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Message: 6475 - Contents - Hide Contents

Date: Thu, 13 Feb 2003 15:48:38

Subject: Re: "Ultimate" 5-limit again

From: Gene W Smith

On Thu, 13 Feb 2003 22:45:32 -0000 "wallyesterpaulrus
<wallyesterpaulrus@xxxxx.xxx>" <wallyesterpaulrus@xxxxx.xxx> writes:
> > probably i goofed. can you help fill in all the data for the row > that > i would need to add to this table: > > Yahoo groups: /tuning/database? * [with cont.] > method=reportRows&tbl=10&sortBy=5&sortDir=up > > i'll then add the corresponding green line in the relevant et > graphs . . .
Unless you want to send it to me, you'll need to wait until my modem problem is fixed. I'm going to try to install another driver now.
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Message: 6476 - Contents - Hide Contents

Date: Thu, 13 Feb 2003 00:28:26

Subject: Re: vanishing diatonic semitone

From: wallyesterpaulrus

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

> It's been a stretch for me to accept neutral thirds and pelogic as > 5-limit temperaments.
pelogic is among the most useful 5-limit temperaments ever discovered. just try a few different inharmonic timbres and you'll quickly find one that works. be sure to listen to some gamelan music first :)
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Message: 6477 - Contents - Hide Contents

Date: Thu, 13 Feb 2003 01:14:55

Subject: Re: vanishing diatonic semitone

From: Dave Keenan

--- In tuning-math@xxxxxxxxxxx.xxxx "wallyesterpaulrus
<wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:
> --- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan <d.keenan@u...>" > <d.keenan@u...> wrote: >
>> It's been a stretch for me to accept neutral thirds and pelogic as >> 5-limit temperaments. >
> pelogic is among the most useful 5-limit temperaments ever > discovered. just try a few different inharmonic timbres and you'll > quickly find one that works. be sure to listen to some gamelan music > first :)
Pelog may be among the most useful MOS scales ever discovered, but if it _requires_ inharmonic timbres, in what sense is it an approximation of 5-limit JI?
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Message: 6478 - Contents - Hide Contents

Date: Thu, 13 Feb 2003 01:27:39

Subject: Re: vanishing diatonic semitone

From: wallyesterpaulrus

--- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan <d.keenan@u...>" 
<d.keenan@u...> wrote:
> --- In tuning-math@xxxxxxxxxxx.xxxx "wallyesterpaulrus > <wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:
>> --- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan <d.keenan@u...>" >> >
>>> It's been a stretch for me to accept neutral thirds and pelogic as >>> 5-limit temperaments. >>
>> pelogic is among the most useful 5-limit temperaments ever >> discovered. just try a few different inharmonic timbres and you'll >> quickly find one that works. be sure to listen to some gamelan music >> first :) >
> Pelog may be among the most useful MOS scales ever discovered, but if > it _requires_ inharmonic timbres, in what sense is it an approximation > of 5-limit JI?
the timbres that people like sethares talk about, even if they don't always say so, start as harmonic and then each harmonic (up to 6, 8, 12, whatever) is "tweaked" toward the nearest et (or whatever) position. therefore, it's an approximation of an approximation of 5- limit JI :)
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Message: 6479 - Contents - Hide Contents

Date: Thu, 13 Feb 2003 01:52:17

Subject: Re: vanishing diatonic semitone

From: Dave Keenan

--- In tuning-math@xxxxxxxxxxx.xxxx "wallyesterpaulrus
<wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:
> if we had listened to you about badness, you wouldn't be seeing any > green lines on the graph with 494 and 612 on it.
I was about to write "You've got me there", however I realised that it is still the case that I have no interest in 494 or 612 _as_5_limit_temperaments_. Presumably they would appear in my kind of list at much higher limits, although 624 looks like it might replace 612 beyond 17-limit.
> things like this are useful to know. Maybe so.
>> Next you'll be wanting the one where 9:10 vanishes. ;-) >
> not really -- this one just seems like a severe omission at the > moment, if you look at the graphs and charts.
And it probably sounds just great with inharmonic timbres. ;-)
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Message: 6480 - Contents - Hide Contents

Date: Thu, 13 Feb 2003 02:03:52

Subject: Re: 5LimitTemp.xls

From: Dave Keenan

--- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:
> Dave, > > The degeneracy column seems broken. I've got Excel 2000. > > -Carl
I've only got Excel 97. Do you have the Analysis Toolpack (or whatever) installed so the GCD function works? Look it up in Excel Help.
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Message: 6481 - Contents - Hide Contents

Date: Thu, 13 Feb 2003 05:52:15

Subject: Re: 5LimitTemp.xls

From: Dave Keenan

--- In tuning-math@xxxxxxxxxxx.xxxx Carl Lumma <ekin@l...> wrote:
>>> The degeneracy column seems broken. I've got Excel 2000. >>> >>> -Carl >>
>> I've only got Excel 97. Do you have the Analysis Toolpack (or >> whatever) installed so the GCD function works? Look it up in Excel >> Help. >
> Ah, now it works. That is, if only rows 17-19, 27-29, 32-34, > 44-46 are supposed to be degenerate, and the rest blank. That's correct.
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Message: 6482 - Contents - Hide Contents

Date: Thu, 13 Feb 2003 09:31:47

Subject: Re: vanishing diatonic semitone

From: Graham Breed

wallyesterpaulrus  wrote:

> the timbres that people like sethares talk about, even if they don't > always say so, start as harmonic and then each harmonic (up to 6, 8, > 12, whatever) is "tweaked" toward the nearest et (or whatever) > position. therefore, it's an approximation of an approximation of 5- > limit JI :)
That's not true. Many of Sethares' timbres are measured from physical objects. It is true that the ones that start as harmonic timbres start as harmonic timbres. Graham
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Message: 6483 - Contents - Hide Contents

Date: Fri, 14 Feb 2003 13:28:47

Subject: Re: That poor overloaded word "comma"

From: manuel.op.de.coul@xxxxxxxxxxx.xxx

Dave wrote:
>Pth-partial chromas >P ratio cents >---------------------- >13 64:65 26.84c >17 50:51 34.28c >19 95:96 18.13c >23 45:46 35.05c >29 144:145 11.98c >31 30:31 56.77c >Some of these are P/5 commas and some are P*5 commas. They are all >superparticular, and size apparently has little to do with it. Can you >explain this, Manuel? Who named these? In what publication? How long ago?
If I remember correctly either by Jon Fonville or Ben Johnston. In an article in Perspectives of New Music vol. 29 no. 2, 1991. Manuel
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Message: 6484 - Contents - Hide Contents

Date: Fri, 14 Feb 2003 13:32:43

Subject: Re: That poor overloaded word "comma"

From: manuel.op.de.coul@xxxxxxxxxxx.xxx

Carl wrote:
>Another question is 'what do we call blocks?'. While nice, "blocks" >alone is too general. But can an acronym as short as "PBs" really be >taken seriously? Certainly "periodicity blocks" is too long...
Why, letters are cheap.
>And periodicity blocks aren't always block-shaped. etc.
Periodicity blobs then? :-) A more literal translation of the Dutch name is repetition blocks, but that isn't shorter. Manuel
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Message: 6485 - Contents - Hide Contents

Date: Fri, 14 Feb 2003 13:58:29

Subject: Re: scala show data

From: manuel.op.de.coul@xxxxxxxxxxx.xxx

Thanks for the bug report Carl, it will be fixed in the
next version. Only ETs are affected.

>I also notice that "Lumma stability" is the title of the value >in the show data output, but "Lumma instability" is the title >in the help for show data. Oops. >Also in the help, the return type is given as n>1. But if it >really is stability you're returning, it would be 0 <= n <= 1, >right?
No, that's the condition for the value to be given, i.e. only if the number of tones is greater than 1. Manuel
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Message: 6486 - Contents - Hide Contents

Date: Fri, 14 Feb 2003 19:33:46

Subject: Re: A common notation for JI and ETs

From: gdsecor

--- In tuning-math@xxxxxxxxxxx.xxxx David C Keenan <d.keenan@u...> 
wrote:
>
>> --- In tuning-math@xxxxxxxxxxx.xxxx "gdsecor <gdsecor@y...>" >> > --- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan <d.keenan@u...>" >> > 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, >
> Possibly more often. But I expect it _has_ been used to cover larger ones > often enough. >
>> 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. >
> What term do you suggest we use for all these intervals typically less than > a scale step, from schisminas to small semitones?
What about "microtone." As a subdivision of that I would just have two broad terms -- comma and diesis, with the ~37-cent boundary. The former would be divided into comma, kleisma, schisma, and schismina, and the latter into 3 groups (which we have yet to name).
> Here's what my Shorter Oxford (1959) has to say: > > Comma ... > 3. Mus. A minute interval or difference of pitch 1597. > ... > > Diesis ... > 1. Mus. a. In ancient Gr. music, the pythagorean semitone (ratio > 243:256). b. Now, the interval equal to the difference between three major > thirds and an octave (ratio 125:128); usually called enharmonic diesis. > ...
It's my understanding that the ancient Greek "diesis" was an interval in the enharmonic genus (varying considerably in size, but smaller than a limma) and that Italian theorists of the later Middle Ages or Renaissance first used the term "diesis" to include the limma (and it wouldn't surprise me a bit if *that* resulted from a misunderstanding of Greek usage, just as the Greek modes were misinterpreted in a prior century). I did a little checking last night in both the Oxford and Harvard Dictionaries, and they state that the use of the term "diesis" for the limma dates from the Italian Renaissance at the earliest. This is in contrast to Marchettus of Padua (14th century), who used the term "diesis" for a fifth-tone (of varying size) in a 29- tone octave (divided rationally, not an ET); his limma was 2/5 of a tone (two dieses) and apotome 3/5 of a tone. (See Margo Schulter's paper _Enharmonic Excursion to Padua, 1318: Marchettus, the cadential diesis, and neo-Gothic tunings_, <Xenharmonic Excursion to Padua, 1318: * [with cont.] (Wayb.)> (ASCII text) or <http://value.net/~mschulter/marchetmf.zip - Type Ok * [with cont.] (Wayb.)> (text and PostScript) That's just for your information -- we're not debating boundaries, anyway. By the way, I also read that "diesis" is also an Italian word (pronounced dee-EH-sis), so it might not be inappropriate to use prefixes of Latin origin to modify it.
>> ... I tried to >> identify what I would call the prototypical diesis in each group: >
> Shouldn't you instead be looking at the primary interpretation of the most > commonly ocurring sagittal symbol in each group?
The most popular that could be claimed in each group are: small: 25/1 - 256400:6561, ~43.0c and 125/1 – 125:128, ~41.1c and 11/5 – 44:45, ~38.9c medium: 11/1 – 32:33, ~53.3c and 35/1 – 35:36, ~48.8c large: 7/1 – 27:28, ~63.0c 13/1 – 26:27, ~65.3c I'll discuss the small group below. The 11 comma, 32:33, definitely takes the prize in the medium group, so neo- can't be dismissed as a group prefix on the basis of popularity. For the large group, you might think of skipping over 7/1 (since it is much more likely that the 7-comma, 63:64, would be used to notate this, but I see this as an opportunity to point out that it is not a stretch of the imagination that a large diesis *does* function and *sound* like a small semitone, e.g., in the resolution of 21/16 to 5/4. I will have something to say about 26:27 below, in response to your mention of complements.
>> 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. >
> But the minor diesis 125:128 is rarely used in the sagittal notation, > having symbol .//|.
Even though it's the second most popular small diesis. But I would attribute the popularity of both 25/1 and 125/1 as being due to transposition of 5-limit chords within a scale rather than use of a 5^2 or 5^3 harmony in a chord. Now if popularity were restricted to actual use of the diesis as determining an interval that is most likely to occur in a chord, then I think that 11/5, or the 5:11 diesis, would probably be considered the representative interval. But it's third place in overall popularity, so it's not clear-cut. (Hence I don't think that the small group has a good chance of disqualifying the use of the neo- prefix for the middle group.)
> By far the most common in this range will be the 25-
<small>diesis //|. I
> can't find anywhere this has been previously named, presumably because it > is simply a double syntonic comma. So, considered as a "comma" in its own > right it is almost as "neo-" as the 11 and 13 commas below.
Two intervals it produces are 16:25 and 24:25, an augmented fifth and augmented prime, and these are both part of traditional harmony, hence not new. And ratios of 7 are not completely new -- even Partch admitted that the 7th harmonic is implied in 12-ET. It is only with 11 and 13 that radically new intervals are introduced, and I think that 11 is the more radical of the two. So I would stand by the label neo- as characterizing the middle group of dieses.
> And there are > other commas in this group which are probably newer.
You're always going to find new theoretical intervals, but I maintain that 11 has the *newest* and *most exotic* sound once you go beyond the bounds of 12-ET or traditional harmony. 13 comes close, but with 17 and 19 you get intervals that are very similar to what you have in 12-ET (except when you relate them to 11 and 13). This is the sense in which I am using neo- to describe the middle diesis group, and the sound will be characteristic of *any* of the dieses in the group, because they all approximate the 11 and 13 dieses in *size.*
>> 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'. >
> But it _is_ average as far as size goes, and that's what these prefixes are > supposed to be about.
While average in size, it's very un-average, i.e., out-of-the- ordinary, in the characteristic *sound* of the intervals (ratios of 11) that result from its use. I think that there is an advantage in having a label that is musically (rather than strictly mathematically) descriptive.
>> 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. >
> But their complements in the large-diesis group are just as new and > strange.
I disagree. The middle group sound like quartertones, but the large group (third-tones) sound like the small semitones of 17 or 19-ET. Why would the 11 and 13 complementary dieses sound less strange? Take a look at how the symbols are used: 11/8 of C is F/|\, but 11/8 of F is B(!) -- that's a Pythagorean B, rather high (or strange) for a tritone (relative to F) inasmuch as you're not alternating a 9:10 with the 8:9's (as would be done in JI) -- so you need a larger alteration to lower the pitch to make it equivalent to Bb/|\. Likewise, 13/8 of C is A(!/ -- that's a Pythagorean A, 27/16, rather high for a major sixth, which requires a large (65-cent) 13 diesis to bring it down to 13/8 -- but if you had a melody that moved from 5/3 to 13/8, the interval would be around 44 cents -- much closer to a 48- cent 13 diesis.
> And anyway, how long does something remain "new"?
As I said above, it's new relative to 12-ET and traditional harmony, and it will continue to be new to anyone unfamiliar with alternative tunings. At present this includes most of the musical world, and it will always be radically new to anyone who is beginning the study of alternative tunings. I don't expect traditional harmonic values to disappear from the musical scene any time soon.
> Also, I should think that if 125:128 is prototypical of the small group > then 243:250 would be that for the medium group. But again this is not a > common comma to want to notate. It might be notated as /|) or (|~ .
I don't see how you drew that conclusion -- 125:128 has a special place in history as *the meantone diesis* that 243:250 does not share. Besides that, you have 11/1 higher on the popularity list than 125/1.
> The 11-<medium>diesis /|\ will certainly be the most common in this group. >
>> 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 agree that the prototypical diesis in the large group is the major diesis > 625:648, again not something we'd commonly use since it is '(|) . > > Clearly the 11-<large>diesis (|) will be the most common here. >
>> I believe that we agree that meta- is a good >> prefix for this group. >
> Well, no. Only that it applies to this group better than it does to the > medium group. > > The use of "meta-" to mean "beyond" is a recent departure from the Greek > usage. As the Shorter Oxford puts it: > > "In supposed analogy to 'Metaphysics' (misaprehended as meaning 'the > science of that which transcends the physical'), meta- has been prefixed to > the name of a science, to form a designation of a higher science of the > same nature but dealing with ulterior problems."
So then we might want something else besides meta-.
> But why not use prefixes that are a valid description of _all_ the commas > in the group, rather than just ones that may be typical in any sense? i.e. > ones that relate to size. >
>> Need I say more? >
> I'm afraid so. :-)
So I've said more.
> My main objection is that neo- tells one nothing about the size.
But it does tell one about the main characteristic of intervals altered by dieses in this size range: they are the ones that *sound* most foreign to anyone who is twelve-oriented, i.e., like quartertones. The over-57-cent group, on the other hand, sound like small semitones (though they could be most accurately described as third-tones), while the under-45-cent group could be described as fifth-tones.
> And if one adopts the modern sense of meta- one might take a meta- diesis to > be a difference between dieses, in the same way that a diesis is a > difference between other intervals. For example, we might well have used > the term meta-comma to describe the differences between commas that we > instead called schismas and now schisminas. > > If one takes the biological meanings of proto- front and meta- rear (of > organisms) it is unclear that there is any correspondence with small and > large. If one takes the temporal meaning of proto- before or early or > primitive and meta- after or late or advanced, then it is only slightly > more clear.
So if you don't like meta-, then what?
> In regard to having the right _meaning_, the best Greek set I can find are > hypo- > meso- > hyper-
Hypo- and hyper- do not offer the opportunity to distinguish by abbreviation. For example, I might want to use 7-c and 7-h to stand for 7-comma and 7-hyperdiesis in a diagram showing the actual symbols (where words would take up too much space), but I don't have that option if two ranges begin with the same letter. Besides, they sound too much alike when spoken, so one might be misunderstood for the other.
> If we were to depart from the Greek > minor > neutral > major > would be obvious enough, and so would > small > medium (or mean) > large
You've made a better case against meta- than neo-, and I suppose that would also eliminate proto-. I would like to see two short prefixes for large and small that begin with different letters. In fact, I would like to see separate letters for each of the following: Schisma - s Kleisma - k Comma - c [Small] diesis - x [Medium] diesis - y [Large] diesis - z where x, y, and z are letters different from s, k, and c. So we could abbreviate intervals as 5c, 7c, 5s, 7z, 11y, 11z, 13y, 13z, etc. (We don't need a separate letter for schismina, because it isn't a symbol in the notation.) So if you don't like proto-, neo-, and meta-, then what would you suggest?
> It is unfortunate that the word "diesis" already has two more syllables > than we'd like it to have. This is presumably why we feel compelled to > shorten any prefix we might add to it, down to a single syllable.
Or at least a single consonant.
> We might > instead shorten "diesis" to "di" for convenience when spoken (say in > rehearsals) and then not need to shorten the prefixes.
Yes, that's possible.
> Boundaries good. Labels still need work. Yes, still. --George
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Message: 6487 - Contents - Hide Contents

Date: Fri, 14 Feb 2003 19:15:50

Subject: Re: A common notation for JI and ETs

From: Gene W Smith

On Fri, 14 Feb 2003 12:28:10 +0100 manuel.op.de.coul@xxxxxxxxxxx.xxx
writes:

> I haven't followed the thread (300 messages in my inbox), but > unison vector isn't the only term that Fokker used, also > homophonic interval and defining interval. I like the latter > better than unison vector. I agree.
One has the constructing intervals
> and defining intervals which form a periodicity block. > Defining commas would be an alternative.
I think this is what I was calling the commas and chroma, or what people having been calling the "commatic" and "chromatic" unison vectors.
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Message: 6488 - Contents - Hide Contents

Date: Fri, 14 Feb 2003 23:51:36

Subject: Re: A common notation for JI and ETs

From: monz

hi George,


> From: <gdsecor@xxxxx.xxx> > To: <tuning-math@xxxxxxxxxxx.xxx> > Sent: Friday, February 14, 2003 11:33 AM > Subject: [tuning-math] Re: A common notation for JI and ETs > > > It's my understanding that the ancient Greek "diesis" was an > interval in the enharmonic genus (varying considerably in size, > but smaller than a limma) and that Italian theorists of the > later Middle Ages or Renaissance first used the term "diesis" > to include the limma (and it wouldn't surprise me a bit if > *that* resulted from a misunderstanding of Greek usage, just > as the Greek modes were misinterpreted in a prior century). > I did a little checking last night in both the Oxford and > Harvard Dictionaries, and they state that the use of the > term "diesis" for the limma dates from the Italian Renaissance > at the earliest. This is in contrast to Marchettus of Padua > (14th century), who used the term "diesis" for a fifth-tone > (of varying size) in a 29-tone octave (divided rationally, > not an ET); his limma was 2/5 of a tone (two dieses) and > apotome 3/5 of a tone. (See Margo Schulter's paper > _Enharmonic Excursion to Padua, 1318: Marchettus, the > cadential diesis, and neo-Gothic tunings_,
<Xenharmonic Excursion to Padua, 1318: * [with cont.] (Wayb.)> (ASCII text) or <http://value.net/~mschulter/marchetmf.zip - Type Ok * [with cont.] (Wayb.)> (text and PostScript) "diesis" is a musical term which indeed has a long and confusing history. you might profit from reading this: Definitions of tuning terms: diesis, (c) 1998 ... * [with cont.] (Wayb.) and i think you missed this -- which you'd also probably be interested in at least in passing: Onelist Tuning Digest # 483 message 26, (c)200... * [with cont.] (Wayb.) -monz
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Message: 6489 - Contents - Hide Contents

Date: Fri, 14 Feb 2003 02:08:47

Subject: Re: "Ultimate" 5-limit again

From: Gene Ward Smith

--- In tuning-math@xxxxxxxxxxx.xxxx "wallyesterpaulrus 
<wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:

> probably i goofed. can you help fill in all the data for the row that > i would need to add to this table: > > Yahoo groups: /tuning/database? * [with cont.] > method=reportRows&tbl=10&sortBy=5&sortDir=up
The comma is 2^(-69) 3^45 5^(-1). Is that all you need?
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Message: 6490 - Contents - Hide Contents

Date: Fri, 14 Feb 2003 03:13:55

Subject: Re: "Ultimate" 5-limit again

From: wallyesterpaulrus

--- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith 
<genewardsmith@j...>" <genewardsmith@j...> wrote:
> --- In tuning-math@xxxxxxxxxxx.xxxx "wallyesterpaulrus > <wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote: >
>> probably i goofed. can you help fill in all the data for the row > that
>> i would need to add to this table: >> >> Yahoo groups: /tuning/database? * [with cont.] >> method=reportRows&tbl=10&sortBy=5&sortDir=up >
> The comma is 2^(-69) 3^45 5^(-1). Is that all you need?
here's the contents of the database (in very non-database form -- hopefully your modem will heal soon). note that this is intended to go along with the charts on monz's equal temperament dictionary entry: "comma name(s)", "as 2^x*3^y*5^z, [x y z] is . . .", "numerator", "denominator", "cents", "temperament name (s)", "sample ETs/MOSs (notes per octave)", "[period, optimal generator] (cents)", "[2 3 5] map in terms of [per., gen.]", "optimum RMS error (cents)" " large limma", "0 3 -2", "27", "25", "133.237575", "beep", "4, 5, 9", "[1200, 268.056439]", "[[1,0] [2,-2] [3,-3]]", "35.609240" " small diesis", "-10 -1 5", "3125", "3072", "29.613568", "magic", "3, 16, 19, 22, 25, 35, 41, 60, 63, 79", "[1200, 379.967949]", "[[1,0] [0,5] [2,1]]", "4.569472" " minimal diesis", "5 -9 4", "20000", "19683", "27.659848", "tetracot", "7, 27, 34, 41, 48, 61, 75", "[1200, 176.282270]", "[[1,0] [1,4] [1,9]]", "2.504205" " diaschisma", "11 -4 -2", "2048", "2025", "19.552569", "diaschismic, 5-limit pajara", "12, 22, 34, 46, 56, 58, 70, 78, 80, 90", "[600, 105.446531]", "[[2,0] [3,1] [5,-2]]", "2.612822" " pythagorean comma", "-19 12 0", "531441", "524288", "23.460010", "aristoxenean", "12, 48, 60, 72, 84, 96", "[100, 14.663787]", "[[12,0] [19,0] [28,-1]]", "1.382394" "-", "2 9 -7", "78732", "78125", "13.399010", "semisixths", "19, 27, 46, 65, 73, 84", "[1200, 442.979297]", "[[1,0] [-1,7] [- 1,9]]", "1.157498" "-", "26 -12 -3", "67108864", "66430125", "17.598848", "misty", "12, 63, 75, 87, 99, 205", "[400, 96.787939]", "[[3,0] [5,-1] [6,4]]", "0.905187" " würschmidt's comma", "17 1 - 8", "393216", "390625", "11.445290", "würschmidt", "28, 31, 34, 37, 65, 71, 96, 99", "[1200, 387.819673]", "[[1,0] [-1,8] [2,1]]", "1.071950" " kleisma", "-6 -5 6", "15625", "15552", "8.107279", "kleismic, hanson", "15, 19, 23, 34, 53, 72, 83, 87, 91, 125", "[1200, 317.079675]", "[[1,0] [0,6] [1,5]]", "1.029625" " semicomma", "-21 3 7", "2109375", "2097152", "10.061000", "orwell", "9, 22, 31, 53, 75, 84, 97, 128, 243", "[1200, 271.589600]", "[[1,0] [0,7] [3,- 3]]", "0.800410" "-", "9 -13 5", "1600000", "1594323", "6.1535581", "amity", "39, 46, 53, 60, 99, 152, 205, 311", "[1200, 339.508826]", "[[1,0] [3,-5] [6,- 13]]", "0.383104" " minor chroma, classic chromatic semitone", "-3 -1 2", "25", "24", "70.672427", "dicot", "3, 4, 7, 10", "[1200. 350.977500]", "[[1,0] [1,2] [2,1]]", "28.851897" "-", "32 -7 - 9", "4294967296", "4271484375", "9.491569", "escapade", "22, 43, 65, 87, 152, 217", "[1200, 55.275493]", "[[1,0] [2,-9] [2,7]]", "0.483108" " parakleisma", "8 14 - 13", "1224440064", "1220703125", "5.291732", "parakleismic", "19, 42, 61, 80, 99, 118, 217", "[1200, 315.250913]", "[[1,0] [5,13] [6,- 14]]", "0.276603" " schisma", "-15 8 1", "32805", "32768", "1.953721", "schismic, helmholtz/groven", "29, 41, 53, 65, 77, 89, 118, 171, 200", "[1200, 498.272487]", "[[1,0] [2,-1] [-1,8]]", "0.161693" "-", "24 -21 4", "10485760000", "10460353203", "4.199837", "vulture", "48, 53, 58, 217, 270, 323", "[1200, 475.542233]", "[[1,0] [0,4] [- 6,21]]", "0.153767" "-", "23 6 - 14", "6115295232", "6103515625", "3.338011", "semisuper", "16, 18, 34, 50, 84, 118, 152, 270, 388", "[600, 71.146064]", "[[2,0] [4,-7] [5,-3]]", "0.194018" "'19-tone comma'", "-14 -19 19", "19073486328125", "19042491875328", "2.815547", "enneadecal", "19 , 152, 171, 323, 494, 665", "[63.157894, 7.292252]", "[[19,0] [30,1] [44,1]]", "0.104784" "-", "39 -29 3", "68719476736000", "68630377364883", "2.246116", "tricot", "53, 388, 441, 494, 547, 600", "[1200, 565.988015]", "[[1,0] [3,-3] [16,- 29]]", "0.057500" "-", "-68 18 17", "295578376007080078125", "295147905179352825856", "2.523151", "va voom", "118, 311, 547, 665", "[1200, 111.875426]", "[[1,0] [0,17] [4,- 18]]", "0.058853" "-", "38 -2 - 15", "274877906944", "274658203125", "1.384290", "semithirds", "118, 205, 323, 441, 559, 1000", "[1200, 193.199615]", "[[1,0] [4,-15] [2, 2]]", "0.060822" " ennealimma", "1 -27 18", "7629394531250", "7625597484987", "0.861826", "ennealimmal", "72, 99, 171, 243, 270, 441, 612", "[133.333333, 49,008820]", "[[9,0] [15,-2] [22,-3]]", "0.025593" " major chroma, major limma, limma ascendant", "-7 3 1", "135", "128", "92.178716", "pelogic", "7, 9, 16, 23", "[1200, 522.862346]", "[[1,0] [2,-1] [1,3]]", "18.077734" "-", "-16 35 - 17", "50031545098999707", "50000000000000000", "1.091895", "minortone" , "125, 171, 217, 388, 559, 730, 901", "[1200, 182.466089]", "[[1,0] [-1,17] [-3,35]]", "0.025466" "-", "-53 10 16", "9010162353515625", "9007199254740992", "0.569430", "kwazy", "118 , 494, 612, 730, 1342", "[600, 162.741892]", "[[2,0] [1,8] [6,- 5]]", "0.017725" "-", "91 -12 - 31", "2475880078570760549798248448", "2474715001881122589111328125", " 0.814860", "astro", "118, 1171, 2224", "[1200, 132.194511]", "[[1,0] [5,-31] [1,12]]", "0.014993" "-", "37 25 - 33", "116450459770592056836096", "116415321826934814453125", "0.522464 ", "whoosh", "441, 730, 1171, 3072", "[1200, 560.546970]", "[[1,0] [17,-33] [14,-25]]", "0.012388" " monzisma", "54 -37 2", "450359962737049600", "450283905890997363", "0.292396", "monzismic ", "53, 559, 612, 665, 1171, 1783", "[1200, 249.018448]", "[[1,0] [2,- 2] [10,-37]]", "0.005738" "-", "-36 -52 51", "444089209850062616169452667236328125", "444002166576103304796646 509039845376", "0.339362", "egads", "441, 1342, 1783, 3125", "[1200, 315.647874]", "[[1,0] [15,-51] [16,-52]]", "0.004660" "-", "-107 47 14", "162285243890121480027996826171875", "162259276829213363391578010 288128", "0.277035", "fortune", "612, 1901, 2513, 3125", "[1200, 221.567865]", "[[1,0] [-1,14] [11,-47]]", "0.003542" "-", "-17 62 - 35", "381520424476945831628649898809", "381469726562500000000000000000 ", "0.230068", "senior", "171, 1000, 1171, 1342, 2513, 3684", "[1200, 322.801387]", "[[1,0] [11,-35] [19,-62]]", "0.003022" "-", "144 -22 - 47", "22300745198530623141535718272648361505980416", "2229758394562963 9856633730232715606689453125", "0.245429", "gross", "118, 1783, 1901, 3684", "[1200, 91.531021]", "[[1,0] [-2,47] [4,-22]]", "0.002842" "-", "-90 -15 49", "17763568394002504646778106689453125", "1776308649528226802416196 7871623168", "0.046966", "pirate", "730, 1783, 2513, 4296", "[1200, 185.754179]", "[[1,0] [-6,49] [0,15]]", "0.000761" " limma, pythagorean minor second", "8 -5 0", "256", "243", "90.224996", "blackwood", "5, 10, 15, 25", "[240, 84.663787]", "[[5,0] [8,0] [12.-1]]", "12.759741" "-", "71 -99 37", "171798691840000000000000000000000000000000000000", "171792506910 670443678820376588540424234035840667", "0.062327", "raider", "1171, 3125, 4296", "[1200, 343.296099]", "[[1,0] [-9,37] [- 26,99]]", "0.000511" " atom of kirnberger", "161 -84 - 12", "2923003274661805836407369665432566039311865085952", "29229773394 92680612451840826835216578535400390625", "0.015361", "atomic", "(12,) 600, 612, 3072, 3684, 4296", "[100, 1.955169]", "[[12,0] [19,1] [28,- 7]]", "0.000120" " diatonic semitone", "4 -1 - 1", "16", "15", "111.731285", "father", "3, 5, 8", "[1200, 442.179356]", "[[1,0] [2,-1] [2,1]]", "45.614107" " major diesis", "3 4 - 4", "648", "625", "62.565148", "diminished, 'octatonic'", "4, 8, 12, 16, 28", "[300, 94.134357]", "[[4,0] [6,1] [9,1]]", "11.060060" " maximal diesis", "1 -5 3", "250", "243", "49.166137", "porcupine", "7, 8, 15, 22, 29, 37, 59", "[1200, 162.996026]", "[[1,0] [2,-3], [3,-5]]", "7.975801" " diesis, great diesis, minor diesis", "7 0 - 3", "128", "125", "41.058858", "augmented, diesic", "3, 9, 12, 15, 18, 27, 39, 42", "[400, 91.201856]", "[[3,0] [5,-1] [7,0]]", "9.677666" "-", "-14 3 4", "16875", "16384", "51.119858", "negri", "9, 10, 19, 28, 29", "[1200, 126.238272]", "[[1,0] [2,-4] [2,3]]", "5.942563" " comma, syntonic comma, comma of didymus", "-4 4 - 1", "81", "80", "21.506290", "meantone, 'diatonic'", "5, 7, 12, 19, 26, 31, 43, 45, 50, 55, 69, 74, 81, 88", "[1200, 503.835154]", "[[1,0] [2,-1] [4,-4]]", "4.217731"
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Message: 6491 - Contents - Hide Contents

Date: Fri, 14 Feb 2003 12:28:10

Subject: Re: A common notation for JI and ETs

From: manuel.op.de.coul@xxxxxxxxxxx.xxx

Paul wrote:
>> Then wouldn't it have been better if he had called them "period >> vectors" or "periodicity vectors". Could a better translation do so >> even now?
>maybe so. manuel?
I haven't followed the thread (300 messages in my inbox), but unison vector isn't the only term that Fokker used, also homophonic interval and defining interval. I like the latter better than unison vector. One has the constructing intervals and defining intervals which form a periodicity block. Defining commas would be an alternative. Manuel
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Message: 6492 - Contents - Hide Contents

Date: Sat, 15 Feb 2003 17:08:57

Subject: Re: A common notation for JI and ETs

From: manuel.op.de.coul@xxxxxxxxxxx.xxx

>> >ne has the constructing intervals >> and defining intervals which form a periodicity block. >> Defining commas would be an alternative. Gene wrote:
>I think this is what I was calling the commas and chroma, or what people >having been calling the "commatic" and "chromatic" unison vectors.
Not quite, the defining intervals comprise both commatic and chromatic ones. The (same number of) constructing intervals are the "prime" intervals, 3/1, 5/1, etc. So "defining commas" isn't a good term, they aren't necessarily commas. Manuel
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Message: 6494 - Contents - Hide Contents

Date: Sat, 15 Feb 2003 20:58:29

Subject: Re: A common notation for JI and ETs

From: wallyesterpaulrus

--- In tuning-math@xxxxxxxxxxx.xxxx Gene W Smith 
<genewardsmith@j...> wrote:
> > > On Fri, 14 Feb 2003 12:28:10 +0100 manuel.op.de.coul@e... > writes: >
>> I haven't followed the thread (300 messages in my inbox), but >> unison vector isn't the only term that Fokker used, also >> homophonic interval and defining interval. I like the latter >> better than unison vector. > > I agree. >
> One has the constructing intervals
>> and defining intervals which form a periodicity block. >> Defining commas would be an alternative. >
> I think this is what I was calling the commas and chroma, or what people > having been calling the "commatic" and "chromatic" unison vectors.
no. the distinction between commatic and chromatic unison vectors falls completely outside of fokker's conception, or that of wuerschmidt from whom the "defining" and "constructing" labels were, i believe, derived. if i recall correctly, the "constructing intervals" are simply the 1-step intervals in the just intonation periodicity block -- for example, different instances of 12-tone in the 5-limit can have constructing interval sets {243:256, 2187:2048} {243:256, 135:128, 16:15} {25:24, 135:128, 16:15} etc.
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Message: 6495 - Contents - Hide Contents

Date: Sat, 15 Feb 2003 21:02:40

Subject: Re: A common notation for JI and ETs

From: wallyesterpaulrus

--- In tuning-math@xxxxxxxxxxx.xxxx "monz" <monz@a...> 
wrote:

> and i think you missed this -- which you'd also probably > be interested in at least in passing: > Onelist Tuning Digest # 483 message 26, (c)200... * [with cont.] (Wayb.) > > > > -monz hi monz,
i brought this page up to dave and george very recently (last week) here on this list, and they indeed found it very useful for their discussion. unfortunately, several erroneous statements persist on this page, most notably: "It can be seen easily from the lattice that all the intervals are made up of various combinations of the ones described by Paul." of course, we all know you're very busy right now, and i at least appreciate your brief and all too infrequent visits to this list. -paul
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Message: 6496 - Contents - Hide Contents

Date: Sat, 15 Feb 2003 21:03:52

Subject: Re: A common notation for JI and ETs

From: wallyesterpaulrus

--- In tuning-math@xxxxxxxxxxx.xxxx manuel.op.de.coul@e... 
wrote:
> The (same number of) constructing intervals are the > "prime" intervals, 3/1, 5/1, etc.
oh . . . i must have been thinking of the wrong term, or perhaps of wuerschmidt's usage instead of fokker's . . .
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Message: 6497 - Contents - Hide Contents

Date: Sun, 16 Feb 2003 23:55:45

Subject: Re: A common notation for JI and ETs

From: monz

hi paul,


> From: <wallyesterpaulrus@xxxxx.xxx> > To: <tuning-math@xxxxxxxxxxx.xxx> > Sent: Sunday, February 16, 2003 6:25 PM > Subject: [tuning-math] Re: A common notation for JI and ETs > > > --- In tuning-math@xxxxxxxxxxx.xxxx "monz" <monz@a...> wrote: >> hi paul, >> >> >> >>> From: <wallyesterpaulrus@y...> >>> To: <tuning-math@xxxxxxxxxxx.xxx>
>>> Sent: Saturday, February 15, 2003 1:02 PM >>> Subject: [tuning-math] Re: A common notation for JI and ETs >>> >>> >>> --- In tuning-math@xxxxxxxxxxx.xxxx "monz" <monz@a...> >>> wrote: >>>
>>>> and i think you missed this -- which you'd also probably >>>> be interested in at least in passing: >>>> Onelist Tuning Digest # 483 message 26, (c)200... * [with cont.] (Wayb.) > > <etc., snip> thanks!
> your faithful scrutinizer, > paul
just don't become "The Central Scrutinizer"!! ;-) [reference to Frank Zappa's _Joe's Garage_ for those who don't get it ... ] -monz
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Message: 6498 - Contents - Hide Contents

Date: Sun, 16 Feb 2003 10:02:05

Subject: Re: A common notation for JI and ETs

From: David C Keenan

At 10:06 PM 14/02/2003 +0000, you wrote:
>It's my understanding that the ancient Greek "diesis" was an interval >in the enharmonic genus (varying considerably in size, but smaller >than a limma) and that Italian theorists of the later Middle Ages or >Renaissance first used the term "diesis" to include the limma (and it >wouldn't surprise me a bit if *that* resulted from a misunderstanding >of Greek usage, just as the Greek modes were misinterpreted in a >prior century). I did a little checking last night in both the >Oxford and Harvard Dictionaries, and they state that the use of the >term "diesis" for the limma dates from the Italian Renaissance at the >earliest. This is in contrast to Marchettus of Padua (14th century), >who used the term "diesis" for a fifth-tone (of varying size) in a 29- >tone octave (divided rationally, not an ET); his limma was 2/5 of a >tone (two dieses) and apotome 3/5 of a tone. (See Margo Schulter's >paper _Enharmonic Excursion to Padua, 1318: Marchettus, the cadential >diesis, and neo-Gothic tunings_, ><Xenharmonic Excursion to Padua, 1318: * [with cont.] (Wayb.)> (ASCII text) or ><http://value.net/~mschulter/marchetmf.zip - Type Ok * [with cont.] (Wayb.)> (text and PostScript)
I'll go along with that. It seems the 1959 Oxford was wrong about the ancient Greeks using "diesis" for the limma, but they've fixed it now. It seems that in fact they used it to mean quarter-tone. Or half of what's left when you take a "ditone" out of a perfect fourth (as per the enharmonic genus). You say "varying considerably in size" but just how much is it likely to have varied in ancient times? I can't imagine the perfect fourth varying (intentionally) much outside of Pythagorean 3:4 to Aristoxenean (12-ET), 498 to 500 cents. And I can't see the ditone varying much outside Pythagorean 64:81 to Didymus' 4:5, 408 TO 386 cents. See Tutorial on ancient Greek Tetrachord-theory * [with cont.] (Wayb.) So that puts the ancient greek enharmonic diesis at 45 to 57 cents, or almost exactly our middle range of dieses, which would seem to make the prefix "neo-" quite inappropriate for this group.
>By the way, I also read that "diesis" is also an Italian word >(pronounced dee-EH-sis), so it might not be inappropriate to use >prefixes of Latin origin to modify it. >
>>> ... I tried to >>> identify what I would call the prototypical diesis in each group: >>
>> Shouldn't you instead be looking at the primary interpretation of >the most
>> commonly ocurring sagittal symbol in each group? >
>The most popular that could be claimed in each group are: > >small: 25/1 - 256400:6561, ~43.0c > and 125/1 ? 125:128, ~41.1c > and 11/5 ? 44:45, ~38.9c >medium: 11/1 ? 32:33, ~53.3c > and 35/1 ? 35:36, ~48.8c >large: 7/1 ? 27:28, ~63.0c > 13/1 ? 26:27, ~65.3c > >I'll discuss the small group below. > >The 11 comma, 32:33, definitely takes the prize in the medium group, >so neo- can't be dismissed as a group prefix on the basis of >popularity. > >For the large group, you might think of skipping over 7/1 (since it >is much more likely that the 7-comma, 63:64, would be used to notate >this,
Yes. We only have the popularity of the ratios (sans 2's and 3's) and not the different commas that may be used for a given ratio, and I would not think 27:28 would be very popular, particularly since it requires a schisma accent. Although it isn't relevant to this discussion, I take this opportunity to remind us that we only have the popularity of the ratios in the scale archive, and not their popularity in actual use. This could be calculated if we knew the popularity of each scale in actual use, but it seems likely that scales which contain ratios which occur rarely in the archive, would be unpopular scales. Thus our numbers are likely to be exaggerating the popularity (in use) of the less popular (in the archive) ratios.
> but I see this as an opportunity to point out that it is not a >stretch of the imagination that a large diesis *does* function and >*sound* like a small semitone, e.g., in the resolution of 21/16 to >5/4.
Sure. But that doen't have any bearing on the naming of these categories of diesis, does it?
>> But the minor diesis 125:128 is rarely used in the sagittal >notation,
>> having symbol .//|. >
>Even though it's the second most popular small diesis. But I would >attribute the popularity of both 25/1 and 125/1 as being due to >transposition of 5-limit chords within a scale rather than use of a >5^2 or 5^3 harmony in a chord. Certainly! > Now if popularity were restricted to >actual use of the diesis as determining an interval that is most >likely to occur in a chord, then I think that 11/5, or the 5:11 >diesis, would probably be considered the representative interval.
Yes. But popularity isn't, and shouldn't be, restricted in that way.
> But it's third place in overall popularity, so it's not clear-cut. >(Hence I don't think that the small group has a good chance of >disqualifying the use of the neo- prefix for the middle group.) Agreed.
>> By far the most common in this range will be the 25-
><small>diesis //|. I
>> can't find anywhere this has been previously named, presumably >because it
>> is simply a double syntonic comma. So, considered as a "comma" in >its own
>> right it is almost as "neo-" as the 11 and 13 commas below. >
>Two intervals it produces are 16:25 and 24:25, an augmented fifth and >augmented prime, and these are both part of traditional harmony, >hence not new. And ratios of 7 are not completely new -- even Partch >admitted that the 7th harmonic is implied in 12-ET. It is only with >11 and 13 that radically new intervals are introduced, and I think >that 11 is the more radical of the two. So I would stand by the >label neo- as characterizing the middle group of dieses.
I retract my argument that the small group might be considered new.
>> And there are >> other commas in this group which are probably newer. >
>You're always going to find new theoretical intervals, but I maintain >that 11 has the *newest* and *most exotic* sound once you go beyond >the bounds of 12-ET or traditional harmony. 13 comes close, but with >17 and 19 you get intervals that are very similar to what you have in >12-ET (except when you relate them to 11 and 13). This is the sense >in which I am using neo- to describe the middle diesis group, and the >sound will be characteristic of *any* of the dieses in the group, >because they all approximate the 11 and 13 dieses in *size.*
However it would seem that they would not have been new to the ancient Greeks.
>>> 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'. >>
>> But it _is_ average as far as size goes, and that's what these >prefixes are
>> supposed to be about. >
>While average in size, it's very un-average, i.e., out-of-the- >ordinary, in the characteristic *sound* of the intervals (ratios of >11) that result from its use. I think that there is an advantage in >having a label that is musically (rather than strictly >mathematically) descriptive.
I wouldn't call the size of an interval in cents a strictly mathematical description. It certainly realates to how it sounds.
>> And anyway, how long does something remain "new"? >
>As I said above, it's new relative to 12-ET and traditional harmony, >and it will continue to be new to anyone unfamiliar with alternative >tunings. At present this includes most of the musical world, and it >will always be radically new to anyone who is beginning the study of >alternative tunings. I don't expect traditional harmonic values to >disappear from the musical scene any time soon.
This just seems like too specific a viewpoint in time and space. It seems likely that other cultures now, and our culture at other times did-not/do-not/will-not see these as new.
>> Also, I should think that if 125:128 is prototypical of the small >group
>> then 243:250 would be that for the medium group. But again this is >not a
>> common comma to want to notate. It might be notated as /|) or (|~ . >
>I don't see how you drew that conclusion -- 125:128 has a special >place in history as *the meantone diesis* that 243:250 does not >share. Besides that, you have 11/1 higher on the popularity list >than 125/1.
I took "prototypical" to mean "coming first in time" and assumed that a 5-prime-limit diesis would have been noticed in this category before 11.
>So then we might want something else besides meta-. Yes. > My main objection is that neo- tells one nothing about the size. >But it does tell one about the main characteristic of intervals >altered by dieses in this size range: they are the ones that *sound* >most foreign to anyone who is twelve-oriented, i.e., like >quartertones. The over-57-cent group, on the other hand, sound like >small semitones (though they could be most accurately described as >third-tones), while the under-45-cent group could be described as >fifth-tones.
Yes. It's uncanny how well these boundaries correspond to the mid points between 1/3, 1/4 and 1/5 of a Pythagorean tone. But even if we had prefixes that meant 1/3, 1/4 and 1/5 I think this would be a mistake since the symbols don't always come out as these in various ETs.
>So if you don't like meta-, then what? >
>> In regard to having the right _meaning_, the best Greek set I can >find are >> hypo- >> meso- >> hyper- >
>Hypo- and hyper- do not offer the opportunity to distinguish by >abbreviation.
I already suggested the abbreviations "o" and "er" for these, which to me seem reasonably distinct vowel sounds. But I assume you do not find them so.
> For example, I might want to use 7-c and 7-h to stand >for 7-comma and 7-hyperdiesis in a diagram showing the actual symbols >(where words would take up too much space), but I don't have that >option if two ranges begin with the same letter. Besides, they sound >too much alike when spoken, so one might be misunderstood for the >other.
I agree that hypo and hyper are too similar, and few people know which has which meaning or even that they have different meanings.
>> If we were to depart from the Greek >> minor >> neutral >> major >> would be obvious enough, and so would >> small >> medium (or mean) >> large >
>You've made a better case against meta- than neo-, and I suppose that >would also eliminate proto-. I would like to see two short prefixes >for large and small that begin with different letters. In fact, I >would like to see separate letters for each of the following: > >Schisma - s >Kleisma - k >Comma - c >[Small] diesis - x >[Medium] diesis - y >[Large] diesis - z >where x, y, and z are letters different from s, k, and c. So we >could abbreviate intervals as 5c, 7c, 5s, 7z, 11y, 11z, 13y, 13z, >etc. (We don't need a separate letter for schismina, because it >isn't a symbol in the notation.)
This would be nice, but I wouldn't let it stop us from using something if there was sufficient other reason.
>> It is unfortunate that the word "diesis" already has two more >syllables
>> than we'd like it to have. This is presumably why we feel compelled >to
>> shorten any prefix we might add to it, down to a single syllable. >
>Or at least a single consonant.
But not if that consonant is "w" (whose name has 3 syllables).
>So if you don't like proto-, neo-, and meta-, then what would you >suggest?
I think we should use "m" for the middle group, whether it stands for "mid", "middle", medium", "mean", or "meso". I think english speaking folks are used to seeing the letters L M H for low medium, high, on appliances etc. and we could claim lepto- meso- hadro-. So that's a possibility but I can't help thinking there may yet be a better solution. Any other suggestions? -- Dave Keenan Brisbane, Australia Dave Keenan's Home Page * [with cont.] (Wayb.)
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Message: 6499 - Contents - Hide Contents

Date: Sun, 16 Feb 2003 16:25:58

Subject: Re: A common notation for JI and ETs

From: David C Keenan

I wrote
"I think english speaking folks are used to seeing the letters L M H for 
low medium, high, on appliances etc. and we could claim lepto- meso- 
hadro-. So that's a possibility but I can't help thinking there may yet be 
a better solution. Any other suggestions?"

We're also used to seeing S M L on t-shirts etc. It's a pity L can stand 
for either large or low, and S will clash with schisma. We could always use 
sd md ld for the dieses and plain s for the schisma.

We alreadty seem to have both been using small medium large as our default 
terms.


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