Revenge of the Subgroups!!!

Okay folks, I think I've finally finished my project of looking at all the rank-1 5-dimensional pentadic subgroups of the 13-limit from 5-ET to 36-ET. Here's a spreadsheet of the adjusted error for the best (lowest-error) mapping of each ET for each subgroup (so the mapping for a single ET may vary from subgroup to subgroup, to minimize the error):

/tuning/files/IgliashonJones/5D%2013-Limit%20Subgroup%20ET%20Errors.xls

Here's a plot of the above data; it's kind of hard to read, so I will probably do a plot of each subgroup individually:

/tuning/files/IgliashonJones/5D%2013-limit%20Subgroup%20ETs.pdf

Here's a plot of the total 13-limit error, the average 5D subgroup error, the minimum error, and the maximum error of each ET:

/tuning/files/IgliashonJones/5D%2013-limit%20MIN-MAX-AVG.pdf

Here's a list of the best ETs for each subgroup:

13-Limit: 31-TET
2.5.7.11.13: 31-TET
2.3.7.11.13: 36-TET
2.3.5.11.13: 34-TET
2.3.5.7.13: 31-TET
11-Limit: 31-TET
2.5.7.9.11: 31-TET
2.5.7.9.13: 31-TET
2.7.9.11.13: 36-TET
2.5.9.11.13: 34-TET
2.7.9.11.15: 31-TET
2.7.11.13.15: 20-TET
2.9.11.13.15: 34-TET
2.3.5.9.15: 34-TET
2.5/3.7/3.11/3.13/3: 35-TET
2.5.7/3.11/3.13/3: 31-TET
2.3.7/5.11/5.13/5: 25-TET
2.7/5.9/5.11/5.13/5: 35-TET
2.9/7.11/7.13/7.15/7: 25-TET

31 and 34 dominate, unsurprisingly, but there are a few surprise appearances by 20, 25, 35, and 36.

In the "fewer than or equal to 24 notes" category, the winners are:

13-Limit: 22-TET
2.5.7.11.13: 21-TET
2.3.7.11.13: 17-TET
2.3.5.11.13: 24-TET
2.3.5.7.13: 19-TET
11-Limit: 22-TET
2.5.7.9.11: 22-TET
2.5.7.9.13: 19-TET
2.7.9.11.13: 17-TET
2.5.9.11.13: 24-TET
2.7.9.11.15: 20-TET
2.7.11.13.15: 20-TET
2.9.11.13.15: 24-TET
2.3.5.9.15: 19-TET
2.5/3.7/3.11/3.13/3: 23-TET
2.5.7/3.11/3.13/3: 9-TET
2.3.7/5.11/5.13/5: 23-TET
2.7/5.9/5.11/5.13/5: 23-TET
2.9/7.11/7.13/7.15/7: 24-TET

Again, the usual suspects of 19 and 22 appear frequently, but also interspersed with 17, 23, and 24. 9-TET makes a surprising appearance as the 2.5.7/3.11/3.13/3 dominator (i.e., for 3:7:11:13:15 pentads). 20-TET also claims two subgroups, surprisingly, and also takes the overall minimum error of a mere 5.54 cents on the 2.7.11.13.15 subgroup.

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:

> 31 and 34 dominate, unsurprisingly, but there are a few surprise appearances by 20, 25, 35, and 36.

Especially 31, the tuning you hate and couldn't wait to be rid of.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:

> Especially 31, the tuning you hate and couldn't wait to be rid of.

You try playing a 31-tone guitar sometime. It wasn't exactly the sound I hated about it.

-Igs