Tuning-Math Archive Section 7: 6975

Message: 6975 - Contents - Hide Contents 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

Message: 6976 - Contents - Hide Contents Date: Wed, 02 Jul 2003 20:20:40 Subject: Re: Modulatory topology in 22-TET From: wallyesterpaulrus --- In tuning-math@xxxxxxxxxxx.xxxx "Kalle Aho" <kalleaho@m...> wrote:

> Hi! > > The following is quoted from an old message #4498 that was posted > over a year ago to tuning-math by Hans Straub. Please read the > original message before proceeding. > > So Hans Straub says: >

>> Now, how about ET22? All the concepts (they are, after all, quite > simple, not

>> to say trivial) can be applied directly. I did it for Paul Erlich's > pentachordal

>> decatonic scale - with a little surprising result! >> >> Two transposes of the decatonic major scale at the distance of

> fifth (which in

>> ET 22 contains 13 steps) have - exactly like in case of the

> diatonic scale in

>> 12-TET - 4 chords in common. However, this is not the maximum! The >> maximum of 6 common chords is reached by distances of 2 (half tone) > OR

>> 11 steps (tritone). Hence the diagram for the modulatory topology > of the

>> pentachordal decatonic scale in ET22 is not a circle of fifths, but > a 2-

>> dimensional structure, best visualized as two concentric circles of > 11 points

>> each (the half tone steps) with radial connections between the

> inner to the

>> outer (the tritone steps). >> An interesting coincidence is that 2 and 11 happen to be the prime > numbers

>> that compose 22, and the modulatory topology as above is also a >> visualization of the decomposition of Z22 into Z2xZ11. A

> coincidence it is -

>> you can create whatever topology you like if you choose the basic > chords >> appropriately. >> >> Any one of the tuning punks ever thought about this or even used it? >> >> Hans Straub >

> I don't understand this because I get 2 common chords with distance > of 13 steps, 3 with distance of 2 steps and 4 with distance of 11 > steps! > > Kalle

kalle, maybe you're thinking tetrads while hans was thinking of some other kind of chord? thanks for pointing this out!

Message: 6977 - Contents - Hide Contents 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

Message: 6979 - Contents - Hide Contents Date: Wed, 02 Jul 2003 21:00:36 Subject: Re: Names for MIDI units From: wallyesterpaulrus --- In tuning-math@xxxxxxxxxxx.xxxx pitchcolor@a... wrote:

> 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? > > Aaron

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... * [with cont.] (Wayb.) its worst error is about 0.016 cents in the 5-limit.

Message: 6980 - Contents - Hide Contents Date: Wed, 02 Jul 2003 21:29:21 Subject: Re: Micro micro madness From: wallyesterpaulrus --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote:

> I wrote some probably useless Maple code which handles nano > temperaments, and here are some presumably useless results. > > Paul discovered the curious 7-limit nano-et 103169 (unless someone > else wants to claim priority, I suppose.) marc jones: Definitions of tuning terms: list of EDOs used... * [with cont.] (Wayb.)

Message: 6981 - Contents - Hide Contents 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

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

'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

Message: 6982 - Contents - Hide Contents 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... * [with cont.] (Wayb.) > > 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 * [with cont.] Yahoo groups: /tuning/message/40966 * [with cont.] Yahoo groups: /tuning/message/41283 * [with cont.] Yahoo groups: /tuning/message/41287 * [with cont.] Yahoo groups: /tuning/message/41288 * [with cont.] Yahoo groups: /tuning/message/41292 * [with cont.] 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

Message: 6983 - Contents - Hide Contents Date: Thu, 03 Jul 2003 21:53:14 Subject: Re: Modulatory topology in 22-TET From: Kalle Aho

> kalle, maybe you're thinking tetrads while hans was thinking of some > other kind of chord? thanks for pointing this out!

Hi Paul, I think you're right. It's weird that Hans didn't mention the chords he was thinking. Kalle

Message: 6984 - Contents - Hide Contents Date: Thu, 03 Jul 2003 22:43:44 Subject: Re: Names for MIDI units From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "monz" <monz@a...> wrote:

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

I like the longer names better, but would prefer heptamu over eptamu. I haven't seen the "dekatesse" prefix before; does anyone know if there is a standard Greek prefix for 14? Would "tetradecamu" maybe be better?

Message: 6986 - Contents - Hide Contents 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

Message: 6987 - Contents - Hide Contents Date: Thu, 03 Jul 2003 08:10:13 Subject: Re: The Cawapu Comma From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "monz" <monz@a...> wrote:

> 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.

In practice, pitch bends use cawapus; on the other hand, MTS uses midipus. Both terms seem useful.

Message: 6989 - Contents - Hide Contents 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

Message: 6990 - Contents - Hide Contents 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

Message: 6991 - Contents - Hide Contents Date: Fri, 04 Jul 2003 21:31:02 Subject: Re: Greekish names for tuning units. From: Gene Ward Smith --- 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.

Message: 6992 - Contents - Hide Contents 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

Message: 6993 - Contents - Hide Contents Date: Fri, 04 Jul 2003 02:04:17 Subject: Re: Names for MIDI units From: Gene Ward Smith --- 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.

Message: 6994 - Contents - Hide Contents Date: Fri, 04 Jul 2003 10:01:05 Subject: Re: Names for MIDI units From: Gene Ward Smith --- 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"?