Ambulatory: Difference between revisions
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* 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. | * 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] 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 == | == 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. The name "ambulatory" was suggested by [[User:Frostburn|Frostburn]] to more subtly reference the same thing. | ||
Revision as of 02:53, 31 August 2024
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 can be considered the 3/2.5/4.7/4 analog of 3.5.7 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 tunings, 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) (assuming an equivalence of 3/2) with the medium and small steps equated.
Etymology
The temperament was first documented by 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 Frostburn to more subtly reference the same thing.