Ambulatory: Difference between revisions

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''Ambulatory'' is a [[nonoctave]] [[rank-2 temperament]] repeating at [[3/2]] which is generated by a flat ~[[7/5]]. It [[tempers out]] the [[comma]] [[686/675]] in the 3/2.5/4.7/4 fractional [[subgroup]]. This implies a stack of 2 generators represents [[9/7]] fifth-reduced, and a stack of 3 generators represents [[6/5]] fifth-reduced.

'''Ambulatory''' is a [[nonoctave]] [[rank-2 temperament|rank-2]] [[regular temperament|temperament]] repeating at [[3/2]] which is generated by a flat ~[[7/5]]. It [[tempering out|tempers out]] the [[comma]] [[686/675]] in the 3/2.5/4.7/4 fractional [[subgroup]]. This implies a stack of 2 generators represents [[9/7]] fifth-reduced, and a stack of 3 generators represents [[6/5]] fifth-reduced.

Ambulatory can be considered the 3/2.5/4.7/4 analog of 3.5.7 [[Bohlen-Pierce-Stearns|BPS]] or 2.3.5 [[meantone]], using [[5:6:7]] as its fundamental consonant chord in the place of [[3:5:7]] or of [[4:5:6]]. Ambulatory is actually similar to meantone in several ways:

* They are both of low [[badness]].

* In most [[optimal tuning]]s, meantone tunes [[3/2]] flat and [[5/4]] slightly sharp~~. In mots [[optimal tuning]]s~~, ambulatory tunes [[7/5]] flat and [[6/5]] slightly sharp.

* In most [[optimal tuning]]s, meantone tunes [[3/2]] flat and [[5/4]] slightly sharp, while ambulatory tunes [[7/5]] flat and [[6/5]] slightly sharp.

* Meantone[7] has [[5/4]] and [[6/5]] share a scale degree. Ambulatory[5] has [[6/5]] and [[7/6]] share a scale degree.

* Meantone[7] is a tempering of the 7-note [[AGS]](5/4, 6/5) (Ptolemy's intense diatonic) with the large and medium steps equated. Ambulatory[5] is a tempering of the 5-note AGS(6/5, 7/6) with the medium and small steps equated.

* Meantone[7] is a tempering of the 7-note [[AGS]](5/4, 6/5) (Ptolemy's intense diatonic) with the large and medium steps equated. Ambulatory[5] is a tempering of the 5-note AGS(6/5, 7/6) (assuming an equivalence of 3/2) with the medium and small steps equated.

== Etymology ==

The temperament was first documented by [[User:CompactStar|CompactStar]] who originally proposed the name of "emergency", which refers to the North American emergency telephone number 911, because 9\[[11edf]] is a possible generator. ~~The~~ name "ambulatory" was suggested by [[User:Frostburn|Frostburn]] to more subtly reference the same thing.

The temperament was first documented by [[User:CompactStar|CompactStar]] who originally proposed the name of "emergency", which refers to the North American emergency telephone number 911, because 9\[[11edf]] is a possible generator. This was deemed as too dark so the name "ambulatory" was suggested by [[User:Frostburn|Frostburn]] to more subtly reference the same thing.

[[Category:Ambulatory| ]]

[[Category:Rank-2 temperaments]]

[[Category:Non-octave temperaments]]

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-''Ambulatory'' is a [[nonoctave]] [[rank-2 temperament]] repeating at [[3/2]] which is generated by a flat ~[[7/5]]. It [[tempers out]] the [[comma]] [[686/675]] in the 3/2.5/4.7/4 fractional [[subgroup]]. This implies a stack of 2 generators represents [[9/7]] fifth-reduced, and a stack of 3 generators represents [[6/5]] fifth-reduced.
+'''Ambulatory''' is a [[nonoctave]] [[rank-2 temperament|rank-2]] [[regular temperament|temperament]] repeating at [[3/2]] which is generated by a flat ~[[7/5]]. It [[tempering out|tempers out]] the [[comma]] [[686/675]] in the 3/2.5/4.7/4 fractional [[subgroup]]. This implies a stack of 2 generators represents [[9/7]] fifth-reduced, and a stack of 3 generators represents [[6/5]] fifth-reduced.
 Ambulatory can be considered the 3/2.5/4.7/4 analog of 3.5.7 [[Bohlen-Pierce-Stearns|BPS]] or 2.3.5 [[meantone]], using [[5:6:7]] as its fundamental consonant chord in the place of [[3:5:7]] or of [[4:5:6]]. Ambulatory is actually similar to meantone in several ways:
 * They are both of low [[badness]].
-* In most [[optimal tuning]]s, meantone tunes [[3/2]] flat and [[5/4]] slightly sharp. In mots [[optimal tuning]]s, ambulatory tunes [[7/5]] flat and [[6/5]] slightly sharp.
+* In most [[optimal tuning]]s, meantone tunes [[3/2]] flat and [[5/4]] slightly sharp, while ambulatory tunes [[7/5]] flat and [[6/5]] slightly sharp.
 * Meantone[7] has [[5/4]] and [[6/5]] share a scale degree. Ambulatory[5] has [[6/5]] and [[7/6]] share a scale degree.
-* Meantone[7] is a tempering of the 7-note [[AGS]](5/4, 6/5) (Ptolemy's intense diatonic) with the large and medium steps equated. Ambulatory[5] is a tempering of the 5-note AGS(6/5, 7/6) with the medium and small steps equated.
+* Meantone[7] is a tempering of the 7-note [[AGS]](5/4, 6/5) (Ptolemy's intense diatonic) with the large and medium steps equated. Ambulatory[5] is a tempering of the 5-note AGS(6/5, 7/6) (assuming an equivalence of 3/2) with the medium and small steps equated.
 == Etymology ==
-The temperament was first documented by [[User:CompactStar|CompactStar]] who originally proposed the name of "emergency", which refers to the North American  emergency telephone number 911, because 9\[[11edf]] is a possible generator. The name "ambulatory" was suggested by [[User:Frostburn|Frostburn]] to more subtly reference the same thing.
+The temperament was first documented by [[User:CompactStar|CompactStar]] who originally proposed the name of "emergency", which refers to the North American  emergency telephone number 911, because 9\[[11edf]] is a possible generator. This was deemed as too dark so the name "ambulatory" was suggested by [[User:Frostburn|Frostburn]] to more subtly reference the same thing.
+[[Category:Ambulatory| ]] <!-- main article -->
+[[Category:Rank-2 temperaments]]
+[[Category:Non-octave temperaments]]