Re: {MELM: 72} Sagittal in ToneXML

[Robert Walker]

I wonder if the Sagittal way of doing things is of any interest for ToneXML? 

It's set out here:

http://www.ozanyarman.com/misc/sag_et.par

The file format needs explanation though.

For 53-et he uses:

d 53 31
/|  //|  )N(  N\ /N\

That says that there are 53 equal steps to the octave, that the fifth is 31 equal steps, and lists the approved Sagittal accidentals for the notation in Ascii notation (easier to read as accidentals), for 1, 2, 3, 4, and 5 steps of 53-et.

From the size of the fifth you can deduce where the naturals are by going up and down in fifths from the 0th degree of the scale, and can also derive the conventional # and b by continuing further around the circle of fifths in both directions.

It's a reasonable system for an et like 53-et or a near to equal system.

Not sure how you would use it for accidentals based on a 24 out of 53 tone system. You will need some way to specify where the naturals are in the scale and how to map the accidentals to numbers of steps up or down in the scale.

Just going to append a few more details to this email in case anyone is interested, I got involved in Sagittal a few years ago and was going to include it in FTS 3. But it all got just a bit too complex, and I ran out of time, so it remains as an unfinished beta part of the program. It's only in the debug builds for now. But do hope to add it to the release when I get a bit more time.

Robert

THE LIST OF ACCIDENTALS (DETAILS OF THE FORMAT)

This is just in case you want the details.

Also, hope I'm remembering / reconstructing this correctly - this is from a number of years ago and haven't been involved in it since then. 

You can also follow up the links in http://xenharmonic.wikispaces.com/Sagittal+notation

In Sagittal just intonation notations, it is simple enough, each accidental corresponds to a particular just intonation ratio such as 81/80 or 64/63 etc and a "pitch capture zone" around the ratio. 

But it's more complicated in ETs because the 3 element of the ratio uses the tempered fifths rather than the pure 3/2.

To find out what the symbols mean you go over to the sag_descr.par which gives the ratio for each symbol.

Here,

/| 81/80

//| 45/44

N is an abbreviation for || - and these I found in a file that Dave and George gave me while I was working on the notation, not sure where they are in the SCALA distribution:

)||( 25/24

||\ 135/128

/||\ 2187/2048

Robert

[Ozan Yarman]

The sag_et.par file there contains Secor's & Keenan's original approach for 53-et. For a different hybrid usage of Sagittal, refer to the graphic in the lowest portion of the page:

http://www.ozanyarman.com/79toneqanun.html

The font for this hybrid usage can be downloaded here:

http://www.ozanyarman.com/files/79mos159tET.ttf

Oz.

✩ ✩ ✩
www.ozanyarman.com

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[Robert Walker]

Hi Ozan, 

Here is one way to do a 24 out of 53 type tuning using a cycle of fifths and accidentals, similarly to the Sagittal method. 

It's surely just a rough beginning, but maybe it can help to clarify what needs to be done. 

I did it as an extension to the Sagittal / scala type notation rather than xml. I'm not too familiar with xml specifications, so someone else can do that if needed.

Anyway, you just add three more parameters like this:

d 53 31 24 -12 11

First two parameters 53 and 31 as before:

53: it's a 53 pythagorean type tuning (which can be based on tempered fifths as well as pure fifths), with 53 as the moment of symmetry (so all the fifths span the same number of scale degrees).

31: The fifth spans 31 scale degrees of the 53 note MOS

24: The scale is for 24 of those 53 notes only

-12 11: The 24 notes are obtained by going down 12 fifths in the circle of fifths and in the opposite direction, up 11 fifths in the circle of fifths.

Then when you specify the scale, you give any tuning you like for each of those 24 notes, as a 24 note scale. With this notation you are not required to give a tuning for the remaining 29 notes.

ARE THE 24 TONE MAQAM TUNINGS THOUGHT OF AS CIRCLE OF FIFTH TUNINGS IN THIS WAY?

One question I have which one might like to think about:

In maqam tunings - even with all the pitch variations etc - are the 24 tones still thought to be related to each other via fifths (pure or tempered) as in the theoretical 24 tone succession of fifths? 

Or with all the pitch alterations in the various maqams, are some of the notes no longer thought of as related to any of the other notes via  fifths at all?

It might be hard to answer one way or another I suppose.

ACCIDENTALS

For each accidental, you specify the number of steps in the underlying theoretical  53 note MOS just as for Sagittal.

You could give ascii equivalents of each accidental (where they exist) as with Sagittal. 

You could also give an example of a glyph to use for each one. 

Glyphs could be specified using the name of a suitable font (plus version number of the font if needed) and the index of the glyph within the font. Or you could use a unicode number if they occur as unicode symbols.

Robert

[Robert Walker]

Thanks for your link to the 79 MOS out of 159 page. 

Sorry I don't understand the table at the bottom of the page with the correspondence of ascii characters to sagittal accidentals. What is the significance of the ascii characters? Since it's in qwerty keyboard layout order it looks like a keyboard map of some sort. Is it? Does it relate in some way to degrees of 79-et or steps in 159 et or what does it relate to?

Robert

On Sun, Jan 22, 2012 at 11:14 PM, Ozan Yarman <ozany...@ozanyarman.com> wrote:

[Ozan Yarman]

Hey Robert,

The table there signifies the following:

Row 1. from the natural (key 6) to full flat and full sharp by "comma" degrees in 79/80 MOS 159-tET.

Row 2. ditto all the way to double sharp and double flat.

qwerty Row 3. commatic alterations around the sharp (leftmost symbol equivalent of Row 1)

asdfghj Row 4. ditto for the flat (rightmost symbol equivalent of Row 1) 

zxcvbnm Row 5. ditto for the doublesharp

Row 6. ditto for the doubleflat

Row 7. ditto for the natural

The remaining symbols are 24-EDO simplifications for the whole tuning.

The font is a personal attempt to get the most out of the hybrid sagittal notation for 79/80 MOS 159-tET.

Oz.

✩ ✩ ✩

www.ozanyarman.com

[Aaron Andrew Hunt]

On Jan 23, 2012, at 8:50 AM, Robert Walker wrote:
> d 53 31 24 -12 11
>
> First two parameters 53 and 31 as before:
>
> 53: it's a 53 pythagorean type tuning (which can be based on tempered fifths as well as pure fifths), with 53 as the moment of symmetry (so all the fifths span the same number of scale degrees).
>
> 31: The fifth spans 31 scale degrees of the 53 note MOS
>
> 24: The scale is for 24 of those 53 notes only
>
> -12 11: The 24 notes are obtained by going down 12 fifths in the circle of fifths and in the opposite direction, up 11 fifths in the circle of fifths.

The 11 seems superfluous once you know it's 24, isn't it?

The main tag would just be whatever this is called. I use "chainsubset" below, with corresponding child tags.

<chainsubset>
<chain> 53 </chain>
<subset>
<fifth> 31 </fifth>
<start> -12 </start>
<count> 24 </count>
</subset>
</chainsubset>

I hope you can see how converting this to XML improves the whole presentation. The XML should be self-explanatory -- one of the main reasons to use it. If it's not, the tag names and structure should be fixed. A person can't make much sense out of d 53 31 24 -12 11 without explanation, but can get an idea of what's going on with the XML because it is it's own explanation.

[Robert Walker]

Yes the 12 is redundant. Yes it's much easier to read in xml, no surprise really there.

It would still need some documentation to explain what a chain is for instance.

On the other  hand I'm jolly glad the sagittal et file isn't in xml format. It is just as readable once you know how it works, and much easier to read and to edit by hand. The same file would be pages and pages in xml and hard to find anything.

Anyway so long as it is easy to convert between the various types of format then you can keep everyone happy :).  

I'll give a go at Ozan's 79 out of 159 format in same way, 

<chainsubset>
       <chain>159 </chain>
       <subset>
               <fifth> 93</fifth>
               <start> 0 </start>
               <count> 46</count>
       </subset>
        <subset>
               <fifth> 92</fifth>
               <start> 46</start>
               <count> 33</count>
       </subset>
</chainsubset>

There by <start>46</start> I mean start at the 46th fifth in the previous chain, not the 46th fifth in a chain of 92 step fifths. Perhaps it might be better to just make it a convention that if you have several chains of fifths then the first one starts at degree 0, the 1/1. Then other chains start where the previous one left off.

If so then it would be

<chainsubset>
       <chain>159 </chain>
       <subset>
               <fifth> 93</fifth>
               <start> 0 </start>
               <count> 46</count>
       </subset>
        <subset>

              <!-- No start parameter given here, so continues from the end of the previous chain subset -->
               <fifth> 92</fifth>
               <count> 33</count>
       </subset>
</chainsubset>

<start>continues</start>

Is this your tuning Ozan?

Also you might want to rotate a union of two chains like this around, so you might want an extra field at the beginning to say where you start the whole thing,

so maybe can improve the structure. Just ideas to think about.

Robert

[Robert Walker]

Hey Ozan,

Oh right I understand now. I hadn't realised that the table is intended as a way to give a character map for the font.

So, it shows the location of the font glyphs by giving the corresponding ascii character for the same location in a standard font. 

One can see that it's designed to make it easy to type the accidentals from a qwerty layout keyboard.

It all makes sense now.

Thanks,

Robert

[Aaron Andrew Hunt]

Hi Robert.

Thanks for this example. The first notation is clear. The second omitting the start tag could actually omit both start tags; the default start of the first subset would be 0, and multiple subsets would continue from wherever the previous subset left off. So the short notation would be:

<chainsubset>
<chain> 159 </chain>
<subset>
<fifth> 93 </fifth>

<count> 46 </count>
</subset>
<subset>
<fifth> 92 </fifth>

<count> 33 </count>
</subset>
</chainsubset>

However, personally I don't like leaving out information or assumed conventions. XML is verbose and should include the information IMO, so I much prefer the first notation which is completely clear.

[Aaron Andrew Hunt]

On Jan 23, 2012, at 5:58 PM, Robert Walker wrote:

> It would still need some documentation to explain what a chain is for instance.

Well, yes but I think the word "chain" in tuning theory has a pretty clear suggestion of a "chain of fifths". If some other tag would be better, suggestions welcome. Other places in ToneXML use <unit> when it's an equal division on an octave 2/1, but you made it clear earlier that that's not what this is. The actual tuning of the fifth should probably be specified so it's clear whether this is Pythagorean or tempered.

Here would be a Pythagorean chain:

<tone> 3/2 </tone>
<chain> 53 </chain>

... as opposed to a closed tempered circle:

<tone> 2^(31/53) </tone>
<chain> 53 </chain>

P.S. Let's try to make the subject headings reflect the message content.

[Ozan Yarman]

Robert, my tuning is a 79 or 80-tone subset of 159-tET. The jenerator interval is 2 degrees of 159-tET.

If you want to define it in terms of a cycle of fifths, then the following order is needed:

ab ab ab aab

ab ab aab
ab aab

ab ab aab
ab aab

ab ab aab
ab aab

ab ab aab
ab aab

ab ab aab
ab aab

ab ab aab
ab ab

Where A corresponds to the pure 3:2 fifth, and B corresponds to (1200/159) * 92 = 694.339622641509434 cents.

So, I guess the approach yields the tuning.

Oz.

✩ ✩ ✩
www.ozanyarman.com

[Robert Walker]

Oh I rather meant stuff like - somewhere you need to explain how it connects with the rest of the xml for instance. You need to explain that the scale is a tuning of just the subset and not the whole chain.

For that matter one might wonder why the xml seems to have two definitions of a scale in it - are they two separate scales or are they the same scale presented in different ways and if so why and how are they related - all that needs to be documented somehow, or you can almost guarantee some time later it will puzzle someone.

I remember trying to puzzle out an open source project that relied entirely on self commenting code with no documentation and it was impossible to figure out what it did, not without months of work, and just two or three lines of proper comments would have made all the difference. 

Similarly, a complex xml file will surely need some documentation (not necessarily in-line comments, but however it is done in xml).

Thanks,

Robert

[Robert Walker]

Ozan, oh i see, got it wrong. I suppose you could still do that in the xml somehow, would need to define the a and b and then give yoru sequence of as and bs.for the complete cycle.

But - how are the two fifth sizes interpreted in 159 et since it has no exactly pure fifths (though very close to exact fifths)? Do you use 93 steps for the pure fifth and 92 for the tempered fifth?

Also don't understand how 2 degrees of 159 et can be the generator. Unless you mean that it's just the even degrees of 159-et = that's how I'd normally understand a  MOS with a 2 degrees generator (so is a MOS, but not based on fifths as the generating interval). That would also fit with your description of how it is constructed I think.

Thanks,

Robert

[Robert Walker]

I mean of course, even degrees of 159 et excluding 158 so that the last step is 3 instead of 2, that would be a MOS, or of course, any rotation of it, I think your construction is for a rotation of it.

So also would be the same one, but including the 158 (with the two step sizes at the MOS  2 and 1 instead of 2 and 3)

Robert

[Aaron Andrew Hunt]

Well, I am just translating things you guys are talking about into XML. I'm not at all suggesting everything belongs together or that it will all be used.

I wouldn't suggest that a file contain confusing redundancies. I'm also not sure about asking parsers to do a bunch of calculations. The data should just be there to be read and to fill memory registers, IMHO.

But having several different ways to express tunings could be useful, so that for example the chain representation is for graphic purposes, and the scale is given as a series of discrete steps elsewhere in the file, and so on.

Anyway, whatever is suggested as being useful, I will just express it in XML and go from there. How it all will fit together, if it belongs together, is something to decide later.

[Ozan Yarman]

That's exactly what you just said: Even degrees of 159-equal up to the point where you need either 3 steps or 1 step to complete to the octave. The former yields 79, the latter 80 tones from out of 159-tET.

Since they are both MOS, and so close in functionality with almost the same number of tones, I sometimes describe my tuning as 79/80 MOS 159-tET. I remember Gene Ward Smith admitting that they are the only two MOSes that can be derived from 159-tET with these intrinsic properties or something to that effect.

This first method to achieve the tuning using the 2nd degree of 159-equal as the generator inveral yields the "yegah-to-neva" compass. A rotation of the tuning either by 33 or -46 degrees should yield the proper "rast-to-gerdaniye" compass.

The cycle of fifths method directly yields the "rast-to-gerdaniye" compass, which I notate as C-to-c that corresponds to Supurde Ahenk (diapason).

Oz.

✩ ✩ ✩

www.ozanyarman.com

[Robert Walker]

Aaron, the point is - it isn't a confusing redundancy when you understand the reason and motivation for it. It is a way to explain how the scale is constructed so that you can see what other scales are suitable for tuning the notes.

Whatever format we come up with for maqam tunings has to be able to do that in some way. I've no idea if the circle of fifths approach is the way to go.

But something is clearly needed otherwise you get a whole bunch of files saved using different systems depending on the user's preferences for nuances of tunings of maqams, with no easy way to convert them to each other.

I was just saying that at some point as xml gets more complex it does need some documentation. It's not a failure if that happens.

See for instance the music xml documentation:

http://www.recordare.com/musicxml/dtd/note-module

Or for a much simpler example, the xspf play list documentation:

http://www.xspf.org/orig-xspf-v1.html

Hope that's clearer now, and it is good to see your translations into xml.

Robert

[Robert Walker]

Great, glad I understand. It's all completely clear now, I mean the mathematical structure of your tuning. Thanks,

Robert

[Robert Walker]

I also wondered if another way of understanding your tuning in the xml is to consider it as a tempering of a 79 tone circle of fifths type tuning.

But the problem with that approach is that the 92 steps out of 159 MOS has 64 notes, and the 93 out of 159 MOS has 65 notes, and the pure fifths tuning has a MOS at 53 or 94 notes.]#

So it seems that there is no obvious 79 tone fifth based tuning to treat it as a tempering of. Is that right?

Maybe it's better related in some way to the 24 out of 53 chain and nuances of pitch within that?...

Otherwise,  it's back to specifying it as a chain of two sizes of fifths in the sequence

ab ab ab aab  ab ab aab ab aab  ab ab aab ab aab  ab ab aab ab aab  ab ab aab ab aab  ab ab aab ab aab  ab ab aab ab ab 

where presumably though notionally in 159-et, it would be permissible to have temperings of it e.g. with pure fifths instead of the 159-et close approximations in any situation where it makes any difference to do that (if any).

Cheers,

Robert

[Ozan Yarman]

I used to use an XSPF playlist in my older XSPF Flash Player for my musics page (still operative in the 79-tone qanun recipe page containing my "qanun taksims"). Thanks to the format I had to use back then, I'm familiar with how XML works. But simple documentation is a great helper even on topics that would otherwise seem obvious to the designers. I remember the countless hours I had had skimmed the internet for the tidbits that prevented a particular code from working right - obvious to the designers, but not so for dummies.

For ToneXML, documentation on several levels should be strongly considered.

Oz.

✩ ✩ ✩

www.ozanyarman.com

[Aaron Andrew Hunt]

Of course there will be documentation for ToneXML. I'm not sure how anyone got the idea that there would be no documentation.

[Ozan Yarman]

Just to be on the safe side, Aaron. :) Besides, notice my emphasis on "several levels": beginner - intermediate - advanced.

Oz.

✩ ✩ ✩
www.ozanyarman.com

[Ozan Yarman]

Please take a look at my XLS file below for countless possible variations for the 79 MOS 159-tET:

http://www.ozanyarman.com/files/79-tones.xls

Surely, the key idea is to have a chain where one completes a whole tour using at least two types of fifths. There are three kinds of perfect fifths available to the 79-tone palette:

694.5 cents
702 cents
709.5 cents

I'm such a dummy for not remembering that the 79-tone qanun recipe page has an English version availabe already! Please follow the details here:

http://www.ozanyarman.com/79toneqanun.html

Anyway, you cannot have a single type of fifth cycle to acquire the same effect. But you can temper within certain limits the three types of fifths above. The adjustments should nevertheless remain minute, for the property of the 79/80 MOS 159-tET is due to its being very tight.

Play around with the XLS and you'll see what I mean.

In my doctoral dissertation, I mentioned several different paths to acquire the same tuning. See pages 93-106.

So, a ToneXML file should be so defined as to adapt to minutely different situations in the same tuning.

Oz.

✩ ✩ ✩
www.ozanyarman.com

[Ozan Yarman]

Hello Robert, in between the lines:

✩ ✩ ✩

www.ozanyarman.com

On Jan 23, 2012, at 3:50 PM, Robert Walker wrote:

Hi Ozan, 

Here is one way to do a 24 out of 53 type tuning using a cycle of fifths and accidentals, similarly to the Sagittal method. 

It's surely just a rough beginning, but maybe it can help to clarify what needs to be done. 

I did it as an extension to the Sagittal / scala type notation rather than xml. I'm not too familiar with xml specifications, so someone else can do that if needed.

Anyway, you just add three more parameters like this:

d 53 31 24 -12 11

First two parameters 53 and 31 as before:

53: it's a 53 pythagorean type tuning (which can be based on tempered fifths as well as pure fifths), with 53 as the moment of symmetry (so all the fifths span the same number of scale degrees).

31: The fifth spans 31 scale degrees of the 53 note MOS

This would obviously work for a plethora of scales coalescing around equal temperaments, but possibly not highly irregular scales bereft of proper fifth cycles (in simplest terms: a 7-limit JI scale for instance).

24: The scale is for 24 of those 53 notes only

A subset, ok.

-12 11: The 24 notes are obtained by going down 12 fifths in the circle of fifths and in the opposite direction, up 11 fifths in the circle of fifths.

Cool enough.

Then when you specify the scale, you give any tuning you like for each of those 24 notes, as a 24 note scale. With this notation you are not required to give a tuning for the remaining 29 notes.

Great, but still assuming that "any tuning" is functionally resemblant of 53-tET: i.e. possessing a similar cycle of fifths. In highly irregular scale replacements, the mapping will definitely go awry. Pitches ordinarily sought will be wrongly mapped due to looking for the fifth (or its approximations) as the generator interval.

ARE THE 24 TONE MAQAM TUNINGS THOUGHT OF AS CIRCLE OF FIFTH TUNINGS IN THIS WAY?

One question I have which one might like to think about:

In maqam tunings - even with all the pitch variations etc - are the 24 tones still thought to be related to each other via fifths (pure or tempered) as in the theoretical 24 tone succession of fifths? 

I'm sure my senior colleague Ömer will agree on this one. Indeed, if one perde goes up, for instance "segah", another naturally follows its footsteps, "ewdj" in this case. But the nature of the makam seyir (melodic progression) might require a lower segah in general, so as to rupture the perfect fifth relationship in between. There are times, as in the classical description of maqam Hijaz:

A Bb C# D E F# G a

(perde segah notated as a very high Bb, and ewdj as a low F#)

where you would expect to see a perfect fifth interval as you ought to in maqam Rast (B vs F#), but here, the interval is at the most a very acute fifth.

So, the answer is both yes, and no. The nominal aspect is to consider the perdes to be in some kind of a chain-of-fifths relationship, but more often than not this chain will be broken for the sake of intonation.

Or with all the pitch alterations in the various maqams, are some of the notes no longer thought of as related to any of the other notes via  fifths at all?

Exactly.

It might be hard to answer one way or another I suppose.

I did my best. :)

ACCIDENTALS

For each accidental, you specify the number of steps in the underlying theoretical  53 note MOS just as for Sagittal.

You could give ascii equivalents of each accidental (where they exist) as with Sagittal. 

You could also give an example of a glyph to use for each one. 

I notice that it will always be problematic to ascribe any one notation to a particular scale. Trying to make ToneXML universal in this regard (compatible with every notation) shall be no light task!

Glyphs could be specified using the name of a suitable font (plus version number of the font if needed) and the index of the glyph within the font. Or you could use a unicode number if they occur as unicode symbols.

We should look into more possibilities also in the future.

Robert

Oz.

[Robert Walker]

Hello Ozan,

Thanks, again answers all my questions. Since 24 out of 53 is thought of theoretically as a tempered cycle of fifths then that seems reasonable enough to do it as such in the xml to me, even if in practise depending on intonation some of the "fifths" no longer sound like fifths.

Yes many scales can't be handled in this way, even ordinary 5 limit j.i., where you have e.g. 9/8 and 10/9 as separate notes, and in the context of a simple 5 limit scale, it doesn't make sense to distinguish them using positions in a cycle of fifths. As I'm sure you know, in Sagittal that's handled by usijng 81/80 as an accidental (10/9 = 9/8 * 81/80), so the fifths give the framework or skeleton and everything else is done using commas and dieses, e.g. also 64/63 for 7 limit (e.g. 7/4 = 16/9*63/64).

So that's one way to handle them - with suitable commas you can notate any just intonation interval precisely using accidentals applied to notes in a pure circle of fifths tuning.

I think that's probably simpler than trying to define the underlying framework using lattices especially since the scale might be some kind of irregularly shaped subset of a lattice.

Another thought for  this approach - if you have the scale defined in ratios it is easy to derive the lattice structure, So if the scale is thought of as a tempering of a lattice, you could just give the ratio equivalents of each note in the scale. 

You could do that even if the tempered note is a long way  away from the lattice note. The lattiice is just like a grid to help users compare alternate tunings of the structure.

You could do the same for chain subsets but for cycles of fifths the ratios quickly get very complex and the chain approach is probably a much simpler way to present what's happening. 

Anyway that's how it seems to me, just a few thoughts. I think with toneXML the task isn't to try to devise ways of expressing all possible tunings from the outset, so much as to make sure you have the tools available for that to be done, with the format made sufficiently expressive so new tags can easily be added if needed.

So here with maqams then the idea is to have a section of the file where you explain the structure of the scale to make it easy to substitute other tunings of the same notes. So - maybe that part of the file needs to be marked out in a clear way to show that that's what it is for, to show the structure of the scale. Then in future for other tunings if one needs new tags to show the structure of the scale using other methods, it is at least clear where in the file to add your new tags.

Robert