27edt: Difference between revisions

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=Division of the tritave (3/1) into 27 equal parts=
'''27edt''' means '''division of the tritave ([[3/1]]) into 27 equal parts'''.


Dividing the interval of 3/1 into 27 equal parts gives a scale with a basic step of 70.44 [[cent|cent]]s, corresponding to 17.035 edo, which is nearly identical to one step of [[17edo|17edo]] (70.59 cents). Hence it has similar melodic and harmonic properties as 17edo, with the difference that 27 is not a [[prime_number|prime number]].
Dividing the interval of 3/1 into 27 equal parts gives a scale with a basic step of 70.4428 [[cent]]s, corresponding to 17.035 edo, which is nearly identical to one step of [[17edo]] (70.59 cents). Hence it has similar melodic and harmonic properties as 17edo, with the difference that 27 is not a [[prime number]].


27 being the third power of 3, and the base interval being 3/1, 27edt is a tuning where the number 3 prevails. This property seems to predestine 27edt as base tuning for Klingon music (since the tradtional Klingon number system is also based on 3). The rather harsh harmonic character of 27edt would suit very well, too.
27 being the third power of 3, and the base interval being 3/1, 27edt is a tuning where the number 3 prevails. This property seems to predestine 27edt as base tuning for Klingon music (since the tradtional Klingon number system is also based on 3). The rather harsh harmonic character of 27edt would suit very well, too.
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See, e.g., [http://launch.dir.groups.yahoo.com/group/tuning/message/86909 http://launch.dir.groups.yahoo.com/group/tuning/message/86909] and [http://www.klingon.org/smboard/index.php?topic=1810.0 http://www.klingon.org/smboard/index.php?topic=1810.0].
See, e.g., [http://launch.dir.groups.yahoo.com/group/tuning/message/86909 http://launch.dir.groups.yahoo.com/group/tuning/message/86909] and [http://www.klingon.org/smboard/index.php?topic=1810.0 http://www.klingon.org/smboard/index.php?topic=1810.0].


==Intervals==
== Intervals ==


{| class="wikitable"
{| class="wikitable" style="text-align: right"
! Steps !! [[Cent]] !! ~[[17edo]]
|-
|-
! | degrees of 27edt
| 1 || 70.443 || 70.588
! | cents value
! | approximation in 17edo
|-
|-
| | 0
| 2 || 140.886 || 141.176
| | 0.00
| | 0.00
|-
|-
| | 1
| 3 || 211.328 || 211.765
| | 70.44
| | 70.59
|-
|-
| | 2
| 4 || 281.771 || 282.353
| | 140.89
| | 141.18
|-
|-
| | 3
| 5 || 352.214 || 352.941
| | 211.33
| | 211.76
|-
|-
| | 4
| 6 || 422.657 || 423.529
| | 281.77
| | 282.35
|-
|-
| | 5
| 7 || 493.099 || 494.118
| | 352.21
| | 352.94
|-
|-
| | 6
| 8 || 563.542 || 564.706
| | 422.66
| | 423.53
|-
|-
| | 7
| 9 || 633.985 || 635.294
| | 493.10
| | 494.12
|-
|-
| | 8
| 10 || 704.428 || 705.882
| | 563.54
| | 564.71
|-
|-
| | 9
| 11 || 774.871 || 776.471
| | 633.99
| | 635.29
|-
|-
| | 10
| 12 || 845.313 || 847.059
| | 704.43
| | 705.88
|-
|-
| | 11
| 13 || 915.756 || 917.647
| | 774.87
| | 776.47
|-
|-
| | 12
| 14 || 986.199 || 988.235
| | 845.31
| | 847.06
|-
|-
| | 13
| 15 || 1056.642 || 1058.824
| | 915.76
| | 917.65
|-
|-
| | 14
| 16 || 1127.084 || 1129.412
| | 986.20
| | 988.24
|-
|-
| | 15
| 17 || 1197.527 || 1200.000
| | 1056.64
| | 1058.82
|-
|-
| | 16
| 18 || 1267.970 || 1270.588
| | 1127.08
| | 1129.41
|-
|-
| | 17
| 19 || 1338.413 || 1341.176
| | 1197.53
| | 1200.00
|-
|-
| | 18
| 20 || 1408.856 || 1411.765
| | 1267.97
| | 1270.59
|-
|-
| | 19
| 21 || 1479.298 || 1482.353
| | 1338.41
| | 1341.18
|-
|-
| | 20
| 22 || 1549.741 || 1552.941
| | 1408.86
| | 1411.76
|-
|-
| | 21
| 23 || 1620.184 || 1623.529
| | 1479.30
| | 1482.35
|-
|-
| | 22
| 24 || 1690.627 || 1694.118
| | 1549.74
| | 1551.94
|-
|-
| | 23
| 25 || 1761.069 || 1764.706
| | 1620.18
| | 1623.53
|-
|-
| | 24
| 26 || 1831.512 || 1835.294
| | 1690.63
| | 1694.12
|-
|-
| | 25
| 27 || 1901.955 || 1905.882
| | 1761.07
| | 1764.71
|-
| | 26
| | 1831.51
| | 1835.29
|-
| | 27
| | 1901.96
| | 1905.88
|}
|}
[[Category:27edt]]
 
[[Category:edonoi]]
[[Category:Edt]]
[[Category:edt]]
[[Category:Nonoctave]]
[[Category:equal]]
[[Category:nonoctave]]

Revision as of 13:35, 28 October 2018

27edt means division of the tritave (3/1) into 27 equal parts.

Dividing the interval of 3/1 into 27 equal parts gives a scale with a basic step of 70.4428 cents, corresponding to 17.035 edo, which is nearly identical to one step of 17edo (70.59 cents). Hence it has similar melodic and harmonic properties as 17edo, with the difference that 27 is not a prime number.

27 being the third power of 3, and the base interval being 3/1, 27edt is a tuning where the number 3 prevails. This property seems to predestine 27edt as base tuning for Klingon music (since the tradtional Klingon number system is also based on 3). The rather harsh harmonic character of 27edt would suit very well, too.

See, e.g., http://launch.dir.groups.yahoo.com/group/tuning/message/86909 and http://www.klingon.org/smboard/index.php?topic=1810.0.

Intervals

Steps Cent ~17edo
1 70.443 70.588
2 140.886 141.176
3 211.328 211.765
4 281.771 282.353
5 352.214 352.941
6 422.657 423.529
7 493.099 494.118
8 563.542 564.706
9 633.985 635.294
10 704.428 705.882
11 774.871 776.471
12 845.313 847.059
13 915.756 917.647
14 986.199 988.235
15 1056.642 1058.824
16 1127.084 1129.412
17 1197.527 1200.000
18 1267.970 1270.588
19 1338.413 1341.176
20 1408.856 1411.765
21 1479.298 1482.353
22 1549.741 1552.941
23 1620.184 1623.529
24 1690.627 1694.118
25 1761.069 1764.706
26 1831.512 1835.294
27 1901.955 1905.882
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