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Temperament

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Lissajous Figures

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Temperament: Boethius

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Temperament

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Temperament1. Music of the Spheres (musica

mundana)

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Temperament1. Music of the Spheres (musica

mundana)

2. Harmonic overtones

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Temperament: Musica MundanaThe man that hath not music in himself

Nor is moved with concord of sweet sounds

Is fit for treasons, stratagems and spoils,The motions of his spirit are as dull as night

And his affections dark as Erebus.

Let no such man be trusted.

Shakespeare, Merchant of Venice. Act V, sc. 1, l. 54 (1596/8)

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Temperament: Musica MundanaSure there is music even in the beauty,

and the silent note which cupid strikes,

far sweeter than the sound of aninstrument. For there is music whereverthere is harmony, order or proportion,and thus far we may maintain the music

of the spheres.

Thomas Browne (1605 1682), Religio Medici.

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Temperament: Musica Mundana

Robert Fludd (1574 -1637)

Celestial

Monochord

De Musica Mundana (1618)

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Temperament: Musica Mundana

Johannes Kepler (1571 1630)

Mysterium Cosmographicum (1596)

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Temperament: Musica Mundana

Vincenzo Galilei (1520 1591)

A special discourse concerning the diversityof ratios in the octave

A special discourse concerning the unison

Dialogue on ancient and modern music(1581)

Discourse concerning the various opinionsthat the three most famous sects of ancientmusicians had concerning the matter ofsound and tunings

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Temperament: Musica Mundana

Vincenzo Galilei (1520 1591)

Sounds are unisonant only insofar as the

diversity of the materials of which they are

made allows the quantity of sound, the diversity of agents

that strike them, the thickness, height and

length of the body on which they are

stretched and the force with which they arestruck.

Vincenzo Galilei,A special discourse concerning the unison

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Temperament: Musica Mundana

Vincenzo Galilei (1520 1591)

Ancient music is lostand its light has so

dimmed that many consider its wonderful

excellence a dream and a fable After the loss [of ancient music] men began

to derive from instruments rules for

composing and singing several airs together

Vincenzo Galilei, Dialogue on Ancient and Modern Music(1581)

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Temperament: Musica Mundana

Vincenzo Galilei (1520 1591)

Voices, being naturally perfect, cannot singwell a song that is not composed according to

their perfect usage, but an instrumenttempered according to the imperfect usage inwhich the song is imperfectly composed, onthe other hand, can play it.

(Discourse concerning the various opinions that the three mostfamous sects of ancient musicians had concerning the matter ofsound and tunings.)

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Temperament: Tuning Pythagorean tuning

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Temperament: Tuning Pythagorean tuning

Just Intonation

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Temperament: Tuning Pythagorean tuning

Just Intonation

Mean-tone tuning

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Temperament: Tuning Pythagorean tuning

Just Intonation

Mean-tone tuning

The well-tuned

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Temperament: Tuning Pythagorean tuning

Just Intonation

Mean-tone tuning

The well-tuned

Equal Temperament

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Harry Partchs forty-three note

octave

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Some of Harry Partchs instruments

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Planetary Kisses

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References

Clark and rehding

Strunk

Stuart isaacoff Chrstitopher Stembridge

La Monte young

Newband

Kyle Gann

How et ruined harmony