Tuning-Math Archive Section 12: 11500

Message: 11500 - Contents - Hide Contents Date: Sun, 18 Jul 2004 04:23:04 Subject: Re: names and definitions: schismic From: Dave Keenan --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote:

> This is the ***21st century***. I would *not* assume people in the > future are going to ignore complex tunings.

I would, because I don't think their hearing will be significantly better. The limitation is no longer the instrument, but the ear. If you've ever heard a glissando in 72-ET, you'll know that without first-order-discontinuities it would be barely distinguishable from a continuous slide. At some point a temperament's errors are so low and its complexity so high, that you might as well use strict rational intervals (or the best approximation of them you can get on your instrument/computer). If that's the case, why would anyone care about the temperament?

Message: 11501 - Contents - Hide Contents Date: Sun, 18 Jul 2004 17:30:56 Subject: Re: names and definitions: schismic From: monz --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote:

> --- In tuning-math@xxxxxxxxxxx.xxxx "monz" <monz@a...> wrote: >

>> please give me enough data (or point to it if it's already >> posted somewhere) to *make* that 7-limit lattice for my >> webpage. >

> The TM basis is {4375/4374, 32805/32768}, and the > Hahn reduced basis is {4375/4374, 65625/65536}; these are > the two most interesting block commas to use; of course > {32805/32768, 65625/65536} is another possibility, and there > are other commas out there, such as 95703125/95551488.

i totally missed out on "Hahn reduced" ... can you please explain that in a way similar to what's on my "TM-reduced" page? i've made a graphic of the TM-basis version, here: http://tonalsoft.com/enc/tm-reduced-lattice-53-118-schismic.gif - Type Ok * [with cont.] (Wayb.) but without being able to rotate (which i can do here with my software), the static graphic of this tuning is too complex to really convey much information. so i didn't want to put it onto the webpage yet. hope that helps a little, Herman! -monz ________________________________________________________________________ ________________________________________________________________________ ------------------------------------------------------------------------ Yahoo! Groups Links <*> To visit your group on the web, go to: Yahoo groups: /tuning-math/ * [with cont.] <*> To unsubscribe from this group, send an email to: tuning-math-unsubscribe@xxxxxxxxxxx.xxx <*> Your use of Yahoo! Groups is subject to: Yahoo! Terms of Service * [with cont.] (Wayb.)

Message: 11502 - Contents - Hide Contents Date: Sun, 18 Jul 2004 04:44:59 Subject: Re: names and definitions: schismic From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx Herman Miller <hmiller@I...> wrote:

> Gene Ward Smith wrote: >

>> and it's not a good idea to >>

>>> change established names in any case. >> >>

>> We've *been* changing established names; I don't think 7-limit >> schismic was ever as established as some Paul wants to deep-six. >

> I was referring to "meantone".

Who changed that?

Message: 11503 - Contents - Hide Contents Date: Sun, 18 Jul 2004 05:01:55 Subject: Re: names and definitions: schismic From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan" <d.keenan@b...> wrote:

> At some point a temperament's errors are so low and its complexity > so high, that you might as well use strict rational intervals (or > the best approximation of them you can get on your > instrument/computer). If that's the case, why would anyone care > about the temperament?

Try and and you'll see that the Tenney height of your rational intervals quickly grows. You can, to be sure, use rational intervals and rejoice in the fact that if you land 2401/2400 away from where you started, no one is likely to notice. But why do that? It's harder! My 171-et piece Kotekant constantly made use of the "too complex" commas 4375/4374 and 32805/32768, so I'm really not impressed with the idea they are too complex to be made use of. There is something to be said for the theory that if you are going to use ennealimmal or this version of schismic or various other 171-et supported 7-limit temperaments such as sesquiquartififths you may as well simply park yourself in 171-equal, but even if you maintain that, understanding an equal temperament is helped by understanding the linear temperaments it supports. The notion that the only good version of 7-limit schismic is 41&53 is really all wet.

Message: 11504 - Contents - Hide Contents Date: Sun, 18 Jul 2004 05:05:49 Subject: Re: names and definitions: schismic From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx Herman Miller <hmiller@I...> wrote:

> Looking over this reply, I'm wondering if my meaning wasn't clear > enough. I'm not referring to Paul's substitution of new names for the 7- > and 5-limit versions of temperaments; those substitutions don't change > the meanings of the existing names. If for consistency we wanted to give > [<1, 2, 4, 2|, <0, -1, -4, 2|] the same name as [<1, 2, 4|, <0, -1, > -4|], it would be confusing to use the name "meantone", since that name > is already associated with [<1, 2, 4, 7|, <0, -1, -4, -10|]. So we'd > have to come up with a new name, like "syntonic".

Out there in the wide, wide world people may be thinking the right way to get a meantone 7 is as an approximate 16/9, so I don't know how established this really is.

> But of course there could be occasional cases where there's a good > reason to change a higher-limit name. I've argued for #56 [<1, 1, 2, 4|, > <0, 2, 1, -4|] to get the name "dicot" in place of #23 [<1, 1, 2, 1|, > <0, 2, 1, 6|], which would be "pseudo-dicot".

You have? When was that? It sounds like there are

> good arguments for changing "schismic" as well. I'm just not convinced > that 118&171 is the best candidate for the name, and I'm dubious about > applying the same criteria to other temperaments.

It's the only temperament with a decent badness figure and an optimal tuning close to 5-limit schismic; that seems to give it a strong claim.

Message: 11505 - Contents - Hide Contents Date: Sun, 18 Jul 2004 05:12:27 Subject: Atomic notation again From: Gene Ward Smith Here is what we find if we want to take it up to the 23-limit: 3: [19, 1] 1:32805/32768, 5632/5625 5: [28, -7] 7: 126/125 7: [34, -16] 16: 56/55 11: [42, -25] 25: 36/35 13: [43, 72] 72: 6561/6050 17: [47, 105] 105: 260/231 19: [50, 50] 50: 128/121 ~ (36/35)^2 23: [52, 117] 117: 416/363 Atomic is a strong temperament up to the 11-limit, which is therefore where this scheme works best. Here is a list of what we would need to notate all the 11-limit consonances. Dave tells us that 5632/5625, 441/440, 126/125, 99/98, 56/55, 50/49 and 36/35 already have symbols; the rest we could get, if in no other way, by combining these. 1 5632/5625 2 441/440 7 126/125 8 15625/15488 9 99/98 16 56/55 17 28672/28125 18 50/49 25 36/35 26 22528/21875 27 567/550

Message: 11506 - Contents - Hide Contents Date: Sun, 18 Jul 2004 05:20:58 Subject: Re: Extreme precison (Olympian) Sagittal From: Gene Ward Smith --- In tuning-math@xxxxxxxxxxx.xxxx "Dave Keenan" <d.keenan@b...> wrote:

> If you're having to squint to figure out the flag-composition of the > symbols in Table 1, then maybe you need to set the zoom on your PDF > reader to exactly 100%, or maybe 200%. But just in case, here they > are in the same order as in Table 1, in ASCII longhand: > '| )| |( ~| )|( ~|( |~ ./| )|~ /| |) |\ (| (| > ( //| /|) /|\ (|) (|\

If there are 9 flags, can't you just give a vector of nine integers or something of that sort? Or if that is too much, what are the intervals which go to each set of flags in your ascii notation? This stuff should already be in the possession of you and George.

> So you could set up 9 columns, one for each flag, with a row for > each symbol.

It would be easy enough if I had a table, in ascii, posted to this list, which gave a rational number followed by a 9-vector on each line.

Message: 11507 - Contents - Hide Contents Date: Sun, 18 Jul 2004 05:34:44 Subject: Re: Atomic notation again From: Dave Keenan --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote:

> Here is what we find if we want to take it up to the 23-limit: > > 3: [19, 1] 1:32805/32768, 5632/5625 > 5: [28, -7] 7: 126/125 > 7: [34, -16] 16: 56/55 > 11: [42, -25] 25: 36/35 > 13: [43, 72] 72: 6561/6050 > 17: [47, 105] 105: 260/231 > 19: [50, 50] 50: 128/121 ~ (36/35)^2 > 23: [52, 117] 117: 416/363 Gene,

Puhleeease put some column headings on these lists. Is your time really so much more valuable than that of your readers? I haven't a clue what you're on about here.

Message: 11508 - Contents - Hide Contents Date: Sun, 18 Jul 2004 06:11:00 Subject: Re: Extreme precison (Olympian) Sagittal From: Dave Keenan --- In tuning-math@xxxxxxxxxxx.xxxx "Gene Ward Smith" <gwsmith@s...> wrote:

> It would be easy enough if I had a table, in ascii, posted to this > list, which gave a rational number followed by a 9-vector on each line.

The more of our work you duplicate, the more chance of finding our mistakes. But here it is, tab-delimited, with column headings. num den '| )| (| /| ~| |~ |\ |) |( symbol comma name 32768 32805 1 0 0 0 0 0 0 0 0 '| 5-schisma 512 513 0 1 0 0 0 0 0 0 0 )| 19-schisma 5103 5120 0 0 0 0 0 0 0 0 1 |( 5:7-kleisma 2176 2187 0 0 0 0 1 0 0 0 0 ~| 17-kleisma 891 896 0 1 0 0 0 0 0 0 1 )|( 7:11-kleisma 4096 4131 0 0 0 0 1 0 0 0 1 ~|( 17-comma 729 736 0 0 0 0 0 1 0 0 0 |~ 23-comma 2025 2048 -1 0 0 1 0 0 0 0 0 ./| 25-comma 19456 19683 0 1 0 0 0 1 0 0 0 )|~ 19-comma 80 81 0 0 0 1 0 0 0 0 0 /| 5-comma 524288 531441 1 0 0 1 0 0 0 0 0 '/| 3-comma 40960 41553 0 1 0 1 0 0 0 0 0 )/| 5:19-comma 63 64 0 0 0 0 0 0 0 1 0 |) 7-comma 54 55 0 0 0 0 0 0 1 0 0 |\ 55-comma 45056 45927 0 0 1 0 0 0 0 0 0 (| 7:11-comma ? ? 0 0 0 1 0 1 0 0 0 /|~ ? 44 45 0 0 1 0 0 0 0 0 1 (|( 5:11-S-diesis 6400 6561 0 0 0 2 0 0 0 0 0 //| 25-S-diesis 35 36 0 0 0 1 0 0 0 1 0 /|) 35-M-diesis 32 33 0 0 0 1 0 0 1 0 0 /|\ 11-M-diesis ________________________________________________________________________ ________________________________________________________________________ ------------------------------------------------------------------------ Yahoo! Groups Links <*> To visit your group on the web, go to: Yahoo groups: /tuning-math/ * [with cont.] <*> To unsubscribe from this group, send an email to: tuning-math-unsubscribe@xxxxxxxxxxx.xxx <*> Your use of Yahoo! Groups is subject to: Yahoo! Terms of Service * [with cont.] (Wayb.)