Musical chords and ratios, THEORICA MUSICE, by...

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Page 1: Musical chords and ratios, THEORICA MUSICE, by …cs.au.dk/~dsound/DigitalAudio.dir/week2/timbre/timbre.pdf · Musical chords and ratios, as demonstrated by Pythagoras. A woodcut
Page 2: Musical chords and ratios, THEORICA MUSICE, by …cs.au.dk/~dsound/DigitalAudio.dir/week2/timbre/timbre.pdf · Musical chords and ratios, as demonstrated by Pythagoras. A woodcut
Page 3: Musical chords and ratios, THEORICA MUSICE, by …cs.au.dk/~dsound/DigitalAudio.dir/week2/timbre/timbre.pdf · Musical chords and ratios, as demonstrated by Pythagoras. A woodcut

Musical chords and ratios, as demonstrated by Pythagoras. A woodcut from the THEORICA MUSICE, Naples, 1492, by Franchino Gafurio, music theorist and choirmaster of Milan cathedral.

Page 4: Musical chords and ratios, THEORICA MUSICE, by …cs.au.dk/~dsound/DigitalAudio.dir/week2/timbre/timbre.pdf · Musical chords and ratios, as demonstrated by Pythagoras. A woodcut

Frequency ~ 1/length

Page 5: Musical chords and ratios, THEORICA MUSICE, by …cs.au.dk/~dsound/DigitalAudio.dir/week2/timbre/timbre.pdf · Musical chords and ratios, as demonstrated by Pythagoras. A woodcut
Page 6: Musical chords and ratios, THEORICA MUSICE, by …cs.au.dk/~dsound/DigitalAudio.dir/week2/timbre/timbre.pdf · Musical chords and ratios, as demonstrated by Pythagoras. A woodcut
Page 7: Musical chords and ratios, THEORICA MUSICE, by …cs.au.dk/~dsound/DigitalAudio.dir/week2/timbre/timbre.pdf · Musical chords and ratios, as demonstrated by Pythagoras. A woodcut
Page 8: Musical chords and ratios, THEORICA MUSICE, by …cs.au.dk/~dsound/DigitalAudio.dir/week2/timbre/timbre.pdf · Musical chords and ratios, as demonstrated by Pythagoras. A woodcut
Page 9: Musical chords and ratios, THEORICA MUSICE, by …cs.au.dk/~dsound/DigitalAudio.dir/week2/timbre/timbre.pdf · Musical chords and ratios, as demonstrated by Pythagoras. A woodcut
Page 10: Musical chords and ratios, THEORICA MUSICE, by …cs.au.dk/~dsound/DigitalAudio.dir/week2/timbre/timbre.pdf · Musical chords and ratios, as demonstrated by Pythagoras. A woodcut
Page 11: Musical chords and ratios, THEORICA MUSICE, by …cs.au.dk/~dsound/DigitalAudio.dir/week2/timbre/timbre.pdf · Musical chords and ratios, as demonstrated by Pythagoras. A woodcut
Page 12: Musical chords and ratios, THEORICA MUSICE, by …cs.au.dk/~dsound/DigitalAudio.dir/week2/timbre/timbre.pdf · Musical chords and ratios, as demonstrated by Pythagoras. A woodcut
Page 13: Musical chords and ratios, THEORICA MUSICE, by …cs.au.dk/~dsound/DigitalAudio.dir/week2/timbre/timbre.pdf · Musical chords and ratios, as demonstrated by Pythagoras. A woodcut
Page 14: Musical chords and ratios, THEORICA MUSICE, by …cs.au.dk/~dsound/DigitalAudio.dir/week2/timbre/timbre.pdf · Musical chords and ratios, as demonstrated by Pythagoras. A woodcut

Fourier (1768 – 1830)

von Helmholtz (1821 –1894)

Page 15: Musical chords and ratios, THEORICA MUSICE, by …cs.au.dk/~dsound/DigitalAudio.dir/week2/timbre/timbre.pdf · Musical chords and ratios, as demonstrated by Pythagoras. A woodcut
Page 16: Musical chords and ratios, THEORICA MUSICE, by …cs.au.dk/~dsound/DigitalAudio.dir/week2/timbre/timbre.pdf · Musical chords and ratios, as demonstrated by Pythagoras. A woodcut
Page 17: Musical chords and ratios, THEORICA MUSICE, by …cs.au.dk/~dsound/DigitalAudio.dir/week2/timbre/timbre.pdf · Musical chords and ratios, as demonstrated by Pythagoras. A woodcut

Time domain Frequency domain

Page 18: Musical chords and ratios, THEORICA MUSICE, by …cs.au.dk/~dsound/DigitalAudio.dir/week2/timbre/timbre.pdf · Musical chords and ratios, as demonstrated by Pythagoras. A woodcut
Page 19: Musical chords and ratios, THEORICA MUSICE, by …cs.au.dk/~dsound/DigitalAudio.dir/week2/timbre/timbre.pdf · Musical chords and ratios, as demonstrated by Pythagoras. A woodcut
Page 20: Musical chords and ratios, THEORICA MUSICE, by …cs.au.dk/~dsound/DigitalAudio.dir/week2/timbre/timbre.pdf · Musical chords and ratios, as demonstrated by Pythagoras. A woodcut
Page 21: Musical chords and ratios, THEORICA MUSICE, by …cs.au.dk/~dsound/DigitalAudio.dir/week2/timbre/timbre.pdf · Musical chords and ratios, as demonstrated by Pythagoras. A woodcut
Page 22: Musical chords and ratios, THEORICA MUSICE, by …cs.au.dk/~dsound/DigitalAudio.dir/week2/timbre/timbre.pdf · Musical chords and ratios, as demonstrated by Pythagoras. A woodcut
Page 23: Musical chords and ratios, THEORICA MUSICE, by …cs.au.dk/~dsound/DigitalAudio.dir/week2/timbre/timbre.pdf · Musical chords and ratios, as demonstrated by Pythagoras. A woodcut
Page 24: Musical chords and ratios, THEORICA MUSICE, by …cs.au.dk/~dsound/DigitalAudio.dir/week2/timbre/timbre.pdf · Musical chords and ratios, as demonstrated by Pythagoras. A woodcut
Page 25: Musical chords and ratios, THEORICA MUSICE, by …cs.au.dk/~dsound/DigitalAudio.dir/week2/timbre/timbre.pdf · Musical chords and ratios, as demonstrated by Pythagoras. A woodcut
Page 26: Musical chords and ratios, THEORICA MUSICE, by …cs.au.dk/~dsound/DigitalAudio.dir/week2/timbre/timbre.pdf · Musical chords and ratios, as demonstrated by Pythagoras. A woodcut
Page 27: Musical chords and ratios, THEORICA MUSICE, by …cs.au.dk/~dsound/DigitalAudio.dir/week2/timbre/timbre.pdf · Musical chords and ratios, as demonstrated by Pythagoras. A woodcut
Page 28: Musical chords and ratios, THEORICA MUSICE, by …cs.au.dk/~dsound/DigitalAudio.dir/week2/timbre/timbre.pdf · Musical chords and ratios, as demonstrated by Pythagoras. A woodcut
Page 29: Musical chords and ratios, THEORICA MUSICE, by …cs.au.dk/~dsound/DigitalAudio.dir/week2/timbre/timbre.pdf · Musical chords and ratios, as demonstrated by Pythagoras. A woodcut

INANCIAL ANALYSIS AND P LANNING RATIO …...term solvency ratios Leverage Ratio/Long term solvency Ratios Activity Ratios/Efficiency Ratios/Performance Ratios/Turnover ratios Profitability

INANCIAL ANALYSIS AND P LANNING RATIO …...term solvency ratios Leverage Ratio/Long term solvency Ratios Activity Ratios/Efficiency Ratios/Performance Ratios/Turnover ratios Profitability

MUSICAL^ DRAMATIC ATHLETIC. - LA84 Foundationlibrary.la84.org/SportsLibrary/SportingLife/1893/VOL_22_NO_06/SL...terviewer -those crashing chords with ... national everyone' cries out

MUSICAL^ DRAMATIC ATHLETIC. - LA84 Foundationlibrary.la84.org/SportsLibrary/SportingLife/1893/VOL_22_NO_06/SL...terviewer -those crashing chords with ... national everyone' cries out

THE GEOMETRY OF MUSICAL CHORDS - Semantic ScholarHarmony delimits the acceptable chords (simultaneously occurring notes) and chord sequences. Counterpoint (or voice leading) is the

THE GEOMETRY OF MUSICAL CHORDS - Semantic ScholarHarmony delimits the acceptable chords (simultaneously occurring notes) and chord sequences. Counterpoint (or voice leading) is the

Musical Forms - Carleton University · Musical Forms Or, organizing music ... •Instrumental solos (often over verse chords) ... Queen –“Bohemian Rhapsody” •Multiple sections,

Musical Forms - Carleton University · Musical Forms Or, organizing music ... •Instrumental solos (often over verse chords) ... Queen –“Bohemian Rhapsody” •Multiple sections,

Musical Chord Preference - The Heller School at Brandeis ... · MUSICAL CHORD PREFERENCE: CULTURAL OR UNIVERSAL? ... after listening to major or minor chords, but after controlling

Musical Chord Preference - The Heller School at Brandeis ... · MUSICAL CHORD PREFERENCE: CULTURAL OR UNIVERSAL? ... after listening to major or minor chords, but after controlling

#01 - Chords-master > #01 - Chords-master > Chordkey Master Copy

#01 - Chords-master > #01 - Chords-master > Chordkey Master Copy

Consonance and Dissonance of Musical Chords: Neural Correlates ...

Consonance and Dissonance of Musical Chords: Neural Correlates ...

Chords Pananagutan Musical Presentation

Chords Pananagutan Musical Presentation

Musical Ratios From the Human Cochlea

Musical Ratios From the Human Cochlea

Perceived Harmonic Structure of Chords in Three Related Musical Keys

Perceived Harmonic Structure of Chords in Three Related Musical Keys

Finding Alternative Musical Scalespublic.tepper.cmu.edu/jnh/scalesSlidesCMU.pdf · • Pitch frequencies have simple ratios. – Rich and intelligible harmonies • Multiple keys

Finding Alternative Musical Scalespublic.tepper.cmu.edu/jnh/scalesSlidesCMU.pdf · • Pitch frequencies have simple ratios. – Rich and intelligible harmonies • Multiple keys

Guitar Chords

Guitar Chords

Perceived Harmonic Structure of Chords in Three Related ...creel/COGS160/COGS160...Chords in Three Related Musical Keys Carol L. Krumhansl Cornell University Jamshed J. Bharucha and

Perceived Harmonic Structure of Chords in Three Related ...creel/COGS160/COGS160...Chords in Three Related Musical Keys Carol L. Krumhansl Cornell University Jamshed J. Bharucha and

{ 8-1: Ratios and Equivalent Ratios IWBAT read and write ratios and equivalent ratios.

{ 8-1: Ratios and Equivalent Ratios IWBAT read and write ratios and equivalent ratios.

Musical Priorities - Ted Greene...1976/05/25  · c. Chord substitution and reharmonization (replacing given chords with interesting substitutes). d. The addition of moving voices.

Musical Priorities - Ted Greene...1976/05/25  · c. Chord substitution and reharmonization (replacing given chords with interesting substitutes). d. The addition of moving voices.

The Geometry of Musical Chords DRAFT - Freecanonsrythmiques.free.fr/gueststars/voiceleading.pdf · The Geometry of Musical Chords DRAFT ... under translation, reflection, ... including

The Geometry of Musical Chords DRAFT - Freecanonsrythmiques.free.fr/gueststars/voiceleading.pdf · The Geometry of Musical Chords DRAFT ... under translation, reflection, ... including

#01 - Chords-master > Chords a-g -Updated > 4-(d) Key

#01 - Chords-master > Chords a-g -Updated > 4-(d) Key

THE GEOMETRY OF MUSICAL CHORDS - Dmitri Tymoczkodmitri.mycpanel.princeton.edu/voiceleading.pdf · A musical chord can be represented as a point in a geometrical space ... distance

THE GEOMETRY OF MUSICAL CHORDS - Dmitri Tymoczkodmitri.mycpanel.princeton.edu/voiceleading.pdf · A musical chord can be represented as a point in a geometrical space ... distance

SEW.S2 Chords

SEW.S2 Chords

Musical Imagery: Generation of Tones and Chordstimothyhubbard.net/hubbardstoeckig88.pdf · 2009-06-07 · musical events (e.g., tones, chords, and melodies) ideal for the study of

Musical Imagery: Generation of Tones and Chordstimothyhubbard.net/hubbardstoeckig88.pdf · 2009-06-07 · musical events (e.g., tones, chords, and melodies) ideal for the study of