User:Unque/Barbershop Tuning Theory: Difference between revisions

(One intermediate revision by one other user not shown)

Line 29:

== Half-Diminished Seventh (and its inversions) ==

The Half-Diminished Seventh tetrad is officially considered by the Barbershop Harmony Society to be the second-most consonant chord (after the Barbershop Seventh, of course); in common practice 12-EDO, however, this chord is far from consonant, especially compared to other chords that may compete for that title. This difference in interpretation must be owed to conventions either in compositional use or in tuning - so, how do ~~choral~~ performers tend to sing Half-Diminished Seventh chords?

The Half-Diminished Seventh tetrad is officially considered by the Barbershop Harmony Society to be the second-most consonant chord (after the Barbershop Seventh, of course); in common practice 12-EDO, however, this chord is far from consonant, especially compared to other chords that may compete for that title. This difference in interpretation must be owed to conventions either in compositional use or in tuning - so, how do vocal performers tend to sing Half-Diminished Seventh chords?

The tuning of the Half-Diminished Seventh chord and its inversions are some of the most controversial in Barbershop music, especially due to differing preferences for "rooting" the chord on a specific interval. In general, chords tend to feel most rooted when their harmonic segment forms are simplest; for instance, the 8 in 6:7:8:10 sounds more like the root than the 6 does, because the simplest inversion is 4:5:6:7.

Line 35:

If one wishes to root the chord as a Half-Diminished Seventh, then inversions of 5:6:7:9 are the most common interpretation. If one instead wishes to root the chord as a Minor triad with an added Major Sixth, the chord is most commonly tuned as a standard 1/(6:5:4) Minor Triad with some type of Major Sixth (typically 5/3, or less commonly 12/7) added on top.

~~Finally, it~~ should be noted that the iiø7 chord is used as a dominant due to being the negative harmony variant of V7. Because of this, some performers prefer to treat this chord as an undertonal variant of the standard Barbershop Seventh.

It should additionally be noted that the iiø7 chord is used as a dominant due to being the negative harmony variant of V7. Because of this, some performers prefer to treat this chord as an undertonal variant of the standard Barbershop Seventh.

Finally, the half-diminished chord can be seen as a minor tetrad with a lowered fifth degree; this can yield 5:6:7:9 if we consider the 6/5 minor third, or 12:14:17:21 if we consider the 7/6 minor third.

{| class="wikitable"

|+Half-Diminished Tunings

Line 62:

Line 64:

|20/17, 6/5, 5/4, (17/15)

|1/(6:5:4) triad stacked on top of a 17:20 dyad. Most likely conceptualized as tempered tuning, not 17-limit JI.

|-

|12:14:17:21

|7/6, 17/12, 7/4

|7/6, 17/14, 21/17, (8/7)

|12:14:18:21 tetrad, with the fifth lowered. Most likely conceptualized as tempered tuning, not 17-limit JI.

|}

'''See also:''' [[5afdo]] and [[7ifdo]], the low-complexity JI scales from which several of these tunings are derived.

Line 197:

Line 204:

|5/4, 17/12, 7/4

|5/4, 17/15, 21/12, (8/7)

|17-limit ~~hald~~-diminished chord, but with the sixth raised.

|17-limit half-diminished chord, but with the sixth raised.

|-

|10:13:14:18

|13/10, 7/5, 9/5

|13/10, 14/13, 9/7, (10/9)

|Purely theoretical; despite ringing very well, 13/10 is too sharp to be expected of typical Barbershop music

|Purely theoretical; despite ringing very well, 13/10 is too sharp to be expected of typical Barbershop music.

|-

|15:19:21:27

@@ Line 29: / Line 29: @@
 == Half-Diminished Seventh (and its inversions) ==
-The Half-Diminished Seventh tetrad is officially considered by the Barbershop Harmony Society to be the second-most consonant chord (after the Barbershop Seventh, of course); in common practice 12-EDO, however, this chord is far from consonant, especially compared to other chords that may compete for that title.  This difference in interpretation must be owed to conventions either in compositional use or in tuning - so, how do choral performers tend to sing Half-Diminished Seventh chords?
+The Half-Diminished Seventh tetrad is officially considered by the Barbershop Harmony Society to be the second-most consonant chord (after the Barbershop Seventh, of course); in common practice 12-EDO, however, this chord is far from consonant, especially compared to other chords that may compete for that title.  This difference in interpretation must be owed to conventions either in compositional use or in tuning - so, how do vocal performers tend to sing Half-Diminished Seventh chords?
 The tuning of the Half-Diminished Seventh chord and its inversions are some of the most controversial in Barbershop music, especially due to differing preferences for "rooting" the chord on a specific interval.  In general, chords tend to feel most rooted when their harmonic segment forms are simplest; for instance, the 8 in 6:7:8:10 sounds more like the root than the 6 does, because the simplest inversion is 4:5:6:7.
@@ Line 35: / Line 35: @@
 If one wishes to root the chord as a Half-Diminished Seventh, then inversions of 5:6:7:9 are the most common interpretation.  If one instead wishes to root the chord as a Minor triad with an added Major Sixth, the chord is most commonly tuned as a standard 1/(6:5:4) Minor Triad with some type of Major Sixth (typically 5/3, or less commonly 12/7) added on top.
-Finally, it should be noted that the ii<sup>ø7</sup> chord is used as a dominant due to being the negative harmony variant of V<sup>7</sup>.  Because of this, some performers prefer to treat this chord as an undertonal variant of the standard Barbershop Seventh.
+It should additionally be noted that the ii<sup>ø7</sup> chord is used as a dominant due to being the negative harmony variant of V<sup>7</sup>.  Because of this, some performers prefer to treat this chord as an undertonal variant of the standard Barbershop Seventh.
+Finally, the half-diminished chord can be seen as a minor tetrad with a lowered fifth degree; this can yield 5:6:7:9 if we consider the 6/5 minor third, or 12:14:17:21 if we consider the 7/6 minor third.
 {| class="wikitable"
 |+Half-Diminished Tunings
@@ Line 62: / Line 64: @@
 |20/17, 6/5, 5/4, (17/15)
 |1/(6:5:4) triad stacked on top of a 17:20 dyad.  Most likely conceptualized as tempered tuning, not 17-limit JI.
+|-
+|12:14:17:21
+|7/6, 17/12, 7/4
+|7/6, 17/14, 21/17, (8/7)
+|12:14:18:21 tetrad, with the fifth lowered.  Most likely conceptualized as tempered tuning, not 17-limit JI.
 |}
 '''See also:''' [[5afdo]] and [[7ifdo]], the low-complexity JI scales from which several of these tunings are derived.
@@ Line 197: / Line 204: @@
 |5/4, 17/12, 7/4
 |5/4, 17/15, 21/12, (8/7)
-|17-limit hald-diminished chord, but with the sixth raised.
+|17-limit half-diminished chord, but with the sixth raised.
 |-
 |10:13:14:18
 |13/10, 7/5, 9/5
 |13/10, 14/13, 9/7, (10/9)
-|Purely theoretical; despite ringing very well, 13/10 is too sharp to be expected of typical Barbershop music
+|Purely theoretical; despite ringing very well, 13/10 is too sharp to be expected of typical Barbershop music.
 |-
 |15:19:21:27