31edf: Difference between revisions

Line 3:

Lookalikes: [[53edo]], [[84edt]]

=Just Approximation=

= Just Approximation =

31edf provides excellent approximations for the classic 5-limit [[just]] chords and scales, such as the Ptolemy-Zarlino "just major" scale.

{| class="wikitable"

|-

! ~~|interval~~

! Interval

! ~~|ratio~~

! Ratio

! ~~|size~~

! Size

! ~~|difference~~

! Difference

|-

| ~~|perfect~~ octave

| Perfect octave

| |2/1

| 2/1

| style="text-align:center;" |31

| style="text-align: center;" | 31

| | +0.12 cents

| +0.12 cents

|-

| |major third

| major third

| |5/4

| 5/4

| style="text-align:center;" |17

| style="text-align: center;" | 17

| ~~|−1~~.37 cents

| −1.37 cents

|-

| |minor third

| minor third

| |6/5

| 6/5

| style="text-align:center;" |14

| style="text-align: center;" | 14

| | +1.37 cents

| +1.37 cents

|-

| |major tone

| major tone

| |9/8

| 9/8

| style="text-align:center;" |9

| style="text-align: center;" | 9

| ~~|−0~~.12 cents

| −0.12 cents

|-

| |minor tone

| minor tone

| |10/9

| 10/9

| style="text-align:center;" |8

| style="text-align: center;" | 8

| ~~|−1~~.25 cents

| −1.25 cents

|-

| |diat. semitone

| diat. semitone

| |16/15

| 16/15

| style="text-align:center;" |5

| style="text-align: center;" | 5

| | +1.49 cents

| +1.49 cents

|}One notable property of 53EDO is that it offers good approximations for both pure and ~~pythagorean~~ major thirds.

|}

One notable property of 53EDO is that it offers good approximations for both pure and Pythagorean major thirds.

The perfect fifth is almost perfectly equal to the just interval 3/2, with only a 0.07 cent difference! 53EDO is practically equal to an extended Pythagorean. The 14- and 17- degree intervals are also very close to 6/5 and 5/4 respectively, and so 5-limit tuning can also be closely approximated. In addition, the 43-degree interval is only 4.85 cents away from the just ratio 7/4, so 31EDF can also be used for 7-limit harmony, tempering out the [[septimal kleisma]], 225/224.

[[Category:Edf]]

[[Category:Edonoi]]

@@ Line 3: / Line 3: @@
 Lookalikes: [[53edo]], [[84edt]]
-=Just Approximation=
+= Just Approximation =
 edf provides excellent approximations for the classic 5-limit [[just]] chords and scales, such as the Ptolemy-Zarlino "just major" scale.
 {| class="wikitable"
 |-
-! |interval
+! Interval
-! |ratio
+! Ratio
-! |size
+! Size
-! |difference
+! Difference
 |-
-| |perfect octave
+| Perfect octave
-| |2/1
+| 2/1
-| style="text-align:center;" |31
+| style="text-align: center;" | 31
-| | +0.12 cents
+| +0.12 cents
 |-
-| |major third
+| major third
-| |5/4
+| 5/4
-| style="text-align:center;" |17
+| style="text-align: center;" | 17
-| |−1.37 cents
+| &minus;1.37 cents
 |-
-| |minor third
+| minor third
-| |6/5
+| 6/5
-| style="text-align:center;" |14
+| style="text-align: center;" | 14
-| | +1.37 cents
+| +1.37 cents
 |-
-| |major tone
+| major tone
-| |9/8
+| 9/8
-| style="text-align:center;" |9
+| style="text-align: center;" | 9
-| |−0.12 cents
+| &minus;0.12 cents
 |-
-| |minor tone
+| minor tone
-| |10/9
+| 10/9
-| style="text-align:center;" |8
+| style="text-align: center;" | 8
-| |−1.25 cents
+| &minus;1.25 cents
 |-
-| |diat. semitone
+| diat. semitone
-| |16/15
+| 16/15
-| style="text-align:center;" |5
+| style="text-align: center;" | 5
-| | +1.49 cents
+| +1.49 cents
-|}One notable property of 53EDO is that it offers good approximations for both pure and pythagorean major thirds.
+|}
+One notable property of 53EDO is that it offers good approximations for both pure and Pythagorean major thirds.
 The perfect fifth is almost perfectly equal to the just interval 3/2, with only a 0.07 cent difference! 53EDO is practically equal to an extended Pythagorean. The 14- and 17- degree intervals are also very close to 6/5 and 5/4 respectively, and so 5-limit tuning can also be closely approximated. In addition, the 43-degree interval is only 4.85 cents away from the just ratio 7/4, so 31EDF can also be used for 7-limit harmony, tempering out the [[septimal kleisma]], 225/224.
 [[Category:Edf]]
 [[Category:Edonoi]]