From Circle to Hyperspheres
Episode IV:
Visualizing Temperaments
Chapters
- 1 The Pythagorean Example
- 2 One Dimension : Problem
- 3 Two Dimensions : Works
- 4 Comparisons using 2D
- 5 Chords in 2D
- 6 Tempered Chromatic Circle
- 7 Tempered Harmonic Cube
- 8 Planet4D Flashback
- 9 Tempered Planet4D
- 10 Chords in 4D
- 11 Tempered Hypersphere
- 12 Well Tempered Hypersphere
-> Why and what is a Temperament ?
-> Because classical circular visualization of frequency fails to provide temperaments feelings, we will use complex numbers and deform the circle.
We can now compare temperaments shapes visually, and perceive the “dissonances” in the animations.
-> We propose a 3D model for visualizing tempered chords sequence.
-> The simple Planet4D model which was designed for equal temperament will be deformed by altering each Quaternion’s magnitude, to emphasis the audition feelings in historical tempered musical pieces.
Premiered at Technical University / Royal Conservatory of Madrid, 2017
Embeded Youtube Playlist :
Visualizing Temperaments 1: The Pythagorean Example
The well known Pythagorean tuning system, adding fifth until being back on the 1st Note
Visualizing Temperaments 1: The Pythagorean Example
Chap 24 The Pythagorean Example The well known Pythagorean tuning ...
Visualizing Temperaments 2: One Dimension as Usual mp4
Chap 25 One Dimension as usual Distributing frequencies along a circle ...
Visualizing Temperaments 3: TwoDimensions Works
We use the chromatic circle as a basis and associate, this time, each ...
Visualizing Temperaments 4:Two D Comparisons
Chap 27 Two-D Comparisons. By superimposing different temperaments ...
Visualizing Temperaments 5: Two D Chords
Chap 28 Two-D Chords. Pure intervals = Just intonation. In order to ...
Visualizing Temperaments 6: Tempered Chromatic Circle Zarlino
Chap 29 Tempered Chromatic Circle Zarlino Application to Zarlino ...
Visualizing Temperaments 7: Three D Cube
Chap 30 Three-D Cube We model each triad as a box with sides ...
Visualizing Temperaments 8: Tempered Harmonic Cube Bach
Chap 31 Tempered Harmonic Cube Bach Application to the famous Bach ...
Visualizing Temperaments 9: Planet 4D FlashBack
Chap 32 Planet-4D FlashBack Short summary of precedents episodes which ...
Visualizing Temperaments 10: Tempered Planet 4D
Chap 33 Tempered Planet-4D As in 2D, we deform the hypersphere along ...
Visualizing Temperaments 11: Four D Chords
Four-D Chords We add lines representing the fifth on the Planet-4D ...
Visualizing Temperaments 12: Tempered Hypersphere
Tempered Hypersphere As in 2D, We apply the deformation to the Sphere ...
Please refer to my Papers Section for scientific description,