rhythm_pattern_explorer

Progressive Transformation Reference

Overview

This document provides comprehensive test results for implementing progressive transformations in the Rhythm Pattern Explorer plugin. It compares all 8 progressive transformations with the webapp implementation to ensure accurate plugin behavior.

Test Patterns

1. E(8,8)B>1 - Barlow Concentration: 8 to 1 onsets

Algorithm: Barlow Indispensability
Mode: Concentration (removing onsets)

Step	Onsets	Pattern	Description
Base	8	11111111	All beats active
1	7	10111111	Remove position 1 (least indispensable)
2	6	10101111	Remove position 3 (least indispensable)
3	5	10101011	Remove position 5 (least indispensable)
4	4	10101010	Remove position 7 (least indispensable)
5	3	10001010	Remove position 2 (medium indispensable)
6	2	10001000	Remove position 6 (medium indispensable)
7	1	10000000	Remove position 4, keep downbeat

2. E(1,8)B>8 - Barlow Dilution: 1 to 8 onsets

Algorithm: Barlow Indispensability
Mode: Dilution (adding onsets)

Step	Onsets	Pattern	Description
Base	1	10000000	Only downbeat
1	2	10001000	Add position 4 (highest indispensability)
2	3	10101000	Add position 2 (medium indispensability)
3	4	10101010	Add position 6 (medium indispensability)
4	5	11101010	Add position 1 (least indispensable)
5	6	11111010	Add position 3 (least indispensable)
6	7	11111110	Add position 5 (least indispensable)
7	8	11111111	Add position 7 (least indispensable)

3. E(8,8)W>1 - Wolrab Concentration: 8 to 1 onsets

Algorithm: Wolrab (Anti-Barlow)
Mode: Concentration (removing onsets)

Step	Onsets	Pattern	Description
Base	8	11111111	All beats active
1	7	01111111	Remove position 0 (most indispensable - downbeat!)
2	6	01110111	Remove position 4 (highest indispensability)
3	5	01010111	Remove position 2 (medium indispensable)
4	4	01010101	Remove position 6 (medium indispensable)
5	3	00010101	Remove position 1 (least indispensable)
6	2	00000101	Remove position 3 (least indispensable)
7	1	00000001	Remove position 5, keep position 7

4. E(1,8)W>8 - Wolrab Dilution: 1 to 8 onsets

Algorithm: Wolrab (Anti-Barlow)
Mode: Dilution (adding onsets)

Step	Onsets	Pattern	Description
Base	1	10000000	Only downbeat
1	2	11000000	Add position 1 (least indispensable)
2	3	11010000	Add position 3 (least indispensable)
3	4	11010100	Add position 5 (least indispensable)
4	5	11010101	Add position 7 (least indispensable)
5	6	11110101	Add position 2 (medium indispensable)
6	7	11110111	Add position 6 (medium indispensable)
7	8	11111111	Add position 4 (highest indispensability)

5. E(8,8)E>1 - Euclidean Concentration: 8 to 1 onsets

Algorithm: Euclidean (Bjorklund)
Mode: Concentration

Step	Onsets	Pattern	Description
Base	8	11111111	All beats active
1	7	11111011	E(7,8) - maximally even distribution
2	6	11011011	E(6,8) - maximally even distribution
3	5	10110110	E(5,8) - maximally even distribution
4	4	10101010	E(4,8) - maximally even distribution
5	3	10010010	E(3,8) - maximally even distribution
6	2	10010000	E(2,8) - maximally even distribution
7	1	10000000	E(1,8) - single downbeat

6. E(1,8)E>8 - Euclidean Dilution: 1 to 8 onsets

Algorithm: Euclidean (Bjorklund)
Mode: Dilution

Step	Onsets	Pattern	Description
Base	1	10000000	E(1,8) - single downbeat
1	2	10010000	E(2,8) - maximally even distribution
2	3	10010010	E(3,8) - maximally even distribution
3	4	10101010	E(4,8) - maximally even distribution
4	5	10110110	E(5,8) - maximally even distribution
5	6	11011011	E(6,8) - maximally even distribution
6	7	11111011	E(7,8) - maximally even distribution
7	8	11111111	E(8,8) - all beats active

7. E(8,8)D>1 - Dilcue Concentration: 8 to 1 onsets

Algorithm: Dilcue (Anti-Euclidean)
Mode: Concentration

Step	Onsets	Pattern	Description
Base	8	11111111	All beats active
1	7	01111111	Complement of E(1,8)
2	6	01101111	Complement of E(2,8)
3	5	01101101	Complement of E(3,8)
4	4	01010101	Complement of E(4,8)
5	3	01001001	Complement of E(5,8)
6	2	00100100	Complement of E(6,8)
7	1	00000100	Complement of E(7,8)

8. E(1,8)D>8 - Dilcue Dilution: 1 to 8 onsets

Algorithm: Dilcue (Anti-Euclidean)
Mode: Dilution

Step	Onsets	Pattern	Description
Base	1	10000000	Single downbeat
1	2	00100100	Complement of E(6,8)
2	3	01001001	Complement of E(5,8)
3	4	01010101	Complement of E(4,8)
4	5	01101101	Complement of E(3,8)
5	6	01101111	Complement of E(2,8)
6	7	01111111	Complement of E(1,8)
7	8	11111111	All beats active

Algorithm Implementation Details

Barlow Indispensability Algorithm

Based on Clarence Barlow’s concept of indispensability values for different metrical positions.

Indispensability Table for 8 steps:

Position 0: 1.000 (downbeat - most indispensable)
Position 1: 0.333 (least indispensable)
Position 2: 0.666 (medium indispensable)
Position 3: 0.333 (least indispensable)
Position 4: 0.833 (high indispensable - halfway point)
Position 5: 0.333 (least indispensable)
Position 6: 0.666 (medium indispensable)
Position 7: 0.333 (least indispensable)

Transformation Rules:

Concentration (removing onsets): Remove least indispensable onsets first, preserve downbeat
Dilution (adding onsets): Add onsets to most indispensable empty positions first

Wolrab (Anti-Barlow) Algorithm

Inverts the Barlow logic to create anti-metrical patterns.

Transformation Rules:

Concentration (removing onsets): Remove most indispensable onsets first (including downbeat!)
Dilution (adding onsets): Add onsets to least indispensable empty positions first

Euclidean Algorithm

Uses the Bjorklund algorithm to create maximally even distributions.

Transformation Rules:

Always generates the standard Euclidean pattern E(k,n) for k onsets in n steps
Creates the most evenly spaced distribution possible

Dilcue (Anti-Euclidean) Algorithm

Generates the complement of Euclidean patterns.

Transformation Rules:

For k onsets in n steps, generates the complement of E(n-k,n)
Creates maximally uneven distributions (the opposite of Euclidean)

Plugin Implementation Checklist

Base Pattern Generation

E(8,8) generates “11111111” (all 8 positions active)
E(1,8) generates “10000000” (only downbeat active)

Barlow Transformer

Implements indispensability table calculation for any step count
Concentration mode removes least indispensable onsets first
Preserves downbeat (position 0) during concentration
Dilution mode adds onsets to most indispensable empty positions
Progressive stepping works for any start/end onset count

Wolrab Transformer

Uses same indispensability table as Barlow but inverts logic
Concentration mode removes most indispensable onsets first (including downbeat)
Dilution mode adds onsets to least indispensable empty positions
Progressive stepping works for any start/end onset count

Euclidean Transformer

Implements Bjorklund algorithm for any (k,n) combination
Progressive stepping generates E(k,n) for each intermediate k
Handles edge cases (k=0, k=n)

Dilcue Transformer

Generates complement patterns correctly
For k onsets, uses complement of E(n-k,n) pattern
Progressive stepping works through complement sequence

Progressive UPI Notation

Parses patterns like “E(8,8)B>1” correctly
Supports all 4 transformer types (B, W, E, D)
Enables step-by-step progression with Enter key
Displays transformation progress clearly

Test Validation

Use the patterns above to validate your plugin implementation:

Generate base patterns and verify they match expected binary strings
Run progressive transformations and compare each step with the expected output
Test edge cases like same source/target onset counts
Verify algorithm behavior matches the webapp’s mathematical approach

The test file /Users/alex/Documents/Coding/rhythm_pattern_explorer/progressive_test_simple.js can be run to regenerate these results for verification.

Key Differences Between Algorithms

Algorithm	Concentration Strategy	Dilution Strategy	Downbeat Treatment
Barlow (B)	Remove least indispensable	Add to most indispensable	Always preserved
Wolrab (W)	Remove most indispensable	Add to least indispensable	Can be removed
Euclidean (E)	Generate E(k,n)	Generate E(k,n)	Depends on math
Dilcue (D)	Generate complement	Generate complement	Depends on math

This comprehensive reference should enable accurate implementation of all 8 progressive transformations in the plugin, with exact pattern matching to the webapp behavior.

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