Some more unclassified temperaments

Hi all.

Below I'm presenting three lists of "possibly undiscovered" temperaments and I'll be glad to know your opinion on which ones may be worth classifying and naming.

The first is not actually a list of temperaments but rather a list of 5-limit commas. When one of them is tempered out, we get a 2D system which might also have some higher extensions up to the 13-limit.

The second is a list of EDO pairs. Unless a letter is added "like 61d", the patent val is meant. The only exception is 31&49 where I'm not yet decided which of the two 13/1 mappings suggested by Graham's scripts I prefer

The third is a list of equal divisions of other intervals than 2/1 -- i.e. non-octave equal temperaments. For some of them, there are suggested approximated ratios in parentheses. Because I didn't know how to notate Xth root of Y, I used the \ sign -- i.e. 13 equal steps to 3/1 would be "13 \ 3/1"; this one is actually not in the list as that's a familiar one.

--------------------

[47 -15 -10]

[-51 19 9]

[62 -23 -11]

[-66 27 10]

[40 7 -22]

[-67 -9 35]

[-36 11 8]

[-9 -28 23]

------------------------

84&99, 7-limit (I was privately calling it by the cryptic "nessafof" but I'm not against something else)

140&224, 7-limit

140&183, 5-limit

87&164, 7-limit

103&202, 7-limit

111&161, 13-limit (7/1 debatable)

31&49, full 13-limit semisept (which one of the two would be better?)

34&50 -- 13-limit vishnu (7/1 debatable)

37&50, full 13-limit

37&53, full 13-limit

37&72, full 13-limit

50&53, full 13-limit

53&61d, full 13-limit (7/1 more mistuned than the rest)

53&67, full 13-limit

53&77, full 13-limit hemischis (11/1 more mistuned)

61&87, full 13-limit

87&84, full 13-limit mutt

--------------------

31 \ 8/5 (5:6:7:8:11:13)

18 \ 8/5 (5:6:7:8)

53 \ 7/3

30 \ 11/5

15 \ 7/4

13 \ 8/5

96 \ 7/1

25 \ 8/3 (6:7:10:16)

29 \ 20/3 (3:7:8:11:20:26), almost 21 \ 4/1

------------------------

Petr

I wrote:

> 87&164, 7-limit

I see, I should have said "77&87" to make it clear and unambiguous.

Petr

--- In tuning@yahoogroups.com, Petr Pařízek <petrparizek2000@...> wrote:

> The first is not actually a list of temperaments but rather a list of
> 5-limit commas. When one of them is tempered out, we get a 2D system which
> might also have some higher extensions up to the 13-limit.

These commas have pretty high badness figures, and if 13-limit temperaments are the point, it seems to me it would make more sense to give those.

--- In tuning@yahoogroups.com, Petr Pařízek <petrparizek2000@...> wrote:

> 140&224, 7-limit

Yeow--a microtemperament with a 1/28 octave period. This actually makes more sense higher-limit than it does in the 7-limit.

Gene wrote:

> These commas have pretty high badness figures, and if 13-limit > temperaments are the point, it seems to me
> it would make more sense to give those.

#1. Some of them can be extended up to the 13-limit but definitely not that close to JI as in the 5-limit. Others have possible 13-limit extensions but would make the resulting temperament way more complex if anything else than 13/1 is added to the mix.

#2. I understand that they have high complexity but I'm not sure what you mean by saying that they have high badness figures.

Petr

I wrote:

> #1. Some of them can be extended up to the 13-limit but definitely not > that close to JI as in the 5-limit.

Of which the first four listed commas are apparent examples.

Petr