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Definitions of tuning terms
© 1998 by Joseph L. Monzo
All definitions by Joe Monzo unless otherwise cited
bike-chain, bicycle-chain
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.
First, a legend for the notation:
Monzo HEWM-based 72edo notation
Notes which are presented horizontally adjacent are
enharmonically equivalent.
Notes which line up vertically are on the same bike-chain.
[from Joe Monzo,
JustMusic: A New Harmony
]
updated:
lower raise inflection cents
b # semitone 100
v ^ 1/4-tone 50
< > 1/6-tone 331/3
- + 1/12-tone 162/3
72-EDO -- Monzo ASCII adaptation of Sims/Herf notation
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 ----------------------------------------------------------------------
2002.09.23 -- webpage created
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