User:Moremajorthanmajor/18ed7/3: Difference between revisions

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{{Infobox ET}}
{{Infobox ET|18ed7/3}}
{{ED intro|18ed7/3}}
 
This scale is a neutral Dorian mode of the Middletown relative of [[Whitewood]] temperament, or the White Oak scale. The Middletown Valley relatives of [[Blackwood]] temperament are:
 
Fair Terra Rubra: bi-equal tetrad
 
Fair Tritetrachordal: Middletown Valley Double Augmented
 
Fair Montrose: Vesuvius Marcodiminished
 
Unfair Montrose: Annapolis~Oriole Macro-Blackwood
 
Unfair Tritetrachordal: Mt. Airy
 
Unfair Terra Rubra: Westminster
 
== Intervals ==
{| class="wikitable"
!Degrees
! colspan="6" |Enneatonic
!Dodecatonic
!ed7/3
|-
| |1
| colspan="2" |FG
| colspan="4" |G
|1#/2b
|81.4928
|-
| |2
| colspan="2" |G
|J
|''A''
|J
|''A''
|2
|162.9856
|-
| |3
|GJ
|''GA''
|J^/Ab
|''A^/Bb''
|Jv/A\\
|''Av/B\\''
|3
|244.4785
|-
| |4
|J
|''A''
|J^^/Aw
|''A^^/Bw''
|Jw/A^^
|''Aw/B^^''
|3#/4b
|325.9713
|-
| |5
|JA
|''AB''
|J#/Av
|''A#/Bv''
|Jp/A^
|''Ap/B^''
|4
|407.46415
|-
| |6
|A
|''B''
|A
|''B''
|A
|''B''
|5
|488.957
|-
| |7
|AB
|''BH''
|B
|''H''
|B
|''H''
|5#/6b
|570.45
|-
|8
|B
|''H''
|H
|''C''
|H
|''C''
|6
|651.9426
|-
|9
|BH
|''HC''
|H^/Cb
|''C^/Db''
|Hv/C\\
|''Cv/D\\''
|7
|733.43545
|-
|10
|H
|''C''
|H^^/Cw
|''C^^/Dw''
|Hw/C^^
|''Cw/D^^''
|7#/8b
|814.9283
|-
|11
|HC
|''CD''
|H#/Cv
|''C#/Dv''
|Hp/C^
|''Cp/D^''
|8
|896.4211
|-
|12
|C
|''D''
|C
|''D''
|C
|''D''
|9
|977.9139
|-
|13
|CD
|''DS''
|D
|''S''
|D
|''S''
|9#/Xb
|1059.4068
|-
|14
|D
|''S''
| colspan="4" |E
|X
|1140.8996
|-
|15
|DE
|''SE''
| colspan="2" |E^/Fb
| colspan="2" |Ev/F\\
|E
|1222.3924
|-
|16
| colspan="2" |E
| colspan="2" |E^^/Fw
| colspan="2" |Ew/F^^
|E#/0b
|1303.8852
|-
|17
| colspan="2" |EF
| colspan="2" |E#/Fv
| colspan="2" |Ep/F^
|0
|1385.3781
|-
|18
| colspan="6" |F
|1
|1466.8709
|}
 
== Harmonics ==
{{Harmonics in equal
| steps = 18
| num = 7
| denom = 3
}}
{{Harmonics in equal
| steps = 18
| num = 7
| denom = 3
| start = 12
| collapsed = 1
}}

Latest revision as of 05:42, 23 February 2025

← 17ed7/3 18ed7/3 19ed7/3 →
Prime factorization 2 × 32
Step size 81.4928 ¢ 
Octave 15\18ed7/3 (1222.39 ¢) (→ 5\6ed7/3)
Twelfth 23\18ed7/3 (1874.34 ¢)
Consistency limit 2
Distinct consistency limit 2

18 equal divisions of 7/3 (abbreviated 18ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 18 equal parts of about 81.5 ¢ each. Each step represents a frequency ratio of (7/3)1/18, or the 18th root of 7/3.

This scale is a neutral Dorian mode of the Middletown relative of Whitewood temperament, or the White Oak scale. The Middletown Valley relatives of Blackwood temperament are:

Fair Terra Rubra: bi-equal tetrad

Fair Tritetrachordal: Middletown Valley Double Augmented

Fair Montrose: Vesuvius Marcodiminished

Unfair Montrose: Annapolis~Oriole Macro-Blackwood

Unfair Tritetrachordal: Mt. Airy

Unfair Terra Rubra: Westminster

Intervals

Degrees Enneatonic Dodecatonic ed7/3
1 FG G 1#/2b 81.4928
2 G J A J A 2 162.9856
3 GJ GA J^/Ab A^/Bb Jv/A\\ Av/B\\ 3 244.4785
4 J A J^^/Aw A^^/Bw Jw/A^^ Aw/B^^ 3#/4b 325.9713
5 JA AB J#/Av A#/Bv Jp/A^ Ap/B^ 4 407.46415
6 A B A B A B 5 488.957
7 AB BH B H B H 5#/6b 570.45
8 B H H C H C 6 651.9426
9 BH HC H^/Cb C^/Db Hv/C\\ Cv/D\\ 7 733.43545
10 H C H^^/Cw C^^/Dw Hw/C^^ Cw/D^^ 7#/8b 814.9283
11 HC CD H#/Cv C#/Dv Hp/C^ Cp/D^ 8 896.4211
12 C D C D C D 9 977.9139
13 CD DS D S D S 9#/Xb 1059.4068
14 D S E X 1140.8996
15 DE SE E^/Fb Ev/F\\ E 1222.3924
16 E E^^/Fw Ew/F^^ E#/0b 1303.8852
17 EF E#/Fv Ep/F^ 0 1385.3781
18 F 1 1466.8709

Harmonics

Approximation of harmonics in 18ed7/3
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +22.4 -27.6 -36.7 -15.6 -5.2 -27.6 -14.3 +26.3 +6.8 +4.8 +17.2
Relative (%) +27.5 -33.9 -45.0 -19.1 -6.4 -33.9 -17.6 +32.2 +8.4 +5.9 +21.1
Steps
(reduced) 		15
(15) 		23
(5) 		29
(11) 		34
(16) 		38
(2) 		41
(5) 		44
(8) 		47
(11) 		49
(13) 		51
(15) 		53
(17)
Approximation of harmonics in 18ed7/3
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -39.9 -5.2 +38.3 +8.1 -15.4 -32.8 +36.5 +29.2 +26.3 +27.2 +31.7
Relative (%) -49.0 -6.4 +47.0 +9.9 -18.9 -40.3 +44.8 +35.9 +32.2 +33.4 +39.0
Steps
(reduced) 		54
(0) 		56
(2) 		58
(4) 		59
(5) 		60
(6) 		61
(7) 		63
(9) 		64
(10) 		65
(11) 		66
(12) 		67
(13)
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