Bicycle

! bicycle.scl
!
13-limit harmonic bicycle, George Secor, 1963
! Transposition of Wilson's Helix Song, see David Rosenthal, Helix Song, XH 7&8, 1979
! Also Andrew Heathwaite's Rodan scale
12
!
13/12
9/8
7/6
5/4
4/3
11/8
3/2
13/8
5/3
7/4
11/6
2/1

Theory

Bicycle has a very elegant structure consisting of two 2:3:5:7:9:11:13 otonalities, one rooted and one offset by 4/3, octave reduced. It has the constant structure property.

Scott Dakota also refers to this scale as Almond.

Chords

Triads

There are a wide variety of thirds available on roots that have 3/2s in Bicycle. Notable thirds which can be paired with perfect fifths include 5/4, 6/5, 7/6, 9/7, 11/9, 27/22, 13/11, 14/11, 13/10, 15/13, and 16/13.

Tetrads

One notable type of tetrad has a perfect fifth between the root and fifth and another between the third and seventh; the common 12edo major seventh and minor seventh chords are both of this type. Many such tetrads exist in Bicycle. They are listed below with the scale on C:

1/1-5/4-3/2-15/8 (on F)

1/1-6/5-3/2-9/5 (on A)

1/1-7/6-3/2-7/4 (on C)

1/1-9/7-3/2-27/14 (on Eb)

1/1-11/9-3/2-11/6 (on G)

1/1-13/11-3/2-39/22 (on B)

1/1-14/11-3/2-21/11 (on B)

1/1-13/10-3/2-39/20 (on A)

1/1-16/13-3/2-24/13 (on Db)

Pitch classes and harmonics (on C)

F	C	A	Eb	G	B	Db
2	3	5	7	9	11	13
C	G	E	Bb	D	F#	Ab
3	9	15	21	27	33	39

Primodality

Bicycle, rewritten as a harmonic series segment, is 24:26:27:28:30:32:33:36:39:40:42:44:48. This relative simplicity means that modes of Bicycle can be used to evoke primodal sounds. For example, once again treating the root as C, the mode on B allows access to /11 intervals, and the mode on Db to /13; these two are probably the best suited for primodal approaches, since more composite numbers are thought to have less distinct primodal sounds. The simplicity of this scale in the harmonic series also means that an amount of gestalt linear effect can be heard when voicing large chords in the scale with harmonic timbres.