# example 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:

`(circle-pitch-plot '(c4e4g4))`

`(circle-pitch-plot '(c4f4ab4))`

`(circle-pitch-plot '(c4e4gs4))`

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

With :style :fill

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

Example with chord names.

Fully-Diminished 7th Chord

`(circle-pitch-plot 'dim7)`

All 3 fully-diminished 7th chords

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

Whole-Tone Scale

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

The complex of 2 Whole-Tone Scale

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

Chromatic Scale

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

The complex of 6 tritones

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

Tonalities

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

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

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

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

Contrary Motion

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

```(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)```

Example with Forte notation

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

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)```

Circle types

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

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

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

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

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

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

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

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

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

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

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

Chord Diagrams

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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All the Best !!!

Looking Forward to the 1.3 version !!!

Julio

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Dear Janusz,

This function would be great in the 1.3 version.

Best,

Julio

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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.

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

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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:

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

You surely know that..? http://www.dynamictonality.com/xronomorph.htm

Maybe you can get some inspiration from it..

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2 hours ago, opmo said:

(-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

Best, J

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Looking Forward !!!

Any release date ?

All the best !!

Or maybe a Beta Version to the Colaborators ?

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Euclidean Rhythm

```(circle-rhythm-plot
(gen-binary-euclidean 1 16 4 12)

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On 10/13/2018 at 11:05 PM, JulioHerrlein said:

Any release date﻿ ?﻿﻿

soon.

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8 hours ago, opmo said:

Euclidean Rhythm

```
(circle-rhythm-plot
(gen-binary-euclidean 1 16 4 12)

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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Associate a list of symbols (names or better, numbers) to this list of rhythms and map symbols to rhythm for structure.

Look in opmo examples folder the Quartet 1b from Nigel Morgan who use this technique with SUBSTITUTE-MAP.

S.

Perfect, SB !

Best,

Julio

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The CIRCLE-RHYTHM-PLOT will use dash circle ("time like") for a better distinction between the CIRCLE-PITCH-PLOT.

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This is wonderful!

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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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