525edo: Difference between revisions

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== Theory ==

525edo is ~~distinctly~~ [[consistent]] through the [[25-odd-limit]]. It tempers out the [[schisma]], 32805/32768, and {{monzo| 8 77 -56 }} in the 5-limit; [[250047/250000]], [[703125/702464]] and {{monzo| 21 3 1 -10 }} in the 7-limit; [[3025/3024]], 24057/24010, 102487/102400 and 180224/180075 in the 11-limit; [[729/728]], [[1716/1715]], [[2200/2197]], [[4096/4095]] and 14641/14625 in the 13-limit; [[1089/1088]], 1275/1274, and [[2025/2023]] in the 17-limit; 2376/2375 in the 19-limit.

525edo is [[consistency|distinctly consistent]] through the [[25-odd-limit]]. The equal temperament [[tempering out|tempers out]] the [[schisma]], 32805/32768, and {{monzo| 8 77 -56 }} in the 5-limit; [[250047/250000]], [[703125/702464]] and {{monzo| 21 3 1 -10 }} in the 7-limit; [[3025/3024]], 24057/24010, 102487/102400 and 180224/180075 in the 11-limit; [[729/728]], [[1716/1715]], [[2200/2197]], [[4096/4095]] and 14641/14625 in the 13-limit; [[1089/1088]], [[1275/1274]], and [[2025/2023]] in the 17-limit; 2376/2375 in the 19-limit.

It allows [[essentially tempered chord]]s of [[squbemic chords]] and [[petrmic chords]] in the 13-odd-limit.

Line 31:

| 2.3

| {{monzo| 512 -323 }}

| [{{~~val~~| 525 832 }}]

| {{mapping| 525 832 }}

| +0.0759

| 0.0759

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| 2.3.5

| 32805/32768, {{monzo| 8 77 -56 }}

| [{{~~val~~| 525 832 1219 }}]

| {{mapping| 525 832 1219 }}

| +0.0546

| 0.0689

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| 2.3.5.7

| 32805/32768, 250047/250000, {{monzo| 21 3 1 -10 }}

| [{{~~val~~| 525 832 1219 1474 }}]

| {{mapping| 525 832 1219 1474 }}

| +0.0128

| 0.0940

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| 2.3.5.7.11

| 3025/3024, 24057/24010, 32805/32768, 102487/102400

| [{{~~val~~| 525 832 1219 1474 1816 }}]

| {{mapping| 525 832 1219 1474 1816 }}

| +0.0368

| 0.0969

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| 2.3.5.7.11.13

| 729/728, 1716/1715, 2200/2197, 3025/3024, 14641/14625

| [{{~~val~~| 525 832 1219 1474 1816 1943 }}]

| {{mapping| 525 832 1219 1474 1816 1943 }}

| +0.0030

| 0.1164

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| 2.3.5.7.11.13.17

| 729/728, 1089/1088, 1275/1274, 1716/1715, 2025/2023, 2200/2197

| [{{~~val~~| 525 832 1219 1474 1816 1943 2146 }}]

| {{mapping| 525 832 1219 1474 1816 1943 2146 }}

| -0.0040

| 0.1091

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| 2.3.5.7.11.13.17.19

| 729/728, 1089/1088, 1275/1274, 1716/1715, 2025/2023, 2200/2197, 2376/2375

| [{{~~val~~| 525 832 1219 1474 1816 1943 2146 2230 }}]

| {{mapping| 525 832 1219 1474 1816 1943 2146 2230 }}

| +0.0074

| 0.1064

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|+Table of rank-2 temperaments by generator

! Periods per 8ve

! Generator~~ (Reduced)~~

! Generator*

! Cents~~ (Reduced)~~

! Cents*

! Associated Ratio

! Associated Ratio*

! Temperaments

|-

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| [[Vasca]]

|}

<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct

[[Category:Akjayland]]

@@ Line 3: / Line 3: @@
 == Theory ==
-edo is distinctly [[consistent]] through the [[25-odd-limit]]. It tempers out the [[schisma]], 32805/32768, and {{monzo| 8 77 -56 }} in the 5-limit; [[250047/250000]], [[703125/702464]] and {{monzo| 21 3 1 -10 }} in the 7-limit; [[3025/3024]], 24057/24010, 102487/102400 and 180224/180075 in the 11-limit; [[729/728]], [[1716/1715]], [[2200/2197]], [[4096/4095]] and 14641/14625 in the 13-limit; [[1089/1088]], 1275/1274, and [[2025/2023]] in the 17-limit; 2376/2375 in the 19-limit.
+edo is [[consistency|distinctly consistent]] through the [[25-odd-limit]]. The equal temperament [[tempering out|tempers out]] the [[schisma]], 32805/32768, and {{monzo| 8 77 -56 }} in the 5-limit; [[250047/250000]], [[703125/702464]] and {{monzo| 21 3 1 -10 }} in the 7-limit; [[3025/3024]], 24057/24010, 102487/102400 and 180224/180075 in the 11-limit; [[729/728]], [[1716/1715]], [[2200/2197]], [[4096/4095]] and 14641/14625 in the 13-limit; [[1089/1088]], [[1275/1274]], and [[2025/2023]] in the 17-limit; 2376/2375 in the 19-limit.
 It allows [[essentially tempered chord]]s of [[squbemic chords]] and [[petrmic chords]] in the 13-odd-limit.
@@ Line 31: / Line 31: @@
 | 2.3
 | {{monzo| 512 -323 }}
-| [{{val| 525 832 }}]
+| {{mapping| 525 832 }}
 | +0.0759
 | 0.0759
@@ Line 38: / Line 38: @@
 | 2.3.5
 | 32805/32768, {{monzo| 8 77 -56 }}
-| [{{val| 525 832 1219 }}]
+| {{mapping| 525 832 1219 }}
 | +0.0546
 | 0.0689
@@ Line 45: / Line 45: @@
 | 2.3.5.7
 | 32805/32768, 250047/250000, {{monzo| 21 3 1 -10 }}
-| [{{val| 525 832 1219 1474 }}]
+| {{mapping| 525 832 1219 1474 }}
 | +0.0128
 | 0.0940
@@ Line 52: / Line 52: @@
 | 2.3.5.7.11
 | 3025/3024, 24057/24010, 32805/32768, 102487/102400
-| [{{val| 525 832 1219 1474 1816 }}]
+| {{mapping| 525 832 1219 1474 1816 }}
 | +0.0368
 | 0.0969
@@ Line 59: / Line 59: @@
 | 2.3.5.7.11.13
 | 729/728, 1716/1715, 2200/2197, 3025/3024, 14641/14625
-| [{{val| 525 832 1219 1474 1816 1943 }}]
+| {{mapping| 525 832 1219 1474 1816 1943 }}
 | +0.0030
 | 0.1164
@@ Line 66: / Line 66: @@
 | 2.3.5.7.11.13.17
 | 729/728, 1089/1088, 1275/1274, 1716/1715, 2025/2023, 2200/2197
-| [{{val| 525 832 1219 1474 1816 1943 2146 }}]
+| {{mapping| 525 832 1219 1474 1816 1943 2146 }}
 | -0.0040
 | 0.1091
@@ Line 73: / Line 73: @@
 | 2.3.5.7.11.13.17.19
 | 729/728, 1089/1088, 1275/1274, 1716/1715, 2025/2023, 2200/2197, 2376/2375
-| [{{val| 525 832 1219 1474 1816 1943 2146 2230 }}]
+| {{mapping| 525 832 1219 1474 1816 1943 2146 2230 }}
 | +0.0074
 | 0.1064
@@ Line 84: / Line 84: @@
 |+Table of rank-2 temperaments by generator
 ! Periods<br>per 8ve
-! Generator<br>(Reduced)
+! Generator*
-! Cents<br>(Reduced)
+! Cents*
-! Associated<br>Ratio
+! Associated<br>Ratio*
 ! Temperaments
 |-
@@ Line 125: / Line 125: @@
 | [[Vasca]]
 |}
+<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
 [[Category:Akjayland]]