29edt: Difference between revisions
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{{Infobox ET}} | |||
'''29EDT''' is the [[Edt|equal division of the third harmonic]] into 29 parts of 65.5847 [[cent|cents]] each, corresponding to 18.2970 [[edo]]. It is related to the [[Metric microtemperaments #Luminal|luminal temperament]]. | '''29EDT''' is the [[Edt|equal division of the third harmonic]] into 29 parts of 65.5847 [[cent|cents]] each, corresponding to 18.2970 [[edo]]. It is related to the [[Metric microtemperaments #Luminal|luminal temperament]]. | ||
{| class="wikitable" | While not possessing good approximations to most integer harmonics, it does have a few very good rational intervals: notably [[27/26]], [[17/10]], [[45/32]], and [[11/6]]. | ||
==Intervals== | |||
{| class="wikitable right-2 right-3" | |||
|- | |- | ||
! | ! steps | ||
! | ! [[cent]]s | ||
! [[hekt]]s | ! [[hekt]]s | ||
! corresponding <br>JI intervals | ! corresponding <br>JI intervals | ||
! comments | ! comments | ||
|- | |- | ||
! colspan="3" | 0 | |||
| | | [[1/1]] | ||
| | | | ||
|- | |- | ||
| Line 75: | Line 79: | ||
| 11 | | 11 | ||
| 721.4312 | | 721.4312 | ||
| 493. | | 493.1034 | ||
| | | | ||
| pseudo-[[3/2]] | | pseudo-[[3/2]] | ||
| Line 81: | Line 85: | ||
| 12 | | 12 | ||
| 787.0159 | | 787.0159 | ||
| 537. | | 537.9310 | ||
| 63/40, 52/33 | | 63/40, 52/33 | ||
| pseudo-[[8/5]] | | pseudo-[[8/5]] | ||
| Line 111: | Line 115: | ||
| 17 | | 17 | ||
| 1114.9391 | | 1114.9391 | ||
| 772. | | 772.0690 | ||
| 99/52, 40/21 | | 99/52, 40/21 | ||
| pseudo-[[15/8]] | | pseudo-[[15/8]] | ||
| Line 117: | Line 121: | ||
| 18 | | 18 | ||
| 1180.5238 | | 1180.5238 | ||
| 806. | | 806.8966 | ||
| | | | ||
| pseudooctave | | pseudooctave | ||
| Line 183: | Line 187: | ||
| 29 | | 29 | ||
| 1901.9550 | | 1901.9550 | ||
| 1300 | | 1300.0000 | ||
| | | [[3/1]] | ||
| [[3/2|just perfect fifth]] plus an octave | | [[3/2|just perfect fifth]] plus an octave | ||
|} | |} | ||
==Harmonics== | |||
{{Harmonics in equal | |||
| steps = 29 | |||
| num = 3 | |||
| denom = 1 | |||
| intervals = integer | |||
}} | |||
{{Harmonics in equal | |||
| steps = 29 | |||
| num = 3 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
| intervals = integer | |||
}} | |||
{{todo|expand}} | |||