User:Moremajorthanmajor/9edX: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
No edit summary
No edit summary
Line 1: Line 1:
This is the neutral scale of the Middletown temperament family.
This is the neutral scale of the Middletown temperament family. It also gives the period of the 9th-decade White Oak temperament family.
 
==Intervals==
== Intervals ==
{| class="wikitable"
{| class="wikitable" style="text-align: center"
|+
! rowspan="3" |Degrees
! colspan="5" |Decade
! colspan="3" rowspan="2" |Intense Aeolian-Subpental Dorian
!Period
! colspan="9" |Dorian
!Notes
|-
|6\5
|
|
|
|
|160
|Intense Aeolian-Subpental Dorian mode begins
|-
|
|17\14
|
|
|
|161.905
|
|-
|-
! colspan="3" |Subpental
|11\9
! colspan="3" |Pental
|
! colspan="3" |Superpental
|
|
|
|162.{{Overline|962}}
|Intense Aeolian-Subpental Dorian mode ends, Subpental Dorian mode begins
|-
|-
!Min-comma
|
!Med
|
! colspan="2" |Max+comma~Min-comma
|27\22
!Med
|
! colspan="2" |Max+comma~Min-comma
|
!Med
|163.{{Overline|63}}
! colspan="2" |Max+comma~Min-comma
|
!Med
!Max+comma
|-
|-
|1
|
|155.{{Overline|5}}-160
|16\13
|161.905
|
| colspan="2" |158.{{Overline|518}}-167.{{Overline|407}}
|
|
|164.103
|164.103
| colspan="2" |162.{{Overline|2}}-171.{{Overline|1}}
|
|168.{{Overline|8}}
|-
| colspan="2" |165.{{Overline|25}}-174.{{Overline|14}}
|
|170.{{Overline|370}}
|
|171.429-175.873
|21\17
|
|
|164.706
|
|-
|
|
|
|26\21
|
|165.079
|
|-
|-
|2
|5\4
|311.{{Overline|1}}-320
|
|323.8095
|
| colspan="2" |317.{{Overline|037}}-334.{{Overline|814}}
|
|328.205
|
| colspan="2" |324.{{Overline|4}}-342.{{Overline|2}}
| 166.{{Overline|6}}
|337.{{Overline|7}}
|Subpental Dorian mode ends, Pental Dorian mode begins
| colspan="2" |330.{{Overline|50}}-348.{{Overline|28}}
|340.{{Overline|740}}
|342.857-351.746
|-
|-
|3
|
|466.{{Overline|6}}-480
|
|485.714
|
| colspan="2" |475.{{Overline|5}}-502.{{Overline|2}}
|
|492.308
|34\27
| colspan="2" |486.{{Overline|6}}-513.{{Overline|3}}
|167.901
|506.{{Overline|6}}
|
| colspan="2" |495.{{Overline|75}}-522.{{Overline|42}}
|511.{{Overline|1}}
|514.286-527.619
|-
|-
|4
|
|622.{{Overline|2}}-640
|
|647.619
|
| colspan="2" |634.{{Overline|074}}-669.{{Overline|629}}
|29\23
|656.41
|
| colspan="2" |648.{{Overline|8}}-684.{{Overline|4}}
|168.116
|675.{{Overline|5}}
|
| colspan="2" |661.{{Overline|01}}-696.{{Overline|56}}
|681.{{Overline|481}}
|685.714-703.492
|-
|-
|5
|
|777.{{Overline|7}}-800
|
|809.524
|24\19
| colspan="2" |792.{{Overline|592}}-837.{{Overline|037}}
|
|820.512
|
| colspan="2" |811.{{Overline|1}}-855.{{Overline|5}}
|168.421
|844.{{Overline|4}}
|
| colspan="2" |826.{{Overline|26}}-870.{{Overline|70}}
|851.{{Overline|851}}
|857.143-878.365
|-
|-
|6
|
|943.{{Overline|3}}-960
|19\15
|971.429
|
| colspan="2" |951.{{Overline|1}}-1004.{{Overline|4}}
|
|984.615
|
| colspan="2" |973.{{Overline|3}}-1026.{{Overline|6}}
|168.{{Overline|8}}
|1013.{{Overline|3}}
|
| colspan="2" |981.{{Overline|51}}-1044.{{Overline|84}}
|1022.{{Overline|2}}
|1028.571-1055.238
|-
|-
|7
|14\11
|1088.{{Overline|8}}-1120
|
|1133.{{Overline|3}}
|
| colspan="2" |1109.{{Overline|629}}-1171.{{Overline|851}}
|
|1148.718
|
| colspan="2" |1135.{{Overline|5}}-1197.{{Overline|7}}
|169.{{Overline|69}}
|1182.{{Overline|2}}
|Pental Dorian mode ends, Superpental Dorian mode begins
| colspan="2" |1156.{{Overline|76}}.-1218.{{Overline|98}}
|1192.{{Overline|592}}
|1200-1231.{{Overline|1}}
|-
|-
|8
|
|1244.{{Overline|4}}-1280
|23\18
|1295.238
|
| colspan="2" |1238.{{Overline|148}}-1339.{{Overline|259}}
|
|1312.8205
|
| colspan="2" |1297.{{Overline|7}}-1368.{{Overline|8}}
|170.{{Overline|370}}
|1351.{{Overline|1}}
|
| colspan="2" |1322.{{Overline|02}}-1392.{{Overline|12}}
|1362.{{Overline|962}}
|1371.429-1406.984
|}
{| class="wikitable" style="text-align: center"
! rowspan="2" |Degrees
! colspan="4" |Mohajira
! colspan="3" |Beatles
|-
|-
!Min-comma
|9\7
!''r¢''
|
!Med
|
! colspan="2" |Max+comma~Min-comma
|
!Med
|
!Max+comma
|171.429
|Superpental Dorian mode ends, Mohajira Dorian-Mixolydian mode begins
|-
|-
|1
|
|166.984-171.429
|31\24
| colspan="2" |''172.{{Overline|2}}''
|
| colspan="2" |168.105-176.9935
|
|172.8395
|
|173.{{Overline|3}}-177.{{Overline|7}}
|172.{{Overline|2}}
|
|-
|-
|2
|22\17
|333.968-342.857
|
| colspan="2" |''344.{{Overline|4}}''
|
| colspan="2" |336.209-353.987
|
|345.679
|
|346.{{Overline|6}}-355.{{Overline|5}}
|172.549
|Mohajira Dorian-Mixolydian mode ends, Beatles Dorian-Mixolydian mode begins
|-
|-
|3
|
|500.952-514.286
|35\27
| colspan="2" |''516.{{Overline|6}}''
|
| colspan="2" |504.314-530.98
|
|518.{{Overline|518}}
|
|520-533.{{Overline|3}}
|[[Tel:172.8395|172.8395]]
|
|-
|-
|4
|13\10
|667.9365-685.714
|
| colspan="2" |''688.{{Overline|8}}''
|
| colspan="2" |672.418-707.974
|
|691.358
|
|693.{{Overline|3}}-711.{{Overline|1}}
|173.{{Overline|3}}
|Beatles Dorian-Mixolydian mode ends, Subpental Mixolydian mode begins
|-
|-
|5
|17\13
|834.921-857.143
|
| colspan="2" |''861.{{Overline|1}}''
|
| colspan="2" |840.523-885.967
|
|864.1975
|
|866.{{Overline|6}}-888.{{Overline|8}}
|174.358
|
|-
|-
|6
|21\16
|1001.904-1028.571
|
| colspan="2" |''1033.{{Overline|3}}''
|
| colspan="2" |1008.6275-1062.961
|
|1037.{{Overline|037}}
|
|1040-1066.{{Overline|6}}
|175
|Subpental Mixolydian mode ends, Pental Mixolydian mode begins
|-
|-
|7
|
|1168.{{Overline|8}}-1200
|25\19
| colspan="2" |''1205.{{Overline|5}}''
|
| colspan="2" |1176.732-1239.954
|
|1209.8765
|
|1213.{{Overline|3}}-1244.{{Overline|4}}
|175.439
|
|-
|-
|8
|
|1335.873-1371.429
|
| colspan="2" |''1377.{{Overline|7}}''
|29\22
| colspan="2" |1344.837-1416.948
|
|1382.716
|
|1386.{{Overline|6}}-1422.{{Overline|2}}
|175.{{Overline|75}}
|}
|
{| class="wikitable"
|-
|-
! rowspan="4" |Degrees
|
! colspan="12" |Mixolydian
|
! colspan="3" rowspan="3" |Mixolydian-Ionian
|
|33\25
|
|176
|
|-
|-
! colspan="3" rowspan="2" |Subpental
|4\3
! colspan="3" rowspan="2" |Pental
|
! colspan="6" |Superpental
|
|
|
|177.{{Overline|7}}
|Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins
|-
|-
! colspan="3" |Soft
|
! colspan="3" |Intense
|
|
|
|31\23
|179.710
|
|-
|-
!Min-comma
|
!Med
|
! colspan="2" |Max+comma~Min-comma
|
!Med
|27\20
! colspan="2" |Max+comma~Min-comma
|
!Med
|180
! colspan="2" |Max+comma~Min-comma
|
!Med
! colspan="2" |Max+comma~Min-comma
!Med
! |Max+comma
|-
|-
| |1
|
|168.{{Overline|8}}-173.{{Overline|3}}
|
|174.359
|23\17
| colspan="2" |170.{{Overline|5}}-179.{{Overline|4}}
|
|175.439
|
| colspan="2" |173.{{Overline|3}}-182.{{Overline|2}}
|180.392
|179.1{{Overline|6}}
|
| colspan="2" |174.866-183.755
|181.609
| colspan="2" |179.464-188.3525
|184.314
| |186.{{Overline|6}}-191.{{Overline|1}}
|-
|-
| |2
|
|337.{{Overline|7}}-346.{{Overline|6}}
|19\14
|348.718
|
| colspan="2" |341.{{Overline|1}}-358.{{Overline|8}}
|
|350.877
|
| colspan="2" |346.{{Overline|6}}-364.{{Overline|4}}
|180.952
|358.{{Overline|3}}
|
| colspan="2" |349.732-367.51
|363.218
| colspan="2" |368.927-376.705
|[[Tel:368.6275|368.6275]]
| |373.{{Overline|3}}-382.{{Overline|2}}
|-
|-
| |3
|15\11
|506.{{Overline|6}}-520
|
|523.077
|
| colspan="2" |511.{{Overline|6}}-538.{{Overline|3}}
|
|526.316
|
| colspan="2" |520-546.{{Overline|6}}
|181.{{Overline|81}}
|537.5
|Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins
| colspan="2" |524.598-551.264
|544.828
| colspan="2" |538.391-565.0575
|552.941
| |560-573.{{Overline|3}}
|-
|-
| |4
|
|675.{{Overline|5}}-693.{{Overline|3}}
|26\19
|697.436
|
| colspan="2" |682.{{Overline|2}}-717.{{Overline|7}}
|
|701.754
|
| colspan="2" |693.{{Overline|3}}-728.{{Overline|8}}
|182.456
|716.{{Overline|6}}
|
| colspan="2" |699.464-735.019
|726.437
| colspan="2" |717.854-753.41
|737.255
| |746.{{Overline|6}}-764.{{Overline|4}}
|-
|-
| |5
| 11\8
|844.{{Overline|4}}-866.{{Overline|6}}
|
|871.795
|
| colspan="2" |852.{{Overline|7}}-897.{{Overline|2}}
|
|877.193
|
| colspan="2" |866.{{Overline|6}}-911.{{Overline|1}}
|183.{{Overline|3}}
|895.8{{Overline|3}}
|Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins
| colspan="2" |874.3295-918.774
|908.046
| colspan="2" |897.318-942.7625
|921.569
| |933.{{Overline|3}}-955.{{Overline|5}}
|-
|-
| |6
|
|1013.{{Overline|3}}-1040
|18\13
|1046.154
|
| colspan="2" |1023.{{Overline|3}}-1076.{{Overline|6}}
|
|1052.632
|
| colspan="2" |1040-1093.{{Overline|3}}
|184.615
|1075
|
| colspan="2" |1049.195-1102.529
|1089.655
| colspan="2" |1076.782-1130.115
|1105.882
| |1120-1146.{{Overline|6}}
|-
|-
| |7
|
|1182.{{Overline|2}}-1213.{{Overline|3}}
|
|1220.513
|25\18
| colspan="2" |1193.{{Overline|8}}-1256.{{Overline|1}}
|
|1228.07
|
| colspan="2" |1213.{{Overline|3}}-1275.{{Overline|5}}
|185.{{Overline|185}}
|1254.1{{Overline|6}}
|
| colspan="2" |1224.061-1286.2835
|1271.264
| colspan="2" |1256.245-1318.457
|1290.196
| |1306.{{Overline|6}}-1337.{{Overline|7}}
|-
|-
|8
|7\5
|1351.{{Overline|1}}-1386.{{Overline|6}}
|
|1394.872
|
| colspan="2" |1364.{{Overline|4}}-1435.{{Overline|5}}
|
|1403.509
|
| colspan="2" |1386.{{Overline|6}}-1457.{{Overline|7}}
|186.{{Overline|6}}
|1433.{{Overline|3}}
|Mixolydian-Ionian mode ends
| colspan="2" |1398.927-1470.038
|1452.874
| colspan="2" |1438.709-1506.82
|1474.51
|1493.{{Overline|3}}-1528.{{Overline|8}}
|}Relative cents
|}Relative cents


Line 346: Line 327:
|6
|6
|966.{{Overline|6}}
|966.{{Overline|6}}
|1000
| 1000
|1066.{{Overline|6}}
|1066.{{Overline|6}}
|1100
|1100
Line 361: Line 342:
|1422.{{Overline|2}}
|1422.{{Overline|2}}
|1466.{{Overline|6}}
|1466.{{Overline|6}}
|}Golden/Pyrite Tunings±13¢
|}By a surprising coincidence, the 9ed of the Pyrite tenth (7φ+6)\(5φ^2)edo is almost exactly every fifth degree of [[34edo]]. Additionally, those of the Golden Subpental Dorian and Pental and Intense Superpental Mixolydian tenths are almost exactly every third step of [[22edo]], 4edf and equal multiples of 10/9 respectively.
 
{| class="wikitable" style="text-align: center"
! rowspan="2" |Degrees
! rowspan="2" |Intense Aeolian-Subpental Dorian
! colspan="3" |Dorian
|-
!Subpental
!Pental
!Superpental
|-
|1
|160.761-163.65
|162.317-165.2055
|167.6965-170.585
|168.741-171.63
|-
|2
|321.522-327.3
|364.633-330.411
|335.393-341.171
|337.483-343.36
|-
|3
|482.284-490.95
|486.95-495.617
|503.089-511.756
|506.224-514.891
|-
|4
|643.045-654.6
|649.2665-660.822
|670.786-682.341
|674.965-686.521
|-
|5
|803.806-818.25
|811.583-826.028
|838.482-852.927
|843.707-858.151
|-
|6
|964.567-981.9
|973.9-991.233
|1006.179-1023.512
|1012.448-1029.781
|-
|7
|1125.328-1145.55
|1136.216-1156.439
|1173.875-1194.0975
|1181.189-1201.411
|-
|8
|1286.09-1309.2
|1278.2435-1321.644
|1341.572-1343.36
|1349.9305-1373.042
|}
{| class="wikitable" style="text-align: center"
!Degrees
!Mohajira
!Beatles
|-
|1
|170.877-173.776
|171.314-174.203
|-
|2
|341.755-347.513
|342.627-348.405
|-
|3
|512.632-521.2985
|513.941-522.607
|-
|4
|683.509-695.065
|685.255-696.81
|-
|5
|854.386-868.831
|856.568-870.112
|-
|6
|1025.264-1042.597
|1027.882-1045.215
|-
|7
|1196.141-1216.363
|1199.196-1219.418
|-
|8
|1367.018-1389.119
|1370.5095-1393.621
|}
{| class="wikitable" style="text-align: center"
|-
! rowspan="3" |Degrees
! colspan="4" |Mixolydian
! rowspan="3" |Mixolydian-Ionian
|-
! rowspan="2" |Subpental
! rowspan="2" |Pental
! colspan="2" |Superpental
|-
!Soft
!Intense
|-
|1
|173.091-175.98
|173.844-176.733
|177.774-180.663
|180.707-183.596
|182.729-185.618
|-
|2
|346.182-351.96
|347.688-353.466
|355.548-361.325
|361.415-367.193
|365.4585-371.236
|-
|3
|519.2735-527.94
|521.532-530.199
|533.321-541.988
|542.122-550.789
|548.188-556.854
|-
|4
|692.365-703.92
|695.376-706.932
|711.095-722.651
|722.83-734.385
|730.917-742.4725
|-
|5
|865.456-879.9
|869.22-883.6645
|888.896-903.3135
|903.537-917.982
|913.646-928.091
|-
|6
|1038.547-1055.88
|1043.064-1060.3975
|1033.634-1083.976
|1084.245-1101.578
|1096.3755-1113.709
|-
|7
|1211.638-1231.86
|1216.908-1237.13
|1244.417-1264.639
|1264.952-1285.174
|1279.105-1299.327
|-
|8
|1384.729-1407.84
|1390.752-1413.863
|1422.19-1445.3015
|1445.6595-1445.821
|1461.834-1484.945
|}
 
By a surprising coincidence, the 9ed of the Pyrite tenth (7φ+6)\(5φ^2)edo is almost exactly every fifth degree of [[34edo|34edo]]. Additionally, those of the Golden Subpental Dorian and Pental and Intense Superpental Mixolydian tenths are almost exactly every third step of [[22edo]], 4edf and equal multiples of 10/9 respectively.


== See also ==
==See also==
* [[9ed5/2]] - equal division of the classic major tenth
*[[9ed5/2]] - equal division of the classic major tenth
* [[9ed7/3]] - equal division of the septimal minor tent
* [[9ed7/3]] - equal division of the septimal minor tent


[[Category:EdX]]
[[Category:EdX]]

Revision as of 04:10, 16 May 2023

This is the neutral scale of the Middletown temperament family. It also gives the period of the 9th-decade White Oak temperament family.

Intervals

Decade Period Notes
6\5 160 Intense Aeolian-Subpental Dorian mode begins
17\14 161.905
11\9 162.962 Intense Aeolian-Subpental Dorian mode ends, Subpental Dorian mode begins
27\22 163.63
16\13 164.103
21\17 164.706
26\21 165.079
5\4 166.6 Subpental Dorian mode ends, Pental Dorian mode begins
34\27 167.901
29\23 168.116
24\19 168.421
19\15 168.8
14\11 169.69 Pental Dorian mode ends, Superpental Dorian mode begins
23\18 170.370
9\7 171.429 Superpental Dorian mode ends, Mohajira Dorian-Mixolydian mode begins
31\24 172.2
22\17 172.549 Mohajira Dorian-Mixolydian mode ends, Beatles Dorian-Mixolydian mode begins
35\27 [[1]]
13\10 173.3 Beatles Dorian-Mixolydian mode ends, Subpental Mixolydian mode begins
17\13 174.358
21\16 175 Subpental Mixolydian mode ends, Pental Mixolydian mode begins
25\19 175.439
29\22 175.75
33\25 176
4\3 177.7 Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins
31\23 179.710
27\20 180
23\17 180.392
19\14 180.952
15\11 181.81 Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins
26\19 182.456
11\8 183.3 Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins
18\13 184.615
25\18 185.185
7\5 186.6 Mixolydian-Ionian mode ends

Relative cents

Degrees Intense Aeolian-Subpental Dorian Dorian Subpental-Soft Superpental Mixolydian Intense Superpental Mixolydian ~ Mixolydian-Ionian
1 161.1 166.6 177.7 183.3
2 322.2 333.3 355.5 366.6
3 483.3 500 533.3 550
4 644.4 666.6 711.1 733.3
5 805.5 833.3 888.8 916.6
6 966.6 1000 1066.6 1100
7 1127.7 1166.6 1244.4 1283.3
8 1288.8 1333.3 1422.2 1466.6

By a surprising coincidence, the 9ed of the Pyrite tenth (7φ+6)\(5φ^2)edo is almost exactly every fifth degree of 34edo. Additionally, those of the Golden Subpental Dorian and Pental and Intense Superpental Mixolydian tenths are almost exactly every third step of 22edo, 4edf and equal multiples of 10/9 respectively.

See also

  • 9ed5/2 - equal division of the classic major tenth
  • 9ed7/3 - equal division of the septimal minor tent
Retrieved from "https://en.xen.wiki/index.php?title=User:Moremajorthanmajor/9edX&oldid=113415"