User:Xenllium/Xenllium's circulating scales

Below are listed circulating scales introduced by Xenllium.

Xentwelve

Xentwelve is a 12-tone circulating scale based on 12 equal temperament. In summary, it is close to 1/3-comma meantone in the natural keys and Pythagorean tuning in the remote keys. The generator is a perfect fifth, which comes in three sizes, with eight pure fifths (at C–G, C♯–G♯, E♭–B♭, E–B, F–C, F♯–C♯, B♭–F and B–F♯, frequency ratio 3/2), three 1/3-comma meantone fifths (at D–A, G–D and A–E, frequency ratio (10/3)^(1/3)), and one narrow schismic fifth (at G♯–D♯ (A♭–E♭), frequency ratio 16384/10935). It derives two major thirds exact 5/4 (at C–E and G–B) and one minor third exact 6/5 (at E–G).

! xentwelve_a.scl
!
Xentwelve, Xenllium's 12-tone circulating scale, Central A
 12
!
 104.56252207087
 196.74123853187
 308.47252380165
 400.65124026264
 505.21376233352
 602.60752120549
 694.78623766648
 806.51752293626
 898.69623939726
 1010.42752466704
 1102.60624112803
 1200.

Sizes and occurrences of fifth and fourth

Fifth (7-step)				Fourth (5-step)
Occurrences	Ratio	Cents	Error from 3/2	Occurrences	Ratio	Cents	Error from 4/3
D–A G–D A–E	[math]\displaystyle{ \sqrt{10/3} }[/math]	694.78624	−7.16876	D–G E–A A–D	[math]\displaystyle{ \sqrt{12/5} }[/math]	505.21376	+7.16876
G♯–D♯ (A♭–E♭)	[math]\displaystyle{ 16384/10935 }[/math]	700.00128	−1.95372	D♯–G♯ (E♭–A♭)	[math]\displaystyle{ 10935/8192 }[/math]	499.99872	+1.95372
C–G C♯–G♯ E♭–B♭ E–B F–C F♯–C♯ B♭–F B–F♯	[math]\displaystyle{ 3/2 }[/math]	701.95500	+0.00000	C–F C♯–F♯ F–B♭ F♯–B G–C G♯–C♯ B♭–E♭ B–E	[math]\displaystyle{ 4/3 }[/math]	498.04500	+0.00000