25ed5/2: Difference between revisions

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m Intro, harmonics
 
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{{Stub}}
{{Infobox ET}}
{{ED intro}}
== Intervals ==
== Intervals ==
{| class="wikitable"
{| class="wikitable"
!Degrees
!Degrees
! colspan="3" |Enneatonic
! colspan="3" |Enneatonic
!ed38\29
!Cents
!Golden
!ed5/2
!ed(7φ+6)\5(φ+1)
!ed4\3=''r¢''
|-
|-
|1
|1
|1#
|1#/2bb
| colspan="2" |F#
| colspan="2" |F#/Gbb
|62.897
|62.963
|63.4525
|63.4525
|63.533
|''64''
|-
|-
|2
|2
|2b
|2b/1x
| colspan="2" |Gb
| colspan="2" |Gb/Fx
|125.793
|125.926
|126.905
|126.905
|127.066
|''128''
|-
|-
|3
|3
|2
|2
| colspan="2" |G
| colspan="2" |G
|188.69
|188.889
|190.358
|190.358
|190.599
|''192''
|-
|-
|4
|4
|2#
|2#/3bb
| colspan="2" |G#
|G#/Jbb
|251.586
|G#/''Abb''
|251.854
|253.81
|253.81
|254.1325
|''256''
|-
|-
|5
|5
|3b
|3b/2x
|Jb
|Jb/Gx
|''Ab''
|''Ab/''Gx
|314.483
|314.814
|317.263
|317.263
|317.666
|''320''
|-
|-
|6
|6
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|J
|J
|''A''
|''A''
|377.379
|377.777
|380.715
|380.715
|381.199
|''384''
|-
|-
|7
|7
|3#
|3#/4bb
|J#
|J#/Abb
|''A#''
|''A#/Bbb''
|440.276
|440.74
|444.168
|444.168
|444.732
|''448''
|-
|-
|8
|8
|4b
|4b/3x
|Ab
|Ab/Jx
|''Bb''
|''Bb/Ax''
|503.172
|503.703
|507.62
|507.62
|508.265
|''512''
|-
|-
|9
|9
Line 89: Line 58:
|A
|A
|''B''
|''B''
|566.069
|566.666
|571.073
|571.073
|571.798
|''576''
|-
|-
|10
|10
Line 99: Line 64:
|A#/Bb
|A#/Bb
|''B#/Hb''
|''B#/Hb''
|628.9655
|629.629
|634.5255
|634.5255
|635.331
|''640''
|-
|-
|11
|11
Line 109: Line 70:
|B
|B
|''H''
|''H''
|691.862
|692.5915
|697.978
|697.978
|698.864
|''704''
|-
|-
|12
|12
|5#
|5#/6bb
|B#
|B#/Hbb
|''H#''
|''H#/Cbb''
|754.759
|755.554
|761.431
|761.431
|762.3975
|''768''
|-
|-
|13
|13
|6b
|6b/5x
|Hb
|Hb/Bx
|''Cb''
|''Cb/Hx''
|817.655
|818.517
|824.389
|824.389
|825.931
|''832''
|-
|-
|14
|14
Line 139: Line 88:
|H
|H
|''C''
|''C''
|880.552
|881.48
|888.336
|888.336
|889.464
|''896''
|-
|-
|15
|15
|6#
|6#/7bb
|H#
|H#/Cbb
|''C#''
|''C#/Dbb''
|943.448
|944.443
|951.788
|951.788
|952.997
|''960''
|-
|-
|16
|16
|7b
|7b/6x
|Cb
|Cb/Hx
|''Db''
|''Db/Cx''
|1006.345
|1007.406
|1015.241
|1015.241
|1016.53
|''1024''
|-
|-
|17
|17
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|C
|C
|''D''
|''D''
|1069.241
|1070.369
|1078.693
|1078.693
|1080.063
|''1088''
|-
|-
|18
|18
|7#/
|7#/8bb
|C#
|C#/Dbb
|''D#''
|''D#/Sbb''
|1132.138
|1133.3315
|1142.146
|1142.146
|1143.596
|''1152''
|-
|-
|19
|19
|8b
|8b/7x
|Db
|Db/Cx
|''Sb''
|''Sb/Dx''
|1195.0345
|1196.294
|1205.598
|1205.598
|1207.129
|''1216''
|-
|-
|20
|20
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|D
|D
|''S''
|''S''
|1257.931
|1259.257
|1269.051
|1269.051
|1270.6625
|''1280''
|-
|-
|21
|21
|8#
|8#/9bb
|D#
|D#/Ebb
|''S#''
|''S#/''Ebb
|1320.828
|1322.22
|1332.5035
|1332.5035
|1334.196
|''1344''
|-
|-
|22
|22
|9b
|9b/8x
| colspan="2" |Eb
|Eb/Dx
|1383.724
|Eb/''Sx''
|1385.183
|1395.956
|1395.956
|1397.729
|''1408''
|-
|-
|23
|23
|9
|9
| colspan="2" |E
| colspan="2" |E
|1446.621
|1448.146
|1459.409
|1459.409
|1461.262
|''1472''
|-
|-
|24
|24
|9#/1b
|9#/1b
| colspan="2" |E#/Fb
| colspan="2" |E#/Fb
|1509.517
|1511.109
|1522.961
|1522.961
|1524.795
|''1536''
|-
|-
|25
|25
|1
|1
| colspan="2" |F
| colspan="2" |F
|1572.414
|1574.0715
|1586.314
|1586.314
|1588.328
|''1600''
|}
|}
== Harmonics ==
{{Harmonics in equal
| steps = 25
| num = 5
| denom = 2
}}
{{Harmonics in equal
| steps = 25
| num = 5
| denom = 2
| start = 12
| collapsed = 1
}}

Latest revision as of 08:34, 4 October 2024

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← 24ed5/2 25ed5/2 26ed5/2 →
Prime factorization 52
Step size 63.4525 ¢ 
Octave 19\25ed5/2 (1205.6 ¢)
(semiconvergent)
Twelfth 30\25ed5/2 (1903.58 ¢) (→ 6\5ed5/2)
Consistency limit 10
Distinct consistency limit 7

25 equal divisions of 5/2 (abbreviated 25ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 25 equal parts of about 63.5 ¢ each. Each step represents a frequency ratio of (5/2)1/25, or the 25th root of 5/2.

Intervals

Degrees Enneatonic Cents
1 1#/2bb F#/Gbb 63.4525
2 2b/1x Gb/Fx 126.905
3 2 G 190.358
4 2#/3bb G#/Jbb G#/Abb 253.81
5 3b/2x Jb/Gx Ab/Gx 317.263
6 3 J A 380.715
7 3#/4bb J#/Abb A#/Bbb 444.168
8 4b/3x Ab/Jx Bb/Ax 507.62
9 4 A B 571.073
10 4#/5b A#/Bb B#/Hb 634.5255
11 5 B H 697.978
12 5#/6bb B#/Hbb H#/Cbb 761.431
13 6b/5x Hb/Bx Cb/Hx 824.389
14 6 H C 888.336
15 6#/7bb H#/Cbb C#/Dbb 951.788
16 7b/6x Cb/Hx Db/Cx 1015.241
17 7 C D 1078.693
18 7#/8bb C#/Dbb D#/Sbb 1142.146
19 8b/7x Db/Cx Sb/Dx 1205.598
20 8 D S 1269.051
21 8#/9bb D#/Ebb S#/Ebb 1332.5035
22 9b/8x Eb/Dx Eb/Sx 1395.956
23 9 E 1459.409
24 9#/1b E#/Fb 1522.961
25 1 F 1586.314

Harmonics

Approximation of harmonics in 25ed5/2
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +5.6 +1.6 +11.2 +5.6 +7.2 -5.8 +16.8 +3.2 +11.2 -26.9 +12.8
Relative (%) +8.8 +2.6 +17.6 +8.8 +11.4 -9.2 +26.5 +5.1 +17.6 -42.4 +20.2
Steps
(reduced) 		19
(19) 		30
(5) 		38
(13) 		44
(19) 		49
(24) 		53
(3) 		57
(7) 		60
(10) 		63
(13) 		65
(15) 		68
(18)
Approximation of harmonics in 25ed5/2
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +1.2 -0.2 +7.2 +22.4 -19.1 +8.8 -21.3 +16.8 -4.2 -21.3 +28.6
Relative (%) +1.8 -0.4 +11.4 +35.3 -30.1 +13.9 -33.6 +26.5 -6.6 -33.6 +45.1
Steps
(reduced) 		70
(20) 		72
(22) 		74
(24) 		76
(1) 		77
(2) 		79
(4) 		80
(5) 		82
(7) 		83
(8) 		84
(9) 		86
(11)
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