770edo: Difference between revisions

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== Theory ==

770edo is in[[consistent]] to the [[5-odd-limit]] and [[3/1|harmonic 3]] is about halfway between its steps. It has a reasonable approximation of the 2.9.5.7.11 [[subgroup]], where it notably tempers out [[9801/9800]].

770edo is in[[consistent]] to the [[5-odd-limit]] and [[3/1|harmonic 3]] is about halfway between its steps. It has a reasonable approximation of the 2.9.5.7.11 [[subgroup]], where it notably [[tempering out|tempers out]] [[9801/9800]].

=== Odd harmonics ===

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=== Subsets and supersets ===

Since 770 factors into ~~2 × 5 × 7 × 11~~, 770edo has subset edos {{EDOs| 2, 5, 7, 10, 11, 14, 22, 35, 55, 70, 77, 110, 154, and 385}}. [[1540edo]], which doubles it, gives a good correction to the harmonic 3.

Since 770 factors into {{factorization|770}}, 770edo has subset edos {{EDOs| 2, 5, 7, 10, 11, 14, 22, 35, 55, 70, 77, 110, 154, and 385}}. [[1540edo]], which doubles it, gives a good correction to the harmonic 3.

== Regular temperament properties ==

{| class="wikitable center-4 center-5 center-6"

|-

! rowspan="2" | [[Subgroup]]

! rowspan="2" | [[Comma list~~|Comma List~~]]

! rowspan="2" | [[Comma list]]

! rowspan="2" | [[Mapping]]

! rowspan="2" | Optimal<br>8ve ~~Stretch~~ (¢)

! rowspan="2" | Optimal<br />8ve stretch (¢)

! colspan="2" | Tuning ~~Error~~

! colspan="2" | Tuning error

|-

! [[TE error|Absolute]] (¢)

! [[TE simple badness|Relative]] (%)

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| {{monzo| 2441 -770 }}

| {{mapping| 770 2441 }}

| -0.0388

| −0.0388

| 0.0388

| 2.49

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| {{monzo| 61 2 -29 }}, {{monzo| 40 -28 21 }}

| {{mapping| 770 2441 1788 }}

| -0.0517

| −0.0517

| 0.0365

| 2.34

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| 43046721/43025920, 134217728/133984375, 1220703125/1219784832

| {{mapping| 770 2441 1788 2162 }}

| -0.0855

| −0.0855

| 0.0666

| 4.27

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| 9801/9800, 820125/819896, 1296000/1294139, 1362944/1361367

| {{mapping| 770 2441 1788 2162 2664 }}

| -0.0898

| −0.0898

| 0.0602

| 3.86

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|770}}
+{{ED intro}}
 == Theory ==
-edo is in[[consistent]] to the [[5-odd-limit]] and [[3/1|harmonic 3]] is about halfway between its steps. It has a reasonable approximation of the 2.9.5.7.11 [[subgroup]], where it notably tempers out [[9801/9800]].
+edo is in[[consistent]] to the [[5-odd-limit]] and [[3/1|harmonic 3]] is about halfway between its steps. It has a reasonable approximation of the 2.9.5.7.11 [[subgroup]], where it notably [[tempering out|tempers out]] [[9801/9800]].
 === Odd harmonics ===
@@ Line 9: / Line 9: @@
 === Subsets and supersets ===
-Since 770 factors into 2 × 5 × 7 × 11, 770edo has subset edos {{EDOs| 2, 5, 7, 10, 11, 14, 22, 35, 55, 70, 77, 110, 154, and 385}}. [[1540edo]], which doubles it, gives a good correction to the harmonic 3.
+Since 770 factors into {{factorization|770}}, 770edo has subset edos {{EDOs| 2, 5, 7, 10, 11, 14, 22, 35, 55, 70, 77, 110, 154, and 385}}. [[1540edo]], which doubles it, gives a good correction to the harmonic 3.
 == Regular temperament properties ==
 {| class="wikitable center-4 center-5 center-6"
+|-
 ! rowspan="2" | [[Subgroup]]
-! rowspan="2" | [[Comma list|Comma List]]
+! rowspan="2" | [[Comma list]]
 ! rowspan="2" | [[Mapping]]
-! rowspan="2" | Optimal<br>8ve Stretch (¢)
+! rowspan="2" | Optimal<br />8ve stretch (¢)
-! colspan="2" | Tuning Error
+! colspan="2" | Tuning error
 |-
 ! [[TE error|Absolute]] (¢)
 ! [[TE simple badness|Relative]] (%)
@@ Line 25: / Line 26: @@
 | {{monzo| 2441 -770 }}
 | {{mapping| 770 2441 }}
-| -0.0388
+| −0.0388
 | 0.0388
 | 2.49
@@ Line 32: / Line 33: @@
 | {{monzo| 61 2 -29 }}, {{monzo| 40 -28 21 }}
 | {{mapping| 770 2441 1788 }}
-| -0.0517
+| −0.0517
 | 0.0365
 | 2.34
@@ Line 39: / Line 40: @@
 | 43046721/43025920, 134217728/133984375, 1220703125/1219784832
 | {{mapping| 770 2441 1788 2162 }}
-| -0.0855
+| −0.0855
 | 0.0666
 | 4.27
@@ Line 46: / Line 47: @@
 | 9801/9800, 820125/819896, 1296000/1294139, 1362944/1361367
 | {{mapping| 770 2441 1788 2162 2664 }}
-| -0.0898
+| −0.0898
 | 0.0602
 | 3.86