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Message: 6950 - Contents - Hide Contents Date: Sun, 29 Jun 2003 21:55:11 Subject: Re: The Cawapu Comma From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx pitchcolor@a... wrote:> Gene Ward Smith wrote: > > <<The de facto pitch bend range is +-200 cents, leading to a de facto > pitch resolution of a cawapu, which is 1/4096 of a cent (as opposed to > the midipu, which does not seem important in practice but which would > give you 1/4 cawapu resolution in case you thought you needed it.) >>> > > Be advised that Joe Monzo's definitions of 'midipu' and 'cawapu'are incorrect. I have already informed him of this. Midipu results in 12 x 2^13 = 98,304 units per octave, not 196,608. Cawapu results in 12 x 2^11 = 24576, not 49152. The de facto standard, as I mentioned, is 49152 pitches per octave, so we need a word for it. I presume Cakewalk follows this standard; do you have evidence it does not?
Message: 6951 - Contents - Hide Contents Date: Sun, 29 Jun 2003 17:03:48 Subject: Re: The Cawapu Comma From: monz hi Aaron and Gene,> From: "Gene Ward Smith" <gwsmith@xxxxx.xxx> > To: <tuning-math@xxxxxxxxxxx.xxx> > Sent: Sunday, June 29, 2003 2:55 PM > Subject: [tuning-math] Re: The Cawapu Comma > > > --- In tuning-math@xxxxxxxxxxx.xxxx pitchcolor@a... wrote:>> Gene Ward Smith wrote: >>>>> The de facto pitch bend range is +-200 cents, leading >>> to a de facto pitch resolution of a cawapu, which is >>> 1/4096 of a cent (as opposed to the midipu, which does >>> not seem important in practice but which would >>> give you 1/4 cawapu resolution in case you thought >>> you needed it.) >> >>>> Be advised that Joe Monzo's definitions of 'midipu' >> and 'cawapu' are incorrect. I have already informed >> him of this. Midipu results in 12 x 2^13 = 98,304 units >> per octave, not 196,608. Cawapu results in 12 x 2^11 = >> 24576, not 49152. >> The de facto standard, as I mentioned, is 49152 pitches > per octave, so we need a word for it. I presume Cakewalk > follows this standard; do you have evidence it does not?lately there's been quite a bit of discussion of this subject on both this list and the main tuning list. i've already mentioned that Aaron informed me of the error and that i haven't yet fixed my webpages or definitions. the main reason for the delay is that i simply haven't had any spare time to check up on it. also, when i first created my "MIDI tuning spec" page i was informed of something else there that was not correct, having to do with two different MIDI tuning standards, one for sys-ex and the other for pitch-bend commands. but i didn't fully understand that comment and just ignored it, hoping to get back to it later. can some of you do some digging and establish once and for all what it is that should be correctly stated in my webpages? i'd appreciate that a lot. thanks. -monz
Message: 6952 - Contents - Hide Contents Date: Sun, 29 Jun 2003 19:37:57 Subject: Re: The Cawapu Comma From: monz hi Gene,> From: "Gene Ward Smith" <gwsmith@xxxxx.xxx> > To: <tuning-math@xxxxxxxxxxx.xxx> > Sent: Sunday, June 29, 2003 7:22 PM > Subject: [tuning-math] Re: The Cawapu Comma > > > --- In tuning-math@xxxxxxxxxxx.xxxx "monz" <monz@a...> wrote: >>> can some of you do some digging and establish once and >> for all what it is that should be correctly stated in >> my webpages? i'd appreciate that a lot. thanks. >> I imagine Manuel knows the answer without digging. My concern is > really not with the official standard, but the default standard.understood ... but as the guy to whose work everyone refers in trying to understand the terminology, i'd better make it *all* correct! (in fact, i think it was Manuel who wrote to me about the "two different specs" to which i referred.) -monz
Message: 6955 - Contents - Hide Contents Date: Mon, 30 Jun 2003 18:38:17 Subject: Re: The Cawapu Comma From: wallyesterpaulrus --- In tuning-math@xxxxxxxxxxx.xxxx "Manuel Op de Coul" <manuel.op.de.coul@e...> wrote:> Also the Turkish cent is 10 times too big, should be 10600 per > octave. huh? 53*20=1060.
Message: 6956 - Contents - Hide Contents Date: Mon, 30 Jun 2003 02:22:54 Subject: Re: The Cawapu Comma From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "monz" <monz@a...> wrote:> can some of you do some digging and establish once and > for all what it is that should be correctly stated in > my webpages? i'd appreciate that a lot. thanks.I imagine Manuel knows the answer without digging. My concern is really not with the official standard, but the default standard.
Message: 6957 - Contents - Hide Contents Date: Mon, 30 Jun 2003 22:05:33 Subject: Re: The Cawapu Comma From: Manuel Op de Coul Paul wrote:>huh? 53*20=1060.You corrected me once before on this and then I thought I was wrong, but not. It's 53*200=10600. I've seen it in Karadeniz. Manuel
Message: 6958 - Contents - Hide Contents Date: Mon, 30 Jun 2003 22:11:25 Subject: Re: Cawapu From: Manuel Op de Coul>'cawapu' = 6 x 2^12 = 24576No it's 6 x 8192 = 6 x 2^13. You have 2 midi "bytes" of 7 bits, that's 2^14. In two's complement that's half for positive and half for negative values. The standard pitch bend range is plus or minus a whole tone. Manuel
Message: 6959 - Contents - Hide Contents Date: Mon, 30 Jun 2003 02:58:39 Subject: Re: The Cawapu Comma From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "monz" <monz@a...> wrote:> understood ... but as the guy to whose work everyone > refers in trying to understand the terminology, i'd > better make it *all* correct!I've just been looking at a web page Manuel gave on MMM: MIDI Tuning Specification - RP012 * [with cont.] (Wayb.) According to this, the "de facto standard" I've been talking about is *not* the same as MTS. MTS expresses a pitch by means of a three digit number in base 128, leaving off the last number, which means a number from 0 to 2097150. This number gives the pitch in terms of the 196608-et, where 0 is a pitch of 8.1758 Hz, five octaves below middle C. Middle C itself of course is 5*196608 = 983040, or 3C 00 00 when written in base 128 with hex digits as the computers prefer. A midipu therefore should be 2^(1/196608), which I think is what you already have.
Message: 6960 - Contents - Hide Contents Date: Mon, 30 Jun 2003 21:17:39 Subject: Re: Cawapu From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Manuel Op de Coul" <manuel.op.de.coul@e...> wrote:> The standard pitch bend range is plus or minus a whole tone.And if you use a different range (for instance, with Audio Compositor) you would not only need to reset the default, if you are rendering a midi you'd need to change the midi. I wouldn't bother, personally.
Message: 6961 - Contents - Hide Contents Date: Mon, 30 Jun 2003 11:57:38 Subject: Re: The Cawapu Comma From: Manuel Op de Coul I think Joe's numbers are correct, although the standard pitch bend range isn't something special to Cakewalk. The cawapu value range is wrong though, should be -8192 .. 8191. Also the Turkish cent is 10 times too big, should be 10600 per octave. Manuel
Message: 6962 - Contents - Hide Contents Date: Mon, 30 Jun 2003 21:20:35 Subject: Re: The Cawapu Comma From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx pitchcolor@a... wrote: I know for a fact that what I am saying is correct, because I use pitchbend in the microtonal instruments I build: What happens if you play a standard midi file which uses pitch bends on the the instruments you build?
Message: 6963 - Contents - Hide Contents Date: Mon, 30 Jun 2003 10:21:45 Subject: Re: The Cawapu Comma From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Manuel Op de Coul" <manuel.op.de.coul@e...> wrote:> I think Joe's numbers are correct, although the standard pitch > bend range isn't something special to Cakewalk.I've noticed. But it seems MTS is another kettle of fish, and I think it might be nice to have an entry explaining it. You could start with the post I just made which explains it in terms (equal temperaments and base 128 numbers) which make more sense to me, at least, than what the midi spec has. Add in the crap in the beginning (including that what looks like a bunch of numbers near the start when you run it through mf2t is actually ascii characters which say something or other, though it doesn't much matter what.) Once you know what the seeming gibberish at the beginning is all about and where the actual pitch information starts, it's not too bad.
Message: 6966 - Contents - Hide Contents Date: Mon, 30 Jun 2003 21:37:16 Subject: Re: The Cawapu Comma From: monz hi Gene and Aaron,> From: "Gene Ward Smith" <gwsmith@xxxxx.xxx> > To: <tuning-math@xxxxxxxxxxx.xxx> > Sent: Monday, June 30, 2003 6:44 PM > Subject: [tuning-math] Re: The Cawapu Comma > > > --- In tuning-math@xxxxxxxxxxx.xxxx pitchcolor@a... wrote: >>>>> What happens if you play a standard midi file which >>> uses pitch bends on the the instruments you build? >>> >>>> I'm only building controllers, not tone modules. But >> your question suggests that I'm using a nonstandard >> approach to pitchbend, which is not the case. >> There's a lot of evidence in what you say that you are. I suggest > using a fairly extreme test case--something with pitch bends giving > more or less than 12 notes to the octave--and seeing if the result > makes any sense. >>> My controllers work with all standard MIDI gear having pitch bend >> capabilities. >> I'm talking about playing a midi file. Do you do that?no, Gene, Aaron's instruments are MIDI *controllers*. they *create* MIDI-files, not play them. -monz
Message: 6967 - Contents - Hide Contents Date: Mon, 30 Jun 2003 21:42:28 Subject: Re: The Cawapu Comma From: monz hi Manuel,> From: "Manuel Op de Coul" <manuel.op.de.coul@xxxxxxxxxxx.xxx> > To: <tuning-math@xxxxxxxxxxx.xxx> > Sent: Monday, June 30, 2003 2:57 AM > Subject: Re: [tuning-math] Re: The Cawapu Comma > > > I think Joe's numbers are correct, although the > standard pitch bend range isn't something special > to Cakewalk.thanks for pointing that out. i said as much when i originally uploaded the Tuning Dictionary "cawapu" entry, and solicited suggestions for other names, but no-one responded. i really am not fond of either "cawapu" or "midipu" as tuning terms, but i felt that they were tuning units of measurement which had enough importance to merit names. so, suggestions for other names are still welcome. use of my two terms hasn't become widespread enough to be a concern.> The cawapu value range is wrong though, should be > -8192 .. 8191. > > Also the Turkish cent is 10 times too big, should > be 10600 per octave.hmmm ... can you give the full reference to Karadeniz? so then is my "Türk cent" Dictionary webpage completely wrong? -monz
Message: 6968 - Contents - Hide Contents Date: Tue, 1 Jul 2003 18:04:53 Subject: Re: The Cawapu Comma From: Manuel Op de Coul Joe wrote:>hmmm ... can you give the full reference to Karadeniz?Karadeniz, M. Ekrem. _Türk Mûsikîsinin Nazariye ve Esaslari_ (Theory and principles of Turkish music). Türkiye IS Bankasi Kültür Yayinlari, Publ. no. 237/238, Ankara, 1965, 1983.>so then is my "Türk cent" Dictionary webpage >completely wrong?"Türk sent". Not if you multiply/divide the values by 10. Karadeniz invented it, but it's unclear why he wanted such a fine division, maybe only to surpass Ellis's cent. Manuel
Message: 6969 - Contents - Hide Contents Date: Tue, 1 Jul 2003 10:34:26 Subject: Re: The Cawapu Comma From: monz hi Manuel,> From: "Manuel Op de Coul" <manuel.op.de.coul@xxxxxxxxxxx.xxx> > To: <tuning-math@xxxxxxxxxxx.xxx> > Sent: Tuesday, July 01, 2003 9:04 AM > Subject: Re: [tuning-math] Re: The Cawapu Comma > > Joe wrote:>> hmmm ... can you give the full reference to Karadeniz? >> Karadeniz, M. Ekrem. > _Türk Mûsikîsinin Nazariye ve Esaslari_ > (Theory and principles of Turkish music). > Türkiye IS Bankasi Kültür Yayinlari, > Publ. no. 237/238, Ankara, 1965, 1983. >>> so then is my "Türk cent" Dictionary webpage >> completely wrong? >> "Türk sent". Not if you multiply/divide the values by 10. > Karadeniz invented it, but it's unclear why he wanted such a > fine division, maybe only to surpass Ellis's cent.OK, thanks for that. 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? -monz
Message: 6970 - Contents - Hide Contents Date: Tue, 1 Jul 2003 22:07:30 Subject: Re: The Cawapu Comma From: monz hi Aaron,> From: <pitchcolor@xxx.xxx> > To: <tuning-math@xxxxxxxxxxx.xxx> > Sent: Monday, June 30, 2003 9:34 AM > Subject: [tuning-math] Re: The Cawapu Comma > > > The figures in each case are: > > 'midipu' = 12 x 2^13 = 98304 > > 'cawapu' = 12 x 2^11 = 24576 > > I'm not sure why there is any confusion about this. > The values above are correct. I do not use cakewalk, > but the same logic holds for all pitch bend messages. > The 'middle' value is a midi note number with no bend. > The bend range is thus a semitone below for half the > values and a halfstep above for the other half. For > 7 bit pitch bend we have 0-63 below a midi note, > 64 as the note with no bend, and 65-127 for the > halfstep above. That is a range of a whole step, > not a halfstep. This is the smallest pitch bend range > available. In 14 bit precision, each of the 7 bit > values has 128 values of its own, where 0-127 is a > range from lowest to highest within the 7 bit step. > Any way you look at it, we are talking about a wholestep > range which is a halfstep above and below a given midi > note. So when you try to make an equal division of the > octave out of it, you have to throw out half of the > values. If this still doesn't make sense, I will write > up a better explanation. I know for a fact that what > I am saying is correct, because I use pitchbend in the > microtonal instruments I build: > > MUSIC * [with cont.] (Wayb.)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. -monz
Message: 6971 - Contents - Hide Contents Date: Tue, 01 Jul 2003 01:44:41 Subject: Re: The Cawapu Comma From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx pitchcolor@a... wrote:> << > What happens if you play a standard midi file which uses pitch bends > on the the instruments you build? >>> > > I'm only building controllers, not tone modules. But your questionsuggests that I'm using a nonstandard approach to pitchbend, which is not the case. There's a lot of evidence in what you say that you are. I suggest using a fairly extreme test case--something with pitch bends giving more or less than 12 notes to the octave--and seeing if the result makes any sense.>My controllers work with all standard MIDI gear having pitch bend >capabilities.I'm talking about playing a midi file. Do you do that?
Message: 6972 - Contents - Hide Contents Date: Wed, 02 Jul 2003 16:32:07 Subject: Re: Modulatory topology in 22-TET From: Kalle Aho 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 offifth (which in> ET 22 contains 13 steps) have - exactly like in case of thediatonic 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 theinner 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. Acoincidence 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 StraubI 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
Message: 6974 - Contents - Hide Contents Date: Wed, 02 Jul 2003 00:46:19 Subject: Micro micro madness From: Gene Ward Smith 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.) Turing my new code loose on this, I found that the 7-limit TM basis for it (in monzo format) is: [[9, -28, 37, -18], [-92, -17, 21, 25], [110, -71, -11, 10]] If you take the first two commas, you get a temperament with an even more absurdly low badness figure than ennealimmal: Wedgie: [1303, 1006, 41, -1431, -3593, -2729] Mapping: [[1, -469, -361, -12], [0, 1303, 1006, 41]] I wish I knew a potential use for this fact, but I can't think of one. Some time back I found that 3125 is an excellent 7-limit et; somewhere in the universe there is a race of beings who use base 5 and who think the obvious way to measure intervals is dividing the octave into 3125 parts. The TM basis for 3125 is this: [[-1, 4, 11, -11], [3, -13, 10, -2], [-48, 0, 11, 8]] The second comma on the above list is the cawapu comma.
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