103edo: Difference between revisions
Contribution (talk | contribs) No edit summary |
Cleanup and consolidate tuning information |
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== Theory == | == Theory == | ||
In 103edo, all intervals within the [[17-odd-limit]] are [[consistent]], with the sole exception of [[9/8]] and its octave complement [[16/9]], which barely miss (relative error 50.2%). Its closest [[zeta peak index]], [[596zpi]], [[stretched and compressed tuning|stretches the octave]] by +0.739 cents. This expansion is uniquely consistent within the 15-integer-limit. | |||
103edo is a good [[miracle]] tuning, especially for the [[7-limit]], and for [[Gamelismic clan #Miracle|benediction]] and [[Gamelismic clan #Miracle|hemisecordite]], two of the [[13-limit]] extensions of miracle. It [[tempering out|tempers out]] [[78732/78125]] in the [[5-limit]]; [[225/224]], [[1029/1024]] and [[2401/2400]] in the 7-limit; [[243/242]], [[441/440]] and [[540/539]] in the [[11-limit]]; [[351/350]] and [[847/845]] in the 13-limit. In the 13-limit it provides the [[optimal patent val]] for [[marvel]] temperament as well as benediction and hemisecordite. | 103edo is a good [[miracle]] tuning, especially for the [[7-limit]], and for [[Gamelismic clan #Miracle|benediction]] and [[Gamelismic clan #Miracle|hemisecordite]], two of the [[13-limit]] extensions of miracle. It [[tempering out|tempers out]] [[78732/78125]] in the [[5-limit]]; [[225/224]], [[1029/1024]] and [[2401/2400]] in the 7-limit; [[243/242]], [[441/440]] and [[540/539]] in the [[11-limit]]; [[351/350]] and [[847/845]] in the 13-limit. In the 13-limit it provides the [[optimal patent val]] for [[marvel]] temperament as well as benediction and hemisecordite. | ||
=== Prime harmonics === | === Prime harmonics === | ||
| Line 29: | Line 29: | ||
| 2.3 | | 2.3 | ||
| {{monzo| -163 103 }} | | {{monzo| -163 103 }} | ||
| | | {{mapping| 103 166 }} | ||
| +0.923 | | +0.923 | ||
| 0.924 | | 0.924 | ||
| Line 36: | Line 36: | ||
| 2.3.5 | | 2.3.5 | ||
| 78732/78125, 34171875/33554432 | | 78732/78125, 34171875/33554432 | ||
| | | {{mapping| 103 166 239 }} | ||
| +0.881 | | +0.881 | ||
| 0.757 | | 0.757 | ||
| Line 43: | Line 43: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 225/224, 1029/1024, 78732/78125 | | 225/224, 1029/1024, 78732/78125 | ||
| | | {{mapping| 103 166 239 289 }} | ||
| +0.824 | | +0.824 | ||
| 0.663 | | 0.663 | ||
| Line 50: | Line 50: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 225/224, 243/242, 385/384, 43923/43750 | | 225/224, 243/242, 385/384, 43923/43750 | ||
| | | {{mapping| 103 166 239 289 356 }} | ||
| +0.876 | | +0.876 | ||
| 0.602 | | 0.602 | ||
| Line 57: | Line 57: | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 225/224, 243/242, 351/350, 385/384, 847/845 | | 225/224, 243/242, 351/350, 385/384, 847/845 | ||
| | | {{mapping| 103 166 239 289 356 381 }} | ||
| +0.806 | | +0.806 | ||
| 0.571 | | 0.571 | ||
| Line 64: | Line 64: | ||
| 2.3.5.7.11.13.17 | | 2.3.5.7.11.13.17 | ||
| 225/224, 243/242, 273/272, 351/350, 375/374, 847/845 | | 225/224, 243/242, 273/272, 351/350, 375/374, 847/845 | ||
| | | {{mapping| 103 166 239 289 356 381 421 }} | ||
| +0.694 | | +0.694 | ||
| 0.595 | | 0.595 | ||
| 5.10 | | 5.10 | ||
|} | |} | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
| Line 75: | Line 74: | ||
|+Table of rank-2 temperaments by generator | |+Table of rank-2 temperaments by generator | ||
! Periods<br>per 8ve | ! Periods<br>per 8ve | ||
! Generator | ! Generator* | ||
! Cents | ! Cents* | ||
! Associated<br>Ratio | ! Associated<br>Ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 84: | Line 83: | ||
| 34.951 | | 34.951 | ||
| 1990656/1953125 | | 1990656/1953125 | ||
| [[ | | [[Gammy]] | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 188: | Line 187: | ||
| [[Neptune]] | | [[Neptune]] | ||
|} | |} | ||
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | |||
== Music == | == Music == | ||