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

lower raise   inflection    cents

  b    #       semitone     100
  v    ^       1/4-tone      50
  <    >       1/6-tone      331/3
  -    +       1/12-tone     162/3

Notes which are presented horizontally adjacent are enharmonically equivalent. Notes which line up vertically are on the same bike-chain.

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  ----------------------------------------------------------------------

[from Joe Monzo, JustMusic: A New Harmony ]

---

updated:

2002.09.23 -- webpage created

(to download a zip file of the entire Dictionary, click here)

For many more diagrams and explanations of historical tunings, see my book. If you don't understand my theory or the terms I've used, start here

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