new names for 5-limit 'anomalies'

Last week, my computer crashed in the middle of my sending
a posting to the List. It looked to me like it didn't go
thru (later I found out it had: TD 483.25), so I worked on
it some more after rebooting, and re-sent it (TD 483.26).

The part added at the end of 483.26 is what I'm forwarding
here, because I had hoped for some feedback on it, but
I fear that most subscribers thought that 483.26 was
simply an exact repeat of 483.25 and so didn't bother
to read it, and didn't catch this additional stuff.

It probably didn't help that the big 5-limit lattice I made
got unintended line-feeds added to each line. I've made
a webpage of the entire posting, and it is much clearer:

http://www.ixpres.com/interval/td/monzo/o483-26new5limitnames.htm

----------- edited forwarded message -------------

Here are some suggestions for a logical system encompassing
more 'commas' than most other systems. It classifies
intervals into seven broad groups: skhisma, kleisma, comma,
small diesis, great diesis, small semitone, and limma (from
smallest to largest).

Each interval is qualified by a pseudo-Graeco-Latin term
indicating the exponent of 5 and its 'tivity', positive
or negative. (Is there a real mathematical term for that?)

I don't particularly like these names, but the set of
these intervals in this lattice fell roughly into 11 groups
(based on the gaps in the graph of their cents-values),
which I condensed into these seven groups, to try to retain
familiar names without introducing new ones. I then devised
a logical system of qualification to accomodate the great
variety. The stem '-pental' immediately betrays the
5-limit dimensionality of these intervals, 'Pythagorean'
designating the ones that don't include 5 as a factor.

Suggested terminology for 5-limit intervals from 0 to 100 cents
with arbitrary boundaries of 3^-15...15 * 5^-7...7
by Joe Monzo 2000.1.11
----------------------------------------------------------------

~cents prime-factor name

100 |- 2 7 | super-septapental limma
98 |-10 6 | super-hexapental limma
94 | 11 2 | super-bipental limma
92 | 3 1 | super-pental limma
90 |- 5 0 | Pythagorean limma
88 |-13 - 1 | sub-pental limma
84 | 8 - 5 | sub-pentapental limma
82 | 0 - 6 | sub-hexapental limma
80 |- 8 - 7 | sub-septapental limma
77 |-14 7 | super-septapental small semitone
73 | 7 3 | super-tripental small semitone
71 |- 1 2 | super-bipental small semitone
69 |- 9 1 | super-pental small semitone
65 | 12 - 3 | sub-tripental small semitone
63 | 4 - 4 | sub-tetrapental small semitone
61 |- 4 - 5 | sub-pentapental small semitone
59 |-12 - 6 | sub-hexapental small semitone
53 | 11 5 | super-pentapental great diesis
51 | 3 4 | super-tetrapental great diesis
49 |- 5 3 | super-tripental great diesis
47 |-13 2 | super-bipental great diesis
43 | 8 - 2 | sub-bipental great diesis
41 | 0 - 3 | sub-tripental diesis
39 |- 8 - 4 | sub-tetrapental great diesis
34 | 15 7 | super-septapental small diesis
32 | 7 6 | super-hexapental small diesis
30 |- 1 5 | super-pentapental small diesis
28 |- 9 4 | super-tetrapental small diesis
23 | 12 0 | Pythagorean comma
22 | 4 - 1 | sub-pental comma (syntonic comma)
20 |- 4 - 2 | sub-bipental comma (Ellis diaskhisma)
18 |-12 - 3 | sub-tripental comma
13 | 9 - 7 | sub-septapental kleisma
10 | 3 7 | super-septapental kleisma
8 |- 5 6 | super-hexapental kleisma (Tanaka kleisma)
6 |-13 5 | super-pentapental kleisma
2 | 8 1 | super-pental skhisma (Ellis skhisma)
0 | 0 0 | reference pitch

-monz

Joseph L. Monzo Philadelphia monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
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