Re: Greekish names for tuning units.

The well-formed Greek term for 14- is tetrakaidek(a)-, but organic chemists have
shortened it to tetradec(a)- as in tetradecane, a saturated hydrocarbon with 14
carbon atoms. The 14-sided space-filling solid is thus a tetrakaidekahedron.

Dekatesserany - is one of Erv Wilson's names for the 14-tone stellated hexany.

--John

--- In tuning-math@yahoogroups.com, John Chalmers <JHCHALMERS@U...>
wrote:

> The well-formed Greek term for 14- is tetrakaidek(a)-, but organic
chemists have
> shortened it to tetradec(a)- as in tetradecane, a saturated
hydrocarbon with 14
> carbon atoms. The 14-sided space-filling solid is thus a
tetrakaidekahedron.

Tetradecamu works for me.

hello all,

there's been some discussion the last few days
on the tuning-math list about a good, consistent
set of names for the units of MIDI tuning resolution.

some of us have come to agree on using Greek
prefixes followed by "mu" for "midi unit".
the prefixes indicate the numbers up to 14,
which is the greatest number of bits resolution
in the MIDI tuning specification.

> From: "Gene Ward Smith" <gwsmith@svpal.org>
> To: <tuning-math@yahoogroups.com>
> Sent: Friday, July 04, 2003 2:31 PM
> Subject: [tuning-math] Re: Greekish names for tuning units.
>
>
> --- In tuning-math@yahoogroups.com, John Chalmers <JHCHALMERS@U...>
> wrote:
>
> > The well-formed Greek term for 14- is
> > tetrakaidek(a)-, but organic chemists have
> > shortened it to tetradec(a)- as in tetradecane,
> > a saturated hydrocarbon with 14 carbon atoms.
> > The 14-sided space-filling solid is thus a
> > tetrakaidekahedron.
>
> Tetradecamu works for me.

yes, i too prefer the shorter version.
"tetrakaidek(a)-" simply means "4 + 10"
of something.

a pedantic theorist might prefer to keep the
"kai", because the normal form for 14 has
"deka" first and *then* "tessera" (= 10 + 4),
and i could see how the "tetradek(a)-" form
might be mistaken for 40 (= 4 * 10, "four tens").

(40 actually has a totally different word: "saranta".)

the "tetradekamu" form comes by way of analogy
with "en-dek(a)-" for 11 and "do-dek(a)-" for 12.
but then at 13 the normal form switches and puts
the word for 10 first.

thus, the regular form for 12 is "dodek(a(-",
which has been used for a long time as prefix
to refer to 12-tone serialism as "dodecaphonic".
i think we can stretch the analogy to use
"tridekamu" for 13 and "tetradekamu" for 14.

OK, then how's this for the whole set? ...

bits EDO name

1 24 enamu (quarter-tone)
2 48 duomu / doamu (eighth-tone)
3 96 triamu
4 192 tesseramu / tetramu
5 384 pentemu / pentamu
6 768 heximu / hexamu
7 1536 heptamu
8 3072 oktomu /oktamu
9 6144 enneamu
10 12288 dekamu
11 24576 endekamu
12 49152 dodekamu (cawapu)
13 98304 dekatriamu / tridekamu
14 196608 dekatesseramu / tetradekamu (midipu)

the first term in the "name" column follows
strict Greek linguistic derivation.

the ones after the slashes are alternates which
i prefer. for one thing, they all end the
prefix with "a", so it's a nice, consistent
naming scheme, which i think others will
probably go along with. also note that i
prefer to use "k" instead of "c" for the
"k" sound, but if there's a lot of disagreement
about this i can be flexible. :)

so, a unit of tuning resolution which is used
on many electronic instruments which give 64
(= 2^6) units per semitone, and which AFAIK has
never had a name, can now be called a "hexamu".

and back in the late 1980s and early 1990s, when
the software MIDI sequencer i used was Texture,
my microtonal music had heptamu precision.

if i have my information straight about Quicktime,
then its finest resolution is oktamus.

"cawapus" now thus become "dodekamus".
i don't think we really need to be concerned
with precision beyond that level of resolution.

and "midipus" become "tetradekamus".
i'm *certain* that we don't need to go
beyond *that*.

any big objections to this naming scheme?
speak now, or forever be condemned to using
this terminology for MIDI tuning! ;-)

... well, OK ... i doubt that "enamu" is
going to replace "quarter-tone" ...

... and so, would something like "midenamu"
(zero bits for tuning, i.e., a plain MIDI-note
in 12edo) be the equivalent for "semitone"?

-monz

Hi, Joe. You wrote:

> bits EDO name
>
> 1 24 enamu (quarter-tone)
> 2 48 duomu / doamu (eighth-tone)
> 3 96 triamu
> 4 192 tesseramu / tetramu
> 5 384 pentemu / pentamu
> 6 768 heximu / hexamu
> 7 1536 heptamu
> 8 3072 oktomu /oktamu
> 9 6144 enneamu
> 10 12288 dekamu
> 11 24576 endekamu
> 12 49152 dodekamu (cawapu)
> 13 98304 dekatriamu / tridekamu
> 14 196608 dekatesseramu / tetradekamu (midipu)

In each case the numbers in the EDO column should be half of those you
give here. This is the initial problem that started the whole discussion.
Remember, 7 bits is 768 ET, not 1536. 14 bits is 98304 ET, not 196608. In
each case, for the number of bits n, the number of divisions in the ED2 is 6 x
2^n, not 12 x 2^n. Just to keep this straight, I think it might help to have a
standard form for the expression as:

n-mu = 6 x 2^n = x ED2

for example,

heptamu = 6 x 2^7 = 768 ED2

Second point: for all the discussion of Greek for 14, I'm glad that John
Chalmers spoke up - I had seen tetra kai deka as three words before but not
one... BUT, I think the best solution to the name for the 14-bit mu is just to
call it 'mu' = 'MIDI unit' because it is the MIDI tuning standard, after all. I'm not
sure of the necessity to name mus under 4, but here is a revised list based on
Joe's suggestions:

bits - ED2 - name
1 - 12 - enamu
2 - 24 - duomu
3 - 48 - triamu
4 - 96 - tetramu
5 - 192 - pentamu
6 - 384 - hexamu
7 - 768 - heptamu
8 - 1536 - octamu
9 - 3072 - enneamu
10 - 6144 - dekamu
11 - 12288 - endekamu
12 - 24576 - dodekamu
13 - 49152 - tridekamu
14 - 98304 - mu

The other idea that comes to mind if we call 14-but 'mu' is to name the others
as versions of 'mu-minus-n' instead of 'n-mu'. Not sure how this would
translate into a name,. but it would make sense. I think it makes a lot of sense
to call the MTS simply 'mu'.

Aaron