Xenharmonic Wiki

Tertiaseptal: Difference between revisions

← Older editNewer edit →

FloraC (talk | contribs)

4 user groups
27,879 edits
VisualWikitext
m + category
Improve intro; cleanup
Line 1: Line 1:
{{Todo|inline=1|improve synopsis|improve readability|comment= Add infobox. Cut huge tables to reasonable sizes.}}
{{Todo|inline=1|improve synopsis|improve readability|comment= Add infobox. Cut huge tables to reasonable sizes.}}


'''Tertiaseptal''' is a [[regular temperament|temperament]] for the 7, 11, 13, and 17 limit. EDOs that support tertiaseptal include [[31edo]], [[140edo]], [[171edo]] and [[311edo]].
'''Tertiaseptal''' is a [[regular temperament|temperament]] generated by a small semitone of about 77 cents, which is 1/3 of an [[8/7]] septimal whole tone. Edos that support tertiaseptal include [[31edo]], [[140edo]], [[171edo]] and [[311edo]].


See [[Breedsmic temperaments #Tertiaseptal]] for more information.
See [[Breedsmic temperaments #Tertiaseptal]] for technical data. See [[Tertiaseptal extensions]] for a discussion on the 11-limit extensions.  


== Interval chain ==
== Interval chain ==
=== Tertiaseptal and tertia ===
=== Tertia and septia ===
 
{| class="wikitable"
{| class="wikitable"
|-
|-
! rowspan="2"| generator
! rowspan="2"| #
! rowspan="2"| cents value <sup>a</sup><br>(octave-reduced)
! rowspan="2"| Cents*
! colspan="2"| 17-limit ratio<br>(octave-reduced)
! colspan="2"| Approximate ratio
|-
|-
! tertiaseptal <br>(31&amp;171)
! Septia
! tertia <br>(31&amp;140)
! Tertia
|-
|-
| 1
| 1
Line 586: Line 585:
|  
|  
|}
|}
<sup>a</sup> in 7-limit POTE tuning
<nowiki/>* In 7-limit POTE tuning, octave reduced


=== Hemitert ===
=== Hemitert ===
{| class="wikitable"
{| class="wikitable"
|-
|-
! generator
! #
! cents value <sup>a</sup><br>(octave-reduced)
! Cents
! 11-limit ratio<br>(octave-reduced)
! Approximate ratios
|-
|-
| 1
| 1
Line 988: Line 986:
| '''[[10/9]]'''
| '''[[10/9]]'''
|}
|}
<sup>a</sup> in 11-limit POTE tuning
<nowiki/>* In 11-limit POTE tuning, octave reduced


== Tuning spectra ==
== Tuning spectra ==
=== Tertiaseptal ===
=== Tertiaseptal ===
Gencom: [2 68/65; 243/242 375/374 441/440 625/624 3584/3575]
Gencom mapping: [{{val|1 3 2 3 7 1 1}}, {{val|0 -22 5 -3 -55 42 48}}]
{| class="wikitable center-all"
{| class="wikitable center-all"
|-
|-
! [[eigenmonzo|eigenmonzo<br>(unchanged-interval]])
! [[Eigenmonzo|eigenmonzo<br>(Unchanged-interval]])
! generator<br>(¢)
! Generator (¢)
! comments
! Comments
|-
|-
| 8/7
| 8/7
Line 1,064: Line 1,058:
| 7/5
| 7/5
| 77.1860
| 77.1860
| 7 and 9-odd-limit minimax
| 7- and 9-odd-limit minimax
|-
|-
| 17/16
| 17/16
Line 1,088: Line 1,082:
| 13/11
| 13/11
| 77.2083
| 77.2083
| 13, 15 and 17-odd-limit minimax
| 13-, 15- and 17-odd-limit minimax
|-
|-
| 22/17
| 22/17
Line 1,128: Line 1,122:


=== Tertia ===
=== Tertia ===
Gencom: [2 22/21; 352/351 385/384 561/560 625/624 715/714]
Gencom mapping: [{{val|1 3 2 3 5 1 1}}, {{val|0 -22 5 -3 -24 42 48}}]
{| class="wikitable center-all"
{| class="wikitable center-all"
|-
|-
! eigenmonzo<br>(unchanged interval)
! Eigenmonzo<br>(Unchanged interval)
! generator<br>(¢)
! Generator (¢)
! comments
! Comments
|-
|-
| 12/11
| 12/11
Line 1,196: Line 1,186:
| 18/13
| 18/13
| 77.1700
| 77.1700
| 13, 15 and 17-odd-limit minimax
| 13-, 15- and 17-odd-limit minimax
|-
|-
| 20/17
| 20/17
Line 1,228: Line 1,218:
| 7/5
| 7/5
| 77.1860
| 77.1860
| 7 and 9-odd-limit minimax
| 7- and 9-odd-limit minimax
|-
|-
| 17/16
| 17/16
Line 1,264: Line 1,254:


=== Hemitert ===
=== Hemitert ===
Gencom: [2 45/44; 2401/2400 3025/3024 65625/65536]
Gencom mapping: [{{val|1 3 2 3 6}}, {{val|0 -44 10 -6 -79}}]
{| class="wikitable center-all"
{| class="wikitable center-all"
|-
|-
! eigenmonzo<br>(unchanged interval)
! Eigenmonzo<br>(Unchanged interval)
! generator<br>(¢)
! Generator (¢)
! comments
! Comments
|-
|-
| 8/7
| 8/7
Line 1,300: Line 1,286:
| 7/5
| 7/5
| 38.5930
| 38.5930
| 7, 9 and 11-odd-limit minimax
| 7-, 9- and 11-odd-limit minimax
|-
|-
| 11/10
| 11/10
Retrieved from "https://en.xen.wiki/w/Tertiaseptal"