17edt: Difference between revisions

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== Intervals ==
== Intervals ==
The notation schemes below are based on the BPS-Lambda enneatonic scale presented in the symmetric (sLsLsLsLs, Cassiopeian) mode in J, and the Mintaka macrodiatonic scale presented in the macro-Phrygian (sLLLsLL) mode in E.
{| class="wikitable"
{| class="wikitable"
|-
|-
! | degree
! | Degree
! | note name
! | Note ([[4L 5s (3/1-equivalent)#Notation|BPS-Lambda notation]])
! | Note (Macrodiatonic notation)
! | Approximate 3.5.7.11.17 subgroup interval
! | cents value
! | cents value
! | hekts
! | hekts
! | cents value <br>octave reduced
|-
|-
| | 0
| | 0
| | C
| | J
| colspan="2" | 0
| | E
| |  
| | [[1/1]]
| | 0
| | 0
|-
|-
| | 1
| | 1
| | Db = B#
| | K
| | F
| | [[27/25]], [[35/33]], [[49/45]], [[81/77]]
| | 111.9
| | 111.9
| | 76.5
| | 76.5
| |
|-
|-
| | 2
| | 2
| | Eb = C#
| | K#
| | Gb = Dx
| | [[17/15]], [[63/55]]
| | 223.8
| | 223.8
| | 152.9
| | 152.9
| |
|-
|-
| | 3
| | 3
| | D
| | Lb
| | F#
| | [[11/9]]
| | 335.6
| | 335.6
| | 229.4
| | 229.4
| |
|-
|-
| | 4
| | 4
| | E
| | L
| | G
| | [[9/7]], [[35/27]]
| | 447.5
| | 447.5
| | 305.9
| | 305.9
| |
|-
|-
| | 5
| | 5
| | F = D#
| | M
| | Ab
| | [[15/11]], [[51/35]]
| | 559.4
| | 559.4
| | 382.35
| | 382.35
| |
|-
|-
| | 6
| | 6
| | Gb = E#
| | M#
| | G#
| | [[49/33]], [[81/55]]
| | 671.3
| | 671.3
| | 458.8
| | 458.8
| |
|-
|-
| | 7
| | 7
| | Hb = F#
| | Nb
| | A
| | [[11/7]], [[17/11]]
| | 783.2
| | 783.2
| | 535.3
| | 535.3
| |
|-
|-
| | 8
| | 8
| | G
| | N
| | Bb
| | [[5/3]], [[27/17]]
| | 895.1
| | 895.1
| | 611.8
| | 611.8
| |
|-
|-
| | 9
| | 9
| | H
| | O
| | A#
| | [[9/5]], [[17/9]]
| | 1006.9
| | 1006.9
| | 688.2
| | 688.2
| |
|-
|-
| | 10
| | 10
| | Jb = G#
| | O#
| | B
| | [[21/11]], [[33/17]]
| | 1118.8
| | 1118.8
| | 764.7
| | 764.7
| |
|-
|-
| | 11
| | 11
| | Ab = H#
| | Pb
| | C
| | [[55/27]], [[99/49]]
| | 1230.7
| | 1230.7
| | 841.2
| | 841.2
| | 30.7
|-
|-
| | 12
| | 12
| | J
| | P
| | Db
| | [[11/5]], [[35/17]]
| | 1342.6
| | 1342.6
| | 917.65
| | 917.65
| | 142.6
|-
|-
| | 13
| | 13
| | A
| | Q
| | C#
| | [[7/3]], [[81/35]]
| | 1454.4
| | 1454.4
| | 994.1
| | 994.1
| | 254.4
|-
|-
| | 14
| | 14
| | Bb = J#
| | Q#
| | D
| | [[27/11]]
| | 1566.3
| | 1566.3
| | 1070.6
| | 1070.6
| | 366.3
|-
|-
| | 15
| | 15
| | Cb = A#
| | Rb
| | Eb
| | [[45/17]], [[55/21]]
| | 1642.598
| | 1122.727
|-
| | 16
| | R
| | D#
| | [[25/9]], [[77/27]], [[99/35]], [[135/49]]
| | 1678.2
| | 1678.2
| | 1147.1
| | 1147.1
| | 478.2
|-
| | 16
| | B
| | 1790.1
| | 1223.5
| | 590.1
|-
|-
| | 17
| | 17
| | C
| | J
| | 1902
| | E
| | 1300
| | [[3/1]]
| | 702
| | 1901.955
|-
| | 1300.
| | 18
| |
| | 2013.8
| | 1376.5
| | 813.8
|-
| | 19
| |
| | 2125.7
| | 1452.9
| | 925.7
|-
| | 20
| |
| | 2237.6
| | 1529.4
| | 1037.6
|-
| | 21
| |
| | 2349.5
| | 1605.9
| | 1149.5
|-
| | 22
| |
| | 2461.35
| | 1682.35
| | 61.35
|-
| | 23
| |
| | 2573.2
| | 1758.8
| | 173.2
|-
| | 24
| |
| | 2685.1
| | 1835.3
| | 285.1
|-
| | 25
| |
| | 2797
| | 1911.8
| | 397
|-
| | 26
| |
| | 2908.9
| | 1988.2
| | 508.9
|-
| | 27
| |
| | 3020.75
| | 2064.7
| | 620.75
|-
| | 28
| |
| | 3132.6
| | 2141.2
| | 732.6
|-
| | 29
| |
| | 3244.5
| | 2217.65
| | 844.5
|-
| | 30
| |
| | 3356.4
| | 2294.1
| | 956.4
|-
| | 31
| |
| | 3468.3
| | 2370.6
| | 1068.3
|-
| | 32
| |
| | 3580.15
| | 2447.1
| | 1180.15
|-
| | 33
| |
| | 3692
| | 2523.5
| | 92
|-
| | 34
| |
| | 3803.9
| | 2600
| | 203.9
|}
|}


<ul><li>Notes named so that C D E F G H J A B C = Lambda mode</li></ul>It's a weird coincidence how the schemes of 17EDO and 17EDT diatonicism are so similar and how their approximations of 9/7 are off by such similar amounts in opposite directions (17EDO -11.6 cents and 17EDT +12.4 cents).
It's a weird coincidence how the schemes of 17EDO and 17EDT diatonicism are so similar and how their approximations of 9/7 are off by such similar amounts in opposite directions (17EDO -11.6 cents and 17EDT +12.4 cents).


== Regular temperament ==
== Regular temperament ==