16ed5/3: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Ayceman (talk | contribs)
autopatrolled, emailconfirmed
173 edits
Major additions
Ayceman (talk | contribs)
autopatrolled, emailconfirmed
173 edits
EDIII and EDIV comparison
Line 178: Line 178:
|+
|+
!
!
!ed16\22
!16ed16\22
!ed5/3
![[7ed5/4]]
!16ed5/3
![[Noleta|9ed4/3]]
![[43ed4]]
![[43ed4]]
!ed16\21
!16ed16\21
|-
|-
|1
|1
|54.54545
|54.54545
|55.188
|55.2724
|55.2724
|55.338
|55.81395
|55.81395
|57.1429
|57.1429
Line 191: Line 195:
|2
|2
|109.0909
|109.0909
|110.375
|110.5448
|110.5448
|110.677
|111.6729
|111.6729
|114.2857
|114.2857
Line 197: Line 203:
|3
|3
|163.6364
|163.6364
|165.563
|165.8173
|165.8173
|166.015
|167.4419
|167.4419
|171.4286
|171.4286
Line 203: Line 211:
|4
|4
|218.1818
|218.1818
|220.751
|221.0897
|221.0897
|221.353
|223.2558
|223.2558
|228.5714
|228.5714
Line 209: Line 219:
|5
|5
|272.7273
|272.7273
|275.938
|276.3621
|276.3621
|276.692
|279.0698
|279.0698
|285.7143
|285.7143
Line 215: Line 227:
|6
|6
|327.2727
|327.2727
|331.126
|331.6345
|331.6345
|332.030
|334.8837
|334.8837
|342.8571
|342.8571
Line 221: Line 235:
|7
|7
|381.8182
|381.8182
|386.314
|386.9069
|386.9069
|387.368
|390.6977
|390.6977
|400
|400
Line 227: Line 243:
|8
|8
|436.3636
|436.3636
|441.501
|442.1794
|442.1794
|442.707
|446.5116
|446.5116
|457.1429
|457.1429
Line 233: Line 251:
|9
|9
|490.9091
|490.9091
|496.689
|497.4517
|497.4517
|498.045
|502.3256
|502.3256
|514.2857
|514.2857
Line 239: Line 259:
|10
|10
|545.54545
|545.54545
|551.877
|552.7242
|552.7242
|553.383
|558.1395
|558.1395
|571.4286
|571.4286
Line 245: Line 267:
|11
|11
|600
|600
|607.064
|607.9966
|607.9966
|608.722
|613.9535
|613.9535
|628.5714
|628.5714
Line 251: Line 275:
|12
|12
|654.54545
|654.54545
|662.252
|663.269
|663.269
|664.060
|669.7674
|669.7674
|685.7143
|685.7143
Line 257: Line 283:
|13
|13
|709.0909
|709.0909
|717.440
|718.54145
|718.54145
|719.398
|725.5814
|725.5814
|742.8571
|742.8571
Line 263: Line 291:
|14
|14
|763.6364
|763.6364
|772.627
|773.8129
|773.8129
|774.737
|781.39535
|781.39535
|800
|800
Line 269: Line 299:
|15
|15
|818.1818
|818.1818
|827.815
|829.0863
|829.0863
|830.075
|837.7209
|837.7209
|857.1429
|857.1429
Line 275: Line 307:
|16
|16
|872.7273
|872.7273
|883.003
|884.3587
|884.3587
|885.413
|893.0233
|893.0233
|914.2857
|914.2857

Revision as of 17:35, 15 May 2021

16ed5/3 (or less accurately 16edVI) is the equal division of the just major sixth into sixteen parts of 55.2724 cents each, corresponding to 21.7106 edo. It is very closely related to the escapade temperament.

It very accurately approximates a number of low complexity just intervals, such as: 4/3 (<1¢), 5/4 (<1¢), 11/8 (<2¢), 11/10 (<1¢), 16/15 (<2¢), and 25/16 (<2¢). It also approximates the just fifth and octave to within 20¢, making it a flexible non-octave scale.

Intervals

16ed5/3 can be notated using steps 7 (~5/4) and 9 (~4/3) as generators, as these are accurate to within 0.6¢. The resulting scale is a heptatonic 2L 5s (similar to the octave repeating antidiatonic).

Degree Cents Approximate intervals Mos-interval Diatonic interval Notation
0 0 1 unison unison A
1 55.2724 31/30, 33/32 aug unison quatertone A#
2 110.5448 16/15 min mos2nd minor second Bb
3 165.8173 11/10 maj mos2nd neutral second B
4 221.0897 8/7, 17/15 min mos3rd major second Cb
5 276.3621 7/6, 20/17, 75/64 maj mos3rd subminor third C
6 331.6345 6/5, 17/14 dim mos4th minor third Db
7 386.9069 5/4 perf mos4th major third D
8 442.1794 9/7, 22/17 aug mos4th supermajor third D#
9 497.4517 4/3 perf mos5th just fourth E
10 552.7242 11/8 aug mos5th wide fourth E#
11 607.9966 10/7 min mos6th large tritone Fb
12 663.269 22/15, 72/49 maj mos6th narrow fifth F
13 718.54145 3/2, 50/33 min mos7th acute fifth F#
14 773.8129 25/16 maj mos7th subminor sixth G
15 829.0863 8/5, 13/8 dim mos8ave minor sixth G#
16 884.3587 5/3 mosoctave major sixth A
17 939.6311 12/7, 19/11 aug mos8ave supermajor sixth A#
18 994.9035 16/9 min mos9th minor seventh Bb
19 1050.1760 11/6 maj mos9th neutral seventh B
20 1105.4484 17/9, 40/21 min mos10th major seventh Cb
21 1160.7208 35/18, 43/22 maj mos10th narrow octave C
22 1215.9932 2/1 dim mos11th octave C#

These intervals are close to a few other related non-octave scales:

16ed16\22 7ed5/4 16ed5/3 9ed4/3 43ed4 16ed16\21
1 54.54545 55.188 55.2724 55.338 55.81395 57.1429
2 109.0909 110.375 110.5448 110.677 111.6729 114.2857
3 163.6364 165.563 165.8173 166.015 167.4419 171.4286
4 218.1818 220.751 221.0897 221.353 223.2558 228.5714
5 272.7273 275.938 276.3621 276.692 279.0698 285.7143
6 327.2727 331.126 331.6345 332.030 334.8837 342.8571
7 381.8182 386.314 386.9069 387.368 390.6977 400
8 436.3636 441.501 442.1794 442.707 446.5116 457.1429
9 490.9091 496.689 497.4517 498.045 502.3256 514.2857
10 545.54545 551.877 552.7242 553.383 558.1395 571.4286
11 600 607.064 607.9966 608.722 613.9535 628.5714
12 654.54545 662.252 663.269 664.060 669.7674 685.7143
13 709.0909 717.440 718.54145 719.398 725.5814 742.8571
14 763.6364 772.627 773.8129 774.737 781.39535 800
15 818.1818 827.815 829.0863 830.075 837.7209 857.1429
16 872.7273 883.003 884.3587 885.413 893.0233 914.2857

MOS Scales

16edVI supports the same MOS scales as 16edo, as such it contains the following scales:

Periods

per octave

Generator Pattern
1 1\16 1L ns (pathological)
1 3\16 1L 4s, 5L 1s
1 5\16 3L 4s, 3L 7s
1 7\16 2L 5s, 7L 2s
2 1\16 2L 8s, 2L 10s, 2L 12s
2 3\16 4L 2s, 6L 4s
4 1\16 4L 4s, 4L 8s

For the 2L 5s scale, the genchain is this:

B# F# C# G# D# A# E# B F C G D A E Bb Fb Cb Gb Db Ab Eb Bbb Fbb Cbb Gbb
A2 A6 A3 A7 A5 A1 A4 M2 M6 M3 M7 P5 P1 P4 m2 m6 m3 m7 d5 d1 d4 d2 d6 d3 d7
Retrieved from "https://en.xen.wiki/index.php?title=16ed5/3&oldid=69881"