1:1 Ionian Species Counterpoint in Pythagorean Tuning
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4 سال پیش
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Hello. Here are 4 species
Hello. Here are 4 species counterpoint examples from Johann Joseph Fux's Gradus ad Parnassum (1725). Each video demonstrates one of Fux’s cantus firmi (1) by itself, (2) with Fux’s counterpoint, & (3) with my counterpoint.
INSPIRATION
Friend & Music Theory Prof., Dr. Gordon Root, emailed on 7-16-20:
“Fux models his teachings on the polyphonic style of the high Renaissance, in particular, on the music of Giovanni Pierluigi da Palestrina (1525-1594). As Knud Jeppesen and others have noted, Fux’s renderings of Renaissance music and of the principles that guided its structure could not help but be colored somewhat anachronistically by the two hundred years that separated his era from that of Palestrina’s. And yet, Fux’s method has dominated the landscape of composition pedagogy for centuries since its publication. And perhaps this is its most enduring legacy (rather than any claim to absolute authenticity of Renaissance style). Nearly every important composer since its publication has studied from Fux’s little book,”
including Mozart, Haydn, Beethoven, Schubert, Bruckner, Brahms, Cherubini, Berlioz, Meyerbeer, Chopin, Rosini, Auber, Paganini, Moscheles, Hummel, & Liszt (Alfred Mann’s intro. to _Gradus ad Parnassum_: http://www.opus28.co.uk/Fux_Gradus.pdf)
MODES
Modes used in the Renaissance were based on the white keys of the keyboard. Black keys were used for temporary functions (to ⇧ 7 at cadences, & to avoid tritones & aug. 2nds). With 7 white notes before the octave, there are 7 modes with Greek city-state names. Locrian was not used due to its dim. 5. In earlier music, only Dorian, Phrygian, Lydian, Mixolydian & their 4 plagal counterparts were used. Different intervals give each mode a different color, inspiring jazz, classical & film composers.
7 Modes
Dorian: D ⇨ D (minor w/⇧ 6)
Phrygian: E ⇨ E (minor w/⇩ 2)
Lydian: F ⇨ F (major w/⇧ 4)
Mixolydian: G ⇨ G (major w/⇩ 7)
Aeolian: A ⇨ A (♮ minor)
Locrian: B ⇨ B (minor w/ ⇩ 2 & 5)
Ionian: C ⇨ C (major)
TUNING & TEMPERAMENT
These modes were limited primarily to white keys because the the church organs were originally tuned to pure math ratios (just intonation) that were not suitable to distant modulations.
JUST INTONATION
In 5-limit just intonation, 3rds & 5ths are both pure, but one cannot comfortably modulate or even use the D to A 5th, which is so bad, it is called a “wolf.”
PYTHAGOREAN TUNING
The main version of just intonation used into the early Renaissance was Pythagorean tuning, with ratio-based 5ths…but impure 3rds.
MEANTONE TEMPERAMENT
Since 3rds & 6ths became favored in the Renaissance, theorists developed a modified “tuning” system called quarter-comma meantone temperament. They divided the dissonance (comma) of the major 3rds in Pythagorean tuning among four 5ths (hence “quarter-comma”). This temperament pervaded Europe during much of the Renaissance until the late Baroque period.
Keys with more sharps/flats were more dissonant & thus used to express intense affects. Extreme keys were deemed unplayable. According to Willard A. Palmer’s introduction to _J.S. Bach: Inventions & Sinfonias_, because of meantone’s limitations, Bach used only 15 keys in his _Inventions and Sinfonias_(1720).
WELL TEMPERAMENT
Contrast that to all 24 keys being displayed by Bach in both books of _The Well-Tempered Clavier_(1722 & 1742). Well temperament is usable but not equal in every key. Intervalic differences were celebrated. Some keys use some ratio-based intervals. Dissonant keys were used expressively.
EQUAL TEMPERAMENT
Theorists modified well temperament to arrive at true equal temperament in the early 20th century. We can now play equally well in all keys with beautiful symmetry, yet we have lost both the harmony of ratio-based intervals & the colorful differences between keys.
TUNING & TEMPERAMENT SYSTEMS USED
Each set of exercises is rendered in 5 systems:
1) Just intonation (tuned to the tonic)
2) Pythagorean tuning (tuned to C)
3) Quarter-comma meantone temperament (tuned to C)
4) Well temperament (Kirnberger III, tuned to C)
5) Equal temperament (tuned to C)
Of the many possible ratios in just intonation, I chose these via just_intonation.scl:
16/15
9/8
6/5
5/4
4/3
7/5 (used in Lydian)
3/2
8/5
5/3
9/5
15/8
2/1
https://usermanuals.garritan.com/ARIA...
This link, Cam Taylor, Prof. Scott Marcus’ Tuning & Temperament course at UCSB, & the following articles were helpful in writing this section:
http://www.early-music.info/octaves_t...
https://en.wikipedia.org/wiki/Musical...
God bless you & yours,
Mark Lybarger-Monson, Ph.D.
(music composition from UCSB)
www.ml-m.net
“The Lord bless you and keep you;
the Lord make his face to shine upon you and be gracious to you;
the Lord lift up his countenance upon you and give you peace.”
(Num. 6:24-26, ESV)
“And the peace of God, which surpasses all understanding, will guard your hearts and your minds in Christ Jesus.”
(Phil. 4:7, ESV)
INSPIRATION
Friend & Music Theory Prof., Dr. Gordon Root, emailed on 7-16-20:
“Fux models his teachings on the polyphonic style of the high Renaissance, in particular, on the music of Giovanni Pierluigi da Palestrina (1525-1594). As Knud Jeppesen and others have noted, Fux’s renderings of Renaissance music and of the principles that guided its structure could not help but be colored somewhat anachronistically by the two hundred years that separated his era from that of Palestrina’s. And yet, Fux’s method has dominated the landscape of composition pedagogy for centuries since its publication. And perhaps this is its most enduring legacy (rather than any claim to absolute authenticity of Renaissance style). Nearly every important composer since its publication has studied from Fux’s little book,”
including Mozart, Haydn, Beethoven, Schubert, Bruckner, Brahms, Cherubini, Berlioz, Meyerbeer, Chopin, Rosini, Auber, Paganini, Moscheles, Hummel, & Liszt (Alfred Mann’s intro. to _Gradus ad Parnassum_: http://www.opus28.co.uk/Fux_Gradus.pdf)
MODES
Modes used in the Renaissance were based on the white keys of the keyboard. Black keys were used for temporary functions (to ⇧ 7 at cadences, & to avoid tritones & aug. 2nds). With 7 white notes before the octave, there are 7 modes with Greek city-state names. Locrian was not used due to its dim. 5. In earlier music, only Dorian, Phrygian, Lydian, Mixolydian & their 4 plagal counterparts were used. Different intervals give each mode a different color, inspiring jazz, classical & film composers.
7 Modes
Dorian: D ⇨ D (minor w/⇧ 6)
Phrygian: E ⇨ E (minor w/⇩ 2)
Lydian: F ⇨ F (major w/⇧ 4)
Mixolydian: G ⇨ G (major w/⇩ 7)
Aeolian: A ⇨ A (♮ minor)
Locrian: B ⇨ B (minor w/ ⇩ 2 & 5)
Ionian: C ⇨ C (major)
TUNING & TEMPERAMENT
These modes were limited primarily to white keys because the the church organs were originally tuned to pure math ratios (just intonation) that were not suitable to distant modulations.
JUST INTONATION
In 5-limit just intonation, 3rds & 5ths are both pure, but one cannot comfortably modulate or even use the D to A 5th, which is so bad, it is called a “wolf.”
PYTHAGOREAN TUNING
The main version of just intonation used into the early Renaissance was Pythagorean tuning, with ratio-based 5ths…but impure 3rds.
MEANTONE TEMPERAMENT
Since 3rds & 6ths became favored in the Renaissance, theorists developed a modified “tuning” system called quarter-comma meantone temperament. They divided the dissonance (comma) of the major 3rds in Pythagorean tuning among four 5ths (hence “quarter-comma”). This temperament pervaded Europe during much of the Renaissance until the late Baroque period.
Keys with more sharps/flats were more dissonant & thus used to express intense affects. Extreme keys were deemed unplayable. According to Willard A. Palmer’s introduction to _J.S. Bach: Inventions & Sinfonias_, because of meantone’s limitations, Bach used only 15 keys in his _Inventions and Sinfonias_(1720).
WELL TEMPERAMENT
Contrast that to all 24 keys being displayed by Bach in both books of _The Well-Tempered Clavier_(1722 & 1742). Well temperament is usable but not equal in every key. Intervalic differences were celebrated. Some keys use some ratio-based intervals. Dissonant keys were used expressively.
EQUAL TEMPERAMENT
Theorists modified well temperament to arrive at true equal temperament in the early 20th century. We can now play equally well in all keys with beautiful symmetry, yet we have lost both the harmony of ratio-based intervals & the colorful differences between keys.
TUNING & TEMPERAMENT SYSTEMS USED
Each set of exercises is rendered in 5 systems:
1) Just intonation (tuned to the tonic)
2) Pythagorean tuning (tuned to C)
3) Quarter-comma meantone temperament (tuned to C)
4) Well temperament (Kirnberger III, tuned to C)
5) Equal temperament (tuned to C)
Of the many possible ratios in just intonation, I chose these via just_intonation.scl:
16/15
9/8
6/5
5/4
4/3
7/5 (used in Lydian)
3/2
8/5
5/3
9/5
15/8
2/1
https://usermanuals.garritan.com/ARIA...
This link, Cam Taylor, Prof. Scott Marcus’ Tuning & Temperament course at UCSB, & the following articles were helpful in writing this section:
http://www.early-music.info/octaves_t...
https://en.wikipedia.org/wiki/Musical...
God bless you & yours,
Mark Lybarger-Monson, Ph.D.
(music composition from UCSB)
www.ml-m.net
“The Lord bless you and keep you;
the Lord make his face to shine upon you and be gracious to you;
the Lord lift up his countenance upon you and give you peace.”
(Num. 6:24-26, ESV)
“And the peace of God, which surpasses all understanding, will guard your hearts and your minds in Christ Jesus.”
(Phil. 4:7, ESV)
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در تاریخ 1399/05/03 منتشر شده
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