5 Finger Chord Sequences With No Finger Reuse

chords.py

#!/usr/bin/env python3

import itertools

def same_finger(ngram):
    fingers = 0
    for chord in ngram:
        if chord & fingers:
            return False
        fingers |= chord
    return True

def get_fingers(ngram):
    return [f"{chord:05b}" for chord in ngram]

def count_fingers(ngram):
    return sum([f"{chord:b}".count("1") for chord in ngram])

chords = list(range(1, 32))
bigrams = list(filter(same_finger, itertools.permutations(chords, 2)))
trigrams = list(filter(same_finger, itertools.permutations(chords, 3)))
lf_chords = sorted([[chord] for chord in chords], key=count_fingers)
lf_bigrams = sorted(bigrams, key=count_fingers)
lf_trigrams = sorted(trigrams, key=count_fingers)

print(*[(get_fingers(chord), count_fingers(chord)) for chord in lf_chords], sep='\n')
print(*[(get_fingers(bigram), count_fingers(bigram)) for bigram in lf_bigrams], sep='\n')
print(*[(get_fingers(trigram), count_fingers(trigram)) for trigram in lf_trigrams], sep='\n')

chords.txt

(['00001'], 1)
(['00010'], 1)
(['00100'], 1)
(['01000'], 1)
(['10000'], 1)
(['00011'], 2)
(['00101'], 2)
(['00110'], 2)
(['01001'], 2)
(['01010'], 2)
(['01100'], 2)
(['10001'], 2)
(['10010'], 2)
(['10100'], 2)
(['11000'], 2)
(['00111'], 3)
(['01011'], 3)
(['01101'], 3)
(['01110'], 3)
(['10011'], 3)
(['10101'], 3)
(['10110'], 3)
(['11001'], 3)
(['11010'], 3)
(['11100'], 3)
(['01111'], 4)
(['10111'], 4)
(['11011'], 4)
(['11101'], 4)
(['11110'], 4)
(['11111'], 5)
(['00001', '00010'], 2)
(['00001', '00100'], 2)
(['00001', '01000'], 2)
(['00001', '10000'], 2)
(['00010', '00001'], 2)
(['00010', '00100'], 2)
(['00010', '01000'], 2)
(['00010', '10000'], 2)
(['00100', '00001'], 2)
(['00100', '00010'], 2)
(['00100', '01000'], 2)
(['00100', '10000'], 2)
(['01000', '00001'], 2)
(['01000', '00010'], 2)
(['01000', '00100'], 2)
(['01000', '10000'], 2)
(['10000', '00001'], 2)
(['10000', '00010'], 2)
(['10000', '00100'], 2)
(['10000', '01000'], 2)
(['00001', '00110'], 3)
(['00001', '01010'], 3)
(['00001', '01100'], 3)
(['00001', '10010'], 3)
(['00001', '10100'], 3)
(['00001', '11000'], 3)
(['00010', '00101'], 3)
(['00010', '01001'], 3)
(['00010', '01100'], 3)
(['00010', '10001'], 3)
(['00010', '10100'], 3)
(['00010', '11000'], 3)
(['00011', '00100'], 3)
(['00011', '01000'], 3)
(['00011', '10000'], 3)
(['00100', '00011'], 3)
(['00100', '01001'], 3)
(['00100', '01010'], 3)
(['00100', '10001'], 3)
(['00100', '10010'], 3)
(['00100', '11000'], 3)
(['00101', '00010'], 3)
(['00101', '01000'], 3)
(['00101', '10000'], 3)
(['00110', '00001'], 3)
(['00110', '01000'], 3)
(['00110', '10000'], 3)
(['01000', '00011'], 3)
(['01000', '00101'], 3)
(['01000', '00110'], 3)
(['01000', '10001'], 3)
(['01000', '10010'], 3)
(['01000', '10100'], 3)
(['01001', '00010'], 3)
(['01001', '00100'], 3)
(['01001', '10000'], 3)
(['01010', '00001'], 3)
(['01010', '00100'], 3)
(['01010', '10000'], 3)
(['01100', '00001'], 3)
(['01100', '00010'], 3)
(['01100', '10000'], 3)
(['10000', '00011'], 3)
(['10000', '00101'], 3)
(['10000', '00110'], 3)
(['10000', '01001'], 3)
(['10000', '01010'], 3)
(['10000', '01100'], 3)
(['10001', '00010'], 3)
(['10001', '00100'], 3)
(['10001', '01000'], 3)
(['10010', '00001'], 3)
(['10010', '00100'], 3)
(['10010', '01000'], 3)
(['10100', '00001'], 3)
(['10100', '00010'], 3)
(['10100', '01000'], 3)
(['11000', '00001'], 3)
(['11000', '00010'], 3)
(['11000', '00100'], 3)
(['00001', '01110'], 4)
(['00001', '10110'], 4)
(['00001', '11010'], 4)
(['00001', '11100'], 4)
(['00010', '01101'], 4)
(['00010', '10101'], 4)
(['00010', '11001'], 4)
(['00010', '11100'], 4)
(['00011', '01100'], 4)
(['00011', '10100'], 4)
(['00011', '11000'], 4)
(['00100', '01011'], 4)
(['00100', '10011'], 4)
(['00100', '11001'], 4)
(['00100', '11010'], 4)
(['00101', '01010'], 4)
(['00101', '10010'], 4)
(['00101', '11000'], 4)
(['00110', '01001'], 4)
(['00110', '10001'], 4)
(['00110', '11000'], 4)
(['00111', '01000'], 4)
(['00111', '10000'], 4)
(['01000', '00111'], 4)
(['01000', '10011'], 4)
(['01000', '10101'], 4)
(['01000', '10110'], 4)
(['01001', '00110'], 4)
(['01001', '10010'], 4)
(['01001', '10100'], 4)
(['01010', '00101'], 4)
(['01010', '10001'], 4)
(['01010', '10100'], 4)
(['01011', '00100'], 4)
(['01011', '10000'], 4)
(['01100', '00011'], 4)
(['01100', '10001'], 4)
(['01100', '10010'], 4)
(['01101', '00010'], 4)
(['01101', '10000'], 4)
(['01110', '00001'], 4)
(['01110', '10000'], 4)
(['10000', '00111'], 4)
(['10000', '01011'], 4)
(['10000', '01101'], 4)
(['10000', '01110'], 4)
(['10001', '00110'], 4)
(['10001', '01010'], 4)
(['10001', '01100'], 4)
(['10010', '00101'], 4)
(['10010', '01001'], 4)
(['10010', '01100'], 4)
(['10011', '00100'], 4)
(['10011', '01000'], 4)
(['10100', '00011'], 4)
(['10100', '01001'], 4)
(['10100', '01010'], 4)
(['10101', '00010'], 4)
(['10101', '01000'], 4)
(['10110', '00001'], 4)
(['10110', '01000'], 4)
(['11000', '00011'], 4)
(['11000', '00101'], 4)
(['11000', '00110'], 4)
(['11001', '00010'], 4)
(['11001', '00100'], 4)
(['11010', '00001'], 4)
(['11010', '00100'], 4)
(['11100', '00001'], 4)
(['11100', '00010'], 4)
(['00001', '11110'], 5)
(['00010', '11101'], 5)
(['00011', '11100'], 5)
(['00100', '11011'], 5)
(['00101', '11010'], 5)
(['00110', '11001'], 5)
(['00111', '11000'], 5)
(['01000', '10111'], 5)
(['01001', '10110'], 5)
(['01010', '10101'], 5)
(['01011', '10100'], 5)
(['01100', '10011'], 5)
(['01101', '10010'], 5)
(['01110', '10001'], 5)
(['01111', '10000'], 5)
(['10000', '01111'], 5)
(['10001', '01110'], 5)
(['10010', '01101'], 5)
(['10011', '01100'], 5)
(['10100', '01011'], 5)
(['10101', '01010'], 5)
(['10110', '01001'], 5)
(['10111', '01000'], 5)
(['11000', '00111'], 5)
(['11001', '00110'], 5)
(['11010', '00101'], 5)
(['11011', '00100'], 5)
(['11100', '00011'], 5)
(['11101', '00010'], 5)
(['11110', '00001'], 5)
(['00001', '00010', '00100'], 3)
(['00001', '00010', '01000'], 3)
(['00001', '00010', '10000'], 3)
(['00001', '00100', '00010'], 3)
(['00001', '00100', '01000'], 3)
(['00001', '00100', '10000'], 3)
(['00001', '01000', '00010'], 3)
(['00001', '01000', '00100'], 3)
(['00001', '01000', '10000'], 3)
(['00001', '10000', '00010'], 3)
(['00001', '10000', '00100'], 3)
(['00001', '10000', '01000'], 3)
(['00010', '00001', '00100'], 3)
(['00010', '00001', '01000'], 3)
(['00010', '00001', '10000'], 3)
(['00010', '00100', '00001'], 3)
(['00010', '00100', '01000'], 3)
(['00010', '00100', '10000'], 3)
(['00010', '01000', '00001'], 3)
(['00010', '01000', '00100'], 3)
(['00010', '01000', '10000'], 3)
(['00010', '10000', '00001'], 3)
(['00010', '10000', '00100'], 3)
(['00010', '10000', '01000'], 3)
(['00100', '00001', '00010'], 3)
(['00100', '00001', '01000'], 3)
(['00100', '00001', '10000'], 3)
(['00100', '00010', '00001'], 3)
(['00100', '00010', '01000'], 3)
(['00100', '00010', '10000'], 3)
(['00100', '01000', '00001'], 3)
(['00100', '01000', '00010'], 3)
(['00100', '01000', '10000'], 3)
(['00100', '10000', '00001'], 3)
(['00100', '10000', '00010'], 3)
(['00100', '10000', '01000'], 3)
(['01000', '00001', '00010'], 3)
(['01000', '00001', '00100'], 3)
(['01000', '00001', '10000'], 3)
(['01000', '00010', '00001'], 3)
(['01000', '00010', '00100'], 3)
(['01000', '00010', '10000'], 3)
(['01000', '00100', '00001'], 3)
(['01000', '00100', '00010'], 3)
(['01000', '00100', '10000'], 3)
(['01000', '10000', '00001'], 3)
(['01000', '10000', '00010'], 3)
(['01000', '10000', '00100'], 3)
(['10000', '00001', '00010'], 3)
(['10000', '00001', '00100'], 3)
(['10000', '00001', '01000'], 3)
(['10000', '00010', '00001'], 3)
(['10000', '00010', '00100'], 3)
(['10000', '00010', '01000'], 3)
(['10000', '00100', '00001'], 3)
(['10000', '00100', '00010'], 3)
(['10000', '00100', '01000'], 3)
(['10000', '01000', '00001'], 3)
(['10000', '01000', '00010'], 3)
(['10000', '01000', '00100'], 3)
(['00001', '00010', '01100'], 4)
(['00001', '00010', '10100'], 4)
(['00001', '00010', '11000'], 4)
(['00001', '00100', '01010'], 4)
(['00001', '00100', '10010'], 4)
(['00001', '00100', '11000'], 4)
(['00001', '00110', '01000'], 4)
(['00001', '00110', '10000'], 4)
(['00001', '01000', '00110'], 4)
(['00001', '01000', '10010'], 4)
(['00001', '01000', '10100'], 4)
(['00001', '01010', '00100'], 4)
(['00001', '01010', '10000'], 4)
(['00001', '01100', '00010'], 4)
(['00001', '01100', '10000'], 4)
(['00001', '10000', '00110'], 4)
(['00001', '10000', '01010'], 4)
(['00001', '10000', '01100'], 4)
(['00001', '10010', '00100'], 4)
(['00001', '10010', '01000'], 4)
(['00001', '10100', '00010'], 4)
(['00001', '10100', '01000'], 4)
(['00001', '11000', '00010'], 4)
(['00001', '11000', '00100'], 4)
(['00010', '00001', '01100'], 4)
(['00010', '00001', '10100'], 4)
(['00010', '00001', '11000'], 4)
(['00010', '00100', '01001'], 4)
(['00010', '00100', '10001'], 4)
(['00010', '00100', '11000'], 4)
(['00010', '00101', '01000'], 4)
(['00010', '00101', '10000'], 4)
(['00010', '01000', '00101'], 4)
(['00010', '01000', '10001'], 4)
(['00010', '01000', '10100'], 4)
(['00010', '01001', '00100'], 4)
(['00010', '01001', '10000'], 4)
(['00010', '01100', '00001'], 4)
(['00010', '01100', '10000'], 4)
(['00010', '10000', '00101'], 4)
(['00010', '10000', '01001'], 4)
(['00010', '10000', '01100'], 4)
(['00010', '10001', '00100'], 4)
(['00010', '10001', '01000'], 4)
(['00010', '10100', '00001'], 4)
(['00010', '10100', '01000'], 4)
(['00010', '11000', '00001'], 4)
(['00010', '11000', '00100'], 4)
(['00011', '00100', '01000'], 4)
(['00011', '00100', '10000'], 4)
(['00011', '01000', '00100'], 4)
(['00011', '01000', '10000'], 4)
(['00011', '10000', '00100'], 4)
(['00011', '10000', '01000'], 4)
(['00100', '00001', '01010'], 4)
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(['00100', '00001', '11000'], 4)
(['00100', '00010', '01001'], 4)
(['00100', '00010', '10001'], 4)
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(['00100', '01000', '00011'], 4)
(['00100', '01000', '10001'], 4)
(['00100', '01000', '10010'], 4)
(['00100', '01001', '00010'], 4)
(['00100', '01001', '10000'], 4)
(['00100', '01010', '00001'], 4)
(['00100', '01010', '10000'], 4)
(['00100', '10000', '00011'], 4)
(['00100', '10000', '01001'], 4)
(['00100', '10000', '01010'], 4)
(['00100', '10001', '00010'], 4)
(['00100', '10001', '01000'], 4)
(['00100', '10010', '00001'], 4)
(['00100', '10010', '01000'], 4)
(['00100', '11000', '00001'], 4)
(['00100', '11000', '00010'], 4)
(['00101', '00010', '01000'], 4)
(['00101', '00010', '10000'], 4)
(['00101', '01000', '00010'], 4)
(['00101', '01000', '10000'], 4)
(['00101', '10000', '00010'], 4)
(['00101', '10000', '01000'], 4)
(['00110', '00001', '01000'], 4)
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(['00110', '01000', '00001'], 4)
(['00110', '01000', '10000'], 4)
(['00110', '10000', '00001'], 4)
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(['01000', '00001', '00110'], 4)
(['01000', '00001', '10010'], 4)
(['01000', '00001', '10100'], 4)
(['01000', '00010', '00101'], 4)
(['01000', '00010', '10001'], 4)
(['01000', '00010', '10100'], 4)
(['01000', '00011', '00100'], 4)
(['01000', '00011', '10000'], 4)
(['01000', '00100', '00011'], 4)
(['01000', '00100', '10001'], 4)
(['01000', '00100', '10010'], 4)
(['01000', '00101', '00010'], 4)
(['01000', '00101', '10000'], 4)
(['01000', '00110', '00001'], 4)
(['01000', '00110', '10000'], 4)
(['01000', '10000', '00011'], 4)
(['01000', '10000', '00101'], 4)
(['01000', '10000', '00110'], 4)
(['01000', '10001', '00010'], 4)
(['01000', '10001', '00100'], 4)
(['01000', '10010', '00001'], 4)
(['01000', '10010', '00100'], 4)
(['01000', '10100', '00001'], 4)
(['01000', '10100', '00010'], 4)
(['01001', '00010', '00100'], 4)
(['01001', '00010', '10000'], 4)
(['01001', '00100', '00010'], 4)
(['01001', '00100', '10000'], 4)
(['01001', '10000', '00010'], 4)
(['01001', '10000', '00100'], 4)
(['01010', '00001', '00100'], 4)
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(['01010', '00100', '00001'], 4)
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(['01100', '00001', '00010'], 4)
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(['10000', '01010', '00001'], 4)
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(['10100', '01000', '00010'], 4)
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(['11000', '00001', '00100'], 4)
(['11000', '00010', '00001'], 4)
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(['00011', '00100', '11000'], 5)
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