User:Unque/Barbershop Tuning Theory: Difference between revisions
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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 choral 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, | 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. | ||
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. | 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. | ||
Additionally, the chord can theoretically be rooted as an inversion of a | Additionally, the chord can theoretically be rooted as an inversion of a 1 - M2 - P4 - M6 tetrad, which could be interpreted as 9:10:12:13 or 9:10:12:14. While not technically invalid, however, this approach is purely theoretical, and does not seem to be used or even attested anywhere. | ||
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. | 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. | ||
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|1/(6:5:4) triad stacked on top of a 17:20 dyad. Most likely conceptualized as tempered tuning, not 17-limit JI. | |1/(6:5:4) triad stacked on top of a 17:20 dyad. Most likely conceptualized as tempered tuning, not 17-limit JI. | ||
|- | |- | ||
| | |10:12:13:18 | ||
| | |6/5, 13/10, 9/5 | ||
| | |6/5, 13/12, 18/13, (10/9) | ||
|Purely theoretical. Seemingly unattested, despite ringing very well. | |Purely theoretical. Seemingly unattested, despite ringing very well. | ||
|} | |} | ||
'''See also:''' [[5afdo]] | '''See also:''' [[5afdo]] and [[7ifdo]], the low-complexity JI scales from which several of these tunings are derived. | ||
== Add-Nine Chords == | == Add-Nine Chords == | ||
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The only attested tuning of this chord seems to be permutations of 16:20:25, though it may be tempered to better approximate [[3edo|3-EDO]]. | The only attested tuning of this chord seems to be permutations of 16:20:25, though it may be tempered to better approximate [[3edo|3-EDO]]. | ||
Alternatively, one of the thirds could theoretically be tuned a flat by a Magic Comma in order to add the more consonant 9/7 on top of the chord; while this is technically valid and rings very well, it is purely theoretical and not attested as a tuning of the Augmented triad in barbershop. | Alternatively, one of the thirds could theoretically be tuned a flat by a Magic Comma in order to add the more consonant 9/7 on top of the chord; while this is technically valid and rings very well, it is purely theoretical and does not seem to be attested as a tuning of the Augmented triad in barbershop. | ||
Some performers add the Dominant Seventh (9/5) or a Barbershop Seventh (7/4) over the top of an Augmented Triad, but this is usually used as a flourish and not considered a part of the chord. | Some performers add the Dominant Seventh (9/5) or a Barbershop Seventh (7/4) over the top of an Augmented Triad, but this is usually used as a flourish and not considered a part of the chord. | ||
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|Purely theoretical. Seemingly unattested, despite ringing very well. | |Purely theoretical. Seemingly unattested, despite ringing very well. | ||
|} | |} | ||
'''See also:''' [[128/125|Augmented]], [[361/360|Dudon]], and [[225/224|Magic]], temperaments whose characteristic essentially | '''See also:''' [[128/125|Augmented]], [[361/360|Dudon]], and [[225/224|Magic]], temperaments whose characteristic essentially tempered chords approximate the ones shown here. | ||