The Jacobins: Difference between revisions

(3 intermediate revisions by 3 users not shown)

Line 1:

'''The Jacobins''' is a collection of microtemperaments of different ranks which all temper out the jacobin comma, [[6656/6655]].

Line 63:

Line 64:

Barton may be described as the 11 & 13 temperament in the 2.5.11.13 subgroup. It was named after [[Jacob Barton]] by [[Gene Ward Smith]] and [[Carl Lumma]] in 2006<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_14632.html Yahoo! Tuning Group | "father" variant?]</ref>.

Barton may be described as the 11 & 13 temperament in the 2.5.11.13 subgroup. It was named after [[Jacob Barton]] by [[Gene Ward Smith]] and [[Carl Lumma]] in 2006<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_14632.html Yahoo! Tuning Group | "father" variant?]</ref>. [[Scott Dakota]] rediscovered this same temperament in 2025 and named it "hem"{{idio}}.

[[Subgroup]]: 2.5.11.13

Line 187:

Line 188:

== Sextilimeans ==

Sextilimeans is like ~~sextilififths~~, but the fourth that is divided into 6 in ~~sextilififths~~ is tuned to a meantone fourth in the optimal tuning, or about 1/4.26-commma meantone. It should be noted, however, that this meantone fourth is not ~4/3 despite that the name may suggest so. In fact, the 3rd harmonic is not mapped in this temperament at all. It is described as the 229 & 1789 temperament.

Sextilimeans is like [[sextilifourths]], but the fourth that is divided into 6 in sextilifourths is tuned to a meantone fourth in the optimal tuning, or about 1/4.26-commma meantone. It should be noted, however, that this meantone fourth is not ~4/3 despite that the name may suggest so. In fact, the 3rd harmonic is not mapped in this temperament at all. It is described as the 229 & 1789 temperament.

[[Subgroup]]: 2.5.7.11.13

Line 227:

Line 228:

{{Optimal ET sequence|legend=1|1789, 2814, }} ...

== ~~Acrosextilififths~~ ==

== Acrosextilifourths ==

Discovered by [[Aura]] and defined as the 159 & 1619 temperament, with prefix acro- denoting the fact that it's a more precise version of ~~sextilififths~~, with fourth divided into 6 parts in 1619edo just as it is in 159edo.

Discovered by [[Aura]] and defined as the 159 & 1619 temperament, with prefix acro- denoting the fact that it's a more precise version of sextilifourths, with fourth divided into 6 parts in 1619edo just as it is in 159edo.

[[Subgroup]]: 2.3.5.7.11.13

@@ Line 1: / Line 1: @@
+{{Technical data page}}
 '''The Jacobins''' is a collection of microtemperaments of different ranks which all temper out the jacobin comma, [[6656/6655]].
@@ Line 63: / Line 64: @@
 {{See also| Chromatic pairs #Barton }}
-Barton may be described as the 11 &amp; 13 temperament in the 2.5.11.13 subgroup. It was named after [[Jacob Barton]] by [[Gene Ward Smith]] and [[Carl Lumma]] in 2006<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_14632.html Yahoo! Tuning Group | "father" variant?]</ref>.
+Barton may be described as the 11 &amp; 13 temperament in the 2.5.11.13 subgroup. It was named after [[Jacob Barton]] by [[Gene Ward Smith]] and [[Carl Lumma]] in 2006<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_14632.html Yahoo! Tuning Group | "father" variant?]</ref>. [[Scott Dakota]] rediscovered this same temperament in 2025 and named it "hem"{{idio}}.
 [[Subgroup]]: 2.5.11.13
@@ Line 187: / Line 188: @@
 == Sextilimeans ==
-Sextilimeans is like sextilififths, but the fourth that is divided into 6 in sextilififths is tuned to a meantone fourth in the optimal tuning, or about 1/4.26-commma meantone. It should be noted, however, that this meantone fourth is not ~4/3 despite that the name may suggest so. In fact, the 3rd harmonic is not mapped in this temperament at all. It is described as the 229 & 1789 temperament.
+Sextilimeans is like [[sextilifourths]], but the fourth that is divided into 6 in sextilifourths is tuned to a meantone fourth in the optimal tuning, or about 1/4.26-commma meantone. It should be noted, however, that this meantone fourth is not ~4/3 despite that the name may suggest so. In fact, the 3rd harmonic is not mapped in this temperament at all. It is described as the 229 & 1789 temperament.
 [[Subgroup]]: 2.5.7.11.13
@@ Line 227: / Line 228: @@
 {{Optimal ET sequence|legend=1|1789, 2814, }} ...
-== Acrosextilififths ==
+== Acrosextilifourths ==
-Discovered by [[Aura]] and defined as the 159 & 1619 temperament, with prefix acro- denoting the fact that it's a more precise version of sextilififths, with fourth divided into 6 parts in 1619edo just as it is in 159edo.
+Discovered by [[Aura]] and defined as the 159 & 1619 temperament, with prefix acro- denoting the fact that it's a more precise version of sextilifourths, with fourth divided into 6 parts in 1619edo just as it is in 159edo.
 [[Subgroup]]: 2.3.5.7.11.13