Barium - Revision history

Lucius Chiaraviglio: /* Music */ Johann Pachelbel's ''Canon in D, P 37'': Add arrangement for bassoon and 3 oboes (2026)

2026-08-27T07:11:29Z

Music: Johann Pachelbel's ''Canon in D, P 37'': Add arrangement for bassoon and 3 oboes (2026)

← Older revision		Revision as of 07:11, 27 August 2026
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	; {{W\|Johann Pachelbel}}		; {{W\|Johann Pachelbel}}
	* ~~[https://www.youtube.com/shorts/zh-obmZNSJM~~ ''Canon in D, P 37''] (unknown date in range 1680 to 1706) — ~~arranged for Organ and~~ tuned into Adaptive Just Intonation, and rendered by [[Claudi Meneghin]] (2026)		* ''Canon in D, P 37'' (unknown date in range 1680 to 1706) — tuned into Adaptive Just Intonation and rendered by [[Claudi Meneghin]] (2026)
			** [https://www.youtube.com/shorts/zh-obmZNSJM Arranged for organ]
			** [https://www.youtube.com/shorts/EFaancQpYWY Arranged for 3 oboes and bassoon]

	[[Category:Barium\| ]] <!-- main article -->		[[Category:Barium\| ]] <!-- main article -->
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]

Lucius Chiaraviglio: /* Music */ Convert existing entry to Modern Renderings format; add Pachelbel's Canon in D, P37 (unknown date in range 1680 to 1706) — arranged for Organ and tuned into Adaptive Just Intonation, and rendered by Claudi Meneghin (2026)

2026-08-27T05:26:51Z

Music: Convert existing entry to Modern Renderings format; add Pachelbel's Canon in D, P37 (unknown date in range 1680 to 1706) — arranged for Organ and tuned into Adaptive Just Intonation, and rendered by Claudi Meneghin (2026)

← Older revision		Revision as of 05:26, 27 August 2026
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	== Music ==		== Music ==

	Although full gamuts for barium start at 224 notes per octave, it is possible to use what is effectively a subset of barium temperament of much smaller gamut to produce the good major thirds of quarter-comma meantone while still getting good fifths, although any stacking of fifths will rapidly increase the size of gamut needed.		Although full gamuts for barium start at 224 notes per octave, it is possible to use what is effectively a subset of barium temperament of much smaller gamut to produce the good major thirds of quarter-comma meantone while still getting good fifths (and perhaps more importantly good minor thirds), although any stacking of fifths will rapidly increase the size of gamut needed.

	* [https://www.youtube.com/watch?v=Hmjx4wvLG7Q ~~Uccellini -~~ «Aria Sopra La Bergamasca» (1642), arranged for Organ, tuned into Adaptive Just Intonation] rendered by [[Claudi Meneghin]] (~~2024~~)		=== Modern renderings ===
			; {{W\|Marco Uccellini}}
			* [https://www.youtube.com/watch?v=Hmjx4wvLG7Q ''«Aria Sopra La Bergamasca»''] (1642) — arranged for Organ and tuned into Adaptive Just Intonation, and rendered by [[Claudi Meneghin]] (2024)

			; {{W\|Johann Pachelbel}}
			* [https://www.youtube.com/shorts/zh-obmZNSJM ''Canon in D, P 37''] (unknown date in range 1680 to 1706) — arranged for Organ and tuned into Adaptive Just Intonation, and rendered by [[Claudi Meneghin]] (2026)

	[[Category:Barium\| ]] <!-- main article -->		[[Category:Barium\| ]] <!-- main article -->
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]

Eliora: /* Theory */

2025-08-22T22:41:52Z

Theory

← Older revision		Revision as of 22:41, 22 August 2025
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	For technical data see: [[56th-octave temperaments#Barium]]		For technical data see: [[56th-octave temperaments#Barium]]
	== Theory ==		== Theory ==
	An octave is equal to <math>\frac{1}{\~~log~~{2}{\frac{81}{80}}} \approx 55.79763</math> syntonic commas, which when rounded to the closest integer yields 56. The associated comma in the 5-limit is {{monzo\|-225 224 -56}}, and therefore is tempered if and only if the EDO divides 56. The comma is about 4 cents wide, but since each 81/80 is flattened by only about 0.07 cents as a consequence, barium is a very precise microtemperament.		An octave is equal to <math>\frac{1}{\log_{2}{\frac{81}{80}}} \approx 55.79763</math> syntonic commas, which when rounded to the closest integer yields 56. The associated comma in the 5-limit is {{monzo\|-225 224 -56}}, and therefore is tempered if and only if the EDO divides 56. The comma is about 4 cents wide, but since each 81/80 is flattened by only about 0.07 cents as a consequence, barium is a very precise microtemperament.

	Because the period is set to 81/80, interval stacking scheme works the same way as in [[meantone]], with the only difference being that the resulting intervals are represented in different 56ths of the octave. When the interval 3/2 is stacked 4 times, it also mirrors the pattern in every 1/56th of the octave, reaching [[5/4]] in 4 steps just as meantone would.		Because the period is set to 81/80, interval stacking scheme works the same way as in [[meantone]], with the only difference being that the resulting intervals are represented in different 56ths of the octave. When the interval 3/2 is stacked 4 times, it also mirrors the pattern in every 1/56th of the octave, reaching [[5/4]] in 4 steps just as meantone would.

FloraC: - parent category

2025-04-28T13:47:38Z

- parent category

← Older revision		Revision as of 13:47, 28 April 2025
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	* [https://www.youtube.com/watch?v=Hmjx4wvLG7Q Uccellini - «Aria Sopra La Bergamasca» (1642), arranged for Organ, tuned into Adaptive Just Intonation] rendered by [[Claudi Meneghin]] (2024)		* [https://www.youtube.com/watch?v=Hmjx4wvLG7Q Uccellini - «Aria Sopra La Bergamasca» (1642), arranged for Organ, tuned into Adaptive Just Intonation] rendered by [[Claudi Meneghin]] (2024)

	[[Category:~~Temperaments~~]]		[[Category:Barium\| ]] <!-- main article -->
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]

Lériendil at 22:59, 19 April 2025

2025-04-19T22:59:31Z

← Older revision		Revision as of 22:59, 19 April 2025
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	Barium in the 7-limit also tempers out the [[akjaysma]], meaning that 40 periods are set to [[105/64]].		Barium in the 7-limit also tempers out the [[akjaysma]], meaning that 40 periods are set to [[105/64]].

	~~[[Category:Temperaments]]~~
	~~[[Category:Rank 2]]~~

	== Music ==		== Music ==
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	* [https://www.youtube.com/watch?v=Hmjx4wvLG7Q Uccellini - «Aria Sopra La Bergamasca» (1642), arranged for Organ, tuned into Adaptive Just Intonation] rendered by [[Claudi Meneghin]] (2024)		* [https://www.youtube.com/watch?v=Hmjx4wvLG7Q Uccellini - «Aria Sopra La Bergamasca» (1642), arranged for Organ, tuned into Adaptive Just Intonation] rendered by [[Claudi Meneghin]] (2024)

			[[Category:Temperaments]]
			[[Category:Rank-2 temperaments]]

BudjarnLambeth: added links

2025-04-13T10:53:33Z

added links

← Older revision		Revision as of 10:53, 13 April 2025
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	'''Barium''' is a rank-2 temperament defined in the 5-limit by tempering out the comma which sets 56 syntonic commas equal to the octave. Extensions exist in the 7-limit and the 11-limit. It is named after the 56th chemical element.		'''Barium''' is a [[rank-2 temperament]] defined in the [[5-limit]] by [[tempering out]] the comma which sets 56 syntonic commas equal to the octave. Extensions exist in the 7-limit and the 11-limit. It is named after the 56th chemical element.

	For technical data see: [[56th-octave temperaments#Barium]]		For technical data see: [[56th-octave temperaments#Barium]]

Lucius Chiaraviglio: Add section about and link to musical demonstration

2024-10-23T20:31:06Z

Add section about and link to musical demonstration

← Older revision		Revision as of 20:31, 23 October 2024
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	[[Category:Temperaments]]		[[Category:Temperaments]]
	[[Category:Rank 2]]		[[Category:Rank 2]]

			== Music ==

			Although full gamuts for barium start at 224 notes per octave, it is possible to use what is effectively a subset of barium temperament of much smaller gamut to produce the good major thirds of quarter-comma meantone while still getting good fifths, although any stacking of fifths will rapidly increase the size of gamut needed.

			* [https://www.youtube.com/watch?v=Hmjx4wvLG7Q Uccellini - «Aria Sopra La Bergamasca» (1642), arranged for Organ, tuned into Adaptive Just Intonation] rendered by [[Claudi Meneghin]] (2024)

Eliora at 14:17, 12 July 2023

2023-07-12T14:17:55Z

← Older revision		Revision as of 14:17, 12 July 2023
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	'''Barium''' is a rank-2 temperament defined in the 5-limit by tempering out the comma which sets 56 syntonic commas equal to the octave. Extensions exist in the 7-limit and the 11-limit. It is named after the 56th chemical element.		'''Barium''' is a rank-2 temperament defined in the 5-limit by tempering out the comma which sets 56 syntonic commas equal to the octave. Extensions exist in the 7-limit and the 11-limit. It is named after the 56th chemical element.

	For technical data see: [[~~Fractional~~-octave temperaments#Barium]]		For technical data see: [[56th-octave temperaments#Barium]]
	== Theory ==		== Theory ==
	An octave is equal to <math>\frac{1}{\log{2}{\frac{81}{80}}} \approx 55.79763</math> syntonic commas, which when rounded to the closest integer yields 56. The associated comma in the 5-limit is {{monzo\|-225 224 -56}}, and therefore is tempered if and only if the EDO divides 56. The comma is about 4 cents wide, but since each 81/80 is flattened by only about 0.07 cents as a consequence, barium is a very precise microtemperament.		An octave is equal to <math>\frac{1}{\log{2}{\frac{81}{80}}} \approx 55.79763</math> syntonic commas, which when rounded to the closest integer yields 56. The associated comma in the 5-limit is {{monzo\|-225 224 -56}}, and therefore is tempered if and only if the EDO divides 56. The comma is about 4 cents wide, but since each 81/80 is flattened by only about 0.07 cents as a consequence, barium is a very precise microtemperament.

Eliora: /* Theory */

2023-01-03T16:47:51Z

Theory

← Older revision		Revision as of 16:47, 3 January 2023
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	For technical data see: [[Fractional-octave temperaments#Barium]]		For technical data see: [[Fractional-octave temperaments#Barium]]
	== Theory ==		== Theory ==
	An octave is equal to ~~about~~ <math>\frac{1}{\log{2}{\frac{81}{80}}} = 55.79763</math> syntonic commas, which when rounded to the closest integer yields 56. The associated comma in the 5-limit is {{monzo\|-225 224 -56}} ~~(see infobox on~~ the ~~right)~~. The comma is about 4 cents wide, but since each 81/80 is flattened by only about 0.07 cents as a consequence, barium is a very precise microtemperament.		An octave is equal to <math>\frac{1}{\log{2}{\frac{81}{80}}} \approx 55.79763</math> syntonic commas, which when rounded to the closest integer yields 56. The associated comma in the 5-limit is {{monzo\|-225 224 -56}}, and therefore is tempered if and only if the EDO divides 56. The comma is about 4 cents wide, but since each 81/80 is flattened by only about 0.07 cents as a consequence, barium is a very precise microtemperament.

	Because the period is set to 81/80, interval stacking scheme works the same way as in [[meantone]], with the only difference being that the resulting intervals are represented in different 56ths of the octave. When the interval 3/2 is stacked 4 times, it also mirrors the pattern in every 1/56th of the octave, reaching [[5/4]] in 4 steps just as meantone would.		Because the period is set to 81/80, interval stacking scheme works the same way as in [[meantone]], with the only difference being that the resulting intervals are represented in different 56ths of the octave. When the interval 3/2 is stacked 4 times, it also mirrors the pattern in every 1/56th of the octave, reaching [[5/4]] in 4 steps just as meantone would.

Eliora: Removing infobox interval because the template automatically adds categories.

2023-01-03T16:46:37Z

Removing infobox interval because the template automatically adds categories.

← Older revision		Revision as of 16:46, 3 January 2023
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	For technical data see: [[Fractional-octave temperaments#Barium]]		For technical data see: [[Fractional-octave temperaments#Barium]]
	== Theory ==		== Theory ==
	~~{{Infobox Interval\|Monzo=-225 224 -56\|Name=barium comma\|Comma=yes}}~~
	An octave is equal to about <math>\frac{1}{\log{2}{\frac{81}{80}}} = 55.79763</math> syntonic commas, which when rounded to the closest integer yields 56. The associated comma in the 5-limit is {{monzo\|-225 224 -56}} (see infobox on the right). The comma is about 4 cents wide, but since each 81/80 is flattened by only about 0.07 cents as a consequence, barium is a very precise microtemperament.		An octave is equal to about <math>\frac{1}{\log{2}{\frac{81}{80}}} = 55.79763</math> syntonic commas, which when rounded to the closest integer yields 56. The associated comma in the 5-limit is {{monzo\|-225 224 -56}} (see infobox on the right). The comma is about 4 cents wide, but since each 81/80 is flattened by only about 0.07 cents as a consequence, barium is a very precise microtemperament.