User:Unque/Barbershop Tuning Theory - Revision history

FilterNashi at 05:16, 17 April 2025

2025-04-17T05:16:26Z

← Older revision		Revision as of 05:16, 17 April 2025
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	\|5/4, 17/12, 7/4		\|5/4, 17/12, 7/4
	\|5/4, 17/15, 21/12, (8/7)		\|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		\|10:13:14:18
	\|13/10, 7/5, 9/5		\|13/10, 7/5, 9/5
	\|13/10, 14/13, 9/7, (10/9)		\|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		\|15:19:21:27

Unque: Noted that the half-diminished chord is equivalent to a minor tetrad with a flattened fifth, adding new possible tunings of the chord (thanks to FilterNashi for suggesting the 12:14:17:21 tetrad!)

2025-04-17T02:15:29Z

Noted that the half-diminished chord is equivalent to a minor tetrad with a flattened fifth, adding new possible tunings of the chord (thanks to FilterNashi for suggesting the 12:14:17:21 tetrad!)

← Older revision		Revision as of 02:15, 17 April 2025
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	== Half-Diminished Seventh (and its inversions) ==		== 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.		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.
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	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.

	~~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"		{\| class="wikitable"
	\|+Half-Diminished Tunings		\|+Half-Diminished Tunings
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	\|20/17, 6/5, 5/4, (17/15)		\|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.		\|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.		'''See also:''' [[5afdo]] and [[7ifdo]], the low-complexity JI scales from which several of these tunings are derived.

Unque: Removed the 13-limit chord under the "half-diminished" section (thanks to FilterNashi for noticing this error), and expanded the theories on dominant diminished tunings.

2025-04-17T02:02:52Z

Removed the 13-limit chord under the "half-diminished" section (thanks to FilterNashi for noticing this error), and expanded the theories on dominant diminished tunings.

← Older revision		Revision as of 02:02, 17 April 2025
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	While Barbershop music is typically said to use 7-limit Just Intonation, in practice it contains a number of idiosyncrasies and dialectal variation that differ from one performer to another, often dipping into tempered tunings or even into higher prime limits. On this page, I plan to document the chords of Barbershop harmony and the variations that occur among them; additionally, I will discuss the theoretical reasoning behind a performer's choice of one tuning over another, and theoretical extensions that could provide other potential tunings for a given chord. Any purely theoretical or otherwise unattested tunings will be explicitly disclaimed as such.		While Barbershop music is typically said to use 7-limit Just Intonation, in practice it contains a number of idiosyncrasies and dialectal variation that differ from one performer to another, often dipping into tempered tunings or even into higher prime limits. On this page, I plan to document the chords of Barbershop harmony and the variations that occur among them; additionally, I will discuss the theoretical reasoning behind a performer's choice of one tuning over another, and theoretical extensions that could provide other potential tunings for a given chord. Any purely theoretical or otherwise unattested tunings will be explicitly disclaimed as such.

	Note that the ratios given here are ''approximations'', not precise measurements. Most performers don't analyze the intervals as JI ratios, but rather slightly adjust the tunings to make the chords ring better. Even if they did analyze the ratios, the voice would not be precise enough to articulate certain minute differences, and as such these ratios would still not precisely represent the actual practical sounds being sung.		Note that the ratios given here are ''approximations'', not precise measurements. Most performers don't analyze the intervals as JI ratios (with the common exception of certain extremely simple chords, such as the famous 4:5:6:7 tetrad), but rather slightly adjust the tunings to make the chords ring better. Even if they did analyze the ratios, the voice would not be precise enough to articulate certain minute differences, and as such these ratios would still not precisely represent the actual practical sounds being sung.

	Chords are given here as harmonic segments within the octave unless otherwise specified; true Barbershop performance often uses more open voicings, inversions, or other kinds of permutations with respect to the equivalent octaves.		Chords are given here as harmonic segments within the octave unless otherwise specified; true Barbershop performance often uses more open voicings, inversions, or other kinds of permutations with respect to the equivalent octaves.
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	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 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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	\|20/17, 6/5, 5/4, (17/15)		\|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.		\|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.~~
	\|}		\|}
	'''See also:''' [[5afdo]] and [[7ifdo]], the low-complexity JI scales from which several of these tunings are derived.		'''See also:''' [[5afdo]] and [[7ifdo]], the low-complexity JI scales from which several of these tunings are derived.
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	\|7/6, 9/7, 7/6, (8/7)		\|7/6, 9/7, 7/6, (8/7)
	\|Standard 7-limit Minor Tetrad; much less common than 5-limit.		\|Standard 7-limit Minor Tetrad; much less common than 5-limit.
			\|-
			\|32:38:48:57
			\|19/16, 3/2, 57/32
			\|19/16, 24/19, 19/16, (64/57)
			\|Much closer to 12edo's minor third. Most likely conceptualized as tempered tuning, not 19-limit JI.
	\|}		\|}

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	The Full Diminished tetrad is rarely used in Barbershop music, but is considered a part of the vocabulary by the Barbershop Harmony Society nonetheless. The simplest way to tune this tetrad is by stacking up intervals of 6/5, but this becomes complex and dissonant quite quickly.		The Full Diminished tetrad is rarely used in Barbershop music, but is considered a part of the vocabulary by the Barbershop Harmony Society nonetheless. The simplest way to tune this tetrad is by stacking up intervals of 6/5, but this becomes complex and dissonant quite quickly.

	Another option is to use the Half-Diminished tetrad, but flatten the seventh to yield a Full Diminished form; in order to do this, however, one must have a determined tuning for the Half-Diminished Seventh chord, which is already controversial. Additionally, the amount by which the seventh is flattened varies idiolectally, since there is no low-complexity tuning for the Diminished Seventh interval aside from the ~~enharmonically-equivalent~~ Major Sixth.		Another option is to use the Half-Diminished tetrad, but flatten the seventh to yield a Full Diminished form; in order to do this, however, one must have a determined tuning for the Half-Diminished Seventh chord, which is already controversial. Additionally, the amount by which the seventh is flattened varies idiolectally, since there is no low-complexity tuning for the Diminished Seventh interval aside from the enharmonic Major Sixth.

	Due to the Diminished Chord's nature as a symmetrical chord in Western classical practices, rotations of the tetrad are also valid options.		Due to the Diminished Chord's nature as a symmetrical chord in Western classical practices, rotations of the tetrad are also valid options.
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	While the Dominant Diminished tetrad (a dominant chord with a diminished fifth) is officially recognized as part of the Barbershop vocabulary, it is rarely used in practice, and as such there are very few attestations of how to tune it. It is also called a Major Diminished chord, or simply a Flat-Five chord.		While the Dominant Diminished tetrad (a dominant chord with a diminished fifth) is officially recognized as part of the Barbershop vocabulary, it is rarely used in practice, and as such there are very few attestations of how to tune it. It is also called a Major Diminished chord, or simply a Flat-Five chord.

	The Major Diminished chord is a barbershop tetrad with the fifth diminished; this interpretation yields the tuning 20:25:28:35. It can also be thought of as a Half-Diminished tetrad with the third raised, which may instead yield 20:25:28:36.		The Major Diminished chord can be seen as a barbershop tetrad with the fifth diminished; this interpretation yields the tuning 20:25:28:35. It can also be thought of as a Half-Diminished tetrad with the third raised, which may instead yield 20:25:28:36.

			Additionally, rooting a Half-Diminished chord on the perfect fifth rather than the root yields a chord with intervals 1 - M3 - Aug4 - M6, which is very close to a Dominant Diminished chord, especially considering how sharp the M6 is tuned and how flat the dominant seventh is in Barbershop music. The major sixth can be raised to a typical minor seventh in tunings where it would be more beneficial to do so.

	It can also be thought of as a Lydian Dominant chord with the fifth omitted; thus, 8:10:11:14 or 4:5:7:11. This tuning is seldom used in Barbershop practice, but is often used as the tuning of this chord in harmonic contexts.		It can also be thought of as a Lydian Dominant chord with the fifth omitted; thus, 8:10:11:14 or 4:5:7:11. This tuning is seldom used in Barbershop practice, but is often used as the tuning of this chord in harmonic contexts.
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	\|5/4, 28/25, 9/7, (10/9)		\|5/4, 28/25, 9/7, (10/9)
	\|Half-diminished chord with raised third.		\|Half-diminished chord with raised third.
			\|-
			\|7:9:10:12
			\|9/7, 10/7, 12/7
			\|9/7, 10/9, 6/5, (7/6)
			\|Rotation of half-diminished chord.
			\|-
			\|12:15:17:21
			\|5/4, 17/12, 7/4
			\|5/4, 17/15, 21/12, (8/7)
			\|17-limit hald-diminished chord, but with the sixth raised.
	\|-		\|-
	\|10:13:14:18		\|10:13:14:18
	\|13/10, 7/5, 9/5		\|13/10, 7/5, 9/5
	\|13/10, 14/13, 9/7, (10/9)		\|13/10, 14/13, 9/7, (10/9)
	\|~~Most likely conceptualized as tempered tuning~~, ~~not~~ 13~~-limit JI.~~		\|Purely theoretical; despite ringing very well, 13/10 is too sharp to be expected of typical Barbershop music
	\|-		\|-
	\|15:19:21:27		\|15:19:21:27

Unque: /* Dominant Diminished */

2025-01-12T17:57:45Z

Dominant Diminished

← Older revision		Revision as of 17:57, 12 January 2025
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	\|Close voicing with eleventh reduced.		\|Close voicing with eleventh reduced.
	\|}		\|}
	'''See also:''' [[8afdo]], the JI scale from which Lydian ~~Diminished~~ is derived.		'''See also:''' [[8afdo]], the JI scale from which Lydian Dominant is derived.

	== Augmented Chord ==		== Augmented Chord ==

Unque at 17:57, 3 December 2024

2024-12-03T17:57:16Z

← Older revision		Revision as of 17:57, 3 December 2024
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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, ~~a chord tends~~ to feel most rooted when ~~its~~ harmonic segment ~~form is~~ 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.		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 ~~root~~-~~second~~-~~fourth~~-~~sixth~~ tetrad, which could ~~yield a subset of the [[8afdo\|Acoustic Scale]]~~. While not technically invalid, however, this approach is purely theoretical, and is not used or even attested anywhere.		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.
	\|-		\|-
	\|9:11:13:16		\|10:12:13:18
	\|11/9, 13/9~~, 16~~/9		\|6/5, 13/10, 9/5
	\|11/9, 13/11, 16/13, (9/8)		\|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]]~~, [[8afdo]],~~ and [[7ifdo]] the low-complexity JI scales from which several of these tunings are derived.		'''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-tempered chords approximate the ones shown here.		'''See also:''' [[128/125\|Augmented]], [[361/360\|Dudon]], and [[225/224\|Magic]], temperaments whose characteristic essentially tempered chords approximate the ones shown here.

Unque at 17:39, 22 November 2024

2024-11-22T17:39:02Z

← Older revision		Revision as of 17:39, 22 November 2024
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	Although officially considered as part of the Barbershop vocabulary, the Major Seventh tetrad is officially recognized as a dissonance due to the "grinding" effect that occurs between the root and the seventh.		Although officially considered as part of the Barbershop vocabulary, the Major Seventh tetrad is officially recognized as a dissonance due to the "grinding" effect that occurs between the root and the seventh.

	The seventh is almost always tuned as 15/8 above the root, though it is occasionally tempered to reduce grinding ~~against the root~~.		The seventh is almost always tuned as 15/8 above the root, though it is occasionally tempered to reduce grinding.
	{\| class="wikitable"		{\| class="wikitable"
	\|+Major Seventh Tunings		\|+Major Seventh Tunings

Unque at 14:28, 14 November 2024

2024-11-14T14:28:47Z

← Older revision		Revision as of 14:28, 14 November 2024
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	\|Purely theoretical. Seemingly unattested, despite ringing very well.		\|Purely theoretical. Seemingly unattested, despite ringing very well.
	\|}		\|}
	'''See also:''' [[5afdo]] ~~and~~ [[8afdo]], the low-complexity JI scales from which several of these tunings are derived.		'''See also:''' [[5afdo]], [[8afdo]], 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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	\|Most likely conceptualized as tempered tuning, not 17-limit JI.		\|Most likely conceptualized as tempered tuning, not 17-limit JI.
	\|}		\|}
			'''See also:''' [[Kleisma\|Kleismic]] and [[648/625\|Diminished]], temperaments who provide essentially-tempered versions of the diminished tetrad.

	== Dominant Diminished ==		== Dominant Diminished ==
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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 ~~fifths~~ 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 not 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.

Unque at 13:59, 14 November 2024

2024-11-14T13:59:38Z

← Older revision		Revision as of 13:59, 14 November 2024
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	Additionally, the chord can theoretically be rooted as an inversion of a root-second-fourth-sixth tetrad, which could yield a subset of the [[8afdo\|Acoustic Scale]]. While not technically invalid, however, this approach is purely theoretical, and is not used or even attested anywhere.		Additionally, the chord can theoretically be rooted as an inversion of a root-second-fourth-sixth tetrad, which could yield a subset of the [[8afdo\|Acoustic Scale]]. While not technically invalid, however, this approach is purely theoretical, and is not 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.
	{\| class="wikitable"		{\| class="wikitable"
	\|+Half-Diminished Tunings		\|+Half-Diminished Tunings
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	== Add-Nine Chords ==		== Add-Nine Chords ==
	The Major Add9 tetrad (and by extension, the sus2 triad) is officially considered as part of the Barbershop vocabulary, but is not treated as fundamental on the same level as the previous two chords. This chord is ~~perhaps~~ the ~~single least variable~~, with the ninth being ~~unambiguously~~ a 9/4 above the tonic.		The Major Add9 tetrad (and by extension, the sus2 triad) is officially considered as part of the Barbershop vocabulary, but is not treated as fundamental on the same level as the previous two chords. This chord is much less variable than some of the other chords, with the ninth being almost unanimously considered a 9/4 above the tonic.
	{\| class="wikitable"		{\| class="wikitable"
	\|+Major Ninth Tunings		\|+Major Ninth Tunings
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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 ~~that respectively analyze 3~~-~~EDO as these three chord tunings~~.		'''See also:''' [[128/125\|Augmented]], [[361/360\|Dudon]], and [[225/224\|Magic]], temperaments whose characteristic essentially-tempered chords approximate the ones shown here.

Unque at 21:15, 12 November 2024

2024-11-12T21:15:01Z

← Older revision		Revision as of 21:15, 12 November 2024
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	While Barbershop music ~~primarily uses~~ 7-limit Just Intonation, it contains a number of idiosyncrasies and dialectal variation that differ from one performer to another, often dipping into tempered tunings or even into higher prime limits. On this page, I plan to document the chords of Barbershop harmony and the variations that occur among them; additionally, I will discuss the theoretical reasoning behind ~~choosing~~ one tuning over another, and ~~potential~~ theoretical extensions that could provide other potential tunings for a chord. Any purely theoretical or otherwise unattested tunings will be explicitly disclaimed as such.		While Barbershop music is typically said to use 7-limit Just Intonation, in practice it contains a number of idiosyncrasies and dialectal variation that differ from one performer to another, often dipping into tempered tunings or even into higher prime limits. On this page, I plan to document the chords of Barbershop harmony and the variations that occur among them; additionally, I will discuss the theoretical reasoning behind a performer's choice of one tuning over another, and theoretical extensions that could provide other potential tunings for a given chord. Any purely theoretical or otherwise unattested tunings will be explicitly disclaimed as such.

	Note that the ratios given here are ''approximations'', not precise measurements. Most performers don't analyze the intervals as JI ratios, but rather slightly adjust the tunings to make the chords ring better. Even if they did analyze the ratios, the voice would not be precise enough to articulate certain minute differences, and as such these ratios would still not precisely represent the actual practical sounds being sung.		Note that the ratios given here are ''approximations'', not precise measurements. Most performers don't analyze the intervals as JI ratios, but rather slightly adjust the tunings to make the chords ring better. Even if they did analyze the ratios, the voice would not be precise enough to articulate certain minute differences, and as such these ratios would still not precisely represent the actual practical sounds being sung.

	Chords are given here as harmonic segments within the octave unless otherwise specified; true Barbershop performance often uses more open voicings, inversions, or other kinds of permutations ~~due~~ to octaves ~~being perceived as equivalent~~.		Chords are given here as harmonic segments within the octave unless otherwise specified; true Barbershop performance often uses more open voicings, inversions, or other kinds of permutations with respect to the equivalent octaves.

	== The Barbershop Seventh ==		== The Barbershop Seventh ==

Unque at 17:39, 12 November 2024

2024-11-12T17:39:21Z

← Older revision		Revision as of 17:39, 12 November 2024
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	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, a chord tends to feel most rooted when its harmonic segment form is 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.		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, a chord tends to feel most rooted when its harmonic segment form is 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 ~~Add6~~, the chord is most commonly tuned as a standard 1/(6:5:4) Minor Triad with some type of Major Sixth (typically ~~either~~ 5/3 or 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 root-second-fourth-sixth tetrad, which could yield a subset of the [[8afdo\|Acoustic Scale]]. While not technically invalid, however, this approach is purely theoretical, and is not used or even attested anywhere.		Additionally, the chord can theoretically be rooted as an inversion of a root-second-fourth-sixth tetrad, which could yield a subset of the [[8afdo\|Acoustic Scale]]. While not technically invalid, however, this approach is purely theoretical, and is not used or even attested anywhere.