2.3.7 subgroup: Difference between revisions

Line 27:

==== Semaphore ====

'''Semaphore''' temperament tempers out the comma [[49/48]] = S7 in the 2.3.7 subgroup, which equates [[8/7]] with [[7/6]], creating a single neutral semifourth. Similarly to [[dicot]], semaphore can be regarded as an exotemperament that elides fundamental distinctions within the subgroup (from the perspective of a pentatonic framework, this is equivalent to erasing the major-minor distinction as dicot does), though the comma involved is half the size of dicot's [[25/24]].

'''Semaphore''' temperament tempers out the comma [[49/48]] = S7 in the 2.3.7 subgroup, which equates [[8/7]] with [[7/6]], creating a single neutral semifourth which serves as the generator. Similarly to [[dicot]], semaphore can be regarded as an exotemperament that elides fundamental distinctions within the subgroup (from the perspective of a pentatonic framework, this is equivalent to erasing the major-minor distinction as dicot does), though the comma involved is half the size of dicot's [[25/24]].

The [[DKW theory|DKW]] (2.3.7) optimum tuning states ~3/2 is tuned to 696.230c (though most other optimizations tune this a few cents flatter); a chart of mistunings of simple intervals is below.

Line 40:

| 9/8 || 203.910 || 192.460 || -11.450

|-

| 8/7 || 231.174 || 251.885 || +20.711

| '''8/7''' || 231.174 || 251.885 || +20.711

|-

| 7/6 || 266.871 || 251.885 || -14.986

| '''7/6''' || 266.871 || 251.885 || -14.986

|-

| 9/7 || 435.084 || 444.345 || +9.261

@@ Line 27: / Line 27: @@
 ==== Semaphore ====
-'''Semaphore''' temperament tempers out the comma [[49/48]] = S7 in the 2.3.7 subgroup, which equates [[8/7]] with [[7/6]], creating a single neutral semifourth. Similarly to [[dicot]], semaphore can be regarded as an exotemperament that elides fundamental distinctions within the subgroup (from the perspective of a pentatonic framework, this is equivalent to erasing the major-minor distinction as dicot does), though the comma involved is half the size of dicot's [[25/24]].
+'''Semaphore''' temperament tempers out the comma [[49/48]] = S7 in the 2.3.7 subgroup, which equates [[8/7]] with [[7/6]], creating a single neutral semifourth which serves as the generator. Similarly to [[dicot]], semaphore can be regarded as an exotemperament that elides fundamental distinctions within the subgroup (from the perspective of a pentatonic framework, this is equivalent to erasing the major-minor distinction as dicot does), though the comma involved is half the size of dicot's [[25/24]].
 The [[DKW theory|DKW]] (2.3.7) optimum tuning states ~3/2 is tuned to 696.230c (though most other optimizations tune this a few cents flatter); a chart of mistunings of simple intervals is below.
@@ Line 40: / Line 40: @@
 | 9/8 || 203.910 || 192.460 || -11.450
 |-
-| 8/7 || 231.174 || 251.885 || +20.711
+| '''8/7''' || 231.174 || 251.885 || +20.711
 |-
-| 7/6 || 266.871 || 251.885 || -14.986
+| '''7/6''' || 266.871 || 251.885 || -14.986
 |-
 | 9/7 || 435.084 || 444.345 || +9.261