Diminished (temperament): Difference between revisions

Revision as of 12:45, 2 August 2024

Diminished is a rank-2 temperament that tempers out the diminished comma, 648/625, in the 5-limit, and 36/35 and 50/49 in the 7-limit. It has a 1/4-octave period and is generated by a ~3/2 perfect fifth. The main interest in this temperament is in its mos scales, featuring tetrawood (4L 4s) when properly tuned.

In the following table, odd harmonics 1–9 are in bold.

#	Period 0		Period 1		Period 2		Period 3
#	Cents*	Approx. Ratios	Cents*	Approx. Ratios	Cents*	Approx. Ratios	Cents*	Approx. Ratios
0	0.0	1/1	300.0	6/5, 7/6	600.0	7/5, 10/7	900.0	5/3, 12/7
1	92.0	15/14, 21/20, 25/24, 49/48	392.0	5/4, 9/7	692.0	3/2	992.0	7/4, 9/5
2	183.9	9/8	483.9	21/16	783.9	45/28, 63/40	1083.9	15/8

* in 7-limit CTE tuning

@@ Line 6: / Line 6: @@
 See [[Dimipent family #Diminished]] for technical data.
+== Interval chain ==
+In the following table, odd harmonics 1–9 are in '''bold'''.
+{| class="wikitable center-1 right-2 right-4 right-6 right-8"
+! rowspan="2" | #
+! colspan="2" | Period 0
+! colspan="2" | Period 1
+! colspan="2" | Period 2
+! colspan="2" | Period 3
+|-
+! Cents*
+! Approx. Ratios
+! Cents*
+! Approx. Ratios
+! Cents*
+! Approx. Ratios
+! Cents*
+! Approx. Ratios
+|-
+| 0
+| 0.0
+| '''1/1'''
+| 300.0
+| 6/5, 7/6
+| 600.0
+| 7/5, 10/7
+| 900.0
+| 5/3, 12/7
+|-
+| 1
+| 92.0
+| 15/14, 21/20, 25/24, 49/48
+| 392.0
+| '''5/4''', 9/7
+| 692.0
+| '''3/2'''
+| 992.0
+| '''7/4''', 9/5
+|-
+| 2
+| 183.9
+| '''9/8'''
+| 483.9
+| 21/16
+| 783.9
+| 45/28, 63/40
+| 1083.9
+| 15/8
+|}
+<nowiki>*</nowiki> in 7-limit CTE tuning
+== Scales ==
+* [[Diminished12]] – in [[44edo]] tuning
 == See also ==