The Xing Metrology

The Xing Metrology

Double sharp
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Dec 5 2017, 01:56 PM #1

OP's edit: This thread was originally titled "Sketches of an Octal Metrology", with an eye to changing it later, as a name for this octal DGW metrology had not yet been decided on then. The name "Xing" emerged in later discussions, and the title has since been edited to reflect this.

So, here's the post that started it all:
Oschkar @ Jan 2 2017, 08:00 PM wrote:
Double sharp @ Jan 2 2017, 03:34 PM wrote: (Maybe I should make that an actual metrology. Out of the Stevinian bases, {8, 10, 12} are surely the top tier. Decimal already has SI and duodecimal has Primel, so that leaves octal. But that's another topic.)
Well, the true decimal equivalent to Primel wouldn't be SI, but Donald Sauter’s system, which uses the microday, acceleration due to gravity, and the density of water as base units, and then derives everything else coherently from there. It even goes as far as saying that names for units are unnecessary, because the quantities they represent are already transparent enough. (That's a little further than Kodegadulo wants to go with Quantitels, though, but at least Quantitels are transparently derived from the name of the quantity they are the base unit of.) Their "bip" and "bop" syllables for scientific notation are almost isofunctional to SDN's "qua" and "cia", but represent powers of ten rather than twelve.

Let's see. I'll use a clone of SDN with the syllable "os" representing octal base. I'll assume Dan's calculated average of Earth's gravity, 9.797582719616393 m/s2, and the maximum density of water, 999.972 kg/m3, and round the values to 8 significant figures.

1 hexosquatimel = 1 day
1 pentosquatimel = 3 hours (= Roman vigilia)
1 quadosquatimel = 22.5 minutes (≈ Indian ghatika)
1 trinosquatimel = 2.8125 minutes
1 binosquatimel = 21.09275 seconds (≈ Indian pala)
1 unosquatimel = 2.6367188 seconds
1 timel = 0.32958984 seconds (≈ Indian vipala)

1 accelerel = 9.7875829 m/s2

1 velocitel = 3.2291838 m/s
1 unosquavelocitel = 25.833470 m/s (almost exactly 93 km/h)

1 lengthel = 1.0643062 metres
1 unosqualengthel = 8.5144494 metres
1 binosqualenthel = 68.115594 metres
1 trinosqualengthel = 544.92476 metres (≈ Chinese li)
1 quadosqualengthel = 4.3593981 kilometres (≈ French lieue)

1 unoscialengthel = 133.03827 millimetres (≈ English shaftment)
1 binoscialengthel = 16.629784 millimetres (≈ Roman digitus)
1 trinoscialengthel = 2.0787230 millimetres

1 volumel = 1.2055903 m3
1 unosciavolumel = 150.69879 litres (≈ oil barrel)
1 binosciavolumel = 18.837348 litres
1 trinosciavolumel = 2.3546685 litres (≈ Imperial pottle)
1 quadosciavolumel = 294.33357 millilitres (≈ Imperial cup)
1 pentosciavolumel = 36.791696 millilitres

Octal Primel actually looks really promising!
So now we can start suggesting some preliminaries, such as an actual name for this hexosciaday-based system, and some colloquialisms for what we have described up there already (since, being immersed in unit names like "centimetre", "kilogram", and "gigapascal", I am not sure I have a very good idea what sounds "natural").
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Kodegadulo
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Dec 5 2017, 07:26 PM #2

Double sharp @ Dec 5 2017, 01:56 PM wrote:So now we can start suggesting some preliminaries, such as an actual name for this hexosciaday-based system
Well, to quote you from another thread:
Double sharp @ Dec 2 2017, 06:45 AM wrote:For the "branding symbol", the circled eight-pointed star ❂ looks quite promising, if you can see it properly.
That seems an excellent choice of brand mark.
As I think you suggested, we could use "oc-" as the branding prefix, and maybe "Octel" as the name of the metrology.
If this works for you, you could certainly go with this. But I hesitate to recommend it as it seems at first blush rather derivative of the name "Primel". You ought to look at Primel as a sister metrology, not a progenitor. Well, perhaps I'm splitting hairs, since either way there's going to be a "family resemblance". But Oschkar for instance has designated his own unqua·decimal system the "Ashtrian" metrology, and you certainly have the option to come up with something equally fanciful.  I mean, what's the Mandarin word for "eight"? Or "octopus"?

Or "spider"?  :)  蛛 zhū? Perhaps you could call this the "Zhū" metrology, and pronounce ❂ as the prefix-syllable "zhū". So for example:

1 ❂timel ("zhū-timel") = 0.32958984d s
1 ❂lengthel ("zhū-lengthel ") = 1.0643062d m
1 ❂velocitel ("zhū-velocitel") = 3.2291838d m/s
1 ❂volumel ("zhū-volumel") = 1.2055903d m3
1 ❂massel ("zhū-massel") =  1201.86897d kg
...
Last edited by Kodegadulo on May 29 2018, 10:45 PM, edited 1 time in total.
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Double sharp
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Dec 6 2017, 01:46 AM #3

I rather think that "zhū" is inadvisable, since it is pronounced very close to the English word "Jew". (The initial affricate is retroflex rather than alveolar, but I think that distinction is going to be lost on most English speakers). Mandarin for eight is 八 bā, which to English speakers I think is going to sound rather like the "bah metrology".

Mandarin for "octopus" is 章魚 zhāngyú, though I worry that the vowel at the end (it's like German ü) - forget about the tones - is going to be murdered by English speakers. And maybe it's the fact that I speak Mandarin but calling something the "Octopus metrology" sounds a little too unserious for my taste. "Zhang" alone could work, but that is also a surname, so it sounds like it is the metrology of one Mr. or Ms. Zhang.

I agree though that "Octel" is a bit unsatisfying, so for now I'll mentally pronounce ❂ as "oc", while reserving the right to change it when something better comes up.
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Kodegadulo
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Dec 6 2017, 01:50 AM #4

Double sharp @ Dec 6 2017, 01:46 AM wrote: I rather think that "zhū" is inadvisable,...
Oh well, might've been exotically fun for English-speakers, despite the inevitable mangling. :) But, no matter.
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Kodegadulo
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Dec 6 2017, 02:00 AM #5

Hmm, how about the "Octagram" (八角星 bājiǎo xīng) metrology? Or perhaps just use the final syllable 星 xīng ("star")? That would make it the "Xīng" metrology, with for example:

1 ❂timel ("xīng-timel") = 0.32958984d s
1 ❂lengthel ("xīng-lengthel ") = 1.0643062d m
1 ❂velocitel ("xīng-velocitel") = 3.2291838d m/s
1 ❂volumel ("xīng-volumel") = 1.2055903d m3
1 ❂massel ("xīng-massel") = 1201.86897d kg
...

Even mangled by Anglophones as "shing" or "zing", it still sounds cool. :) And you would be saying exactly what the brand mark looks like. :)

Now please don't tell me that untoned "xing" or mangled "zing" sounds like some expletive in Mandarin... :)
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Double sharp
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Dec 6 2017, 02:45 AM #6

I like that; it'd then be a bit like Ashtrian with its vague shade of aster (at least, I picked up on that; no idea if Oschkar meant for it, though).

It is quite acceptable to pronounce Mandarin alveolo-palatal /ɕ/ (romanised x) as a palatalised s /sj/. In fact this is pretty common among native speakers; historically all instances of /ɕ/ come from [sj] or [xj]. So I'd think sing is a better approximation, since the front vowel is going to allophonically palatalise the s anyway.
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Kodegadulo
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Dec 6 2017, 03:15 AM #7

Double sharp @ Dec 6 2017, 02:45 AM wrote: It is quite acceptable to pronounce Mandarin alveolo-palatal /ɕ/ (romanised x) as a palatalised s /sj/. In fact this is pretty common among native speakers; historically all instances of /ɕ/ come from [sj] or [xj]. So I'd think sing is a better approximation, since the front vowel is going to allophonically palatalise the s anyway.
Interesting. Listening to the audio at the Google translate page for 星, it sounds to my ears closer to /ʃɪŋ/ ("shing") than to /sɪŋ/ ("sing"). In all the English dialects I've heard, I've never discerned any tendency to palatalize "single" so that it would sound like "shingle". The words are quite distinct. Quite a shibboleth, I'd say. :)

Granted, /ɪ/ is somewhat less fronted than /i/, but by the same token, I've never detected any tendency for the word "sealed" to be palatalized to sound like "shield".

I think if you simply transliterate 星 as "Xing", and let anglophones pronounce it either /ʃɪŋ/ or /zɪŋ/, it would be quite ... um ... palatable. ;)
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Double sharp
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Dec 6 2017, 03:40 AM #8

I didn't mean palatalisation far enough to actually move the primary place of articulation, but just as a secondary place of articulation, i.e. a raising of the middle of the tongue, as you would need to do for the following /i/ or /j/ anyway.

From Google Translate, I'm hearing of course the standard /ɕ/, which indeed sounds more like /ʃ/ than /s/. I think you would be understood with either anyway because of this acceptable variation between /ɕ/ and /sj/, while /z/ might be more confusing.

I think we can leave off the tone mark anyway, and just call them the xing-timel, the xing-massel, the xing-lengthel, and so on.
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Shaun
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Dec 6 2017, 08:34 AM #9

Just for amusement ...

When discussing number bases with a group of eleven-year olds many years ago, we used first base four (doggie), then base eight.

1 ,2 ,3, 4, 5, 6, 7, 10 (octy)
with twocty, throcty, forocty, fivocty, soxty, sennocty (I can't remember the rest of the invented names).
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wendy.krieger
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Dec 6 2017, 11:44 AM #10

Evidently Kode has not heard of an "e" or "i" palitising a dental. It's quite common in English. John > Ʒohn > Sean > Shaun is common. Here the vowel is 'ia', has caused the S to palitise into sh. You see the same effect where the i-glide palatising in many dithongs, (sugar -> siugar -> shuga. Tuesday -> choosday, and due date to dʒu: date.).

It's just not palatising because we don't have a dithong.
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Kodegadulo
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Dec 6 2017, 01:40 PM #11

wendy.krieger @ Dec 6 2017, 11:44 AM wrote: Evidently Kode has not heard of an "e" or "i" palitising a dental
You know Wendy, for someone who protests her complete innocence of any enmity against me, you seem to be quite adept at finding the most insulting way to inject your disagreement. Methinks the lady doth protest too much. Are you able to participate at all in civil discussion without injecting a note of rancor and divisiveness? I'm sure DS does not appreciate you pursuing your vendetta against me into yet another of his threads.

I most certainly do have an understanding of palatalization as an effect that occurs in some languages, in some dialects, in some instances. I've commented before on the fact that my son surprised me when he was in first grade learning to write, by misspelling "tree" as "chree". I realized that indeed there is some palatalization occurring in the /tri/ cluster in our dialect of American English, even though most adult speakers still perceive it as just an allophone of the same morpheme. But my son was just spelling it the way he heard it.

But as in all things linguistic, we witness once again Wendy's willful ignorance of the fact that language is always a matter of usage and habit and custom. It is not a matter of physical law. Wendy has been chided about this numerous times, but refuses to learn. Simply because one can cite one instance where an effect is observed does not mean that it occurs everywhere in all instances. As I have already said, I can cite instances where English "si" has not palatalized to "shi", and we could conjecture that this may have been suppressed due to the existence of contrasting words such as "single" vs "shingle". This does not mean that I'm contradicting DS's observations of such palatalization in Mandarin. But I am suggesting that we should expect the English pronunciation of this "xing" prefix to wind up as "shing" or "zing", rather than "sing". Particularly since "sing" is already a word in English with a contrasting meaning, that also has shown no signs of ever going palatal.
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wendy.krieger
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Dec 6 2017, 02:13 PM #12

What happens with s,z,t,d, is that before /j/ they palatise to sh,zh,ch,j. Dithongs with a leading i, the i becomes a i-glide, ie a /j/. t and d can palitise before an r too. In old english, c palatised into ch, such as kirk -> church. Most k are norse borrowings.

In terms of chinese, they have two labial stops, like english, but the articulation is different. Two labial stops is 'p' and 'b', but the chinese points are b and b'. So we get Peking -> Beijing.

A word spelt 'Xing' would be pronounced 'zing' in english, or even 'ksing'. The X is a kind of 'sh' so it would be shing. Chinese has tones as well, which we don't generally preserve in english.

I'd rather D.S. pick his own prefix, since there are implied naunces in english and chinese that non-fluent speakers may be aware of.
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Double sharp
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Dec 6 2017, 03:01 PM #13

During the Tang Dynasty (618-907), Middle Chinese had a three-way contrast in initial stops: voiced, voiceless aspirated, and voiceless unaspirated. This distinction collapsed to a two-way one in the modern Mandarin dialect: voiceless aspirated and voiceless unaspirated. Nevertheless the former voicing or unvoicing of the initial consonant potentially triggered a tone change - which incidentally explains why there are quite a few lexical gaps in the sense that many syllables exist with first or second tone, but not both.

Incidentally, the very rare context which allow the u-umlaut ü to carry a tone mark (it must be the only vowel in the syllable, and the umlaut is only written when it would be ambiguous, forcing the initial consonant to be either n or l - a sonorant, meaning that there is no normal historical route to reach a first tone) mean that curiously, one of the 30 combinations of vowel and tone mark in Pinyin, the official Chinese romanisation (6 vowels {a, o, e, i, u, ü}, 4 tone marks, plus the "zero tone mark" for neutral tone) never actually gets used: ǖ. All the other tone-marks on ü exist: lǘ 驴 "donkey", lǚ 铝 "aluminium", lǜ 绿 "green", lüè 略 "slightly, strategy, outline".

Some other romanisation systems for Mandarin Chinese render the syllable under discussion as "hsing" or "shing".

Regardless, I'll adopt Kode's &#26143; x&#299;ng as the brand-marker since I don't see much of a problem with it, with the understanding that English speakers should approximate it as "shing". I would probably ASCII-fy it by stripping off the tone mark and writing "xing" anyway, since like it or not, this transliteration with <x> is standard.

P.S. In Mandarin Chinese, underlying medial /i/ is always realised as palatalisation of the preceding consonant, unless that is already one of the palatals, in which case it is just deleted. In other words, underlying /Cj/ is always pronounced [C&#690;], unless the consonant C is already one of the palatals /t&#597; t&#597;&#688; &#597;/, in which case the result is just [C]. C cannot be /f/, a retroflex, or a velar: the reason for the last is because these palatals historically come from palatalisation of the velars /k k&#688; x/ or or dentals /ts ts&#688; s/ by a following high vowel /i/ or /y/. Similarly, medial /u/ is realised as labialisation of the preceding consonant, and medial /y/ is realised as simultaneous labialisation and palatalisation of the preceding consonant (unless that is a palatal, in which case only labialisation occurs).

So now we can get back to colloquialisms for the units, I suppose.
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Kodegadulo
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Dec 6 2017, 04:21 PM #14

Double sharp @ Dec 6 2017, 03:01 PM wrote: Some other romanisation systems for Mandarin Chinese render the syllable under discussion as "hsing" or "shing".

Regardless, I'll adopt Kode's &#26143; x&#299;ng as the brand-marker since I don't see much of a problem with it, with the understanding that English speakers should approximate it as "shing". I would probably ASCII-fy it by stripping off the tone mark and writing "xing" anyway, since like it or not, this transliteration with <x> is standard.
Cool. I'd say leave some flexibility in what Romanization people can use, even if you settle on your own preference. Unless one is actually writing introductory prose describing the entire system itself, in practice it will mostly be a moot point, because one will be using the brand mark on the unit names the vast majority of the time. The only reason I'd advocate "xing" for the full spelling is that it's rather exotic for most Anglophones, so it adds colorful distinction to your metrology, reflecting your background as its author.
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Oschkar
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Dec 6 2017, 05:25 PM #15

Well, at least you’ll have a very convenient &#26143;&#37324; x&#299;ngl&#464; available at 545 metres!
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Kodegadulo
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Dec 6 2017, 08:50 PM #16

Oschkar @ Dec 6 2017, 05:25 PM wrote:Well, at least you’ll have a very convenient &#26143;&#37324; x&#299;ngl&#464; available at 545 metres!
Indeed, and that's a perfect colloquial to use for it in Mandarin. The last time we mentioned the metric l&#464; (&#37324;), I suggested translating that as the colloquial name rustical, from Latin rus "farm, field, village", based on the idea that the Chinese l&#464; is considered the typical size of a farming village and its fields. So you could certainly translate &#26143;&#37324; x&#299;ngl&#464; as &#10050;rustical. You could also call it a &#10050;turrial, based on it being a "towering" height, typical of skyscrapers
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Double sharp
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Dec 7 2017, 09:00 AM #17

Given the Chinese element introduced by the name (and also because traditional Chinese units of mass are hexadecimal, which meshes well with the octality of this system), I'm more inclined to call the trinosqualengthel the &#10050;rustical, since that is more akin to the derivation of the Chinese &#37324;. It's just difficult to adapt Chinese names to the phonotactics that Latin-style suffixes work well with, hence the translation.

Another happy coincidence is that since eight squared is just over sixty, the Indian sexagesimal subdivisions of the day are very close to every other octal power of the day. Normally I would be loath to coopt existing names like this, but here they are so very close that the temptation is justified (all figures to 6 s.f. at most):

binosciaday = 22.5 min, close to ghatika = 24 min
quadosciaday = 21.0375 s, close to pala = 24 s
hexosciaday = 329.590 ms, close to vipala = 400 ms
unnilosciaday = 5.14984 ms, close to leekshaka = 6.66667 ms
unbinosciaday = 80.4663 &#956;s, close to lava = 111.111 &#956;s
unquadosciaday = 1.25729 &#956;s, close to renu = 1.85185 &#956;s
unhexosciaday = 19.6451 ns, close to truti = 30.8642 ns

Okay, at the very bottom they're not all that close anymore, but I doubt anyone is looking for colloquialisms in the microsecond or nanosecond range. Except that this is trying to be an octal metrology, not a tetrasexagesimal metrology, and taking over the Indian names wholesale results in blanks on every other octal power. The unosciaday could be called a &#10050;vigil, certainly, following the Romans, but I don't think the Indian names are going to fit well with that and the &#10050;rustical either.

I suppose we can call the &#10050;rustical the &#26143;&#37324; in Mandarin Chinese and coopt those names for Hindi, with a disambiguating marker being whatever Hindi for "star" happens to be. I just don't think they work as English colloquialisms, though &#10050;vigil for the 3-hour-long unosciaday certainly does.
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Kodegadulo
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Dec 7 2017, 10:47 AM #18

Double sharp @ Dec 7 2017, 09:00 AM wrote:The unosciaday could be called a &#10050;vigil, certainly, following the Romans
Ah, that's a nice find for the octinfra·day (8\day or o\day). The best I could come up with for that in the past was sesqui·dwell or semi·phase, but this is much better! :)

Now where did I put that table of fractions of the day ? ... :rolleyes:
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Double sharp
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Dec 7 2017, 11:15 AM #19

Let me try once more properly for a few negative binary powers of the day. Now it seems go me that in order to harmonise octal and hexadecimal properly we need a full binary range, and also that this is a very natural way to bring in regular numbers as auxiliaries; 8 and 16 only have powers of 2 as regulars, so why not use them?

(Please assume the brand marker &#10050; is in front of all those names, of course.)

Half a day is 12 hours, and Kode has previously suggested to call it a clock-period, since it fits am vs pm. A quarter is 6 hours, for which he's suggested "phase"; and I've suggested "vigil" for the eighth-day of 3 hours.

The untesciaday weighs in at 1.5 hours; Kode's suggested "dodrell" for it, since it is 3/4 of a dwell. While it is opaque enough to feel like a single name, I don't find it totally binary. Now 90 minutes feels quite reasonable for a family-entertainment film to while away time on a holiday (not one of those two-hour-or-more serious epics), so we might as well call it a "whiling", since that was one of Kode's early rejected names for the dwell. The next power of two down leads us to 45 minutes, which is quite possible for a Classical-era serenade (though many are shorter, so this is perhaps an upper limit); as you can see I can't think of a good colloquialism for it at the moment, so I'll just use "serenade-period" for now. Half of that is the binosciaday, 22.5 minutes: like Oschkar suggested for the 24-minute sexagesimal unit, we could call it the "chime".

Half of that leads us to 11.25 minutes, which makes a reasonable analogue of the Primel "bout" of ten minutes; half again is the bitesciaday of 5.625 minutes, close to a "block" of five minutes; half of that is the trinosciaday of 2.8125 minutes, close to the passage of 2.5 minutes from the Phasic metrology, and might as well be called a "passage" as well.

The next power down is 1.40625 minutes or about 84 seconds, which we could call a "moment" like the similarly short Ashtrian counterpart. Half again is about 42 seconds, not far from a Primel "trice" (though it does lose the play on "thrice", it is still an English word). Next is the tritesciaday or quadosciaday of about 21 seconds; this could be a reasonable "strain" of music.

Half again is about 10.5 seconds, or about a "verse" in Primel; then about 5.3 seconds, or about a "lull". The pentosciaday of about 2.64 seconds works out to be a reasonable "hesit" (if a bit on the long side, it still feels like a brief interruption), allowing me to call its half of about 1.32 seconds, the quadtesciaday, a "beat". Half again is 0.659 seconds, a reasonably lively pace, rather andante if you ask me (well, under a more Romantic idea of tempo this time); we could call it the "pacing". Half once more gives us the hexosciaday, my preferred choice of timel at about a third of a second, very close to a Primel "twinkling". Half of that is about 165 milliseconds, something like the TGM Tim; well, "tick" seems quite as good here.

If this were a hexadecimal metrology, of course, I would definitely continue the halving a tiny bit further. Half again is the penttesciaday of about 82.4 ms, close to a Phasic "flicker". Ashtrian "instant" and Primel "jiff" (maybe "jiffy", as I'm hesitant to coopt a base unit) give us enough space to reach the septosciaday.

So:
Two clock-periods to the day,
Two phases to a clock-period,
Two vigils to a phase, (8^-1)
Two whilings to a vigil, (16^-1)
Two serenade-periods to a whiling,
Two chimes to a serenade-period, (8^-2)
Two bouts to a chime,
Two blocks to a bout, (16^-2)
Two passages to a block, (8^-3)
Two moments to a passage,
Two trices to a moment,
Two strains to a trice, (8^-4 and 16^-3)
Two verses to a strain,
Two lulls to a verse,
Two hesits to a lull, (8^-5)
Two beats to a hesit, (16^-4)
Two pacings to a beat,
Two twinklings to a pacing, (8^-6)
Two ticks to a twinkling,
Two flickers to a tick (16^-5),
Two instants to a flicker,
Two jiffies to an instant. (8^-7)

I'd want to reach 8^-8 = 16^-6, but I think that's too far outside the range of human perception to be seen as anything but periods of piano key frequencies.

I can't help but feel that this binary spacing for octal or hexadecimal auxiliaries is far too much, but given that Imperial volume units are already binary, and {8, 16} as bases force you to stick to binary powers anyway, I wonder how well it seems to work for someone not immersed in millesimal metric culture.
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Double sharp
Dozens Demigod
Double sharp
Dozens Demigod
Joined: Sep 19 2015, 11:02 AM

Dec 7 2017, 12:39 PM #20

Actually, we can probably go a little bit further, since this is binary (and octal and hexadecimal). So the old dozenalist idea of "vic" (vibration of C-sharp) - here it is a "vig" (vibration of G) - can be consistently applied with just a mark of the octave: two jiffies would make a contra-vig, two contra-vigs a great vig, and two great vigs a small vig. Instead of "one-line", "two-line", and so on for the next octaves, we could certainly substitute "tenor vig", "soprano vig", "altissimo vig", "piccolo vig", or something like that. But this is starting to be overkill, I would imagine, although it certainly does get us to the unnilosciaday as the small vig (frequency of G3).
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wendy.krieger
wendy.krieger

Dec 7 2017, 12:57 PM #21

{a}
The nautical measure is a day of six watches, of eight bells.

For units as long as 8^-2 day, you could use a word meaning bell, the indian 'gurry' means bell, and 'pali' is 'while'. So eg

day = 8 watches
watch = 8 bells
bell = 64 whiles.

The other thing is that some of this system is close enough to metrics that you could use a binmetric to navigate. I do this sort of thing occasionally.

point = 1/64 digit = 256 oum (as in printer's point, or point of rain).
line = 1/8 digit = 2 omm (a french line = 1/12 inch ~ 2 mm)
digit = 16 omm
metre = 64 digit = 1 o2lengthals (si metre = 60)
okm = 2o5 lengthels (65536 v 60000)

{8}
One can have an absolute temperature scale, where freezing is set to 326 'degrees' There are then 1x5thremmels to a 'degree', and 1°C = 0.62 thremmel.
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Double sharp
Dozens Demigod
Double sharp
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Joined: Sep 19 2015, 11:02 AM

Dec 7 2017, 03:38 PM #22

Shaun @ Dec 6 2017, 08:34 AM wrote: Just for amusement ...

When discussing number bases with a group of eleven-year olds many years ago, we used first base four (doggie), then base eight.

1 ,2 ,3, 4, 5, 6, 7, 10 (octy)
with twocty, throcty, forocty, fivocty, soxty, sennocty (I can't remember the rest of the invented names).
Oschkar suggested an octal nomenclature here, based on trying to make the compounds with the existing Indo-European roots for one through eight and developing them into English:

{8}

1 through 10: one, two, three, four, five, six, seven, eight

10 through 100 by decades: eight, twaught, thright, foraight, fivaight, sixaight, sevenaight, thaured (with -aight pronounced "it")

Not sure if he put the octal "teens" anywhere, though it strikes me that the way things worked in this world would lead to 11 and 12 being read as "eleven" and "twelve", since they are still "one left" and "two left". So something needs to be done, perhaps regularisation of 11 and 12 to be like the rest of the octal "teens" through analogy. Since his linguistic abilities far outstrip mine, I shall let him suggest how things would work there, while I carry on saying "eight-one, eight-two, ..., eight-seven". And might I perhaps suggest a completion allowing one to say bigger numbers in a way that sounds to the average English speaker (well, in this pentadactyl universe) no more unnatural than arbiteroftruth's dozenal use of "dozen, gross, great gross, ..., zillion, ..., bizillion, ..., trizillion" for powers of the dozen? Already this brief range for the octal nomenclature sounds very fine to my ears!

I must confess that I am very fond of the idea of a mixed octal-hexadecimal system, in which octal and hexadecimal languages coexist, with octal numbers being read in fours and hexadecimal numbers being read in threes, because the fourth power of eight is equal to the cube of sixteen (both are two to the twelfth power). So you could use the other nomenclature whenever you liked, something like one of my old suggestions:

0 zero, 1 one, 2 two, 3 three, 4 four, 5 five, 6 six, 7 seven
10 oct, 11 nine, 12 tolve, 13 threlve, 14 forlif, 15 fivelif, 16 sixlif, 17 sevenlif
20 tess, 21 tess-one, 22 tess-two, 23 tess-three, 24 tess-four, 25 tess-five, 26 tess-six, 27 tess-seven
30 tess-oct, 31 tess-nine, 32 tess-tolve, 33 tess-threlve, 34 tess-forlif, 35 tess-fivelif, 36 tess-sixlif, 37 tess-sevenlif
40 two-tess, 50 two-tess-oct, 60 three-tess, 70 three-tess-oct, 74 three-tess-forlif
100 octent, 200 two octent, 300 three octent, 400 tessent, 500 five octent, 600 six octent, 700 seven octent
1000 octcue, 2000 two octcue, 3000 three octcue, 4000 four octcue, 5000 five octcue, 6000 six octcue, 7000 seven octcue
10000 octinent = tescue

And you could, if you wanted, call 100 "four-tess" instead and so on in this suggestion. But I'm not sure how to build up this massive radix-mixing in a quasi-historical manner, like Oschkar's octades. Maybe it isn't the natural way of speaking anywhere originally, but prolonged contact between octal and hexadecimal cultures should allow this sort of thing without either having to give up their native base.

EDIT: Eleven cubed posts!
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Kodegadulo
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Kodegadulo
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Joined: Sep 10 2011, 11:27 PM

Dec 7 2017, 05:40 PM #23

Nice job with your binary time series. But because it overloads some Primel colloquials, and because these overloading are reasonable, it does rather preclude the hope that those colloquials could be deemed "absolute" and not require brand-qualification. For instance, all metrologies might agree that "clock", "shift" (8 hrs), "phase", "watch" (4 hrs) , "vigil", "dwell", "hour" always mean the same things, without further qualification. but we will now need to distinguish e.g. "prime-twinkling" from "xing-twinkling".
Double sharp @ Dec 7 2017, 11:15 AM wrote:(Please assume the brand marker &#10050; is in front of all those names, of course.)
Perhaps we can come up with a convention of signalling metrologies as well as bases. Just as we might place

{8}

before a block of text to indicate that it is all in base 8, by the same token we might place

{&#10050;}

to indicate "default to Xing metrology until further notice".
As of 1202/03/01[z]=2018/03/01[d] I use:
ten,eleven = ↊↋, ᘔƐ, ӾƐ, XE or AB.
Base-neutral base annotations
Systematic Dozenal Nomenclature
Primel Metrology
Western encoding (not by choice)
Greasemonkey + Mathjax + PrimelDozenator
(Links to these and other useful topics are in my index post;
click on my user name and go to my "Website" link)
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Oschkar
Dozens Disciple
Oschkar
Dozens Disciple
Joined: Nov 19 2011, 01:07 AM

Dec 7 2017, 06:06 PM #24

You could take inspiration from French, and the way it follows vigesimal in the upper decades.

In the alternative octal history we’ve been discussing, French numbers could be something like:

zéro, un, deux, trois, quatre, cinq, six, sept
huit, huint, doit, truit, quattoirt, quint, sît, setteint
vif, vif-et-un, vif-deux, vif-trois, vif-quatre, vif-cinq, vif-six, vif-sept
trive, trive-et-un, trive-deux, trive-trois,...
quarave, quarave-et-un,... quarave-huit, quarave-et-huint,... quarave-setteint
trois-vifs, trois-vif-un,... trois-vif-huit, trois-vif-huint,... trois-vif-setteint
teuf, deux teufs, trois teufs, sanstre, cinq teufs, six teufs, sept teufs
stoirent, huint teufs, doit teufs, truit teufs, stoirent-sanstre, quint teufs, sît teufs, setteint teufs
deux stoirents, deux stoirents teuf,... deux stoirents sept-teufs
trois stoirents, quatre stoirents,...


For 1000 I took the IE root for "star", formed a feminine active participle out of it (*h&#8322;stérn&#805;tih&#8322;) and ran it through the sound changes from PIE to French. 400 then follows as "half a star" (*s&#275;&#769;mih&#8322;st&#275;r).

I don't know what I want the word for 1 0000 to be. Probably a Greek borrowing into Latin, but I’m not sure what word I want to take it from. (Or how to distinguish six from sît under liaison.)
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