Secor - Revision history

Squib at 13:27, 15 May 2026

2026-05-15T13:27:03Z

← Older revision		Revision as of 13:27, 15 May 2026
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	{{Wikipedia\|Secor (interval)}}		{{Wikipedia\|Secor (interval)}}
	The '''secor''' is a [[unit of interval size]] named after [[George Secor]]. ~~It's~~ original technical definition is [[19ed18/5\|(18/5)<sup>1/19</sup>]], or 116.716{{cent}}, the [[11-limit]] minimax [[generator]] for [[miracle]] [[temperament]], but it can be used for any interval of similar size that fulfils the requirements for Miracle and its [[extension]]s.		The '''secor''' is a [[unit of interval size]] named after [[George Secor]]. Its original technical definition is [[19ed18/5\|(18/5)<sup>1/19</sup>]], or 116.716{{cent}}, the [[11-limit]] minimax [[generator]] for [[miracle]] [[temperament]], but the name can be used for any interval of similar size that fulfils the requirements for Miracle and its [[extension]]s.

	The secor was first derived by George Secor in 1975, in his article "[http://www.anaphoria.com/secor.pdf A new look at the Partch Monophonic Fabric]", published in ''[[Xenharmonikôn]] 3'': "If the above keyboard is tuned so that each key plays 116.89 cents different in pitch from the one beside it, a temperament will result in which none of the 29 primary ratios within the 11-limit will be more than about 3.32 cents false." At this time, the interval was yet unnamed. The name "secor" was proposed in 2001 by [[Dave Keenan]], both in honor of Secor and as a contraction of "SECond, minOR"<ref>https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_27028#27062</ref>.		The secor was first derived by George Secor in 1975, in his article "[http://www.anaphoria.com/secor.pdf A new look at the Partch Monophonic Fabric]", published in ''[[Xenharmonikôn]] 3'': "If the above keyboard is tuned so that each key plays 116.89 cents different in pitch from the one beside it, a temperament will result in which none of the 29 primary ratios within the 11-limit will be more than about 3.32 cents false." At this time, the interval was yet unnamed. The name "secor" was proposed in 2001 by [[Dave Keenan]], both in honor of Secor and as a contraction of "SECond, minOR"<ref>https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_27028#27062</ref>.

BudjarnLambeth: Add links

2024-12-24T09:09:54Z

Add links

← Older revision		Revision as of 09:09, 24 December 2024
Line 1:		Line 1:
	{{Wikipedia\|Secor (interval)}}		{{Wikipedia\|Secor (interval)}}
	The '''secor''' is a [[unit of interval size]] named after [[George Secor]]. It's original technical definition is [[19ed18/5\|(18/5)<sup>1/19</sup>]], or 116.716{{cent}}, the [[11-limit]] minimax [[generator]] for [[miracle]] [[temperament]], but it can be used for any interval of similar size that fulfils the requirements for Miracle and its ~~extensions~~.		The '''secor''' is a [[unit of interval size]] named after [[George Secor]]. It's original technical definition is [[19ed18/5\|(18/5)<sup>1/19</sup>]], or 116.716{{cent}}, the [[11-limit]] minimax [[generator]] for [[miracle]] [[temperament]], but it can be used for any interval of similar size that fulfils the requirements for Miracle and its [[extension]]s.

	The secor was first derived by George Secor in 1975, in his article "[http://www.anaphoria.com/secor.pdf A new look at the Partch Monophonic Fabric]", published in Xenharmonikôn 3: "If the above keyboard is tuned so that each key plays 116.89 cents different in pitch from the one beside it, a temperament will result in which none of the 29 primary ratios within the 11-limit will be more than about 3.32 cents false." At this time, the interval was yet unnamed. The name "secor" was proposed in 2001 by [[Dave Keenan]], both in honor of Secor and as a contraction of "SECond, minOR"<ref>https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_27028#27062</ref>.		The secor was first derived by George Secor in 1975, in his article "[http://www.anaphoria.com/secor.pdf A new look at the Partch Monophonic Fabric]", published in ''[[Xenharmonikôn]] 3'': "If the above keyboard is tuned so that each key plays 116.89 cents different in pitch from the one beside it, a temperament will result in which none of the 29 primary ratios within the 11-limit will be more than about 3.32 cents false." At this time, the interval was yet unnamed. The name "secor" was proposed in 2001 by [[Dave Keenan]], both in honor of Secor and as a contraction of "SECond, minOR"<ref>https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_27028#27062</ref>.

	For more information, see: http://anaphoria.com/SecorMiracle.pdf		For more information, see: http://anaphoria.com/SecorMiracle.pdf
Line 9:		Line 9:
	[[File:Derivation of the secor.png\|thumb\|600px\|center\|A diagram taken from George Secor's article "The Miracle Temperament and Decimal Keyboard" which was published in Xenharmonikôn 18 (2006). This version includes minor revisions for clarity, done by Douglas Blumeyer on Dave Keenan's request.]]		[[File:Derivation of the secor.png\|thumb\|600px\|center\|A diagram taken from George Secor's article "The Miracle Temperament and Decimal Keyboard" which was published in Xenharmonikôn 18 (2006). This version includes minor revisions for clarity, done by Douglas Blumeyer on Dave Keenan's request.]]

	This diagram visually demonstrates how the secor is found as the interval that nearly-equally subdivides all six of the smallest odd ~~harmonics~~ — 1, 3, 5, 7, 9, and 11 — where the width of the error band is narrowest, thus minimizing the maximum error of any interval in the 11-odd-limit [[tonality diamond]].		This diagram visually demonstrates how the secor is found as the interval that nearly-equally subdivides all six of the smallest odd [[harmonic]]s — 1, 3, 5, 7, 9, and 11 — where the width of the error band is narrowest, thus minimizing the maximum error of any interval in the 11-odd-limit [[tonality diamond]].

	Note that the method here is not to minimize the ''absolute'' deviation from 0{{cent}} in each harmonic individually, but to minimize the ''relative'' difference between the errors of the harmonic with the greatest positive error and the harmonic with the greatest negative error. In other words, the method is not to minimize the maximum distance of the diagonal harmonic lines from the horizontal 0{{cent}} axis, but to minimize the width of the band between the highest harmonic line and the lowest harmonic line at any given vertical slice through the chart.		Note that the method here is not to minimize the ''absolute'' deviation from 0{{cent}} in each harmonic individually, but to minimize the ''relative'' difference between the errors of the harmonic with the greatest positive error and the harmonic with the greatest negative error. In other words, the method is not to minimize the maximum distance of the diagonal harmonic lines from the horizontal 0{{cent}} axis, but to minimize the width of the band between the highest harmonic line and the lowest harmonic line at any given vertical slice through the chart.
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	== See also ==		== See also ==
	* [[19ed18/5]] - equal-step nonoctave tuning based on the secor interval		* [[19ed18/5]] - equal-step [[nonoctave]] tuning based on the secor interval

	== References ==		== References ==

ArrowHead294: Shouldn't image captions not be this big?

2024-10-02T11:50:03Z

Shouldn't image captions not be this big?

← Older revision		Revision as of 11:50, 2 October 2024
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	For more information, see: http://anaphoria.com/SecorMiracle.pdf		For more information, see: http://anaphoria.com/SecorMiracle.pdf

	[[File:Derivation of the secor.png\|thumb\|600px\|A diagram taken from George Secor's article "The Miracle Temperament and Decimal Keyboard" which was published in Xenharmonikôn 18 (2006). This version includes minor revisions for clarity, done by Douglas Blumeyer on Dave Keenan's request. ~~<br><br>~~This diagram visually demonstrates how the secor is found as the interval that nearly-equally subdivides all six of the smallest odd harmonics — 1, 3, 5, 7, 9, and 11 — where the width of the error band is narrowest, thus minimizing the maximum error of any interval in the 11-odd-limit [[tonality diamond]]. ~~<br><br>~~Note that the method here is not to minimize the ''absolute'' deviation from 0{{cent}} in each harmonic individually, but to minimize the ''relative'' difference between the errors of the harmonic with the greatest positive error and the harmonic with the greatest negative error. In other words, the method is not to minimize the maximum distance of the diagonal harmonic lines from the horizontal 0{{cent}} axis, but to minimize the width of the band between the highest harmonic line and the lowest harmonic line at any given vertical slice through the chart. ~~<br><br>~~Interestingly, the case of the secor, both methods would happen to give the same result. This is because at the point where the difference in errors of the harmonic is least here, all errors are non-positive. So the odd harmonic with the most positive error is actually 1, with an error of 0{{cent}}, because it is purely tuned of course, and therefore its harmonic line is identical with the horizontal 0{{cent}} axis. And the odd harmonic with the most negative error is a tie between 5 and 9, both of which have an error of -3.323{{cent}}.]]
			[[File:Derivation of the secor.png\|thumb\|600px\|center\|A diagram taken from George Secor's article "The Miracle Temperament and Decimal Keyboard" which was published in Xenharmonikôn 18 (2006). This version includes minor revisions for clarity, done by Douglas Blumeyer on Dave Keenan's request.]]

			This diagram visually demonstrates how the secor is found as the interval that nearly-equally subdivides all six of the smallest odd harmonics — 1, 3, 5, 7, 9, and 11 — where the width of the error band is narrowest, thus minimizing the maximum error of any interval in the 11-odd-limit [[tonality diamond]].

			Note that the method here is not to minimize the ''absolute'' deviation from 0{{cent}} in each harmonic individually, but to minimize the ''relative'' difference between the errors of the harmonic with the greatest positive error and the harmonic with the greatest negative error. In other words, the method is not to minimize the maximum distance of the diagonal harmonic lines from the horizontal 0{{cent}} axis, but to minimize the width of the band between the highest harmonic line and the lowest harmonic line at any given vertical slice through the chart.

			Interestingly, the case of the secor, both methods would happen to give the same result. This is because at the point where the difference in errors of the harmonic is least here, all errors are non-positive. So the odd harmonic with the most positive error is actually 1, with an error of 0{{cent}}, because it is purely tuned of course, and therefore its harmonic line is identical with the horizontal 0{{cent}} axis. And the odd harmonic with the most negative error is a tie between 5 and 9, both of which have an error of -3.323{{cent}}.

	== See also ==		== See also ==
	* [[19ed18/5]] - equal-step nonoctave tuning based on the secor interval		* [[19ed18/5]] - equal-step nonoctave tuning based on the secor interval

	== References ==		== References ==
	<references/>		<references/>

Eliora at 23:04, 1 February 2024

2024-02-01T23:04:13Z

← Older revision		Revision as of 23:04, 1 February 2024
Line 1:		Line 1:
	{{Wikipedia\|Secor (interval)}}		{{Wikipedia\|Secor (interval)}}
	The '''secor''' is a [[unit of interval size]] named after [[George Secor]]. It's original technical definition is (18/5)<sup>1/19</sup>, or 116.716{{cent}}, the [[11-limit]] minimax [[generator]] for [[miracle]] [[temperament]], but it can be used for any interval of similar size that fulfils the requirements for Miracle and its extensions.		The '''secor''' is a [[unit of interval size]] named after [[George Secor]]. It's original technical definition is [[19ed18/5\|(18/5)<sup>1/19</sup>]], or 116.716{{cent}}, the [[11-limit]] minimax [[generator]] for [[miracle]] [[temperament]], but it can be used for any interval of similar size that fulfils the requirements for Miracle and its extensions.

	The secor was first derived by George Secor in 1975, in his article "[http://www.anaphoria.com/secor.pdf A new look at the Partch Monophonic Fabric]", published in Xenharmonikôn 3: "If the above keyboard is tuned so that each key plays 116.89 cents different in pitch from the one beside it, a temperament will result in which none of the 29 primary ratios within the 11-limit will be more than about 3.32 cents false." At this time, the interval was yet unnamed. The name "secor" was proposed in 2001 by [[Dave Keenan]], both in honor of Secor and as a contraction of "SECond, minOR"<ref>https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_27028#27062</ref>.		The secor was first derived by George Secor in 1975, in his article "[http://www.anaphoria.com/secor.pdf A new look at the Partch Monophonic Fabric]", published in Xenharmonikôn 3: "If the above keyboard is tuned so that each key plays 116.89 cents different in pitch from the one beside it, a temperament will result in which none of the 29 primary ratios within the 11-limit will be more than about 3.32 cents false." At this time, the interval was yet unnamed. The name "secor" was proposed in 2001 by [[Dave Keenan]], both in honor of Secor and as a contraction of "SECond, minOR"<ref>https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_27028#27062</ref>.
Line 7:		Line 7:

	[[File:Derivation of the secor.png\|thumb\|600px\|A diagram taken from George Secor's article "The Miracle Temperament and Decimal Keyboard" which was published in Xenharmonikôn 18 (2006). This version includes minor revisions for clarity, done by Douglas Blumeyer on Dave Keenan's request. <br><br>This diagram visually demonstrates how the secor is found as the interval that nearly-equally subdivides all six of the smallest odd harmonics — 1, 3, 5, 7, 9, and 11 — where the width of the error band is narrowest, thus minimizing the maximum error of any interval in the 11-odd-limit [[tonality diamond]]. <br><br>Note that the method here is not to minimize the ''absolute'' deviation from 0{{cent}} in each harmonic individually, but to minimize the ''relative'' difference between the errors of the harmonic with the greatest positive error and the harmonic with the greatest negative error. In other words, the method is not to minimize the maximum distance of the diagonal harmonic lines from the horizontal 0{{cent}} axis, but to minimize the width of the band between the highest harmonic line and the lowest harmonic line at any given vertical slice through the chart. <br><br>Interestingly, the case of the secor, both methods would happen to give the same result. This is because at the point where the difference in errors of the harmonic is least here, all errors are non-positive. So the odd harmonic with the most positive error is actually 1, with an error of 0{{cent}}, because it is purely tuned of course, and therefore its harmonic line is identical with the horizontal 0{{cent}} axis. And the odd harmonic with the most negative error is a tie between 5 and 9, both of which have an error of -3.323{{cent}}.]]		[[File:Derivation of the secor.png\|thumb\|600px\|A diagram taken from George Secor's article "The Miracle Temperament and Decimal Keyboard" which was published in Xenharmonikôn 18 (2006). This version includes minor revisions for clarity, done by Douglas Blumeyer on Dave Keenan's request. <br><br>This diagram visually demonstrates how the secor is found as the interval that nearly-equally subdivides all six of the smallest odd harmonics — 1, 3, 5, 7, 9, and 11 — where the width of the error band is narrowest, thus minimizing the maximum error of any interval in the 11-odd-limit [[tonality diamond]]. <br><br>Note that the method here is not to minimize the ''absolute'' deviation from 0{{cent}} in each harmonic individually, but to minimize the ''relative'' difference between the errors of the harmonic with the greatest positive error and the harmonic with the greatest negative error. In other words, the method is not to minimize the maximum distance of the diagonal harmonic lines from the horizontal 0{{cent}} axis, but to minimize the width of the band between the highest harmonic line and the lowest harmonic line at any given vertical slice through the chart. <br><br>Interestingly, the case of the secor, both methods would happen to give the same result. This is because at the point where the difference in errors of the harmonic is least here, all errors are non-positive. So the odd harmonic with the most positive error is actually 1, with an error of 0{{cent}}, because it is purely tuned of course, and therefore its harmonic line is identical with the horizontal 0{{cent}} axis. And the odd harmonic with the most negative error is a tie between 5 and 9, both of which have an error of -3.323{{cent}}.]]
			== See also ==
			* [[19ed18/5]] - equal-step nonoctave tuning based on the secor interval
	== References ==		== References ==
	<references/>		<references/>

FloraC: Recategorize

2023-11-26T11:24:09Z

Recategorize

← Older revision		Revision as of 11:24, 26 November 2023
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	[[Category:Tuning]]		[[Category:Tuning]]
	[[Category:Interval size ~~measure~~]]		[[Category:Interval size measures]]
	[[Category:Secor]]		[[Category:Secor]]
	[[Category:Regular temperament theory]]		[[Category:Regular temperament theory]]
	[[Category:Terms]]		[[Category:Terms]]
	[[Category:Math]]		[[Category:Math]]

Sintel: typo

2023-09-13T20:19:05Z

typo

← Older revision		Revision as of 20:19, 13 September 2023
Line 2:		Line 2:
	The '''secor''' is a [[unit of interval size]] named after [[George Secor]]. It's original technical definition is (18/5)<sup>1/19</sup>, or 116.716{{cent}}, the [[11-limit]] minimax [[generator]] for [[miracle]] [[temperament]], but it can be used for any interval of similar size that fulfils the requirements for Miracle and its extensions.		The '''secor''' is a [[unit of interval size]] named after [[George Secor]]. It's original technical definition is (18/5)<sup>1/19</sup>, or 116.716{{cent}}, the [[11-limit]] minimax [[generator]] for [[miracle]] [[temperament]], but it can be used for any interval of similar size that fulfils the requirements for Miracle and its extensions.

	The secor was first derived by George Secor in 1975, in his article "[http://www.anaphoria.com/secor.pdf A new look at the Partch ~~Monotphonic~~ Fabric]", published in Xenharmonikôn 3: "If the above keyboard is tuned so that each key plays 116.89 cents different in pitch from the one beside it, a temperament will result in which none of the 29 primary ratios within the 11-limit will be more than about 3.32 cents false." At this time, the interval was yet unnamed. The name "secor" was proposed in 2001 by [[Dave Keenan]], both in honor of Secor and as a contraction of "SECond, minOR"<ref>https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_27028#27062</ref>.		The secor was first derived by George Secor in 1975, in his article "[http://www.anaphoria.com/secor.pdf A new look at the Partch Monophonic Fabric]", published in Xenharmonikôn 3: "If the above keyboard is tuned so that each key plays 116.89 cents different in pitch from the one beside it, a temperament will result in which none of the 29 primary ratios within the 11-limit will be more than about 3.32 cents false." At this time, the interval was yet unnamed. The name "secor" was proposed in 2001 by [[Dave Keenan]], both in honor of Secor and as a contraction of "SECond, minOR"<ref>https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_27028#27062</ref>.

	For more information, see: http://anaphoria.com/SecorMiracle.pdf		For more information, see: http://anaphoria.com/SecorMiracle.pdf

Fredg999: Minor improvement to lead section

2023-08-22T04:36:09Z

Minor improvement to lead section

← Older revision		Revision as of 04:36, 22 August 2023
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	{{Wikipedia\|Secor (interval)}}		{{Wikipedia\|Secor (interval)}}
	'''~~Secor~~''' is an interval size ~~measure~~ named after [[George Secor]]. It's original technical definition is (18/5)<sup>1/19</sup>, or 116.716{{cent}}, the [[11-limit]] minimax [[generator]] for [[miracle]] [[temperament]], but it can be used for any interval of similar size that fulfils the requirements for Miracle and its extensions.		The '''secor''' is a [[unit of interval size]] named after [[George Secor]]. It's original technical definition is (18/5)<sup>1/19</sup>, or 116.716{{cent}}, the [[11-limit]] minimax [[generator]] for [[miracle]] [[temperament]], but it can be used for any interval of similar size that fulfils the requirements for Miracle and its extensions.

	The secor was first derived by George Secor in 1975, in his article "[http://www.anaphoria.com/secor.pdf A new look at the Partch Monotphonic Fabric]", published in Xenharmonikôn 3: "If the above keyboard is tuned so that each key plays 116.89 cents different in pitch from the one beside it, a temperament will result in which none of the 29 primary ratios within the 11-limit will be more than about 3.32 cents false." At this time, the interval was yet unnamed. The name "secor" was proposed in 2001 by [[Dave Keenan]], both in honor of Secor and as a contraction of "SECond, minOR"<ref>https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_27028#27062</ref>.		The secor was first derived by George Secor in 1975, in his article "[http://www.anaphoria.com/secor.pdf A new look at the Partch Monotphonic Fabric]", published in Xenharmonikôn 3: "If the above keyboard is tuned so that each key plays 116.89 cents different in pitch from the one beside it, a temperament will result in which none of the 29 primary ratios within the 11-limit will be more than about 3.32 cents false." At this time, the interval was yet unnamed. The name "secor" was proposed in 2001 by [[Dave Keenan]], both in honor of Secor and as a contraction of "SECond, minOR"<ref>https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_27028#27062</ref>.

Xenllium at 09:50, 29 April 2023

2023-04-29T09:50:01Z

← Older revision		Revision as of 09:50, 29 April 2023
Line 2:		Line 2:
	'''Secor''' is an interval size measure named after [[George Secor]]. It's original technical definition is (18/5)<sup>1/19</sup>, or 116.716{{cent}}, the [[11-limit]] minimax [[generator]] for [[miracle]] [[temperament]], but it can be used for any interval of similar size that fulfils the requirements for Miracle and its extensions.		'''Secor''' is an interval size measure named after [[George Secor]]. It's original technical definition is (18/5)<sup>1/19</sup>, or 116.716{{cent}}, the [[11-limit]] minimax [[generator]] for [[miracle]] [[temperament]], but it can be used for any interval of similar size that fulfils the requirements for Miracle and its extensions.

	The secor was first derived by George Secor in 1975, in his article "[http://www.anaphoria.com/secor.pdf A new look at the Partch Monotphonic Fabric]", published in Xenharmonikôn 3: "If the above keyboard is tuned so that each key plays 116.89 cents different in pitch from the one beside it, a temperament will result in which none of the 29 primary ratios within the 11-~~lmit~~ will be more than about 3.32 cents false." At this time, the interval was yet unnamed. The name "secor" was proposed in 2001 by [[Dave Keenan]], both in honor of Secor and as a contraction of "SECond, minOR"<ref>https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_27028#27062</ref>.		The secor was first derived by George Secor in 1975, in his article "[http://www.anaphoria.com/secor.pdf A new look at the Partch Monotphonic Fabric]", published in Xenharmonikôn 3: "If the above keyboard is tuned so that each key plays 116.89 cents different in pitch from the one beside it, a temperament will result in which none of the 29 primary ratios within the 11-limit will be more than about 3.32 cents false." At this time, the interval was yet unnamed. The name "secor" was proposed in 2001 by [[Dave Keenan]], both in honor of Secor and as a contraction of "SECond, minOR"<ref>https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_27028#27062</ref>.

	For more information, see: http://anaphoria.com/SecorMiracle.pdf		For more information, see: http://anaphoria.com/SecorMiracle.pdf

	[[File:Derivation of the secor.png\|thumb\|600px~~\|center~~\|A diagram taken from George Secor's article "The Miracle Temperament and Decimal Keyboard" which was published in Xenharmonikôn 18 (2006). This version includes minor revisions for clarity, done by Douglas Blumeyer on Dave Keenan's request.		[[File:Derivation of the secor.png\|thumb\|600px\|A diagram taken from George Secor's article "The Miracle Temperament and Decimal Keyboard" which was published in Xenharmonikôn 18 (2006). This version includes minor revisions for clarity, done by Douglas Blumeyer on Dave Keenan's request. <br><br>This diagram visually demonstrates how the secor is found as the interval that nearly-equally subdivides all six of the smallest odd harmonics — 1, 3, 5, 7, 9, and 11 — where the width of the error band is narrowest, thus minimizing the maximum error of any interval in the 11-odd-limit [[tonality diamond]]. <br><br>Note that the method here is not to minimize the ''absolute'' deviation from 0{{cent}} in each harmonic individually, but to minimize the ''relative'' difference between the errors of the harmonic with the greatest positive error and the harmonic with the greatest negative error. In other words, the method is not to minimize the maximum distance of the diagonal harmonic lines from the horizontal 0{{cent}} axis, but to minimize the width of the band between the highest harmonic line and the lowest harmonic line at any given vertical slice through the chart. <br><br>Interestingly, the case of the secor, both methods would happen to give the same result. This is because at the point where the difference in errors of the harmonic is least here, all errors are non-positive. So the odd harmonic with the most positive error is actually 1, with an error of 0{{cent}}, because it is purely tuned of course, and therefore its harmonic line is identical with the horizontal 0{{cent}} axis. And the odd harmonic with the most negative error is a tie between 5 and 9, both of which have an error of -3.323{{cent}}.]]
	<br><br>
	This diagram visually demonstrates how the secor is found as the interval that nearly-equally subdivides all six of the smallest odd harmonics — 1, 3, 5, 7, 9, and 11 — where the width of the error band is narrowest, thus minimizing the maximum error of any interval in the 11-odd-limit [[tonality diamond]].
	<br><br>
	Note that the method here is not to minimize the ''absolute'' deviation from 0{{cent}} in each harmonic individually, but to minimize the ''relative'' difference between the errors of the harmonic with the greatest positive error and the harmonic with the greatest negative error. In other words, the method is not to minimize the maximum distance of the diagonal harmonic lines from the horizontal 0{{cent}} axis, but to minimize the width of the band between the highest harmonic line and the lowest harmonic line at any given vertical slice through the chart.
	<br><br>
	Interestingly, the case of the secor, both methods would happen to give the same result. This is because at the point where the difference in errors of the harmonic is least here, all errors are non-positive. So the odd harmonic with the most positive error is actually 1, with an error of 0{{cent}}, because it is purely tuned of course, and therefore its harmonic line is identical with the horizontal 0{{cent}} axis. And the odd harmonic with the most negative error is a tie between 5 and 9, both of which have an error of -3.323{{cent}}.]]

	== References ==		== References ==

Fredg999: Added Wikipedia box, misc. edits

2022-03-31T02:39:23Z

Added Wikipedia box, misc. edits

← Older revision		Revision as of 02:39, 31 March 2022
Line 1:		Line 1:
	'''Secor''' is an interval size measure named after [[George Secor]]. It's original technical definition is (18/5)^(1/19), or 116.716 ~~cents~~, the [[11 limit]] [[minimax]] [[generator]] for [[~~Miracle~~]] [[temperament]], but it can be used for any interval of similar size that fulfils the requirements for Miracle and its extensions.		{{Wikipedia\|Secor (interval)}}
			'''Secor''' is an interval size measure named after [[George Secor]]. It's original technical definition is (18/5)<sup>1/19</sup>, or 116.716{{cent}}, the [[11-limit]] minimax [[generator]] for [[miracle]] [[temperament]], but it can be used for any interval of similar size that fulfils the requirements for Miracle and its extensions.

	The secor was first derived by George Secor in 1975, in his article "[http://www.anaphoria.com/secor.pdf A new look at the Partch Monotphonic Fabric]", published in Xenharmonikôn 3: "If the above keyboard is tuned so that each key plays 116.89 cents different in pitch from the one beside it, a temperament will result in which none of the 29 primary ratios within the 11-lmit will be more than about 3.32 cents false." At this time, the interval was yet unnamed. The name "secor" was proposed in 2001 by [[Dave Keenan]], both in honor of Secor and as a contraction of "SECond, minOR"<ref>https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_27028#27062</ref>.		The secor was first derived by George Secor in 1975, in his article "[http://www.anaphoria.com/secor.pdf A new look at the Partch Monotphonic Fabric]", published in Xenharmonikôn 3: "If the above keyboard is tuned so that each key plays 116.89 cents different in pitch from the one beside it, a temperament will result in which none of the 29 primary ratios within the 11-lmit will be more than about 3.32 cents false." At this time, the interval was yet unnamed. The name "secor" was proposed in 2001 by [[Dave Keenan]], both in honor of Secor and as a contraction of "SECond, minOR"<ref>https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_27028#27062</ref>.
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	This diagram visually demonstrates how the secor is found as the interval that nearly-equally subdivides all six of the smallest odd harmonics — 1, 3, 5, 7, 9, and 11 — where the width of the error band is narrowest, thus minimizing the maximum error of any interval in the 11-odd-limit [[tonality diamond]].		This diagram visually demonstrates how the secor is found as the interval that nearly-equally subdivides all six of the smallest odd harmonics — 1, 3, 5, 7, 9, and 11 — where the width of the error band is narrowest, thus minimizing the maximum error of any interval in the 11-odd-limit [[tonality diamond]].
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	Note that the method here is not to minimize the ''absolute'' deviation from 0¢ in each harmonic individually, but to minimize the ''relative'' difference between the errors of the harmonic with the greatest positive error and the harmonic with the greatest negative error. In other words, the method is not to minimize the maximum distance of the diagonal harmonic lines from the horizontal 0¢ axis, but to minimize the width of the band between the highest harmonic line and the lowest harmonic line at any given vertical slice through the chart.		Note that the method here is not to minimize the ''absolute'' deviation from 0{{cent}} in each harmonic individually, but to minimize the ''relative'' difference between the errors of the harmonic with the greatest positive error and the harmonic with the greatest negative error. In other words, the method is not to minimize the maximum distance of the diagonal harmonic lines from the horizontal 0{{cent}} axis, but to minimize the width of the band between the highest harmonic line and the lowest harmonic line at any given vertical slice through the chart.
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	Interestingly, the case of the secor, both methods would happen to give the same result. This is because at the point where the difference in errors of the harmonic is least here, all errors are non-positive. So the odd harmonic with the most positive error is actually 1, with an error of 0¢, because it is purely tuned of course, and therefore its harmonic line is identical with the horizontal 0¢ axis. And the odd harmonic with the most negative error is a tie between 5 and 9, both of which have an error of -3.~~323¢~~.]]		Interestingly, the case of the secor, both methods would happen to give the same result. This is because at the point where the difference in errors of the harmonic is least here, all errors are non-positive. So the odd harmonic with the most positive error is actually 1, with an error of 0{{cent}}, because it is purely tuned of course, and therefore its harmonic line is identical with the horizontal 0{{cent}} axis. And the odd harmonic with the most negative error is a tie between 5 and 9, both of which have an error of -3.323{{cent}}.]]

			== References ==
			<references/>

	[[Category:Tuning]]		[[Category:Tuning]]

Cmloegcmluin at 13:37, 25 December 2021

2021-12-25T13:37:21Z

← Older revision		Revision as of 13:37, 25 December 2021
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	[[Category:Interval size measure]]		[[Category:Interval size measure]]
	[[Category:Secor]]		[[Category:Secor]]
	~~[[Category:Temperament]]~~
	[[Category:Regular temperament theory]]		[[Category:Regular temperament theory]]
	~~[[Category:Theory]]~~
	[[Category:Terms]]		[[Category:Terms]]
	[[Category:Math]]		[[Category:Math]]