Xenharmonic Wiki

Equable heptatonic: Difference between revisions

← Older edit
VisualWikitext
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
5,024 edits
mNo edit summary
ArrowHead294 (talk | contribs)
15,213 edits
mNo edit summary
 
(3 intermediate revisions by 2 users not shown)
Line 1: Line 1:
In the theory of [[Margo Schulter]], '''equable heptatonic''' is a category of intervals which occupy regions intermediate between [[11/10]] and [[10/9]], or [[9/5]] and [[20/11]]. There are two heartland regions given below, with approximate cents ranges from Schulter's article [http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum]:
In the theory of [[Margo Schulter]], '''equable heptatonic''' is a category of intervals which occupy regions intermediate between [[11/10]] and [[10/9]], or [[9/5]] and [[20/11]]. There are two heartland regions given below, with approximate cents ranges from Schulter's article [http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum]:


* Neut2–Maj2 – intermediate between [[11/10]] and [[10/9]] – 160¢–182¢
* Neut2–Maj2 – intermediate between [[11/10]] and [[10/9]] – 160–182{{c}} (~submajor second)
* min7–Neut7 – intermediate between [[9/5]] and [[20/11]] – 1018¢–1040¢
* min7–Neut7 – intermediate between [[9/5]] and [[20/11]] – 1018–1040{{c}} (~supraminor seventh)


Equable heptatonic intervals are well-represented in [[7edo]] at 171.429¢ (1＼7) and 1028.571¢ (6＼7). They also appear in [[27edo]], [[34edo]] and [[41edo]]. As they fall in ambiguous zones between simpler categories, they are inevitably xenharmonic.
Equable heptatonic intervals are well-represented in [[7edo]] at 171.429{{c}} (1\7) and 1028.571{{c}} (6\7). They also appear in [[27edo]], [[34edo]] and [[41edo]]. As they fall in ambiguous zones between simpler categories, they are inevitably xenharmonic.


== Examples ==
== Examples ==
Line 11: Line 11:
=== Neut2–Maj2 (submajor second) ===
=== Neut2–Maj2 (submajor second) ===
{| class="wikitable center-1 right-2"
{| class="wikitable center-1 right-2"
|-
! Interval
! Interval
! Cents Value
! Size<br />(cents)
! Prime Limit (if applicable)
! Prime limit<br />(if applicable)
|-
|-
| [[34/31]]
| [[34/31]]
Line 19: Line 20:
| 31
| 31
|-
|-
| 2＼[[15edo|15]]
| 2\[[15edo|15]]
| 160.000
| 160.000
| -
| —
|-
|-
| [[79/72]]
| [[79/72]]
Line 31: Line 32:
| 41
| 41
|-
|-
| 7＼[[52edo|52]]
| 7\[[52edo|52]]
| 161.538
| 161.538
| -
| —
|-
|-
| [[101/92]]
| [[101/92]]
Line 43: Line 44:
| 17
| 17
|-
|-
| 5＼[[37edo|37]]
| 5\[[37edo|37]]
| 162.162
| 162.162
| -
| —
|-
|-
| [[67/61]]
| [[67/61]]
Line 63: Line 64:
| 13
| 13
|-
|-
| 3＼[[22edo|22]]
| 3\[[22edo|22]]
| 163.636
| 163.636
| -
| —
|-
|-
| 7＼[[51edo|51]]
| 7\[[51edo|51]]
| 164.706
| 164.706
| -
| —
|-
|-
| [[11/10]]
| [[11/10]]
Line 75: Line 76:
| 11
| 11
|-
|-
| 4＼[[29edo|29]]
| 4\[[29edo|29]]
| 165.517
| 165.517
| -
| —
|-
|-
| 5＼[[36edo|36]]
| 5\[[36edo|36]]
| 166.667
| 166.667
| -
| —
|-
|-
| [[98/89]]
| [[98/89]]
Line 95: Line 96:
| 23
| 23
|-
|-
| 6＼[[43edo|43]]
| 6\[[43edo|43]]
| 167.442
| 167.442
| -
| —
|-
|-
| [[65/59]]
| [[65/59]]
Line 103: Line 104:
| 59
| 59
|-
|-
| 7＼[[50edo|50]]
| 7\[[50edo|50]]
| 168.000
| 168.000
| -
| —
|-
|-
| [[54/49]]
| [[54/49]]
Line 131: Line 132:
| 17
| 17
|-
|-
| 1＼[[7edo|7]]
| 1\[[7edo|7]]
| 171.429
| 171.429
| -
| —
|-
|-
| [[53/48]]
| [[53/48]]
Line 159: Line 160:
| 77
| 77
|-
|-
| 7＼[[48edo|48]]
| 7\[[48edo|48]]
| 175.000
| 175.000
| -
| —
|-
|-
| [[52/47]]
| [[52/47]]
Line 171: Line 172:
| 83
| 83
|-
|-
| 6＼[[41edo|41]]
| 6\[[41edo|41]]
| 175.610
| 175.610
| -
| —
|-
|-
| [[31/28]]
| [[31/28]]
Line 179: Line 180:
| 31
| 31
|-
|-
| 5＼[[34edo|34]]
| 5\[[34edo|34]]
| 176.471
| 176.471
| -
| —
|-
|-
| [[72/65]]
| [[72/65]]
Line 191: Line 192:
| 41
| 41
|-
|-
| 4＼[[27edo|27]]
| 4\[[27edo|27]]
| 177.778
| 177.778
| -
| —
|-
|-
| [[92/83]]
| [[92/83]]
Line 203: Line 204:
| 23
| 23
|-
|-
| 7＼[[47edo|47]]
| 7\[[47edo|47]]
| 178.723
| 178.723
| -
| —
|-
|-
| [[61/55]]
| [[61/55]]
Line 215: Line 216:
| 71
| 71
|-
|-
| 3＼[[20edo|20]]
| 3\[[20edo|20]]
| 180.000
| 180.000
| -
| —
|-
|-
| [[81/73]]
| [[81/73]]
Line 227: Line 228:
| 41
| 41
|-
|-
| 5＼[[33edo|33]]
| 5\[[33edo|33]]
| 181.818
| 181.818
| -
| —
|-
|-
| [[10/9]]
| [[10/9]]
Line 235: Line 236:
| 5
| 5
|-
|-
| 7＼[[46edo|46]]
| 7\[[46edo|46]]
| 182.609
| 182.609
| -
| —
|-
|-
| 2＼[[13edo|13]]
| 2\[[13edo|13]]
| 184.615
| 184.615
| -
| —
|}
|}


=== min7–Neut7 (supraminor seventh) ===
=== min7–Neut7 (supraminor seventh) ===
{| class="wikitable center-1 right-2"
{| class="wikitable center-1 right-2"
|-
! Interval
! Interval
! Cents Value
! Size<br />(cents)
! Prime Limit (if applicable)
! Prime limit<br />(if applicable)
|-
|-
| 11＼[[13edo|13]]
| 11\[[13edo|13]]
| 1015.385
| 1015.385
| -
| —
|-
|-
| 39＼[[46edo|46]]
| 39\[[46edo|46]]
| 1017.391
| 1017.391
| -
| —
|-
|-
| [[9/5]]
| [[9/5]]
Line 262: Line 264:
| 5
| 5
|-
|-
| 28＼[[33edo|33]]
| 28\[[33edo|33]]
| 1018.182
| 1018.182
| -
| —
|-
|-
| 17＼[[20edo|20]]
| 17\[[20edo|20]]
| 1020.000
| 1020.000
| -
| —
|-
|-
| 40＼[[47edo|47]]
| 40\[[47edo|47]]
| 1021.277
| 1021.277
| -
| —
|-
|-
| [[92/51]]
| [[92/51]]
Line 282: Line 284:
| 83
| 83
|-
|-
| 23＼[[27edo|27]]
| 23\[[27edo|27]]
| 1022.222
| 1022.222
| -
| —
|-
|-
| [[74/41]]
| [[74/41]]
Line 294: Line 296:
| 13
| 13
|-
|-
| 29＼[[34edo|34]]
| 29\[[34edo|34]]
| 1023.529
| 1023.529
| -
| —
|-
|-
| [[56/31]]
| [[56/31]]
Line 302: Line 304:
| 31
| 31
|-
|-
| 35＼[[41edo|41]]
| 35\[[41edo|41]]
| 1024.390
| 1024.390
| -
| —
|-
|-
| [[47/26]]
| [[47/26]]
Line 310: Line 312:
| 47
| 47
|-
|-
| 41＼[[48edo|48]]
| 41\[[48edo|48]]
| 1025.000
| 1025.000
| -
| —
|-
|-
| [[85/47]]
| [[85/47]]
Line 320: Line 322:
| [[38/21]]
| [[38/21]]
| 1026.732
| 1026.732
|  
| 19
|-
|-
| [[67/37]]
| [[67/37]]
Line 326: Line 328:
| 67
| 67
|-
|-
| 6＼[[7edo|7]]
| 6\[[7edo|7]]
| 1028.571
| 1028.571
| -
| —
|-
|-
| [[29/16]]
| [[29/16]]
| 1029.577
| 1029.577
| 19
| 29
|-
|-
| [[78/43]]
| [[78/43]]
Line 342: Line 344:
| 7
| 7
|-
|-
| 43＼[[50edo|50]]
| 43\[[50edo|50]]
| 1032.000
| 1032.000
| -
| —
|-
|-
| [[69/38]]
| [[69/38]]
Line 350: Line 352:
| 23
| 23
|-
|-
| 37＼[[43edo|43]]
| 37\[[43edo|43]]
| 1032.558
| 1032.558
| -
| —
|-
|-
| [[89/49]]
| [[89/49]]
Line 358: Line 360:
| 89
| 89
|-
|-
| 31＼[[36edo|36]]
| 31\[[36edo|36]]
| 1033.333
| 1033.333
| -
| —
|-
|-
| 25＼[[29edo|29]]
| 25\[[29edo|29]]
| 1034.483
| 1034.483
| -
| —
|-
|-
| [[20/11]]
| [[20/11]]
Line 370: Line 372:
| 11
| 11
|-
|-
| 44＼[[51edo|51]]
| 44\[[51edo|51]]
| 1035.294
| 1035.294
| -
| —
|-
|-
| 19＼[[22edo|22]]
| 19\[[22edo|22]]
| 1036.364
| 1036.364
| -
| —
|-
|-
| [[91/50]]
| [[91/50]]
| 1036.726
| 1036.726
|  
| 13
|-
|-
| [[71/39]]
| [[71/39]]
Line 386: Line 388:
| 71
| 71
|-
|-
| 32＼[[37edo|37]]
| 32\[[37edo|37]]
| 1037.838
| 1037.838
| -
| —
|-
|-
| [[51/28]]
| [[51/28]]
| 1038.085
| 1038.085
|  
| 17
|-
|-
| 45＼[[52edo|52]]
| 45\[[52edo|52]]
| 1038.462
| 1038.462
| -
| —
|-
|-
| [[82/45]]
| [[82/45]]
Line 402: Line 404:
| 41
| 41
|-
|-
| 13＼[[15edo|15]]
| 13\[[15edo|15]]
| 1040.000
| 1040.000
| -
| —
|-
|-
| [[31/17]]
| [[31/17]]
Line 412: Line 414:


== See also ==
== See also ==
* [[Interseptimal interval|Interseptimal regions]]
* [[Interseptimal interval]]
* [[Gentle region]]
* [[Gentle region]]
* [[Gallery of just intervals]]
* [[Gallery of just intervals]]
Retrieved from "https://en.xen.wiki/w/Equable_heptatonic"