Secor: Difference between revisions

Line 1:

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

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.]]

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.

Line 16:

== 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 ==

@@ Line 1: / Line 1: @@
 {{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
@@ 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.]]
-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.
@@ Line 16: / Line 16: @@
 == 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 ==