Yahoo Tuning Groups Ultimate Backup tuning New member here with brief intro. and an idea for notation/nomenclature

Hello everyone! ^_^ First of all, I would like to keep my true name hidden....I don't want random strangers on the Internet to know it and stalk me so I use an alias (pseudonym) here.

For over a year I've been using various tunings but I don't ever recall producing an intelligent piece of music that isn't based on the omnipresent twelve tone system even though I have software, Linux MultiMedia Studio (LMMS, music composition) and ZynAddSubFX (Microtonal plug-in) that can allow for just about any sort of tuning. I'll admit I don't have particularly great level of intelligence nor a long attention span for active working but I still think I may be lacking something else that others on this forum have but I don't know what that is.

Obviously, one problem I face is the issue of notation and nomenclature; if I am going to use some pitches I need some names for them! So I came up with this idea over the past week: instead of using the letters A B C D E F G ~~ I want to make it usable in other alphabets! Knowing that the Roman alphabet has direct correspondences with the Greek, Hebrew, Arabic and Phoenician alphabets I imagined twenty-two notes within an interval of {1:2} in a chain of {2:3} and {3:4} intervals and assigned one letter of the Phoenician alphabet to each note. Here is the result, with numbers corresponding roughly to 53rd part of a {1:2} interval, Phoenician letter name and Greek letter name:
(+11) 23 Tau - Tau/Tav/Taw - Tau
(+10) 45 Sin/Shin - Sin/Shin - Sigma
(+9) 14 Re - Resh - Rho
(+8) 36 Qof - Qoph - (Qoppa)
(+7) 05 Sah/San - Sade - (San)
(+6) 27 Pe - Pe - Pi
(+5) 49 Ain - Ain - Omicron
(+4) 18 Sem/Sen - Samekh/Semkath - Xi
(+3) 40 Nun - Nun - Nu
(+2) 09 Mem/Mim - Mem/Mim - Mu
(+1) 31 Lam - Lamedh - Lambda
(00) 00 Kaf - Kaph - Kappa
(-1) 22 Yod - Yodh - Iota
(-2) 44 Tet - Teth - Theta
(-3) 13 Het - Heth - Eta
(-4) 35 Zain - Zain - Zeta
(-5) 04 Waw - Waw - (Digamma)/Upsilon
(-6) 26 He - He - E(psilon)
(-7) 48 Dal/Del - Daleth - Delta
(-8) 17 Gam - Gamel/Gimel - Gamma
(-9) 39 Bet - Beth - Beta
(-10) 08 Al - Aleph - Alpha
((NOTE: Spellings of these letters' names in Roman letters may vary because *no* Romanization is *perfect*.))

Now, let's arrange these in order of increasing frequency of vibration, starting on 'Kaf' :
00-00 Kaf
04-05 Waw-San
08-09 Al-Mim
13-14 Het-Re
17-18 Gam-Sem
22-23 Yod-Tau
26-27 He-Pe
31-31 Lam
35-36 Zain-Qof
39-40 Bet-Nun
44-45 Tet-Shin
48-49 Dal-Ain
53-53 Kaf

See how 'Kaf' and 'Lam' are isolate while the others come in pairs that differ by a small interval? Twelve iterations of {2:3, 3:4} kept in the frame of {1:2} lead to two pitches that sound very much alike yet are different; it's like two posts are set near but there is no closure. In other words, it's a *schism* , a split, a division! Is there a special name for this particular schism? I tried to think of one but I can't seem to come up with a coherent and etymologically plausible name!

I wanted this sort of thing to be adaptable to different tunings so if there aren't more than twenty-two tones to a frame of {1:2} then this idea shouldn't pose difficulties. For example, if a pentatonic scale is the basis of a system then I can use e.g. Sen@-Kaf-Lam-Mim-Nun-Sen-Kaf# for five nominals and symbols for altered pitches, which in this case @ denotes a raised pitch and # denotes a lowered pitch.

Of course, the basis of this notation only has fractions and rations with factors of {2} and {3} , what can we do about {5} ? There's another schism that is much smaller than the first schism mentioned here, it's the difference between eight iterations of {2:3, 3:4} in {1:2} and one of {4:5, 5:8}. This is represented by, e.g. Kaf-Gam which has 17 steps of 53 as shown in the above tables. 17/53{1:2} is very close to {4:5}, within one part in 850 of a {1:2} interval! Very close indeed! This schism is so small that it can practically be ignored, though of course it doesn't have to be ignored.

Sorry if this post is difficult to understand, I'm still fairly new to this sort of thing and I am well aware that I may come across as being obsessed with reading textbooks but if you have questions about anything I wrote here don't hesitate to ask! I wrote this assuming that most of the members here know what fractions and rations of frequencies are, though the way I write them may cause a little discomfort for some readers; if that is the case, please let me know!

~~ Glacia the Frosty Musician ~~

<< P.S. In case anyone is curious, the ratio of the first schism is {524288:531441} and the second schism is {32768:32805} >>

🔗genewardsmith <genewardsmith@...>

🔗glacia_frost <frostycake99@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "glacia_frost" <frostycake99@> wrote:
>
> >Twelve iterations of {2:3, 3:4} kept in the frame of {1:2} lead to two pitches that sound very much alike yet are different; it's like two posts are set near but there is no closure. In other words, it's a *schism* , a split, a division! Is there a special name for this particular schism? I tried to think of one but I can't seem to come up with a coherent and etymologically plausible name!
>
> It already has one--the Pythagorean comma.

Hmm~ Did Pythagoras describe a system like what I described here? That name seems familiar but I wasn't aware if Pythagoras had something to do with it. Is there a shorter name for this same interval?

>
> > << P.S. In case anyone is curious, the ratio of the first schism is {524288:531441} and the second schism is {32768:32805} >>
> >
>
> The second one is called the schisma.
>

So it's just another form of the word "schism"? Now that's interesting..... I thought there would be more descriptive names for these rations/intervals. The first small ratio {524288:531441} = {2^19:3^12} seems more like a real "schisma" (i.e. split) in my mind so recognition of "the schisma" for {32768:32805} is something that doesn't come naturally to me because it's so small that it's practically non-existent! Perhaps one can say "great schisma" and "tiny schisma" or something like that to differentiate between the two?

Oh, by the way, what do you think of this notation scheme? Does it seem like a good idea, if not, what can I do to make it a better idea?

~~Glacia ^_^

🔗Mike Battaglia <battaglia01@...>

On Fri, Dec 7, 2012 at 7:19 PM, glacia_frost <frostycake99@...> wrote:
>
> Hello everyone! ^_^ First of all, I would like to keep my true name
> hidden....I don't want random strangers on the Internet to know it and stalk
> me so I use an alias (pseudonym) here.

Alright, fair enough. I really hope that you're a famous person or
something, because we could use more of both of those. Anyway,
welcome!

> I'll admit I don't have
> particularly great level of intelligence nor a long attention span for
> active working but I still think I may be lacking something else that others
> on this forum have but I don't know what that is.

We've thoroughly mapped out the problem that you introduce below,
which is to be able to systematically identify tuning systems which
equate these various "schisms," which we call commas. The basic idea,
in a nutshell, is to not limit yourself to only looking at chains of
3/2 and 2/1, but to consider chains of 5/4 as well, or chains of 6/5,
or of 7/4, or 11/8, or 13/9, etc - basically we first construct this
idealized "perfect" or "just" tuning system which has all possible
intervals. Since this can be rather unwieldy, we typically limit
ourselves to intervals which have some maximum prime factor, such as 3
or 5 or 7 or 11.

After doing that, we look at all of the places where combinations of
these intervals come close to one another. For each instance where
this occurs, there is an associated "comma" (what you called a
"schism") between these combinations. It can be useful to temper
commas like these, as they not only allow us to reduce the amount of
notes we need to worry about in the tuning system and also the number
of separate "chains" of intervals involved, but also allow us to
create some very beautiful musical effects.

Of course, as you can see, it can be annoying to do the math by hand,
which is why we have computers to do all of this stuff for us
instantly.

> Is there a special name
> for this particular schism? I tried to think of one but I can't seem to come
> up with a coherent and etymologically plausible name!

This is called the Pythagorean comma.

> I wanted this sort of thing to be adaptable to different tunings so if
> there aren't more than twenty-two tones to a frame of {1:2} then this idea
> shouldn't pose difficulties. For example, if a pentatonic scale is the basis
> of a system then I can use e.g. Sen@-Kaf-Lam-Mim-Nun-Sen-Kaf# for five
> nominals and symbols for altered pitches, which in this case @ denotes a
> raised pitch and # denotes a lowered pitch.

I gotta be honest, I admire your enthusiasm here but I'm not sure my
brain can handle it :)

> Of course, the basis of this notation only has fractions and rations with
> factors of {2} and {3} , what can we do about {5} ? There's another schism
> that is much smaller than the first schism mentioned here, it's the
> difference between eight iterations of {2:3, 3:4} in {1:2} and one of {4:5,
> 5:8}. This is represented by, e.g. Kaf-Gam which has 17 steps of 53 as shown
> in the above tables. 17/53{1:2} is very close to {4:5}, within one part in
> 850 of a {1:2} interval! Very close indeed! This schism is so small that it
> can practically be ignored, though of course it doesn't have to be ignored.

Yep, this is the "schisma."

> I wrote this assuming that most of the
> members here know what fractions and rations of frequencies are, though the
> way I write them may cause a little discomfort for some readers

Challenge accepted!

-Mike

🔗glacia_frost <frostycake99@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Fri, Dec 7, 2012 at 7:19 PM, glacia_frost <frostycake99@...> wrote:
> >
> > Hello everyone! ^_^ First of all, I would like to keep my true name
> > hidden....I don't want random strangers on the Internet to know it and stalk
> > me so I use an alias (pseudonym) here.
>
> Alright, fair enough. I really hope that you're a famous person or
> something, because we could use more of both of those. Anyway,
> welcome!
>

I'm not famous in any way; I simply prefer not to publicly disclose my true name on the Internet :)

> > I'll admit I don't have
> > particularly great level of intelligence nor a long attention span for
> > active working but I still think I may be lacking something else that others
> > on this forum have but I don't know what that is.
>
> We've thoroughly mapped out the problem that you introduce below,
> which is to be able to systematically identify tuning systems which
> equate these various "schisms," which we call commas. The basic idea,
> in a nutshell, is to not limit yourself to only looking at chains of
> 3/2 and 2/1, but to consider chains of 5/4 as well, or chains of 6/5,
> or of 7/4, or 11/8, or 13/9, etc - basically we first construct this
> idealized "perfect" or "just" tuning system which has all possible
> intervals. Since this can be rather unwieldy, we typically limit
> ourselves to intervals which have some maximum prime factor, such as 3
> or 5 or 7 or 11.
>
> After doing that, we look at all of the places where combinations of
> these intervals come close to one another. For each instance where
> this occurs, there is an associated "comma" (what you called a
> "schism") between these combinations. It can be useful to temper
> commas like these, as they not only allow us to reduce the amount of
> notes we need to worry about in the tuning system and also the number
> of separate "chains" of intervals involved, but also allow us to
> create some very beautiful musical effects.
>

I am well aware of that; the "chain" of {3}n (mod {2}) merely gives a framework from which pitch classes can be derived; of course there are other possible bases for a "chain", I used {3} (mod {2}) because it is the simplest possible with {1:2} as the interval of repetition. Though if there are multiple chains of {3}|{2}, such as in the decatonic scale that I like to use, I do something like this:
Kaf-Lam-Mim-Nun-Sen
Pe -San-Qof-Rei-Sin
with "Ain" skipped as the region around 4/53{1:2} below "Kaf" is blank and "Pe" is nearly 1/2{1:2} offset "Kaf" So the scale from "Kaf" in ascending order is
Kaf-San-Mim-Rei-Sen--Pe -Lam-Qof-Nun-Sin--Kaf
with semitone (around {15:16}) steps in Kaf-San-Mim-Rei-Sen and Pe -Lam-Qof-Nun-Sin and small tone (around {9:10}) steps Sen--Pe and Sin--Kaf. Does that make sense?

I've also known of an heptatonic scale with six small steps around 3/22{1:2} and one long step around 4/22{1:2} so it has three separate "chains" of {3}|{2} e.g. Kaf-Lam-Mim, Shin-Tau and Bet-Gam so the scale runs Kaf--Mim-Gam-Tau-Lam-Bet-Sin-Kaf with Kaf:Gam:Tau:Lam an approximate 8:10:11:12 and Kaf:Mim an approximate 7:8 ; I think it's useful so long as there aren't more than a few "chains" of {3}|{2} in the scale!

> Of course, as you can see, it can be annoying to do the math by hand,
> which is why we have computers to do all of this stuff for us
> instantly.
>
> > Is there a special name
> > for this particular schism? I tried to think of one but I can't seem to come
> > up with a coherent and etymologically plausible name!
>
> This is called the Pythagorean comma.
>
> > I wanted this sort of thing to be adaptable to different tunings so if
> > there aren't more than twenty-two tones to a frame of {1:2} then this idea
> > shouldn't pose difficulties. For example, if a pentatonic scale is the basis
> > of a system then I can use e.g. Sen@-Kaf-Lam-Mim-Nun-Sen-Kaf# for five
> > nominals and symbols for altered pitches, which in this case @ denotes a
> > raised pitch and # denotes a lowered pitch.
>
> I gotta be honest, I admire your enthusiasm here but I'm not sure my
> brain can handle it :)
>

Hah~ That was just an example of the utility of this notation scheme :) There are many more I can give but it can take a while to explain many examples!

> > Of course, the basis of this notation only has fractions and rations with
> > factors of {2} and {3} , what can we do about {5} ? There's another schism
> > that is much smaller than the first schism mentioned here, it's the
> > difference between eight iterations of {2:3, 3:4} in {1:2} and one of {4:5,
> > 5:8}. This is represented by, e.g. Kaf-Gam which has 17 steps of 53 as shown
> > in the above tables. 17/53{1:2} is very close to {4:5}, within one part in
> > 850 of a {1:2} interval! Very close indeed! This schism is so small that it
> > can practically be ignored, though of course it doesn't have to be ignored.
>
> Yep, this is the "schisma."
>

Or a "tiny schisma" as I would like to call it!

> > I wrote this assuming that most of the
> > members here know what fractions and rations of frequencies are, though the
> > way I write them may cause a little discomfort for some readers
>
> Challenge accepted!
>
> -Mike
>

Are all my notation/conventions clear from the context or should I explain them more clearly?

~~Glacia ^_^~~

🔗martinsj013 <martinsj@...>

I second Mike's "welcome" and indeed pretty much everything else he said!

--- In tuning@yahoogroups.com, "glacia_frost" <frostycake99@...> wrote:
> Are all my notation/conventions clear from the context or should I explain them more clearly?

They seemed pretty clear to me although slightly different from those normally used here. e.g your 31/53{1:2} would be 31\53 and it would be called the "generator" for the system (with the "period" assumed to be 1:2).

As for the names, I like the idea in principle, but in the current case where the generator is an approximate (or indeed an exact) 2:3, why not just use common practice notation? We can equate Kaf=C, Lam=G and would find that Al=Ebb at one end of the chain and Tau=E# at the other.

> Or a "tiny schisma" as I would like to call it!

I wouldn't try to change that name which has a much longer history than anyone on this list! Similarly for Pythagorean comma which if you don't like I can only suggest to abbreviate to PC :-) You may have noticed from Mike's post that the usual name for intervals around this size is "commas"; e.g. also the syntonic comma (SC!) of 81/80. In fact the schisma is the ratio PC/SC (I think).

Now, your system has 22 notes, right? And Kaf and Lam sit in splendid isolation, each with no near neighbour, whereas all the others come in pairs? This is I believe identical (or near identical) to the Indian or "sruti" system, although descriptions of that vary. I can say more if you wish, or you may prefer to look it up yourself.

One more suggestion below; I hope it will help.

> ... decatonic scale that I like to use, I do something like this:
> Kaf-Lam-Mim-Nun-Sen
> Pe -San-Qof-Rei-Sin
> ... Kaf-San-Mim-Rei-Sen--Pe -Lam-Qof-Nun-Sin--Kaf
> with semitone (around {15:16}) steps in Kaf-San-Mim-Rei-Sen and Pe -Lam-Qof-Nun-Sin and small tone (around {9:10}) steps Sen--Pe and Sin--Kaf. Does that make sense?

Yes; actually Kaf-San is 512:729 (approx 5\53) while San-Mim is 2048:2187 (approx 4/53); the latter differs from 15:16 by the schisma (I think). Similarly Sen--Pe is 9\53 and Sin--Kaf is 8\53 - I've not worked out the actual ratios - one is approx 9:10 but the latter is approx 8:9 (and what is the ratio of these two? this question has didactic intent - I can't help it; although not a teacher myself, my parents both are).

While I'm at it, you have not mentioned that Kaf-Sen is around 4:5 - any reason for that?

You could diagram this as follows (use Courier font to view):

Pe - San - Qof - Rei - Sin
/ \ / \ / \ / \ /
Kaf - Lam - Mim - Nun - Sen

or, for anyone else who's reading :-)

F# - C# - G# - D# - A#
/ \ / \ / \ / \ /
C - G - D - A - E

where:
* the "-" interval is 2:3 (approx 31\53)
* the "/" interval is 512:729 (approx 27\53)
* the "\" interval is 243:256 (approx 4\53)

I find this kind of thing useful because parallel moves are identical in size; where such a move is not available, you know you have to use a different interval (it may or may not be close).

> I've also known of an heptatonic scale with six small steps around 3/22{1:2} and one long step around 4/22{1:2} so it has three separate "chains" of {3}|{2} e.g. Kaf-Lam-Mim, Shin-Tau and Bet-Gam so the scale runs Kaf--Mim-Gam-Tau-Lam-Bet-Sin-Kaf with Kaf:Gam:Tau:Lam an approximate 8:10:11:12 and Kaf:Mim an approximate 7:8 ; I think it's useful so long as there aren't more than a few "chains" of {3}|{2} in the scale!

I don't understand the 3\22 and 4\22 - (a) why change from expressing as x\53? (b) if you mean to count steps within the ordered 22 they are not equal in size (a confusion often seen in the context of Indian sruti) so this doesn't seem useful. In fact the steps in the scale seem to me to be 9, 8, 6, 8, 8, 6, 8.

Note, I am not saying the scale is bad; I don't know (it looks highly original to me). I like the description of an approximate 8:10:11:12 - that's exactly the kind of thing people do around here (the only question would be, how good does it sound).

Again you could use a diagram:

Bet - Gam
/ \ /
Kaf - Lam - Mim
/ \ /
Sin - Tau

or,

Bbb - Fb
/ \ /
C - G - D
/ \ /
A# - E#

where now:
* the "-" interval is "31\53"
* the "/" interval is "8\53"
* the "\" interval is "23\53"

A final question; you wrote:

> ... which in this case @ denotes a raised pitch and # denotes a lowered pitch.

By how much would the pitch be raised?

Steve M.

🔗glacia_frost <frostycake99@...>

--- In tuning@yahoogroups.com, "martinsj013" <martinsj@...> wrote:
>
> I second Mike's "welcome" and indeed pretty much everything else he said!
>
> --- In tuning@yahoogroups.com, "glacia_frost" <frostycake99@> wrote:
> > Are all my notation/conventions clear from the context or should I explain them more clearly?
>
> They seemed pretty clear to me although slightly different from those normally used here. e.g your 31/53{1:2} would be 31\53 and it would be called the "generator" for the system (with the "period" assumed to be 1:2).
>

Ahh~ I see, I specified {1:2} by 31/53 to ensure that it is that fraction of {1:2} instead of some other ratio such as {2:3} etc. so 22/31{2:3} is very close to 22/53{1:2} and therefore close to 22/84{1:3} ; see how this is more flexible that merely stating "31\53" ?

> As for the names, I like the idea in principle, but in the current case where the generator is an approximate (or indeed an exact) 2:3, why not just use common practice notation? We can equate Kaf=C, Lam=G and would find that Al=Ebb at one end of the chain and Tau=E# at the other.
>

Common practice notation is limited to seven nominals and the Roman alphabet; I wanted to use up to 22 nominals and be adaptable to other alphabets ~~ and besides, having at least twelve notes on a chain of {1:3}|{2} is desirable because the scale from a twelve-tone chain (sLsLssLsLsLs) has near-equal steps while the seven-tone scale (LLsLLsL) has a three step interval (LLL {512:729}) longer than a four step interval (sLLs {729:1024}) ; to see that the first is longer, multiply 729/512 by 729/1024 then check the result :P

> > Or a "tiny schisma" as I would like to call it!
>
> I wouldn't try to change that name which has a much longer history than anyone on this list! Similarly for Pythagorean comma which if you don't like I can only suggest to abbreviate to PC :-) You may have noticed from Mike's post that the usual name for intervals around this size is "commas"; e.g. also the syntonic comma (SC!) of 81/80. In fact the schisma is the ratio PC/SC (I think).
>

I've known about the syntonic comma being tempered to an identity in much of Western common practice music, called "Meantone" though I haven't used meantone tunings much when I try to compose new music :P

> Now, your system has 22 notes, right? And Kaf and Lam sit in splendid isolation, each with no near neighbour, whereas all the others come in pairs? This is I believe identical (or near identical) to the Indian or "sruti" system, although descriptions of that vary. I can say more if you wish, or you may prefer to look it up yourself.
>

It can have any subset of the 22 nominals; the main idea here is that two notes of a scale separate by {1:3}|{2} (includes {2:3, 3:4, 3:8} etc. but not {4:5, 4:9} etc.) have nominals on adjacent positions on a 22 letter alphabet though the converse need not hold true, which it won't if a 22 tone scale has more than one chain of {1:3}|{2} intervals. I suppose it can be used for the "sruti" system in some way though the nomenclature may sound rather strange to mainstream Hindustani and Carnatic practitioners

> One more suggestion below; I hope it will help.
>
> > ... decatonic scale that I like to use, I do something like this:
> > Kaf-Lam-Mim-Nun-Sen
> > Pe -San-Qof-Rei-Sin
> > ... Kaf-San-Mim-Rei-Sen--Pe -Lam-Qof-Nun-Sin--Kaf
> > with semitone (around {15:16}) steps in Kaf-San-Mim-Rei-Sen and Pe -Lam-Qof-Nun-Sin and small tone (around {9:10}) steps Sen--Pe and Sin--Kaf. Does that make sense?
>
> Yes; actually Kaf-San is 512:729 (approx 5\53) while San-Mim is 2048:2187 (approx 4/53); the latter differs from 15:16 by the schisma (I think). Similarly Sen--Pe is 9\53 and Sin--Kaf is 8\53 - I've not worked out the actual ratios - one is approx 9:10 but the latter is approx 8:9 (and what is the ratio of these two? this question has didactic intent - I can't help it; although not a teacher myself, my parents both are).
>

{512:729} is near 5/53{1:2} ? It's more like 27/53{1:2} !!

The way I use that particular decatonic scale, Sen--Pe and Sin--Kaf are tempered {9:10} and the eight small steps are tempered {15:16} such that two small steps are a tempered {8:9} such as Kaf--Mim and San--Rei. The idea of successive nominals e.g. Kaf-Lam, Lam-Mim etc. separate by {2:3} holds; what the other intervals are depends on in the interpretation of the scale.

> While I'm at it, you have not mentioned that Kaf-Sen is around 4:5 - any reason for that?
>

Kaf-Sen represents an interval near 18/53{1:2} ; this can be {4:5} in a meantone system but usually, as in the decatonic scale described above, does not represent {4:5}. Kaf-Gam is more often {4:5} than Kaf-Sen but that does not need to hold true either!

> You could diagram this as follows (use Courier font to view):
>
> Pe - San - Qof - Rei - Sin
> / \ / \ / \ / \ /
> Kaf - Lam - Mim - Nun - Sen
>
((Note: Try putting filler characters, e.g. full stops "..." before the first character of the line and in multiple spaces so that in normal view it looks more clear))

> or, for anyone else who's reading :-)
>
> F# - C# - G# - D# - A#
> / \ / \ / \ / \ /
> C - G - D - A - E
>
> where:
> * the "-" interval is 2:3 (approx 31\53)
> * the "/" interval is 512:729 (approx 27\53)
> * the "\" interval is 243:256 (approx 4\53)
>

I normally would use the "/" interval to represent {32:45} and {45:64} simultaneously, and "\" to represent {15:16} which infact does *not* represent {243:256} for this particular scale; rather, {243:256} is equal with {24:25} here and can be notated with extra symbols.

> I find this kind of thing useful because parallel moves are identical in size; where such a move is not available, you know you have to use a different interval (it may or may not be close).
>

That's a neat way to think about that ^_^

> > I've also known of an heptatonic scale with six small steps around 3/22{1:2} and one long step around 4/22{1:2} so it has three separate "chains" of {3}|{2} e.g. Kaf-Lam-Mim, Shin-Tau and Bet-Gam so the scale runs Kaf--Mim-Gam-Tau-Lam-Bet-Sin-Kaf with Kaf:Gam:Tau:Lam an approximate 8:10:11:12 and Kaf:Mim an approximate 7:8 ; I think it's useful so long as there aren't more than a few "chains" of {3}|{2} in the scale!
>
> I don't understand the 3\22 and 4\22 - (a) why change from expressing as x\53? (b) if you mean to count steps within the ordered 22 they are not equal in size (a confusion often seen in the context of Indian sruti) so this doesn't seem useful. In fact the steps in the scale seem to me to be 9, 8, 6, 8, 8, 6, 8.
>

The "x\53" values given in the second table of my first post are merely guidelines on what names to use for each interval; notes in the gaps of 3 or 4 steps of 53 can be named by either side of the gap. I intended this to be adaptable to various tunings and temperament systems so it can be used for any sort of scale with plenty of {1:3}|{2} and no more than 22 notes. So this heptatonic scale from Kaf has steps [4, 3, 3, 3, 3, 3, 3]/22/{1:2} ; for example, Mim-Gam has 8 steps of 53 in the original table which is near {9:10} and the small step of this scale is {9:10} tempered narrow so it fits here~~

> Note, I am not saying the scale is bad; I don't know (it looks highly original to me). I like the description of an approximate 8:10:11:12 - that's exactly the kind of thing people do around here (the only question would be, how good does it sound).
>
> Again you could use a diagram:
>
> Bet - Gam
> / \ /
> Kaf - Lam - Mim
> / \ /
> Sin - Tau
>
> or,
>
> Bbb - Fb
> / \ /
> C - G - D
> / \ /
> A# - E#
>
> where now:
> * the "-" interval is "31\53"
> * the "/" interval is "8\53"
> * the "\" interval is "23\53"
>
> A final question; you wrote:
>
> > ... which in this case @ denotes a raised pitch and # denotes a lowered pitch.
>
> By how much would the pitch be raised?
>

In the pentatonic scale with alterations Sen@-Kaf-Lam-Mim-Nun-Sen-Kaf# the alteration is a (tempered) {243:256} ; the decatonic scale described above is basically two pentatonic scales separate by 1/2{1:2} where {24:25} and {243:256} are equal. So Kaf:Rei:Lam and Mim:Pe#:Nun are minor triads (10:12:15 == 1/6:1/5:1/4) while Kaf:Rei@:Lam and Mim:Pe:Nun are major triads (4:5:6)

~~Glacia~~

🔗martinsj013 <martinsj@...>

It seems from this post that you know more than I assumed when writing my post; sorry about my assumption.

Also I realise I am not quite clear if your main topic was the nomenclature or the tuning system itself - if the former, then I am not able to say much.

--- In tuning@yahoogroups.com, "glacia_frost" <frostycake99@...> wrote:
> ... besides, having at least twelve notes on a chain of {1:3}|{2} is desirable because the scale from a twelve-tone chain (sLsLssLsLsLs) has near-equal steps while the seven-tone scale (LLsLLsL) has a three step interval (LLL {512:729}) longer than a four step interval (sLLs {729:1024}) ; to see that the first is longer, multiply 729/512 by 729/1024 then check the result :P

I think this is what folks around here call an "improper" scale (but I see I made a few mistakes in my last post; hope this is not another one); but still, my point was about the familiarity of the existing system.

> the main idea here is that two notes of a scale separate by {1:3}|{2} (includes {2:3, 3:4, 3:8} etc. but not {4:5, 4:9} etc.) have nominals on adjacent positions on a 22 letter alphabet

Ah, I think I missed the point there - but not sure it's advantageous to do this.

> {512:729} is near 5/53{1:2} ? It's more like 27/53{1:2} !!

My mistake; 512:729 is 27\53 as can be seen from the diagram; I was intending to contrasting 4\53 and 5\53 and actually got them both wrong I think!

> Kaf-Sen represents an interval near 18/53{1:2} ; this can be {4:5} in a meantone system but usually, as in the decatonic scale described above, does not represent {4:5}. Kaf-Gam is more often {4:5} than Kaf-Sen but that does not need to hold true either!

This is interesting - what do you mean by represent 4:5?

> That's a neat way to think about that ^_^

Thank goodness there was something useful in my post ...

> ... so it can be used for any sort of scale with plenty of {1:3}|{2} and no more than 22 notes. So this heptatonic scale from Kaf has steps [4, 3, 3, 3, 3, 3, 3]/22/{1:2}

I see what you mean, but I don't find the notation so apt for this. e.g there may be confusion with 22-edo.

> So Kaf:Rei:Lam and Mim:Pe#:Nun are minor triads (10:12:15 == 1/6:1/5:1/4) while Kaf:Rei@:Lam and Mim:Pe:Nun are major triads (4:5:6)

Did you mean that? If so, I am confused.

Another question - I now see that you temper the intervals - how?

Steve M.

🔗glacia_frost <frostycake99@...>

--- In tuning@yahoogroups.com, "martinsj013" <martinsj@...> wrote:
>
> It seems from this post that you know more than I assumed when writing my post; sorry about my assumption.
>
> Also I realise I am not quite clear if your main topic was the nomenclature or the tuning system itself - if the former, then I am not able to say much.
>

It's the nomenclature which is designed to be used for various tuning systems.

> --- In tuning@yahoogroups.com, "glacia_frost" <frostycake99@> wrote:
> > ... besides, having at least twelve notes on a chain of {1:3}|{2} is desirable because the scale from a twelve-tone chain (sLsLssLsLsLs) has near-equal steps while the seven-tone scale (LLsLLsL) has a three step interval (LLL {512:729}) longer than a four step interval (sLLs {729:1024}) ; to see that the first is longer, multiply 729/512 by 729/1024 then check the result :P
>
> I think this is what folks around here call an "improper" scale (but I see I made a few mistakes in my last post; hope this is not another one); but still, my point was about the familiarity of the existing system.
>

Well.... familiarity of existing systems is no criterion for what I would prefer to use :)

> > the main idea here is that two notes of a scale separate by {1:3}|{2} (includes {2:3, 3:4, 3:8} etc. but not {4:5, 4:9} etc.) have nominals on adjacent positions on a 22 letter alphabet
>
> Ah, I think I missed the point there - but not sure it's advantageous to do this.
>

The advantage of this is so that relations of {1:3}|{2} are clear from the nominals assuming one knows the order in which the names run.

> > {512:729} is near 5/53{1:2} ? It's more like 27/53{1:2} !!
>
> My mistake; 512:729 is 27\53 as can be seen from the diagram; I was intending to contrasting 4\53 and 5\53 and actually got them both wrong I think!
>
> > Kaf-Sen represents an interval near 18/53{1:2} ; this can be {4:5} in a meantone system but usually, as in the decatonic scale described above, does not represent {4:5}. Kaf-Gam is more often {4:5} than Kaf-Sen but that does not need to hold true either!
>
> This is interesting - what do you mean by represent 4:5?
>

{4:5} as any other interval can be tempered, and the tempered intonation of {4:5} is essentially the *representation* ; in this case, it's Kaf-Gam in a system with a "tiny schisma" {32768:32805} identity, and Kaf-Sen in a meantone system (i.e. {80:81} identity)

There's no specific representation for {4:5} with this scheme; it depends on the scale and tuning system to be used.

> > ... so it can be used for any sort of scale with plenty of {1:3}|{2} and no more than 22 notes. So this heptatonic scale from Kaf has steps [4, 3, 3, 3, 3, 3, 3]/22/{1:2}
>
> I see what you mean, but I don't find the notation so apt for this. e.g there may be confusion with 22-edo.
>

Any ideas on how to resolve this?

> > So Kaf:Rei:Lam and Mim:Pe#:Nun are minor triads (10:12:15 == 1/6:1/5:1/4) while Kaf:Rei@:Lam and Mim:Pe:Nun are major triads (4:5:6)
>
> Did you mean that? If so, I am confused.
>

In the context of the decatonic scale I described, yes; though that wouldn't be the case for a meantone scale.

> Another question - I now see that you temper the intervals - how?
>

It's an adaptable nomenclature scheme; any sensible way to temper the intervals may possibly work with the scheme, as I described with the decatonic and 1/3{3:4} heptatonic scales.

~~Glacia~~

🔗martinsj013 <martinsj@...>

🔗Ryan Avella <domeofatonement@...>

--- In tuning@yahoogroups.com, "glacia_frost" <frostycake99@...> wrote:
> See how 'Kaf' and 'Lam' are isolate while the others come in pairs that differ by a small interval? Twelve iterations of {2:3, 3:4} kept in the frame of {1:2} lead to two pitches that sound very much alike yet are different; it's like two posts are set near but there is no closure. In other words, it's a *schism* , a split, a division! Is there a special name for this particular schism? I tried to think of one but I can't seem to come up with a coherent and etymologically plausible name!

First of all, welcome to the tuning list!

I like your idea of avoiding the roman alphabet, because things can get really confusing if you describe a microtonal piece using conventional notation. The idea has never really caught on in the past though because of the difficulties in learning a new notation, but who knows? Maybe you will be able to convince the naysayers that the pros outweigh the cons.

As Mike already mentioned, this "schism" you have identified is what we call a "comma." If two notes are separated by a comma, we often take advantage of this and temper them together to a single note.

I'd highly reccomend you get familiar with Graham's temperament finder, found at this link below:
http://x31eq.com/temper/uv.html

This is a script that Graham Breed has written which allows you to enter in commas in order to find more information about the resulting temperaments. For example, if you enter in 81:80, it will give you some information about Meantone Temperament.

If you already know all of this, I apologize for preaching to the choir.

On the contrary if you do not know all of this, then feel free to ask questions. When I first joined the community when I was 17, I was overwhelmed by the sheer amount of information. But I am thankful that Keenan Pepper and Mike Battaglia helped explain some of the jargon to me knowing that my background in math/music was not very extensive.

Ryan Avella