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Circle-Pitch-Plot

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A new CIRCLE-PITCH-PLOT function (examples below) will be part of the forthcoming Opusmodus 1.3.

 

The function CIRCLE-PIOTCH-PLOT returns a geometrical representation of relationships among the 12 pitch classes of the chromatic scale in pitch class space and provides an easy way to identify patterns and similarities between harmonic structures.

 

Clockwise motion represents ascending pitch motion, and counterclockwise motion represents descending pitch motion.

 

Examples:

 

Major Triad

(circle-pitch-plot '(c4e4g4))

Pasted Graphic.png

 

Minor Triad

(circle-pitch-plot '(c4f4ab4))

Pasted Graphic 1.pngPasted Graphic 1.png

 

Augmented Triad

(circle-pitch-plot '(c4e4gs4))

Pasted Graphic 2.png

 

All 4 augmented triads

(circle-pitch-plot '(c4e4gs4 db4f4a4 d4fs4bb4 eb4g4b4))

Pasted Graphic 3.png

 

 

With :style :fill

(circle-pitch-plot '(c4e4gs4 db4f4a4 d4fs4bb4 eb4g4b4) :style :fill)

Pasted Graphic 4.png

 

Example with chord names.

Fully-Diminished 7th Chord

(circle-pitch-plot 'dim7)

Pasted Graphic 5.png

 

All 3 fully-diminished 7th chords

(circle-pitch-plot '((c4 dim7) (cs4 dim7) (d4 dim7)))

Pasted Graphic 6.png

 

Whole-Tone Scale

(circle-pitch-plot '(0 2 4 6 8 10))

Pasted Graphic 7.png

 

The complex of 2 Whole-Tone Scale

(circle-pitch-plot '((0 2 4 6 8 10) (1 3 5 7 9 11)) :style :fill)

Pasted Graphic 8.png

 

Chromatic Scale

(circle-pitch-plot 'chromatic :point-radius 4)

Pasted Graphic 9.png

 

The complex of 6 tritones

(circle-pitch-plot '((0 6) (1 7) (2 8) (3 9) (4 10) (5 11)) :point-radius 4)

Pasted Graphic 10.png

 

Tonalities

(circle-pitch-plot 'mixolydian-greek :point-radius 4)

Pasted Graphic 11.png

(circle-pitch-plot 'bartok :point-radius 4)

Pasted Graphic 12.png

(circle-pitch-plot 'messiaen-mode3 :point-radius 4)

Pasted Graphic 13.png

(circle-pitch-plot 'hyojo :point-radius 4)

Pasted Graphic 14.png

 

Contrary Motion

(circle-pitch-plot '(0 1 11 2 10 3 9 4 8 5 7 6)
                   :sort nil :join-first nil)

Pasted Graphic 15.png

(circle-pitch-plot '((0 1) (0 2) (0 3) (0 4) (0 5) (0 6)
                     (0 7) (0 8) (0 9) (0 10) (0 11)) :point-radius 4)

Pasted Graphic 16.png

 

Example with Forte notation

(circle-pitch-plot '(6-32 6-7))

Pasted Graphic 17.png

 

Example with omn-form sequence and :type :pitches

 

(circle-pitch-plot '(((leg s g2 p dbow+sul d3 sul b3 dig1 a3 b3 d3 b3 d3)
                      (leg g2 d3 b3 a3 b3 d3 b3 d3)))
                   :type :pitches)

 

Pasted Graphic 18.png

 

Circle types

(circle-pitch-plot '((4 9 11) (3 5 10) (0 3 6 9)) :style :fill)

Pasted Graphic 19.png

(circle-pitch-plot '((4 9 11) (3 5 10) (0 3 6 9))
                   :type :pitches :style :fill)

 

Pasted Graphic 20.png

(circle-pitch-plot '((4 9 11) (3 5 10) (0 3 6 9))
                   :type :fifths :style :fill)

 

Pasted Graphic 21.png

 

Examples with :sort and :remove-duplicates set to nil

(circle-pitch-plot '(0 2 6 0 3 7 0 4 8))

Pasted Graphic 22.png

(circle-pitch-plot '(0 2 6 0 3 7 0 4 8) :sort nil)

Pasted Graphic 23.png

(circle-pitch-plot '(0 2 6 0 3 7 0 4 8)
                   :sort nil :remove-duplicates nil)

Pasted Graphic 24.png

(circle-pitch-plot '(0 2 6 0 3 7 0 4 8)
                   :sort nil :remove-duplicates nil :join-first nil)

 

Pasted Graphic 25.png

(circle-pitch-plot '(8 4 2 0 10 2 8 10 4 6 8)
                   :sort nil :remove-duplicates nil)

Pasted Graphic 26.png

 

Best wishes,

Janusz

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MARVELLOUS Function ! Thanks !

 

Necklace diagrams are a really important feature for many reasons:

 

1) Visualizing and teaching post tonal theory;

2) Visualizing the Rhythms (in conjuntion with the new Pcs-Rhythm function) and the Rhythm/Pitch Isomorphism;

3) Using the geometry relations to express harmonic properties and proportions;

4) Using the geometry relations to express rhythmic properties and proportions;

5) Visualizing Hauer's Trope Structures.

><><><><><

Database on tone rows and tropes

Harald Fripertinger, Peter Lackner
Last update: September 6, 2018

http://143.50.47.149/music/

><><><><><><

Chord Diagrams

http://143.50.47.149/music/chord_diagrams1.html

 

SUGGESTION:

 

Insert an option that enable to make circles with 3, 4, 5, 12, 16, any number of points.

This can be very useful in modelling rhythms.

 

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On 10/12/2018 at 2:42 PM, JulioHerrlein said:

Insert an option that enable to make circles with 3, 4, 5, 12, 16, any number of points.

This can be very useful in modelling rhythms.

 

In the later date we can make a CIRCLE-RHYTHM-PLOT function especially designed for that.

 

Thank you for the links.

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On 10/11/2018 at 8:10 PM, opmo said:

 

(circle-pitch-plot '(0 2 6 0 3 7 0 4 8) :sort nil)

Should the resulting plot for that example not return to 0 multiple times?

 

Anyway, thanks for doing this! 

 

Best,

Torsten

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On 10/13/2018 at 1:42 AM, torstenanders said:

Should the resulting plot for that example not return to 0 multiple times?

 

(circle-pitch-plot '(0 2 6 0 3 7 0 4 8)
                   :sort nil :remove-duplicates nil)

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2 hours ago, opmo said:

Pasted Graphic.pngPasted Graphic 1.png

 

                              (-e e q e q e)                                                                 (e q e q q) 

Really cool, Janusz! 

Nice to have different necklace sizes. According to Toussaint, the most widespread cycle is the 16 step cycle, typical in drum machines. 

 

All the best! 

 

Julio 

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8 hours ago, opmo said:

Euclidean Rhythm


(circle-rhythm-plot
 (gen-binary-euclidean 1 16 4 12)
 :point-radius 4 :points 16)

Pasted Graphic.pngPasted Graphic 1.png

Pasted Graphic 2.pngPasted Graphic 3.png

 

Great. I wish I had it by the time of writing my doctoral dissertation. It would be easier. Very inspiring to visualize the rhythms. 

What about a looping function, allowing to repeat the material X times? Many of these Euclidean Rhythm are conceived to be repeating ostinatos. Or just the gen-repeat can work... Best Julio 

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A very big thank you. I was waiting for this function because I use it regularly. Pedagogically it is a very useful tool.

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