7edf: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
'''[[EDF|Division of the just perfect fifth]] into 7 equal parts''' (7EDF) is related to [[12edo|12 edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 3.3514 cents stretched and the step size is about 100.2793 cents. The patent val has a generally sharp tendency for harmonics up to 21, with the exception for 11 and 13.
{{ED intro}}


Lookalikes: [[12edo]], [[19ed3]], [[31ed6]], [[43ed12]]
== Theory ==
7edf is related to [[12edo]], but with the 3/2 rather than the 2/1 being just. The octave is about 3.3514 cents stretched and the step size is about 100.2793 cents. The patent val has a generally sharp tendency for harmonics up to 21, with the exception for 11 and 13.


==Harmonics==
Lookalikes: [[12edo]], [[19ed3]], [[31ed6]], [[43ed12]].
 
=== Harmonics ===
{{Harmonics in equal|7|3|2|prec=2|columns=15}}
{{Harmonics in equal|7|3|2|prec=2|columns=15}}


==Intervals==
== Intervals ==
{| class="wikitable"
{| class="wikitable center-1 right-2 center-3"
|-
|-
! #
! #
! Cents
! Cents
! 12edo notation
! 12edo Notation
|-
|-
| 1
| 1
| 100.2793
| 100.3
| C#, Db
| C#, Db
|-
|-
| 2
| 2
| 200.5586
| 200.6
| D
| D
|-
|-
| 3
| 3
| 300.8379
| 300.8
| D#, Eb
| D#, Eb
|-
|-
| 4
| 4
| 401.1171
| 401.1
| E
| E
|-
|-
| 5
| 5
| 501.3964
| 501.4
| F
| F
|-
|-
| 6
| 6
| 601.6757
| 601.7
| F#, Gb
| F#, Gb
|-
|-
| 7
| 7
| 701.955
| 702.0
| G
| G
|-
|-
| 8
| 8
| 802.2343
| 802.2
| G#, Ab
| G#, Ab
|-
|-
| 9
| 9
| 902.5136
| 902.5
| A
| A
|-
|-
| 10
| 10
| 1002.7929
| 1002.8
| A#, Bb
| A#, Bb
|-
|-
| 11
| 11
| 1103.0721
| 1103.1
| B
| B
|-
|-
| 12
| 12
| 1203.3514
| 1203.4
| C
| C
|-
|-
| 13
| 13
| 1303.6307
| 1303.6
| C#, Db
| C#, Db
|-
|-
| 14
| 14
| 1403.91
| 1403.9
| D
| D
|}
|}

Revision as of 06:43, 10 May 2024

← 6edf 7edf 8edf →
Prime factorization 7 (prime)
Step size 100.279 ¢ 
Octave 12\7edf (1203.35 ¢)
(convergent)
Twelfth 19\7edf (1905.31 ¢)
(convergent)
Consistency limit 10
Distinct consistency limit 6

7 equal divisions of the perfect fifth (abbreviated 7edf or 7ed3/2) is a nonoctave tuning system that divides the interval of 3/2 into 7 equal parts of about 100 ¢ each. Each step represents a frequency ratio of (3/2)1/7, or the 7th root of 3/2.

Theory

7edf is related to 12edo, but with the 3/2 rather than the 2/1 being just. The octave is about 3.3514 cents stretched and the step size is about 100.2793 cents. The patent val has a generally sharp tendency for harmonics up to 21, with the exception for 11 and 13.

Lookalikes: 12edo, 19ed3, 31ed6, 43ed12.

Harmonics

Approximation of harmonics in 7edf
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Error Absolute (¢) +3.35 +3.35 +6.70 +21.51 +6.70 +40.67 +10.05 +6.70 +24.86 -39.87 +10.05 -28.24 +44.02 +24.86 +13.41
Relative (%) +3.3 +3.3 +6.7 +21.4 +6.7 +40.6 +10.0 +6.7 +24.8 -39.8 +10.0 -28.2 +43.9 +24.8 +13.4
Steps
(reduced) 		12
(5) 		19
(5) 		24
(3) 		28
(0) 		31
(3) 		34
(6) 		36
(1) 		38
(3) 		40
(5) 		41
(6) 		43
(1) 		44
(2) 		46
(4) 		47
(5) 		48
(6)

Intervals

# Cents 12edo Notation
1 100.3 C#, Db
2 200.6 D
3 300.8 D#, Eb
4 401.1 E
5 501.4 F
6 601.7 F#, Gb
7 702.0 G
8 802.2 G#, Ab
9 902.5 A
10 1002.8 A#, Bb
11 1103.1 B
12 1203.4 C
13 1303.6 C#, Db
14 1403.9 D
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