Tripod Notation update

So far, the only feedback I've had on this is about my Chinese translation. But, anyway, I'm deeming this introduction to tripod notation "finished" so that I'll only update it for corrections, or in response to any more feedback I should get, or if I really want to. So if anybody was waiting for it to reach such a state here it is:

http://x31eq.com/magic/tripod.pdf

The notation examples are looking very nice, which works as a demonstration of what you can do with Lilypond and such a weird notation. All the code you need is here:

http://x31eq.com/magic/tripod-code.zip

I'm still working on this, so not all the big examples have standalone Lilypond files, but they will. I'll also get more polyphonic MIDI files set up so that the pitch bends work properly and you can hear them.

Graham

Though I am more a tourist than an emigre to the micro-notational shores (my "scores" are Csound and SuperCollider code), this is a fascinating and whimsical paper (and beautifully typeset, which is a treat in itself). Very interesting idea, which I'll need to digest and ponder. Thanks for your work.

- Dave

Graham Breed wrote:
> So far, the only feedback I've had on this is about my > Chinese translation. But, anyway, I'm deeming this > introduction to tripod notation "finished" so that I'll only > update it for corrections, or in response to any more > feedback I should get, or if I really want to. So if > anybody was waiting for it to reach such a state here it is:
> > http://x31eq.com/magic/tripod.pdf
> > The notation examples are looking very nice, which works as > a demonstration of what you can do with Lilypond and such a > weird notation. All the code you need is here:
> > http://x31eq.com/magic/tripod-code.zip
> > I'm still working on this, so not all the big examples have > standalone Lilypond files, but they will. I'll also get > more polyphonic MIDI files set up so that the pitch bends > work properly and you can hear them.
> > > Graham

--
~DaveSeidel = [
http://mysterybear.net,
http://daveseidel.tumblr.com,
http://twitter.com/DaveSeidel
];

Dave Seidel wrote:
> Though I am more a tourist than an emigre to the micro-notational shores > (my "scores" are Csound and SuperCollider code), this is a fascinating > and whimsical paper (and beautifully typeset, which is a treat in > itself). Very interesting idea, which I'll need to digest and ponder. > Thanks for your work.

Well, thank you! I noticed a bug in the marvel accidentals in a version that may have gone online yesterday. Sorry if anybody's puzzling over that. It was a side-effect of some of the MIDI files switching to 72-equal:

http://x31eq.com/magic/tripod-code.zip

As for Csound, it would be one way to implement tricycle notation with pitch drift. I haven't thought about how to do it though. You'd have to remember the current positions of the feet, and the pitch drift, which would slowly tend towards zero.

Here, though, is some code for implementing fixed tripod tuning:

--------------- begin code -----------------------------

; Global variables for the tuning
; TOP-RMS
gi_stretch init 1.0009 ; 1.0 for pure octaves
gi_magic_gen init 0.5107 ; 0 for 22, 1 for 19

; gi_magic_gen is (g - 7/22)/(6/19 - 7/22)
; where g is the generating third as a proportion of
; the stretched octave

gi_orwell_gen init 0.0 ; 0 for 22, 1 for 31
gi_tonic init 4.03 ; base 2 log of note 0 (Hz)

; Tripod tuning as a rank 2 tuning
; (Actually may support rank 3 one day!)
opcode R2Tuning, i, ii
inote, ishift xin

ioctaves init int(inote)

itoes init frac(inote)*10 - 1
iinches init int(itoes / 3)

ioctave_size init gi_stretch
itoe_size init gi_stretch*(2/22 \
+ gi_magic_gen*2/19 - gi_magic_gen*2/22 \
+ gi_orwell_gen*3/31- gi_orwell_gen*2/22)
iinch_size init gi_stretch*(1/22 \
- gi_magic_gen/22 \
+ gi_orwell_gen/31 - gi_orwell_gen/22)
ishift_size init gi_stretch*(1/22 \
+ gi_magic_gen/19 - gi_magic_gen/22 \
+ gi_orwell_gen/31- gi_orwell_gen/22)

ipitch = ioctaves*ioctave_size + \
itoes * itoe_size + \
iinches * iinch_size + \
ishift * ishift_size

xout cpsoct(gi_tonic + ipitch)
endop

---------------- end code ------------------------------

It's a UDO that takes the tripod nominal and the semitoe shift relative to it, and returns a frequency in Hz. The nominals are specified in decimal form, like the usual Csound note names, so 4.1 is yan in octave 4 (whatever that is, I forget the definition and I'm only using MIDI so far :-P). The tuning's determined by those global variables at the top, which means you can set up an instrument that changes them. Here are some alternative values to be un-commented:

--------------- begin code -----------------------------

; octave and 7:4 pure
;gi_stretch init 1.0
;gi_magic_gen init 0.3771

; compromise with a moderate 7:4
;gi_stretch init 1.0005
;gi_magic_gen init 0.4

; 11:8 tuned as a noble number and octave stretch optimized
;gi_stretch init 1.0013
;gi_magic_gen init 0.6040

; 60-equal
;gi_stretch init 1
;gi_magic_gen init 0.633333333

---------------- end code ------------------------------

Graham

Graham Breed wrote:
> So far, the only feedback I've had on this is about my > Chinese translation. But, anyway, I'm deeming this > introduction to tripod notation "finished" so that I'll only > update it for corrections, or in response to any more > feedback I should get, or if I really want to. So if > anybody was waiting for it to reach such a state here it is:
> > http://x31eq.com/magic/tripod.pdf
> > The notation examples are looking very nice, which works as > a demonstration of what you can do with Lilypond and such a > weird notation. All the code you need is here:
> > http://x31eq.com/magic/tripod-code.zip
> > I'm still working on this, so not all the big examples have > standalone Lilypond files, but they will. I'll also get > more polyphonic MIDI files set up so that the pitch bends > work properly and you can hear them.

I finally got around to reading the Tripod notation paper today. All in all a very interesting system, although it started to get confusing with the different kinds of inches, which weren't explained very well. Maybe a few examples side by side with Sagittal notation and ratios given to identify the intervals would help.

With a generalized keyboard, you can set up the tuning so the nominals 1-9 follow the same pattern as on a numeric keypad or pocket calculator, with a key in between each of the numbers for the semitoes. You can see the effect of "crossing the river" as the pattern shifts to the right when you go up an octave. Not having a generalized keyboard, I have to use the qwerty keyboard to simulate one, but the fingerings work out okay and it seems like it would be easy enough to follow tripod notation with some practice (a pattern of black and white keys might help).

I've tried developing my own alternative notations for 7-limit tuning systems, but not with much success. 5-limit works out better (with 1/1 10/9 6/5 4/3 3/2 5/3 9/5 for instance), and it's unlikely that anything will replace 3-limit chain-of-fifth notation, but since some of the music I write has a fictional setting, I've been hoping to figure out one or more notation systems that the Zireen people could use to write music. That might be more a topic for the tuning-math list I guess.

Herman Miller wrote:

> I finally got around to reading the Tripod notation paper today. All in > all a very interesting system, although it started to get confusing with > the different kinds of inches, which weren't explained very well. Maybe > a few examples side by side with Sagittal notation and ratios given to > identify the intervals would help.

I avoid ratios because they'll turn off people who aren't familar with them. But I can list them here. The "harpoon" inch is 81:80. The curved/single headed arrow inch is 49:48 or 525:512. I think I got the right Sagittal glyphs for these. The standard semitoe is 36:35 and it's twin, with a different symbol, is 25:24. The toe is like a secor: either 16:15 or 15:14.

I'm working on different Sagittal notations but if I do comparisons they'll be in a different PDF. 72-equal will be good for showing marvel temperament and I can use other standard glyphs for that if I have the font.

> With a generalized keyboard, you can set up the tuning so the nominals > 1-9 follow the same pattern as on a numeric keypad or pocket calculator, > with a key in between each of the numbers for the semitoes. You can see > the effect of "crossing the river" as the pattern shifts to the right > when you go up an octave. Not having a generalized keyboard, I have to > use the qwerty keyboard to simulate one, but the fingerings work out > okay and it seems like it would be easy enough to follow tripod notation > with some practice (a pattern of black and white keys might help).

Looks good, but I don't have a generalized keyboard either. At least, not with me.

> I've tried developing my own alternative notations for 7-limit tuning > systems, but not with much success. 5-limit works out better (with 1/1 > 10/9 6/5 4/3 3/2 5/3 9/5 for instance), and it's unlikely that anything > will replace 3-limit chain-of-fifth notation, but since some of the > music I write has a fictional setting, I've been hoping to figure out > one or more notation systems that the Zireen people could use to write > music. That might be more a topic for the tuning-math list I guess.

Chain-of-fifth notations don't fit magic well because you tend to move a lot by thirds.

Graham