Garibaldi: Difference between revisions

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 The '''garibaldi temperament''' is a 7-limit (and higher) temperament of the [[Schismatic family #Garibaldi|schismatic family]]. It is an extension of [[helmholtz]] temperament beyond the 5-limit but with the same simple chain-of-fifths structure (so that standard notation may be used). As in helmholtz temperament, [[5/4]] is mapped to the diminished fourth (e.g. A-Db), and the new mapping specific to garibaldi is that [[7/4]] is mapped to the double diminished octave (e.g. A-Abb). This makes garibaldi a [[Marvel temperaments|marvel temperament]].
+== Interval chain ==
+In the following table, prime harmonics are in '''bold'''.
+{| class="wikitable center-1 right-2"
+! #
+! Cents*
+! Approximate Ratios
+|-
+| 0
+| 0.0
+| 1/1
+|-
+| 1
+| 702.1
+| '''3/2'''
+|-
+| 2
+| 204.2
+| 9/8
+|-
+| 3
+| 906.3
+| 22/13, 27/16
+|-
+| 4
+| 408.5
+| 33/26, 63/50
+|-
+| 5
+| 1110.6
+| 40/21
+|-
+| 6
+| 612.7
+| 10/7
+|-
+| 7
+| 114.8
+| 15/14, 16/15
+|-
+| 8
+| 816.9
+| '''8/5'''
+|-
+| 9
+| 319.0
+| 6/5
+|-
+| 10
+| 1021.1
+| 9/5
+|-
+| 11
+| 523.2
+| 27/20
+|-
+| 12
+| 25.4
+| 50/49, 64/63, 81/80
+|-
+| 13
+| 727.5
+| 32/21
+|-
+| 14
+| 229.6
+| '''8/7'''
+|-
+| 15
+| 931.7
+| 12/7
+|-
+| 16
+| 433.8
+| 9/7
+|-
+| 17
+| 1135.9
+| 27/14, 48/25
+|-
+| 18
+| 638.0
+| 13/9
+|-
+| 19
+| 140.1
+| 13/12
+|-
+| 20
+| 842.3
+| '''13/8'''
+|-
+| 21
+| 344.4
+| 11/9
+|-
+| 22
+| 1046.5
+| 11/6
+|-
+| 23
+| 548.6
+| '''11/8'''
+|-
+| 24
+| 50.7
+| 33/32, 36/35
+|-
+| 25
+| 752.8
+| 54/35
+|-
+| 26
+| 254.9
+| 81/70
+|-
+| 27
+| 957.0
+| 15/13
+|-
+| 28
+| 459.2
+| 13/10
+|-
+| 29
+| 1161.3
+| 39/20, 96/48
+|}
+<nowiki>*</nowiki> in 13-limit POTE tuning
 == Scales ==