雙和聲大調

$\layout { line-width = #72 ragged-last = ##f \context { \Score \override SpacingSpanner.spacing-increment = #1/2 \remove System_start_delimiter_engraver } } << \new Staff \with { \remove Time_signature_engraver } { \new Voice \with { \consists Horizontal_bracket_engraver \override HorizontalBracket.direction = #UP \override HorizontalBracket.Y-offset = 3.8 } \transpose c c'{ \set Staff.midiExpression = #1 \time 12/4 c4-\tweak HorizontalBracketText.text "半音"\startGroup des\stopGroup e-\tweak HorizontalBracketText.text "半音"\startGroup f\stopGroup g-\tweak HorizontalBracketText.text "半音"\startGroup aes\stopGroup b-\tweak HorizontalBracketText.text "半音"\startGroup \once \override NoteHead.color = "#b0b0b0" \once \override Stem.color = "#b0b0b0" c'1\stopGroup } } \new Staff \with { \remove Bar_engraver \remove Time_signature_engraver \remove Key_engraver \remove Clef_engraver \override StaffSymbol.line-count = 0 } { \set Staff.midiMinimumVolume = 0.0 \set Staff.midiMaximumVolume = 0.0 \new Voice \with { \consists Horizontal_bracket_engraver \override HorizontalBracket.direction = #DOWN \override HorizontalBracket.shorten-pair = #'(0 . 1) \override HorizontalBracket.Y-offset = 3.9 } \transpose c c'{ \hideNotes \time 12/4 c4 des-\tweak HorizontalBracketText.text "半音三度"\startGroup e\stopGroup f-\tweak HorizontalBracketText.text "全音"\startGroup g\stopGroup aes-\tweak HorizontalBracketText.text "半音三度"\startGroup b\stopGroup c'1 } } >>$

C 雙和聲大調。

$\layout { line-width = #72 ragged-last = ##f \context { \Score \override SpacingSpanner.spacing-increment = #1/2 \remove System_start_delimiter_engraver } } << \new Staff \with { \remove Time_signature_engraver } { \new Voice \with { \consists Horizontal_bracket_engraver \override HorizontalBracket.direction = #UP \override HorizontalBracket.Y-offset = 3.8 } \transpose f c'{ \set Staff.midiExpression = #1 \time 12/4 f4-\tweak HorizontalBracketText.text "全音"\startGroup g\stopGroup aes-\tweak HorizontalBracketText.text "半音三度"\startGroup b\stopGroup c'-\tweak HorizontalBracketText.text "半音"\startGroup des'\stopGroup e'-\tweak HorizontalBracketText.text "半音"\startGroup \once \override NoteHead.color = "#b0b0b0" \once \override Stem.color = "#b0b0b0" f'1\stopGroup } } \new Staff \with { \remove Bar_engraver \remove Time_signature_engraver \remove Key_engraver \remove Clef_engraver \override StaffSymbol.line-count = 0 } { \set Staff.midiMinimumVolume = 0.0 \set Staff.midiMaximumVolume = 0.0 \new Voice \with { \consists Horizontal_bracket_engraver \override HorizontalBracket.direction = #DOWN \override HorizontalBracket.shorten-pair = #'(0 . 1) \override HorizontalBracket.Y-offset = 3.9 } \transpose f c'{ \hideNotes \time 12/4 f4 g-\tweak HorizontalBracketText.text "半音"\startGroup aes\stopGroup b-\tweak HorizontalBracketText.text "半音"\startGroup c'\stopGroup des'-\tweak HorizontalBracketText.text "半音三度"\startGroup e'\stopGroup f'1 } } >>$

C 匈牙利小調。

雙和聲大調^{[註 1]}（英文：double harmonic major）係一種七個音嘅音階，相當於將大調第二級同第六級降半音^[1]；音階由七個音程組成，順序係半音、半音三度、半音、全音、半音、半音三度、半音，加埋啱啱一個八度。呢個音階喺印度音樂叫 Bhairav Thaat^[2]^[3]。

雙和聲大調係所謂自反音階^[暫譯]^{[註 2]}（reflective scale），佢嘅倒影^[暫譯]（mirror modal equivalent）係返自己，即係話構成佢嘅音程順序數同逆序數都冇分別，掉轉嚟都仲係雙和聲大調^[4]。

同大調一樣，喺唔同嘅音開始，按音階順序上，攞齊七個音，可以得出七個唔同嘅調式；當中第四級調式就係好多唔同文化嘅音樂都有用嘅匈牙利小調^{[註 3]}（Hungarian minor）^[5]。

順階和弦

構成雙和聲大調嘅七個音，對應下面呢七個順階和弦^[6]：

名		構成音	性質	例（C 和聲大調）
羅馬數字	數字和弦	構成音	性質	例（C 和聲大調）
I	1	1-3-5	大和弦	$\new Staff \with {\remove Time_signature_engraver \remove Bar_engraver} \transpose c c' { <c e g>1 }$
II	2	2♭-4-6♭	大和弦	$\new Staff \with {\remove Time_signature_engraver \remove Bar_engraver} \transpose c c' { <des f aes>1 }$
iii	3-	3-5-7	小和弦	$\new Staff \with {\remove Time_signature_engraver \remove Bar_engraver} \transpose c c' { <e g b>1 }$
iv	4-	4-6♭-1	小和弦	$\new Staff \with {\remove Time_signature_engraver \remove Bar_engraver} \transpose c c' { <f aes c'>1 }$
V^♭5 ^{[註 4]}	未知	5-7-2♭	大和弦降五級^{[註 4]}	$\new Staff \with {\remove Time_signature_engraver \remove Bar_engraver} \transpose c c' { <g b des'>1 }$
VI+	6+	6♭-1-3	增和弦	$\new Staff \with {\remove Time_signature_engraver \remove Bar_engraver} \transpose c c' { <aes c' e'>1 }$
vii°^♭3 ^{[註 5]}	未知	7-2♭-4	減和弦降三級^{[註 5]}	$\new Staff \with {\remove Time_signature_engraver \remove Bar_engraver} \transpose c c' { <b des' f'>1 }$

調式

雙和聲大調對應七個唔同嘅調式，當中第四級起音嘅匈牙利小調其實好常見，因為喺好多唔同文化嘅音樂都有用佢^[5]：

起音音級	名	別名	例（中央 C 起音）
1	雙和聲大調 (double harmonic major)	唔適用	$\layout { line-width = #72 ragged-last = ##f \context { \Score \override SpacingSpanner.spacing-increment = #1/2 \remove System_start_delimiter_engraver } } << \new Staff \with { \remove Time_signature_engraver } { \new Voice \with { \consists Horizontal_bracket_engraver \override HorizontalBracket.direction = #UP \override HorizontalBracket.Y-offset = 3.8 } \transpose c c'{ \set Staff.midiExpression = #1 \time 12/4 c4-\tweak HorizontalBracketText.text "半音"\startGroup des\stopGroup e-\tweak HorizontalBracketText.text "半音"\startGroup f\stopGroup g-\tweak HorizontalBracketText.text "半音"\startGroup aes\stopGroup b-\tweak HorizontalBracketText.text "半音"\startGroup \once \override NoteHead.color = "#b0b0b0" \once \override Stem.color = "#b0b0b0" c'1\stopGroup } } \new Staff \with { \remove Bar_engraver \remove Time_signature_engraver \remove Key_engraver \remove Clef_engraver \override StaffSymbol.line-count = 0 } { \set Staff.midiMinimumVolume = 0.0 \set Staff.midiMaximumVolume = 0.0 \new Voice \with { \consists Horizontal_bracket_engraver \override HorizontalBracket.direction = #DOWN \override HorizontalBracket.shorten-pair = #'(0 . 1) \override HorizontalBracket.Y-offset = 3.9 } \transpose c c'{ \hideNotes \time 12/4 c4 des-\tweak HorizontalBracketText.text "半音三度"\startGroup e\stopGroup f-\tweak HorizontalBracketText.text "全音"\startGroup g\stopGroup aes-\tweak HorizontalBracketText.text "半音三度"\startGroup b\stopGroup c'1 } } >>$
2	利地安升二級升六級調式^[暫譯] (Lydian ♯2 ♯6)	唔適用	$\layout { line-width = #72 ragged-last = ##f \context { \Score \override SpacingSpanner.spacing-increment = #1/2 \remove System_start_delimiter_engraver } } << \new Staff \with { \remove Time_signature_engraver } { \new Voice \with { \consists Horizontal_bracket_engraver \override HorizontalBracket.direction = #UP \override HorizontalBracket.Y-offset = 3.8 } \transpose des c'{ \set Staff.midiExpression = #1 \time 12/4 des4-\tweak HorizontalBracketText.text "半音三度"\startGroup e\stopGroup f-\tweak HorizontalBracketText.text "全音"\startGroup g\stopGroup aes-\tweak HorizontalBracketText.text "半音三度"\startGroup b\stopGroup c'-\tweak HorizontalBracketText.text "半音"\startGroup \once \override NoteHead.color = "#b0b0b0" \once \override Stem.color = "#b0b0b0" des'1\stopGroup } } \new Staff \with { \remove Bar_engraver \remove Time_signature_engraver \remove Key_engraver \remove Clef_engraver \override StaffSymbol.line-count = 0 } { \set Staff.midiMinimumVolume = 0.0 \set Staff.midiMaximumVolume = 0.0 \new Voice \with { \consists Horizontal_bracket_engraver \override HorizontalBracket.direction = #DOWN \override HorizontalBracket.shorten-pair = #'(0 . 1) \override HorizontalBracket.Y-offset = 3.9 } \transpose des c'{ \hideNotes \time 12/4 des4 e-\tweak HorizontalBracketText.text "半音"\startGroup f\stopGroup g-\tweak HorizontalBracketText.text "半音"\startGroup aes\stopGroup b-\tweak HorizontalBracketText.text "半音"\startGroup c'\stopGroup des'1 } } >>$
3	超費里吉安調式^[暫譯] (Ultraphrygian)	唔適用	$\layout { line-width = #72 ragged-last = ##f \context { \Score \override SpacingSpanner.spacing-increment = #1/2 \remove System_start_delimiter_engraver } } << \new Staff \with { \remove Time_signature_engraver } { \new Voice \with { \consists Horizontal_bracket_engraver \override HorizontalBracket.direction = #UP \override HorizontalBracket.Y-offset = 3.8 } \transpose e c'{ \set Staff.midiExpression = #1 \time 12/4 e4-\tweak HorizontalBracketText.text "半音"\startGroup f\stopGroup g-\tweak HorizontalBracketText.text "半音"\startGroup aes\stopGroup b-\tweak HorizontalBracketText.text "半音"\startGroup c'\stopGroup des'-\tweak HorizontalBracketText.text "半音三度"\startGroup \once \override NoteHead.color = "#b0b0b0" \once \override Stem.color = "#b0b0b0" e'1\stopGroup } } \new Staff \with { \remove Bar_engraver \remove Time_signature_engraver \remove Key_engraver \remove Clef_engraver \override StaffSymbol.line-count = 0 } { \set Staff.midiMinimumVolume = 0.0 \set Staff.midiMaximumVolume = 0.0 \new Voice \with { \consists Horizontal_bracket_engraver \override HorizontalBracket.direction = #DOWN \override HorizontalBracket.shorten-pair = #'(0 . 1) \override HorizontalBracket.Y-offset = 3.9 } \transpose e c'{ \hideNotes \time 12/4 e4 f-\tweak HorizontalBracketText.text "全音"\startGroup g\stopGroup aes-\tweak HorizontalBracketText.text "半音三度"\startGroup b\stopGroup c'-\tweak HorizontalBracketText.text "半音"\startGroup des'\stopGroup e'1 } } >>$
4	匈牙利小調^{[註 3]} (Hungarian minor)	唔適用	$\layout { line-width = #72 ragged-last = ##f \context { \Score \override SpacingSpanner.spacing-increment = #1/2 \remove System_start_delimiter_engraver } } << \new Staff \with { \remove Time_signature_engraver } { \new Voice \with { \consists Horizontal_bracket_engraver \override HorizontalBracket.direction = #UP \override HorizontalBracket.Y-offset = 3.8 } \transpose f c'{ \set Staff.midiExpression = #1 \time 12/4 f4-\tweak HorizontalBracketText.text "全音"\startGroup g\stopGroup aes-\tweak HorizontalBracketText.text "半音三度"\startGroup b\stopGroup c'-\tweak HorizontalBracketText.text "半音"\startGroup des'\stopGroup e'-\tweak HorizontalBracketText.text "半音"\startGroup \once \override NoteHead.color = "#b0b0b0" \once \override Stem.color = "#b0b0b0" f'1\stopGroup } } \new Staff \with { \remove Bar_engraver \remove Time_signature_engraver \remove Key_engraver \remove Clef_engraver \override StaffSymbol.line-count = 0 } { \set Staff.midiMinimumVolume = 0.0 \set Staff.midiMaximumVolume = 0.0 \new Voice \with { \consists Horizontal_bracket_engraver \override HorizontalBracket.direction = #DOWN \override HorizontalBracket.shorten-pair = #'(0 . 1) \override HorizontalBracket.Y-offset = 3.9 } \transpose f c'{ \hideNotes \time 12/4 f4 g-\tweak HorizontalBracketText.text "半音"\startGroup aes\stopGroup b-\tweak HorizontalBracketText.text "半音"\startGroup c'\stopGroup des'-\tweak HorizontalBracketText.text "半音三度"\startGroup e'\stopGroup f'1 } } >>$
5	東方調式^[暫譯] (Oriental)	唔適用	$\layout { line-width = #72 ragged-last = ##f \context { \Score \override SpacingSpanner.spacing-increment = #1/2 \remove System_start_delimiter_engraver } } << \new Staff \with { \remove Time_signature_engraver } { \new Voice \with { \consists Horizontal_bracket_engraver \override HorizontalBracket.direction = #UP \override HorizontalBracket.Y-offset = 3.8 } \transpose g c'{ \set Staff.midiExpression = #1 \time 12/4 g4-\tweak HorizontalBracketText.text "半音"\startGroup aes\stopGroup b-\tweak HorizontalBracketText.text "半音"\startGroup c'\stopGroup des'-\tweak HorizontalBracketText.text "半音三度"\startGroup e'\stopGroup f'-\tweak HorizontalBracketText.text "全音"\startGroup \once \override NoteHead.color = "#b0b0b0" \once \override Stem.color = "#b0b0b0" g'1\stopGroup } } \new Staff \with { \remove Bar_engraver \remove Time_signature_engraver \remove Key_engraver \remove Clef_engraver \override StaffSymbol.line-count = 0 } { \set Staff.midiMinimumVolume = 0.0 \set Staff.midiMaximumVolume = 0.0 \new Voice \with { \consists Horizontal_bracket_engraver \override HorizontalBracket.direction = #DOWN \override HorizontalBracket.shorten-pair = #'(0 . 1) \override HorizontalBracket.Y-offset = 3.9 } \transpose g c'{ \hideNotes \time 12/4 g4 aes-\tweak HorizontalBracketText.text "半音三度"\startGroup b\stopGroup c'-\tweak HorizontalBracketText.text "半音"\startGroup des'\stopGroup e'-\tweak HorizontalBracketText.text "半音"\startGroup f'\stopGroup g'1 } } >>$
6	艾奧尼安增和弦升二級調式^[暫譯] (Ionian augmented ♯2)	唔適用	$\layout { line-width = #72 ragged-last = ##f \context { \Score \override SpacingSpanner.spacing-increment = #1/2 \remove System_start_delimiter_engraver } } << \new Staff \with { \remove Time_signature_engraver } { \new Voice \with { \consists Horizontal_bracket_engraver \override HorizontalBracket.direction = #UP \override HorizontalBracket.Y-offset = 3.8 } \transpose aes c'{ \set Staff.midiExpression = #1 \time 12/4 aes4-\tweak HorizontalBracketText.text "半音三度"\startGroup b\stopGroup c'-\tweak HorizontalBracketText.text "半音"\startGroup des'\stopGroup e'-\tweak HorizontalBracketText.text "半音"\startGroup f'\stopGroup g'-\tweak HorizontalBracketText.text "半音"\startGroup \once \override NoteHead.color = "#b0b0b0" \once \override Stem.color = "#b0b0b0" aes'1\stopGroup } } \new Staff \with { \remove Bar_engraver \remove Time_signature_engraver \remove Key_engraver \remove Clef_engraver \override StaffSymbol.line-count = 0 } { \set Staff.midiMinimumVolume = 0.0 \set Staff.midiMaximumVolume = 0.0 \new Voice \with { \consists Horizontal_bracket_engraver \override HorizontalBracket.direction = #DOWN \override HorizontalBracket.shorten-pair = #'(0 . 1) \override HorizontalBracket.Y-offset = 3.9 } \transpose aes c'{ \hideNotes \time 12/4 aes4 b-\tweak HorizontalBracketText.text "半音"\startGroup c'\stopGroup des'-\tweak HorizontalBracketText.text "半音三度"\startGroup e'\stopGroup f'-\tweak HorizontalBracketText.text "全音"\startGroup g'\stopGroup aes'1 } } >>$
7	洛克里安重降三級重降七級調式^[暫譯] (Locrian 𝄫3 𝄫7)	唔適用	$\layout { line-width = #72 ragged-last = ##f \context { \Score \override SpacingSpanner.spacing-increment = #1/2 \remove System_start_delimiter_engraver } } << \new Staff \with { \remove Time_signature_engraver } { \new Voice \with { \consists Horizontal_bracket_engraver \override HorizontalBracket.direction = #UP \override HorizontalBracket.Y-offset = 3.8 } \transpose b c'{ \set Staff.midiExpression = #1 \time 12/4 b4-\tweak HorizontalBracketText.text "半音"\startGroup c'\stopGroup des'-\tweak HorizontalBracketText.text "半音三度"\startGroup e'\stopGroup f'-\tweak HorizontalBracketText.text "全音"\startGroup g'\stopGroup aes'-\tweak HorizontalBracketText.text "半音三度"\startGroup \once \override NoteHead.color = "#b0b0b0" \once \override Stem.color = "#b0b0b0" b'1\stopGroup } } \new Staff \with { \remove Bar_engraver \remove Time_signature_engraver \remove Key_engraver \remove Clef_engraver \override StaffSymbol.line-count = 0 } { \set Staff.midiMinimumVolume = 0.0 \set Staff.midiMaximumVolume = 0.0 \new Voice \with { \consists Horizontal_bracket_engraver \override HorizontalBracket.direction = #DOWN \override HorizontalBracket.shorten-pair = #'(0 . 1) \override HorizontalBracket.Y-offset = 3.9 } \transpose b c'{ \hideNotes \time 12/4 b4 c'-\tweak HorizontalBracketText.text "半音"\startGroup des'\stopGroup e'-\tweak HorizontalBracketText.text "半音"\startGroup f'\stopGroup g'-\tweak HorizontalBracketText.text "半音"\startGroup aes'\stopGroup b'1 } } >>$

參考資料

↑ Beato 2017a, 0:26.
↑ "C Bhairav Thaat scale". The Piano Encyclopedia (英文). 喺2024年12月17號搵到.
↑ Nayak, Ritesh (2024年11月1號). "Understanding Indian Classical Scales: A Western Musician's Guide to Thaats, Raags, and Modes" (英文). 喺2024年12月17號搵到.
↑ Beato 2017b, 4:00, 5:07.
↑ ^5.0 ^5.1 Beato 2024, 1:57.
↑ Beato 2017a, 1:30 開始.

註

↑ 譯名見：〈雙和聲大調〉 (臺灣中文)。黑白格文藝事業。喺2024年12月13號搵到。
↑ 譯名參考：｢數學科常用英漢辭彙｣ 2020年, p. 23
↑ ^3.0 ^3.1 譯名見：〈各式基底音階與調式音階〉 (臺灣中文)。黑白格文藝事業。喺2024年12月16號搵到。
↑ ^4.0 ^4.1 冇標準名，咁叫係跟 Beato 2017a, 2:32。
↑ ^5.0 ^5.1 冇標準名，咁叫係跟 Beato 2017a, 3:34。

書目

Beato, Rick (2017年7月17號). The Darkest Scale Ever (英文). 喺2024年8月25號搵到.
Beato, Rick (2017年11月16號). Musical Palindromes & Negative Harmony (what?) (英文). 喺2024年12月16號搵到.
Beato, Rick (2024年4月2號). The Mystery of the Double Harmonic Major Scale (英文). 喺2024年12月16號搵到.
〈數學科常用英漢辭彙〉 (PDF) (英文、香港中文)。2020年7月8日。喺2024年9月12號搵到。

[FOOTNOTEBeato2017a0:26-2] Beato 2017a, 0:26.

[3] "C Bhairav Thaat scale". The Piano Encyclopedia (英文). 喺2024年12月17號搵到.

[4] Nayak, Ritesh (2024年11月1號). "Understanding Indian Classical Scales: A Western Musician's Guide to Thaats, Raags, and Modes" (英文). 喺2024年12月17號搵到.

[FOOTNOTEBeato2017b4:00,_5:07-6] Beato 2017b, 4:00, 5:07.

[FOOTNOTEBeato20241:57-8] 5.0 ^5.1 Beato 2024, 1:57.

[FOOTNOTEBeato2017a1:30_開始-9] Beato 2017a, 1:30 開始.

[g-8ead1632cb9d4c96f9754553df8a5bb6-1] 譯名見：〈雙和聲大調〉 (臺灣中文)。黑白格文藝事業。喺2024年12月13號搵到。

[g-cb422e837fee53f697e1f3cfd983016a-5] 譯名參考：｢數學科常用英漢辭彙｣ 2020年, p. 23

[g-aac7e344e02c5087f6a59ca28b398d6e-7] 3.0 ^3.1 譯名見：〈各式基底音階與調式音階〉 (臺灣中文)。黑白格文藝事業。喺2024年12月16號搵到。

[chord5-10] 4.0 ^4.1 冇標準名，咁叫係跟 Beato 2017a, 2:32。

[chord7-11] 5.0 ^5.1 冇標準名，咁叫係跟 Beato 2017a, 3:34。

[註 1]

[1]

[2]

[3]

[註 2]

[4]

[註 3]

[5]

[6]

[註 4]

[註 5]