Tuning-Math Digests messages 6975 - 6992

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Message: 6975

Date: Wed, 2 Jul 2003 12:07:14

Subject: Re: The Cawapu Comma

From: monz

hi Aaron,


> From: <pitchcolor@xxx.xxx>
> To: <tuning-math@xxxxxxxxxxx.xxx>
> Sent: Wednesday, July 02, 2003 11:05 AM
> Subject: [tuning-math] Re: The Cawapu Comma
>
>
> Hi Joe,
> 
> You wrote:
> 
> <<i appreciate your pursuing this topic ... but i'm still
> having trouble seeing it.
> i'm sorry that i have to speak in terms of Cakewalk,
> since you don't use it, but i do and i know this works:
> each 12edo semitone is divided in 4096 cawapus.
> thus, each cent is divided into exactly 40.96 cawapus.
> 12 * 4096 = 49152.
> i know that the standard pitch-bend range is a
> whole-step, one half-step on either side of the
> MIDI-note. but Cakewalk uses 8192 as the size of
> a whole-step. 6 * 8192 = 49152.
> please keep this dialog going, because i really want
> to clear this up.>>
> 
> 
> From Manuel's input and what you wrote there,
> it looks like you've got it figured out. Looks like
> the cawapu ET (or ED2) should be what you thought it
> was all along:
> 
> 6 * 8192 = 49152
> 
> The only concern I would raise is that since cakewalk
> uses both data bytes then it is likely that the second
> data byte is ignored by the midi module. I defer to Manuel
> if there is something I am missing, but it looks like if
> the second data byte is ignored, then 7 bit cawapu should
> be the same as standard pitch bend:
> 
> 6 x 2^7 = 768 ET
> 
> According to your webpage giving specifics about the
> data format for cakewalk, this would be correct. I
> raise this point because if the second byte is simply
> ignored, then there are bend messages being sent out
> which are incorrect in 7-bit precision. They will be
> incorrect because they need to be rounded from 12-bits
> to 7-bits. In other words, the MSB needs to be rounded
> up or down according to the value of the LSB. Truncated
> 7-bit values will sometimes be wrong.



hmmm ... well, i use Cakewalk to play MIDI-files thru
my computer's soundcard, and the "cawapu" pitch-bend
data i use gives me the correct tuning.

i have no idea what happens when you play use Cakewalk
to play MIDI-files thru another instrument.

i coined the term "cawapu" to have a handy word to
represent the 4096-pitch-bend-units-per-semitone
unit of interval measurement, which is one degree
of 49152edo.

therefore, it would be incorrect to use the term
"cawapu" when referring to an instrument that only
has 7-bit precision.  as you point out, even if the
MIDI-file uses 49152edo as its tuning basis, the
result is truncated to 768edo resolution.

in view of the fact that so many instruments use
7-bit precision, i suppose we really need another
new term to represent one degree of 768edo.
any suggestions?


PS -- "midipu" covers the full 14-bit resolution
that is possible in MIDI, but "cawapu" seems to
be the resolution which is much more frequently 
implemented in practice.



-monz


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Message: 6977

Date: Wed, 2 Jul 2003 12:27:01

Subject: Re: The Cawapu Comma

From: Manuel Op de Coul

>but i'm still not clear:
>does the division of 1060 per 8ve have any
>historical relevance for Turkish music, or for
>any other for that matter?

No, but 106-tET does. Karadeniz lists some makams
as modes of 106 in his book. I've put them in the
mode list.

Manuel


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Message: 6981

Date: Wed, 2 Jul 2003 23:24:09

Subject: Re: Names for MIDI units

From: monz

----- Original Message -----
From: <pitchcolor@xxx.xxx>
To: <tuning-math@xxxxxxxxxxx.xxx>
Sent: Wednesday, July 02, 2003 1:41 PM
Subject: [tuning-math] Names for MIDI units


> Hi Joe,
> <<in view of the fact that so many instruments use
> 7-bit precision, i suppose we really need another
> new term to represent one degree of 768edo.
> any suggestions?>>
>
> It was mentioned that the 12-bit bend is not unique to cakewalk, and you
said that your names were provisional, so how about we simplify all of the
existing names in the process of finding one for 7-bit?
>
> ( ) Use 'midi unit' = mu instead of 'pitch unit'. So, 'midipu' just
becomes 'mu', pronounced 'mew', pl. 'mus' pronounced 'mews'.
> ( ) Use prefixes for different types of mu ... how about 1 letter for 1
byte and 2 letters for 2 bytes. I dunno, default to Greek? 7 = epta (or
hepta), 12 = dodeca, 14 = dekatessera, so
>
> 7-bit = 'emu', (pronounced 'eemew', pl. 'emus' pronounced 'eemews')
> 12-bit = 'domu', (= 'doemew', pl. 'domus' = 'doemews')
> 14-bit = 'demu', (= 'deemew', pl. 'demus' = 'deemews')
>
> I suppose we could go with 'extra precision' for 14 bit and call it
'exmu', which sounds hip.
>
> Any other ideas?



hmmm ... i think those are some good suggestions!

"domu" and "demu" are both shorter and nicer-sounding
than "cawapu" and "midipu".  they're also a little
too similar, which leads me to preferring "exmu" for
"demu".

i think i might go with this, especially since the
idea of using the Greek prefixes makes it a nice
logical system, which i always like.

so if Quicktime *does* use 9-bit resolution, then
i guess we have "nomu" too?


i'm thinking actually that the longer names which
use a fuller Greek prefix are better:

7-bit = eptamu
12-bit = dodecamu
14-bit = dekatessemu


think about it ... no-one's using 14-bit, so who
cares if you can't spell "dekatessemu"?

ah, maybe i like the shorter versions after all ...


feedback on this from a few others would be most appreciated.




-monz


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Message: 6982

Date: Thu, 3 Jul 2003 10:15:31

Subject: Quicktime pitch resolution (was:: Names for MIDI units)

From: monz

hi paul and Aaron,


i'm consolidating both of your posts about Quicktime,
and responding by quoting the links to the old tuning list
posts about it.


> From: "wallyesterpaulrus" <wallyesterpaulrus@xxxxx.xxx>
> To: <tuning-math@xxxxxxxxxxx.xxx>
> Sent: Wednesday, July 02, 2003 2:00 PM
> Subject: [tuning-math] Re: Names for MIDI units
>
>
> was the quicktime resolution verified to be 3072
> (=9-bit?) parts per octave? if so, it's a *far*
> better choice for emulating 5-limit ji harmonies --
> in fact, it lies on the "atomic" 5-limit uber-temperament
> line (and all the ets that do are multiples of 12, 
> following from kirnberger's construction of 12-tone
> equal temperament by subtracting the schisma from
> the just fifth to approximate the ET fifth, the error
> being 1/12 of the "atomic comma"), as you can see on 
> the deepest zoom level of the graph at:
> 
> Definitions of tuning terms: equal temperament, (c) 1998 by Joe Monzo *
> 
> its worst error is about 0.016 cents in the 5-limit.



> From: <pitchcolor@xxx.xxx>
> To: <tuning-math@xxxxxxxxxxx.xxx>
> Sent: Thursday, July 03, 2003 7:07 AM
> Subject: [tuning-math] Re: Names for MIDI units
>
>
> > [me, monz]
> > so if Quicktime *does* use 9-bit resolution, then
> > i guess we have "nomu" too?
> 
> I searched archives on this and didn't find anything.
> I assume it refers to apple's quicktime documentation.
> Does anyone have proof that quicktime uses 9 bits
> for pitch bend?
>
> Aaron


here is the whole history of our previous discussion
regarding Quicktime's pitch resolution:

Yahoo groups: /tuning/message/40904 *
Yahoo groups: /tuning/message/40966 *
Yahoo groups: /tuning/message/41283 *
Yahoo groups: /tuning/message/41287 *
Yahoo groups: /tuning/message/41288 *
Yahoo groups: /tuning/message/41292 *


be sure to read all of them, and in the correct order,
because Robert Walker contradicted himself several
times as he kept performing his experiments.


in fact, after reading them all again myself, i'm
still confused as to what the pitch resolution of
Quicktime actually is.  it's either 256 (=2^8) units
per semitone (= 3072edo) or 512 (= 2^9) units per
semitone (= 6144edo).

the confusion arises because of Quicktime's use
of signed integers, so one bit represents the sign.




-monz


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Message: 6986

Date: Thu, 3 Jul 2003 21:46:50

Subject: Re: Names for MIDI units

From: monz

----- Original Message ----- 
From: "Gene Ward Smith" <gwsmith@xxxxx.xxx>
To: <tuning-math@xxxxxxxxxxx.xxx>
Sent: Thursday, July 03, 2003 7:04 PM
Subject: [tuning-math] Re: Names for MIDI units


> --- In tuning-math@xxxxxxxxxxx.xxxx pitchcolor@a... wrote:
> 
> > I think 'dekatesse' is standard:
> 
> I don't think modern Greek should be the standard--the usual 
> proceedure is to steal from a dead language--Greek, Latin, or even 
> old Norse.



'dekatesse" is ancient Greek.  the modern version
has "th" instead of "d" at the beginning.

i think perhaps the most correct Greek name
for the 14-bit "midipu" is "dekatesseramu",
which is getting rather long.


-monz


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Message: 6989

Date: Fri, 4 Jul 2003 08:46:25

Subject: Re: Names for MIDI units

From: monz

----- Original Message ----- 
From: "Gene Ward Smith" <gwsmith@xxxxx.xxx>
To: <tuning-math@xxxxxxxxxxx.xxx>
Sent: Friday, July 04, 2003 3:01 AM
Subject: [tuning-math] Re: Names for MIDI units


> --- In tuning-math@xxxxxxxxxxx.xxxx "monz" <monz@a...> wrote:
> 
> > i think perhaps the most correct Greek name
> > for the 14-bit "midipu" is "dekatesseramu",
> > which is getting rather long.
> 
> Could you live with "dekatessamu"?


umm, that was *my* original suggestion!

i like the idea of using these Greek prefixes.
and "mu" at the end sounds better than "pu".


-monz


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Message: 6990

Date: Fri, 04 Jul 2003 11:34:19

Subject: Re: Greekish names for tuning units.

From: John Chalmers

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


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Message: 6992

Date: Fri, 4 Jul 2003 17:12:37

Subject: Re: Greekish names for tuning units.

From: monz

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@xxxxx.xxx>
> To: <tuning-math@xxxxxxxxxxx.xxx>
> Sent: Friday, July 04, 2003 2:31 PM
> Subject: [tuning-math] Re: Greekish names for tuning units.
>
>
> --- In tuning-math@xxxxxxxxxxx.xxxx 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


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