|
|
| Line 13: |
Line 13: |
| Likewise, 293edo also can be interpreted as a dual-interval tuning, with ''two notes'' instead of one assigned to a particular interval. | | Likewise, 293edo also can be interpreted as a dual-interval tuning, with ''two notes'' instead of one assigned to a particular interval. |
|
| |
|
| {| class="wikitable mw-collapsible right-3"
| | == Relation to a calendar reform == |
| |+Selected intervals
| | 33L 19s [[Maximal evenness|maximally even]] scale of 293edo has a real life application - it is a leap year pattern of a proposed calendar. Using MOS, it employs 62\293 as a generator, described as "accumulator" by the creator of the calendar himself. Likewise, a 71-note cycle with 260\293 generator can be constructed by analogy. |
| |-
| | |
| ! Degree
| | The corresponding rank two temperament is therefore '''Sym454''', defined as 52 & 243c. |
| ! Name
| | |
| ! Cents
| | === Symmetry454 calendar temperament === |
| ! Approximate ratios
| | Subgroup: 2.3.5.7.11.13.17 |
| |-
| | |
| | 0
| | Comma list: 225/224, 715/714, 2880/2873, 22750/22627, 60112/60025. |
| | Unison, prime
| | |
| | 0.0000
| | POTE generator: 253.9326 (62\293) |
| | 1/1 exact
| |
| |-
| |
| | 1
| |
| | Limit-tone
| |
| | 4.0596
| |
| | 423/422
| |
| |-
| |
| | 5
| |
| | Minor leap week interval
| |
| | 20.4778
| |
| | 85/84
| |
| |-
| |
| | 6
| |
| | Major leap week interval
| |
| | 24.5734
| |
| | 71/70
| |
| |-
| |
| | 11
| |
| | Bundle of 2
| |
| | 45.0512
| |
| |
| |
| |-
| |
| | 17
| |
| | Bundle of 3
| |
| | 69.6246
| |
| |
| |
| |-
| |
| | 18
| |
| | Vicesimotertial quarter-tone
| |
| | 73.7201
| |
| | [[24/23]]
| |
| |-
| |
| | 45
| |
| | Minor subcycle
| |
| | 184.3003
| |
| |
| |
| |-
| |
| | 47
| |
| | Undevicesimal meantone | |
| | 192.4915
| |
| | [[19/17]]
| |
| |-
| |
| | 56
| |
| | Minor septimal second
| |
| | 229.3515
| |
| | 8/7, 214/187
| |
| |-
| |
| | 57
| |
| | Major septimal second
| |
| | 233.4471
| |
| | 8/7, 266/233
| |
| |-
| |
| | 62
| |
| | Leap week accumulator
| |
| | 253.9249
| |
| | 755/652
| |
| |-
| |
| | 77
| |
| | Minor third
| |
| | 315.3584
| |
| | [[6/5]]
| |
| |-
| |
| | 79
| |
| | Major subcycle
| |
| | 323.5495
| |
| |
| |
| |-
| |
| | 115
| |
| | 21st harmonic
| |
| | 470.9898
| |
| | [[21/16]]
| |
| |-
| |
| | 116
| |
| | 25 over 19
| |
| | 475.0853
| |
| | [[25/19]]
| |
| |-
| |
| | 125
| |
| | 43rd harmonic
| |
| | 511.9454
| |
| | [[43/32]]
| |
| |-
| |
| | 130
| |
| | Vengeance superfourth
| |
| | 532.4232
| |
| | [[34/25]]
| |
| |-
| |
| | 163
| |
| | Vengeance subfifth
| |
| | 667.5768
| |
| | [[25/17]]
| |
| |-
| |
| | 168
| |
| | 43rd subharmonic
| |
| | 688.0546
| |
| | 64/43
| |
| |-
| |
| | 171
| |
| | Perfect fifth
| |
| | 700.3413
| |
| | [[3/2]]
| |
| |-
| |
| | 172
| |
| | "Major" fifth
| |
| | 704.4369
| |
| | 347/231
| |
| |-
| |
| | 191
| |
| | Undecimal minor sixth
| |
| | 782.2526
| |
| | [[11/7]]
| |
| |-
| |
| | 216
| |
| | Major sixth
| |
| | 884.6416
| |
| | [[5/3]]
| |
| |-
| |
| | 236
| |
| | Minor harmonic seventh
| |
| | 966.5529
| |
| | [[7/4]], 187/107
| |
| |-
| |
| | 237
| |
| | Major harmonic seventh
| |
| | 970.6485
| |
| | [[7/4]], 233/133
| |
| |-
| |
| | 260
| |
| | Leap day accumulator
| |
| | 1064.8464
| |
| | 468/253
| |
| |-
| |
| | 293
| |
| | Perfect octave
| |
| | 1200.0000
| |
| | 2/1 exact
| |
| |}
| |
|
| |
|
| == Tempered commas == | | == Tempered commas == |
| Line 178: |
Line 41: |
|
| |
|
| == Scales == | | == Scales == |
| 33L 19s [[Maximal evenness|maximally even]] scale of 293edo has a real life application - it is a leap year pattern of a proposed calendar. Using MOS, it employs 62\293 as a generator, described as "accumulator" by the creator of the calendar himself. Likewise, a 71-note cycle with 260\293 generator can be constructed by analogy.
| |
|
| |
| * LeapWeek[52] | | * LeapWeek[52] |
| * LeapDay[71] | | * LeapDay[71] |