered a better interval for voice leading than [[16/15]] due to its size of 62.96 [[cent]]s, which is much closer to the optimum of around 70 cents<ref>Secor, George. "The 17-tone puzzle — and the Neo-medieval Key That Unlocks It" Xenharmonikôn 18, 2006. http://anaphoria.com/Secor17puzzle.pdf</ref> than 16/15, which is 111.73 cents.		On the dominant, this chord is [[3/2]]–[[27/14]]–[[9/4]]–[[21/8]] above the tonic, which is [[octave equivalence\|octave-equivalent]] to [[28/27\|27/28]]–[[9/8]]–[[21/16]]–3/2. This chord resolves to [[4:5:6]] on the tonic by inflecting the 27/28 up by [[28/27]] to [[1/1]], and the 21/16 down by [[21/20]] to 5/4. 28/27 is often considered a better interval for voice leading than [[16/15]] due to its size of 62.96 [[cent]]s, which is much closer to the optimum of around 70 cents<ref>Secor, George. "The 17-tone puzzle — and the Neo-medieval Key That Unlocks It" Xenharmonikôn 18, 2006. http://anaphoria.com/Secor17puzzle.pdf</ref> than 16/15, which is 111.73 cents.

Overthink: make this clearer

2026-01-26T04:07:33Z

make this clearer

← Older revision		Revision as of 04:07, 26 January 2026
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	This chord occurs on the V of the [[5L 2s\|diatonic]] scale in [[superpyth]] temperament. Note that the [[49/36]] [[tritone]] represents [[15/11]] in undecimal superpyth, which reduces it to a [[15-odd-limit]] [[swetismic chords\|swetismic]] [[essentially tempered chord]].		This chord occurs on the V of the [[5L 2s\|diatonic]] scale in [[superpyth]] temperament. Note that the [[49/36]] [[tritone]] represents [[15/11]] in undecimal superpyth, which reduces it to a [[15-odd-limit]] [[swetismic chords\|swetismic]] [[essentially tempered chord]].

	On the dominant, this chord is [[3/2]]–[[27/14]]–[[9/4]]–[[21/8]] above the tonic, which is [[octave equivalence\|octave-equivalent]] to [[28/27\|27/28]]–[[9/8]]–[[21/16]]–3/2. This chord resolves to [[4:5:6]] on the tonic by inflecting the 27/28 up by [[28/27]], and the 21/16 down by [[21/20]]. 28/27 is often considered a better interval for voice leading than [[16/15]] due to its size of 62.96 [[cent]]s, which is much closer to the optimum of around 70 cents<ref>Secor, George. "The 17-tone puzzle — and the Neo-medieval Key That Unlocks It" Xenharmonikôn 18, 2006. http://anaphoria.com/Secor17puzzle.pdf</ref> than 16/15, which is 111.73 cents.		On the dominant, this chord is [[3/2]]–[[27/14]]–[[9/4]]–[[21/8]] above the tonic, which is [[octave equivalence\|octave-equivalent]] to [[28/27\|27/28]]–[[9/8]]–[[21/16]]–3/2. This chord resolves to [[4:5:6]] on the tonic by inflecting the 27/28 up by [[28/27]] to [[1/1]], and the 21/16 down by [[21/20]] to 5/4. 28/27 is often considered a better interval for voice leading than [[16/15]] due to its size of 62.96 [[cent]]s, which is much closer to the optimum of around 70 cents<ref>Secor, George. "The 17-tone puzzle — and the Neo-medieval Key That Unlocks It" Xenharmonikôn 18, 2006. http://anaphoria.com/Secor17puzzle.pdf</ref> than 16/15, which is 111.73 cents.

	== See also ==		== See also ==

Overthink: fix ref again

2025-12-27T13:48:16Z

fix ref again

← Older revision		Revision as of 13:48, 27 December 2025
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	This chord occurs on the V of the [[5L 2s\|diatonic]] scale in [[superpyth]] temperament. Note that the [[49/36]] [[tritone]] represents [[15/11]] in undecimal superpyth, which reduces it to a [[15-odd-limit]] [[swetismic chords\|swetismic]] [[essentially tempered chord]].		This chord occurs on the V of the [[5L 2s\|diatonic]] scale in [[superpyth]] temperament. Note that the [[49/36]] [[tritone]] represents [[15/11]] in undecimal superpyth, which reduces it to a [[15-odd-limit]] [[swetismic chords\|swetismic]] [[essentially tempered chord]].

	On the dominant, this chord is [[3/2]]–[[27/14]]–[[9/4]]–[[21/8]] above the tonic, which is [[octave equivalence\|octave-equivalent]] to [[28/27\|27/28]]–[[9/8]]–[[21/16]]–3/2. This chord resolves to [[4:5:6]] on the tonic by inflecting the 27/28 up by [[28/27]], and the 21/16 down by [[21/20]]. 28/27 is often considered a better interval for voice leading than [[16/15]] due to its size of 62.96 [[cent]]s, which is much closer to the optimum of around 70 cents<ref>http://anaphoria.com/Secor17puzzle.pdf ~~George Secor's 17-tone puzzle~~</ref> than 16/15, which is 111.73 cents.		On the dominant, this chord is [[3/2]]–[[27/14]]–[[9/4]]–[[21/8]] above the tonic, which is [[octave equivalence\|octave-equivalent]] to [[28/27\|27/28]]–[[9/8]]–[[21/16]]–3/2. This chord resolves to [[4:5:6]] on the tonic by inflecting the 27/28 up by [[28/27]], and the 21/16 down by [[21/20]]. 28/27 is often considered a better interval for voice leading than [[16/15]] due to its size of 62.96 [[cent]]s, which is much closer to the optimum of around 70 cents<ref>Secor, George. "The 17-tone puzzle — and the Neo-medieval Key That Unlocks It" Xenharmonikôn 18, 2006. http://anaphoria.com/Secor17puzzle.pdf</ref> than 16/15, which is 111.73 cents.

	== See also ==		== See also ==

Overthink: fix reference

2025-12-27T13:41:07Z

fix reference

← Older revision		Revision as of 13:41, 27 December 2025
Line 4:		Line 4:
	This chord occurs on the V of the [[5L 2s\|diatonic]] scale in [[superpyth]] temperament. Note that the [[49/36]] [[tritone]] represents [[15/11]] in undecimal superpyth, which reduces it to a [[15-odd-limit]] [[swetismic chords\|swetismic]] [[essentially tempered chord]].		This chord occurs on the V of the [[5L 2s\|diatonic]] scale in [[superpyth]] temperament. Note that the [[49/36]] [[tritone]] represents [[15/11]] in undecimal superpyth, which reduces it to a [[15-odd-limit]] [[swetismic chords\|swetismic]] [[essentially tempered chord]].

	On the dominant, this chord is [[3/2]]–[[27/14]]–[[9/4]]–[[21/8]] above the tonic, which is [[octave equivalence\|octave-equivalent]] to [[28/27\|27/28]]–[[9/8]]–[[21/16]]–3/2. This chord resolves to [[4:5:6]] on the tonic by inflecting the 27/28 up by [[28/27]], and the 21/16 down by [[21/20]]. 28/27 is often considered a better interval for voice leading than [[16/15]] due to its size of 62.96 [[cent]]s, which is much closer to the optimum of around 70 cents<ref>~~Erlich, Paul. "Tuning, Tonality and 22-Tone Temperament." Xenharmonicon 17, 1998. [~~http://~~sethares~~.~~engr.wisc.edu~~/~~paperspdf/Erlich-22~~.pdf ~~http://sethares.engr.wisc.edu/paperspdf/Erlich~~-~~22.pdf]~~</ref> than 16/15, which is 111.73 cents.		On the dominant, this chord is [[3/2]]–[[27/14]]–[[9/4]]–[[21/8]] above the tonic, which is [[octave equivalence\|octave-equivalent]] to [[28/27\|27/28]]–[[9/8]]–[[21/16]]–3/2. This chord resolves to [[4:5:6]] on the tonic by inflecting the 27/28 up by [[28/27]], and the 21/16 down by [[21/20]]. 28/27 is often considered a better interval for voice leading than [[16/15]] due to its size of 62.96 [[cent]]s, which is much closer to the optimum of around 70 cents<ref>http://anaphoria.com/Secor17puzzle.pdf George Secor's 17-tone puzzle</ref> than 16/15, which is 111.73 cents.

	== See also ==		== See also ==

Overthink: + reference

2025-12-27T06:42:34Z

+ reference

← Older revision		Revision as of 06:42, 27 December 2025
Line 4:		Line 4:
	This chord occurs on the V of the [[5L 2s\|diatonic]] scale in [[superpyth]] temperament. Note that the [[49/36]] [[tritone]] represents [[15/11]] in undecimal superpyth, which reduces it to a [[15-odd-limit]] [[swetismic chords\|swetismic]] [[essentially tempered chord]].		This chord occurs on the V of the [[5L 2s\|diatonic]] scale in [[superpyth]] temperament. Note that the [[49/36]] [[tritone]] represents [[15/11]] in undecimal superpyth, which reduces it to a [[15-odd-limit]] [[swetismic chords\|swetismic]] [[essentially tempered chord]].

	On the dominant, this chord is [[3/2]]–[[27/14]]–[[9/4]]–[[21/8]] above the tonic, which is [[octave equivalence\|octave-equivalent]] to [[28/27\|27/28]]–[[9/8]]–[[21/16]]–3/2. This chord resolves to [[4:5:6]] on the tonic by inflecting the 27/28 up by [[28/27]], and the 21/16 down by [[21/20]]. 28/27 is often considered a better interval for voice leading than [[16/15]], due to its size of 62.96 [[cent]]s, which is much closer to the optimum of around 70 cents than 16/15, which is 111.73 cents.		On the dominant, this chord is [[3/2]]–[[27/14]]–[[9/4]]–[[21/8]] above the tonic, which is [[octave equivalence\|octave-equivalent]] to [[28/27\|27/28]]–[[9/8]]–[[21/16]]–3/2. This chord resolves to [[4:5:6]] on the tonic by inflecting the 27/28 up by [[28/27]], and the 21/16 down by [[21/20]]. 28/27 is often considered a better interval for voice leading than [[16/15]] due to its size of 62.96 [[cent]]s, which is much closer to the optimum of around 70 cents<ref>Erlich, Paul. "Tuning, Tonality and 22-Tone Temperament." Xenharmonicon 17, 1998. [http://sethares.engr.wisc.edu/paperspdf/Erlich-22.pdf http://sethares.engr.wisc.edu/paperspdf/Erlich-22.pdf]</ref> than 16/15, which is 111.73 cents.

	== See also ==		== See also ==
	* [[14:18:21]] - a subchord of 28:36:42:49		* [[14:18:21]] - a subchord of 28:36:42:49
	* [[4:6:7]] - another subchord		* [[4:6:7]] - another subchord

			== References ==
			<references/>

Overthink: reword

2025-12-27T06:38:49Z

reword

← Older revision		Revision as of 06:38, 27 December 2025
Line 2:		Line 2:
	'''28:36:42:49''' is a septimal [[dominant seventh chord]]. This chord is similar to the harmonic seventh chord [[4:5:6:7]], except the major third is inflected up by [[36/35]] from [[5/4]] to [[9/7]]. This makes it stand out as a dissonance from the rest of the chord. This is in contrast to the [[5-limit]] [[20:25:30:36]] dominant seventh chord, which has the seventh inflected up by 36/35 from [[7/4]] to [[9/5]] compared to 4:5:6:7.		'''28:36:42:49''' is a septimal [[dominant seventh chord]]. This chord is similar to the harmonic seventh chord [[4:5:6:7]], except the major third is inflected up by [[36/35]] from [[5/4]] to [[9/7]]. This makes it stand out as a dissonance from the rest of the chord. This is in contrast to the [[5-limit]] [[20:25:30:36]] dominant seventh chord, which has the seventh inflected up by 36/35 from [[7/4]] to [[9/5]] compared to 4:5:6:7.

	This chord occurs on the V of the [[5L 2s\|diatonic]] scale in [[superpyth]] temperament. ~~The~~ [[49/36]] [[tritone]] represents [[15/11]] in undecimal superpyth~~, however~~, which reduces it to a [[15-odd-limit]] [[swetismic chords\|swetismic]] [[essentially tempered chord]].		This chord occurs on the V of the [[5L 2s\|diatonic]] scale in [[superpyth]] temperament. Note that the [[49/36]] [[tritone]] represents [[15/11]] in undecimal superpyth, which reduces it to a [[15-odd-limit]] [[swetismic chords\|swetismic]] [[essentially tempered chord]].

	On the dominant, this chord is [[3/2]]–[[27/14]]–[[9/4]]–[[21/8]] above the tonic, which is [[octave equivalence\|octave-equivalent]] to [[28/27\|27/28]]–[[9/8]]–[[21/16]]–3/2. This chord resolves to [[4:5:6]] on the tonic by inflecting the 27/28 up by [[28/27]], and the 21/16 down by [[21/20]]. 28/27 is often considered a better interval for voice leading than [[16/15]], due to its size of 62.96 [[cent]]s, which is much closer to the optimum of around 70 cents than 16/15, which is 111.73 cents.		On the dominant, this chord is [[3/2]]–[[27/14]]–[[9/4]]–[[21/8]] above the tonic, which is [[octave equivalence\|octave-equivalent]] to [[28/27\|27/28]]–[[9/8]]–[[21/16]]–3/2. This chord resolves to [[4:5:6]] on the tonic by inflecting the 27/28 up by [[28/27]], and the 21/16 down by [[21/20]]. 28/27 is often considered a better interval for voice leading than [[16/15]], due to its size of 62.96 [[cent]]s, which is much closer to the optimum of around 70 cents than 16/15, which is 111.73 cents.