Microtonal, just intonation, electronic music software Microtonal, just intonation, electronic music software

Encyclopedia of Microtonal Music Theory

@ 00 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Login   |  Encyclopedia Index

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. Firstly, take a look at the legend for the HEWM 72edo music notation accidentals.

HEWM-base 72edo Music Notation

                         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:

72-EDO, Monzo ASCII adaptation of Sims/Herf notation

                             +        >       ^     #
                             -        <       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.

[Dave Keenan, Yahoo tuning group message 55637]

[Joe Monzo]
. . . . . . . . .

The tonalsoft.com website is almost entirely the work of one person: me, Joe Monzo. Please reward me for my knowledge and effort by choosing your preferred level of financial support. Thank you.

support level