5edo: Difference between revisions

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[[File:5edo scale.mp3|thumb|A chromatic 5edo scale on C.]]

5edo is the smallest edo that contains a usable [[Perfect fifth (interval region)|perfect fifth]] at 720{{C}}, being 18{{C}} sharp of a [[just]]ly tuned [[3/2]] ratio at 702{{C}}. As such, it is the smallest edo where elements of traditional music theory begin to make sense. The 720{{C}} fifth generates an [[equalized]] tuning of the [[pentic]] (2L 3s) scale, where every step is the same size at 240{{C}}, or one step of 5edo. It also generates a [[collapsed]] tuning of the [[diatonic]] (5L 2s) scale, where the [[diatonic semitone]] or minor second is mapped to 0 steps, meaning that E and F as well as B and C are the same note in 5edo.

5edo is the smallest edo that contains a usable [[Perfect fifth (interval region)|perfect fifth]] at 720{{Cent}}, being 18{{C}} sharp of a [[just]]ly tuned [[3/2]] ratio at 702{{C}}. As such, it is the smallest edo where elements of traditional music theory begin to make sense.

The 720{{C}} fifth generates an [[equalized]] tuning of the [[pentic]] (2L 3s) scale, where every step is the same size at 240{{C}}, or one step of 5edo. It also generates a [[collapsed]] tuning of the [[diatonic]] (5L 2s) scale, where the [[diatonic semitone]] or minor second is mapped to 0 steps, meaning that E and F as well as B and C are the same note in 5edo.

5edo is the basic example of an [[equipentatonic]] scale, as in 5edo all steps are exactly the same size.

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| [[144/125]] (-4.969) [[125/108]] (-13.076)

| [[8/7]] (+8.826) [[7/6]] (-26.871)

| [[224/195]] (-0.030)

| [[23/20]] (-1.960) [[31/27]] (+0.829) [[224/195]] (-0.030)

| [[File:0-240 second, third (5-EDO).mp3|frameless]]

|-

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| [[21/16]] (+9.219)

| [[33/25]] (-0.686)

| [[33/25]] (-0.686) [[120/91]] (-1.085)

| [[File:0-480 fourth (5-EDO).mp3|frameless]]

|-

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| [[32/21]] (-9.219)

| [[50/33]] (+0.686)

| [[50/33]] (+0.686) [[91/60]] (+1.085)

[[91/60]] (+1.085)

| [[File:0-720 fifth (5-EDO).mp3|frameless]]

|-

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| [[216/125]] (+13.076) [[125/72]] (+4.969)

| [[12/7]] (+26.871) [[7/4]] (-8.826)

| [[195/112]] (+0.030)

| [[40/23]] (+1.960) [[54/31]] (-0.829) [[195/112]] (+0.030)

| [[File:0-960 sixth, seventh (5-EDO).mp3|frameless]]

|-

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| 111.731

| Gubi

| ~~Dicot~~ comma, classic ~~chroma~~

| Father comma, classic diatonic semitone

|-

| 5

@@ Line 14: / Line 14: @@
 [[File:5edo scale.mp3|thumb|A chromatic 5edo scale on C.]]
-edo is the smallest edo that contains a usable [[Perfect fifth (interval region)|perfect fifth]] at 720{{C}}, being 18{{C}} sharp of a [[just]]ly tuned [[3/2]] ratio at 702{{C}}. As such, it is the smallest edo where elements of traditional music theory begin to make sense. The 720{{C}} fifth generates an [[equalized]] tuning of the [[pentic]] (2L 3s) scale, where every step is the same size at 240{{C}}, or one step of 5edo. It also generates a [[collapsed]] tuning of the [[diatonic]] (5L 2s) scale, where the [[diatonic semitone]] or minor second is mapped to 0 steps, meaning that E and F as well as B and C are the same note in 5edo.
+edo is the smallest edo that contains a usable [[Perfect fifth (interval region)|perfect fifth]] at 720{{Cent}}, being 18{{C}} sharp of a [[just]]ly tuned [[3/2]] ratio at 702{{C}}. As such, it is the smallest edo where elements of traditional music theory begin to make sense.
+The 720{{C}} fifth generates an [[equalized]] tuning of the [[pentic]] (2L 3s) scale, where every step is the same size at 240{{C}}, or one step of 5edo. It also generates a [[collapsed]] tuning of the [[diatonic]] (5L 2s) scale, where the [[diatonic semitone]] or minor second is mapped to 0 steps, meaning that E and F as well as B and C are the same note in 5edo.
 edo is the basic example of an [[equipentatonic]] scale, as in 5edo all steps are exactly the same size.
@@ Line 70: / Line 72: @@
 | [[144/125]] (-4.969)<br>[[125/108]] (-13.076)
 | [[8/7]] (+8.826)<br>[[7/6]] (-26.871)
-| [[224/195]] (-0.030)
+| [[23/20]] (-1.960)<br>[[31/27]] (+0.829)<br>[[224/195]] (-0.030)
 | [[File:0-240 second, third (5-EDO).mp3|frameless]]
 |-
@@ Line 79: / Line 81: @@
 |
 | [[21/16]] (+9.219)
-| [[33/25]] (-0.686)
+| [[33/25]] (-0.686)<br>[[120/91]] (-1.085)
 | [[File:0-480 fourth (5-EDO).mp3|frameless]]
 |-
@@ Line 88: / Line 90: @@
 |
 | [[32/21]] (-9.219)
-| [[50/33]] (+0.686)
+| [[50/33]] (+0.686)<br>[[91/60]] (+1.085)
-[[91/60]] (+1.085)
 | [[File:0-720 fifth (5-EDO).mp3|frameless]]
 |-
@@ Line 98: / Line 99: @@
 | [[216/125]] (+13.076)<br>[[125/72]] (+4.969)
 | [[12/7]] (+26.871)<br>[[7/4]] (-8.826)
-| [[195/112]] (+0.030)
+| [[40/23]] (+1.960)<br>[[54/31]] (-0.829)<br>[[195/112]] (+0.030)
 | [[File:0-960 sixth, seventh (5-EDO).mp3|frameless]]
 |-
@@ Line 294: / Line 295: @@
 | 111.731
 | Gubi
-| Dicot comma, classic chroma
+| Father comma, classic diatonic semitone
 |-
 | 5