Tuning-Math Archive Section 7: 6400

>> --- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan <d.keenan@u...>" >>

>>> Here's another data point relevant to the comma-name boundaries >>> discussion. >>> >>> 49:125 E-13.469 Fb-36.929 >>> >>> 36.929 c must be notated as ~|) which should make it a comma. >>> Therefore 13.469 c ought to be a kleisma, as it would be with a 13.47 >>> c boundary.

Okay, upon reading this again, now I see why the kleisma-comma boundary should be no lower: the 49:125 kleisma is at ~13.469c and the 43 comma is at 13.473c. Looks like this has gotten pretty tight! (And before sending this, I see that you replied to my questions about moving it a little lower.) So the boundaries you now have look okay to me. (I'll summarize them at the end of this message.)

>> ...

>>> As for the names of the categories - how about >>> >>> hypodiesis >>> diesis >>> hyperdiesis >>> >>> Which can be abbreviated to >>> >>> odiesis >>> diesis >>> ediesis >>

>> I think that the idea is good, but I have two suggestions. >> >> 1) I was thinking of having three different prefixes (such as mini, >> midi, and maxi, although probably not those three) and >> allowing "diesis" to remain a more general term that would cover all >> three.

I think that the term "comma" has been used in a broad sense to denote smaller intervals (which we now call kleisma and schisma) more often than larger ones, inasmuch as the term "diesis" has been used for the latter since at least the 14th century. So I would be inclined not to use the term "comma" for anything above ~37 cents, even in a broader sense.

> I was thinking that would be good too. emdiasis? > > Mini- midi- maxi- are not Greek, but then we've already use -ina which > is not Greek.

I didn't like everything beginning with m, anyway.

> Incidentally -ina really means female rather than small, > but it still has the correct implication. > > Sub-, super-, infra-, ultra- are not Greek either. >

>> 2) The three prefixes should be more than just a single letter -- >> odiesis and ediesis sound too much alike. >

> Could be odiesis (pron. oadiesis) and erdiesis. >

>> I was about to suggest three prefixes used in organic chemistry: >> ortho, meta, and para. The original 125:128 diesis would then >> appropriately be termed an orthodiesis. The abbreviations o- diesis, >> m-diesis, and p-diesis would even work. >

> But I thought you objected to single letters?

Just single-vowel prefixes, which sound too much alike.

> Unfortunately these three prefixes do not generally represent 3 > degrees of a single property and I fear that few musicians would be > familiar with the naming of benzene derivatives. Meta- would generally > be more appropriate for the largest, as you suggest below. > >> Unfortunately, the

>> particular dieses that we're using the o and m characters for are >> both in the para category. >

> I wouldn't place too much importance on this. But I note that in the > three categories we have these symbols. > > small dq /|~ (|( ~|\ //| |~) > middle unv /|) (|~ /|\ |)) (/| > large owm |\) (|) (|\ > > But I find there is not much hope of making our prefixes match up with > any of these, except possibly in the large category. >

>> Perhaps we could use meta for the largest >> group (the meaning, "beyond," would still apply) and find a couple of >> other prefixes that wouldn't conflict with (and might even tie in >> with) the letters q and n for the small and middle ranges. > > Good luck! >

> There aren't very many prefixes starting with q. The only one that is > even slightly appropriate is "quasi-" but that means "almost but not > quite" and would be better used for those things that have > historically been called dieses but are smaller than 36.93 cents.

I wasn't expecting to find anything appropriate for q, anyway. I'm just trying to avoid names that might cause confusion.

> "meso-" is _the_ Greek prefix meaning middle.

Yes, I thought of that one, but would rather not use it, since it begins with m.

> It is used with various > other Greek pairs such as: > > hypo- under > meso- middle > hyper- over > > endo- inside > meso- middle > ecto- outside > > proto- (or pro-) earlier or to the front > meso- middle > meta- later or to the rear > > lepto- fine small thin delicate > meso- middle > hadro- thick stout

I also found intra- (within or inside), neo- (new), and peri- (close at hand, near, adjacent). In evaluating all of these, I tried to identify what I would call the prototypical diesis in each group: 37-45 cents -- 125:128, the meantone diesis, is not only in the group with the *smallest size*, but is also the diesis by which three 4:5s *fall short* of (i.e., on the near side of) an octave. So I thought that peri- or intra- might be appropriate. Of these two I prefer peri-. But proto- is also good, for a couple of reasons: it is similar in meaning to peri-, and it is the opposite of meta- (should we use that term for the large group). Besides, 125:128, which is probably the best-known of any diesis in any group (and thus, on account of its prominence, the one with the strongest claim to the label proto-diesis), would validate an additional shade of meaning by which the term could be applied to this group. 45-57 cents -- 32:33, the unidecimal diesis (or quartertone), introduces some of the *strangest new* harmonies encountered in alternative tunings. I thought neo- might be more descriptive of an interval such as this, rather than some nondescript label (such as meso-) that suggests that it might be average or middlin'. Even the 13 diesis (1024:1053, the second most prominent member of the group, and the one that's actually symbolized by an "n") is new and strange. 57-69 cents -- 625:648, besides being a *large* diesis (~27:28, or 1deg19) is also the amount by which four 5:6s *exceed* (i.e., go beyond) an octave. I believe that we agree that meta- is a good prefix for this group. Need I say more? With these labels, the boundaries (in cents) would then be: 0 schismina 0.98 schisma 4.50 kleisma 13.47 comma 36.93 protodiesis 45.11 neodiesis 56.84 metadiasis 68.57 --George