A metaphor coined by Joseph Pehrson to explain one aspect of 72edo, which describes multiple instances of the closed 12edo pitch-set transposed by microtonal (in the sense of "less than a semitone") intervals, as similar to the derailleur mechanism on modern bicycles. The concept can apply to any EDO with a cardinality which is an even multiple of a lower-cardinality EDO. As an example, below is a diagram showing how this works for 72edo, as 6 bicycle-chains of 12edo. Firstly, take a look at the legend for the HEWM 72edo music notation accidentals.
lower raise inflection cents
b # semitone 100
v ^ 1/4-tone 50
< > 1/6-tone 331/3
- + 1/12-tone 162/3
In the "NOTATION" section of the table below, notes which are presented horizontally adjacent are enharmonically equivalent. Notes which line up vertically are on the same bike-chain. 8 different symbols in addition to the letter-names:
+ > ^ #
- < v b
16&2/3 ¢ 33&1/3 ¢ 50 ¢ 100 ¢
1/12 1/6 1/4 1/2 of a 'tone'
DE- SEMI- /------------------------------ NOTATION ------------------------------\
GREE TONES
0 0.00 C ----------|-----------|-----------|-------------|------------|-----
71 11.83 | C- | | | |
70 11.67 | | C< | | |
69 11.50 | | | Cv B^ | |
68 11.33 | | | | B> |
67 11.17 | | | | | B+
66 11.00 B ----------|-----------|-----------|-------------|------------|-----
65 10.83 | B- | | | |
64 10.67 | | B< | | |
63 10.50 | | | Bv Bb^ A#^ | |
62 10.33 | | | | Bb> A#> |
61 10.17 | | | | | Bb+ A#
60 10.00 Bb A# ------|-----------|-----------|-------------|------------|-----
59 9.83 | Bb- A#- | | | |
58 9.67 | | Bb< A#< | | |
57 9.50 | | | Bbv A#v A^ | |
56 9.33 | | | | A> |
55 9.17 | | | | | A+
54 9.00 A ----------|-----------|-----------|-------------|------------|-----
53 8.83 | A- | | | |
52 8.67 | | A< | | |
51 8.50 | | | Av Ab^ G#^ | |
50 8.33 | | | | Ab> G#> |
49 8.17 | | | | | Ab+ G#+
48 8.00 Ab G# ------|-----------|-----------|-------------|------------|-----
47 7.83 | Ab- G#- | | | |
46 7.67 | | Ab< G#< | | |
45 7.50 | | | Abv G#v G^ | |
44 7.33 | | | | G> |
43 7.17 | | | | | G+
42 7.00 G ----------|-----------|-----------|-------------|------------|-----
41 6.83 | G- | | | |
40 6.67 | | G< | | |
39 6.50 | | | F#^ Gv Gb^ | |
38 6.33 | | | | F#> Gb> |
37 6.17 | | | | | F#+ Gb+
36 6.00 F# Gb ------|-----------|-----------|-------------|------------|--------
35 5.83 | F#- Gb- | | | |
34 5.67 | | F#< Gb< | | |
33 5.50 | | | F#v F Gbv | |
32 5.33 | | | | F> |
31 5.17 | | | | | F+
30 5.00 F ----------|-----------|-----------|-------------|------------|--------
29 4.83 | F- | | | |
28 4.67 | | F< | | |
27 4.50 | | | E^ Fv | |
26 4.33 | | | | E> |
25 4.17 | | | | | E+
24 4.00 E ----------|-----------|-----------|-------------|------------|--------
23 3.83 | E- | | | |
22 3.67 | | E< | | |
21 3.50 | | | D#^ Eb^ Ev | |
20 3.33 | | | | D#> Eb> |
19 3.17 | | | | | D#+ Eb+
18 3.00 D# Eb ------|-----------|-----------|-------------|------------|--------
17 2.83 | D#- Eb- | | | |
16 2.67 | | D#< Eb< | | |
15 2.50 | | | D^ D#v Ebv | |
14 2.33 | | | | D> |
13 2.17 | | | | | D+
12 2.00 D ----------|-----------|-----------|-------------|------------|--------
11 1.83 | D- | | | |
10 1.67 | | D< | | |
9 1.50 | | | C#^ Db^ Dv | |
8 1.33 | | | | C#> Db> |
7 1.17 | | | | | C#+ Db+
6 1.00 C# Db ------|-----------|-----------|-------------|------------|--------
5 0.83 | C#- Db- | | | |
4 0.67 | | C#< Db< | | |
3 0.50 | | | C^ C#v Dbv | |
2 0.33 | | | | C> |
1 0.17 | | | | | C+
0 0.00 C ----------|-----------|-----------|-------------|------------|--------
Here are all examples [of scales with bike-chains] no larger than 72-ET.
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