User:Fitzgerald Lee/Sandbox: Difference between revisions

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Fulcrum is kappagamma icosapentacot, as it takes 13 [[2/1]]<nowiki/>s and 25 [[48/25]]<nowiki/>s (-25 [[Periods and generators#Introduction to generators|generators]]<nowiki/>, or gens for short) to reach [[3/2]].
{{Q-odd-limit intervals|46|9}}
 
== Tuning spectra ==
=== Fulcrum ===
{| class="wikitable center-all left-4"
|-
! Edo<br>generator
! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]
! Generator (¢)
! Comments
|-
| [[18edo|1\18]]
|
| 66.667
| 25/24s slightly flatter than this fall under [[sycamore]]
|-
|
| [[125/96]]
| 67.547
| 1/11-comma
|-
| [[71edo|4\71]]
|
| 67.606
|
|-
| [[124edo|7\124]]
|
| 67.742
|
|-
| [[177edo|10\177]]
|
| 67.797
|
|-
|
| [[5/4]]
| 67.807
| 1/12-comma
|-
| [[230edo|13\230]]
|
| 67.826
|
|-
| [[283edo|16\283]]
|
| 67.845
|
|-
| [[336edo|19\336]]
|
| 67.857
|
|-
|
| [[75/64]]
| 67.8657
| 4/49-comma
|-
| [[389edo|22\389]]
|
| 67.8663
|
|-
| [[442edo|25\442]]
|
| 67.873
|
|-
| [[495edo|28\495]]
|
| 67.879
|
|-
| [[548edo|31\548]]
|
| 67.883
|
|-
|
| [[15/8]]
| 67.885
| 3/37-comma
|-
| [[601edo|34\601]]
|
| 67.887
|
|-
|
| [[3/2]]
| 67.922
| 2/25-comma
|-
| [[53edo|3\53]]
|
| 67.925
|
|-
|
| [[10/9]]
| 67.958
| 3/38-comma
|-
|
| [[5/3]]
| 68.028
| 1/13-comma
|-
| [[194edo|11\194]]
|
| 68.041
|
|-
| [[141edo|8\141]]
|
| 68.085
|
|-
| [[88edo|5\88]]
|
| 68.182
|
|-
|
| [[125/72]]
| 68.217
| 1/14-comma
|-
| [[35edo|2\35]]
|
| 68.571
|
|-
|
| [[25/24]]
| 70.672
| Untempered, 25/24s slightly sharper than this fall under [[vishnu]]
|}
=== Septimal Fulcrum ===
{| class="wikitable center-all left-4"
|-
! Edo<br>generator
! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]
! Generator (¢)
! Comments
|-
|
| [[28/25]]
| 65.399
| +3 gens
|-
| [[18edo|1\18]]
|
| 66.667
|
|-
|
| [[7/6]]
| 66.718
| +4 gens
|-
|
| [[15/14]]
| 67.535
| -16 gens
|-
|
| [[9/7]]
| 67.756
| -29 gens
|-
| [[53edo|3\53]]
|
| 67.925
|
|-
|
| [[21/16]]
| 68.027
| -46 gens
|-
| [[194edo|11\194]]
|
| 68.041
|
|-
| [[141edo|8\141]]
|
| 68.085
|
|-
|
| [[21/20]]
| 68.104
| -34 gens
|-
|
| [[7/4]]
| 68.151
| -21 gens
|-
| [[88edo|5\88]]
|
| 68.182
|
|-
|
| [[25/21]]
| 68.266
| +22 gens
|-
| [[35edo|2\35]]
|
| 68.571
|
|-
|
| [[7/5]]
| 68.610
| -9 gens
|}
=== Septimal Extension 1 ===
{| class="wikitable center-all left-4"
|-
! Edo<br>generator
! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]
! Generator (¢)
! Comments
|-
| [[18edo|1\18]]
|
| 66.667
| 18d val
|-
|
| [[21/16]]
| 67.254
| +7 gens
|-
|
| [[21/20]]
| 67.604
| +19 gens
|-
| [[71edo|4\71]]
|
| 67.606
|
|-
|
| [[25/21]]
| 67.682
| -31 gens
|-
| [[124edo|7\124]]
|
| 67.742
|
|-
|
| [[7/4]]
| 67.776
| +32 gens
|-
|
| [[7/5]]
| 67.784
| +44 gens
|-
|
| [[25/14]]
| 67.789
| -56 gens
|-
| [[177edo|10\177]]
|
| 67.797
|
|-
| [[230edo|13\230]]
|
| 67.826
|
|-
|
| [[15/14]]
| 67.834
| -69 gens
|-
|
| [[7/6]]
| 67.840
| +57 gens
|-
|
| [[9/7]]
| 67.865
| -82 gens
|-
| [[53edo|3\53]]
|
| 67.925
|
|-
| [[35edo|2\35]]
|
| 68.571
| 35d val
|}

Latest revision as of 06:02, 3 July 2026

The following table shows how 9-odd-limit intervals are represented in 46edo. Prime harmonics are in bold.

As 46edo is consistent in the 9-odd-limit, the mappings by direct approximation and through the patent val are identical.

9-odd-limit intervals in 46edo
Interval and complement Error (abs, ¢) Error (rel, %)
1/1, 2/1 0.000 0.0
9/5, 10/9 0.205 0.8
3/2, 4/3 2.393 9.2
5/3, 6/5 2.598 10.0
7/4, 8/7 3.609 13.8
9/8, 16/9 4.786 18.3
5/4, 8/5 4.991 19.1
7/6, 12/7 6.001 23.0
9/7, 14/9 8.394 32.2
7/5, 10/7 8.599 33.0
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