5L 3s: Difference between revisions
| Line 480: | Line 480: | ||
! [[31edo]] | ! [[31edo]] | ||
! Optimal ([[POTE]]) tuning | ! Optimal ([[POTE]]) tuning | ||
|- | |- | ||
| generator (g) | | generator (g) | ||
| Line 487: | Line 486: | ||
| 12\31, 464.52 | | 12\31, 464.52 | ||
| 464.39 | | 464.39 | ||
|- | |- | ||
| L (3g - octave) | | L (3g - octave) | ||
| Line 494: | Line 492: | ||
| 5\31, 193.55 | | 5\31, 193.55 | ||
| 193.16 | | 193.16 | ||
|- | |- | ||
| s (-5g + 2 octaves) | | s (-5g + 2 octaves) | ||
| Line 501: | Line 498: | ||
| 2\31, 77.42 | | 2\31, 77.42 | ||
| 78.07 | | 78.07 | ||
|} | |} | ||
| Line 519: | Line 515: | ||
! [[21edo]] | ! [[21edo]] | ||
! [[34edo]] | ! [[34edo]] | ||
|- | |- | ||
| generator (g) | | generator (g) | ||
| Line 525: | Line 520: | ||
| 8\21, 457.14 | | 8\21, 457.14 | ||
| 13\34, 458.82 | | 13\34, 458.82 | ||
|- | |- | ||
| L (3g - octave) | | L (3g - octave) | ||
| Line 531: | Line 525: | ||
| 3\21, 171.43 | | 3\21, 171.43 | ||
| 5\34, 176.47 | | 5\34, 176.47 | ||
|- | |- | ||
| s (-5g + 2 octaves) | | s (-5g + 2 octaves) | ||
| Line 537: | Line 530: | ||
| 2\21, 114.29 | | 2\21, 114.29 | ||
| 3\34, 105.88 | | 3\34, 105.88 | ||
|} | |} | ||
| Line 551: | Line 543: | ||
! [[37edo]] | ! [[37edo]] | ||
! [[45edo]] | ! [[45edo]] | ||
|- | |- | ||
| generator (g) | | generator (g) | ||
| Line 558: | Line 549: | ||
| 14\37, 454.05 | | 14\37, 454.05 | ||
| 17\45, 453.33 | | 17\45, 453.33 | ||
|- | |- | ||
| L (3g - octave) | | L (3g - octave) | ||
| Line 565: | Line 555: | ||
| 5\37, 162.16 | | 5\37, 162.16 | ||
| 6\45, 160.00 | | 6\45, 160.00 | ||
|- | |- | ||
| s (-5g + 2 octaves) | | s (-5g + 2 octaves) | ||
| Line 572: | Line 561: | ||
| 4\37, 129.73 | | 4\37, 129.73 | ||
| 5\45, 133.33 | | 5\45, 133.33 | ||
|} | |} | ||
=== Buzzard === | === Buzzard === | ||
Buzzard is an oneirotonic temperament in the ultrahard-to-[[Step ratio|pseudopaucitonic]] range. | Buzzard is an oneirotonic rank-2 temperament in the ultrahard-to-[[Step ratio|pseudopaucitonic]] range. It represents the only [[harmonic entropy]] minimum of the oneirotonic spectrum. | ||
In the broad sense, [[Buzzard]] can be viewed as any tuning that divides the 3rd harmonic into 4 equal parts. [[23edo]], [[28edo]] and [[33edo]] can nominally be viewed as supporting it, but are still very flat and in an ambiguous zone between 18edo and true Buzzard in terms of harmonies. [[38edo]] & [[43edo]] are good compromises between melodic utility and harmonic accuracy, as the small step is still large enough to be obvious to the untrained ear, but [[48edo]] is where it really comes into it's own in terms of harmonies, providing not only an excellent [[3/2]], but also [[7/4]] and [[The_Archipelago|archipelago]] harmonies, as by dividing the 5th in 4 it obviously also divides it in two as well. | In the broad sense, [[Buzzard]] can be viewed as any tuning that divides the 3rd harmonic into 4 equal parts. [[23edo]], [[28edo]] and [[33edo]] can nominally be viewed as supporting it, but are still very flat and in an ambiguous zone between 18edo and true Buzzard in terms of harmonies. [[38edo]] & [[43edo]] are good compromises between melodic utility and harmonic accuracy, as the small step is still large enough to be obvious to the untrained ear, but [[48edo]] is where it really comes into it's own in terms of harmonies, providing not only an excellent [[3/2]], but also [[7/4]] and [[The_Archipelago|archipelago]] harmonies, as by dividing the 5th in 4 it obviously also divides it in two as well. | ||