53-tone division for computer-assited composition

I have been working on a computer system for music sequencing using arbitrary frequencies that can be constrained to a discrete set, the 53-tone equal division in particular. The system calculates dissonance of groups of tones on the basis of Helmholtz's beat theory, and assists by offering positions for candidate "good tones", that is, tones that are "locally consonant" with an existing tone collection. In this way, I reason, one can explore micro-tonality, while adhering to near-just intonation.

To test the theory, I made a short experimental suite of pieces: variations on Bach's Prelude in C (WTC, BWV 846). The sound files and brief notes can be accessed here:

http://jbnotes.info/mt/Music/

I will greatly appreciate and reply to any comments that you can provide. Thank you all very much for your time.

Ian

HI Ian;

If you are intending to worki with 53 edo you will find that you can map 53edo to a meantone-type note assignment with Large (L) and small (s) intervals.

53 edo would use:
9 steps to be the Large interval and
4 steps to be the small interval:

i.e. (9*5) + ( 4*2) = 53 steps = 5L+2s.

see this page for details:

http://www.lucytune.com/tuning/equal_temp.html

On 26 Sep 2009, at 21:38, igb.33143 wrote:

> I have been working on a computer system for music sequencing using > arbitrary frequencies that can be constrained to a discrete set, the > 53-tone equal division in particular. The system calculates > dissonance of groups of tones on the basis of Helmholtz's beat > theory, and assists by offering positions for candidate "good > tones", that is, tones that are "locally consonant" with an existing > tone collection. In this way, I reason, one can explore micro-> tonality, while adhering to near-just intonation.
>
> To test the theory, I made a short experimental suite of pieces: > variations on Bach's Prelude in C (WTC, BWV 846). The sound files > and brief notes can be accessed here:
>
> http://jbnotes.info/mt/Music/
>
> I will greatly appreciate and reply to any comments that you can > provide. Thank you all very much for your time.
>
> Ian
>
>
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

Thank you, Charles. My original intent was to work (or better, investigate how such work can be done - I am better an engineer than a musician) with any pitches that would be found as local minima in the dissonance function. It turned out that having some granularity would be beneficial to cut down computational complexity and also to control the drift; I think that 53-edo is a very good choice for that, mainly because it approximates just intervals very well, its step is fine, yet still large enough that it can be heard.

Since the dissonance is calculated from beats, the minima that occur in the dissonance function (I call it "landscape", since it looks like one) are just intervals apart, that is the close ones are 17, 14, 9, 8, 5, and 3 steps. The "landscape" changes its shape as tones come in and out. 4-step interval also occurs (when I take my hands off and let algorithms run, like in "Glockenspiel"), but less frequently. The method seems to prefer either the diatonic or chromatic semitone (at least I believe that is what 5 and 3 steps in 53-edo correspond to).

Regards,
Ian

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
> If you are intending to work with 53 edo you will find that you can
> map 53edo to a meantone-type note assignment with Large (L) and small
> (s) intervals.
>
> 53 edo would use:
> 9 steps to be the Large interval and
> 4 steps to be the small interval:
>
> i.e. (9*5) + ( 4*2) = 53 steps = 5L+2s.
>
> see this page for details:
>
> http://www.lucytune.com/tuning/equal_temp.html

--- In tuning@yahoogroups.com, "igb.33143" <ian.burleigh@...> wrote:
>
> I have been working on a computer system for music sequencing
> using arbitrary frequencies that can be constrained to a
> discrete set, the 53-tone equal division in particular.
[snip]
> To test the theory, I made a short experimental suite of
> pieces: variations on Bach's Prelude in C (WTC, BWV 846).
> The sound files and brief notes can be accessed here:
> http://jbnotes.info/mt/Music/
> I will greatly appreciate and reply to any comments that you
> can provide. Thank you all very much for your time.

Hi Ian,

Thanks for posting. Your app is one of a few piano roll -style microtonal sequencers demonstrated recently, which is incredibly
exciting for folks like me who have watched microtonal music
slowly become more popular over the years. And, who have been
incredibly lazy, waiting for someone like you to create such a
thing. I presume you're familiar with the Rationale sequencer
by Chuckk Hubbard?
http://www.badmuthahubbard.com/cgi-bin/rationaleinfo.py

It looks like yours is a Java application. Have you thought
about sharing it as an applet?

One question. You say, "can be constrained to any number
of steps: namely twelve, forty eight, or fifty three". Do
you really mean any number of steps, or just 12, 48 and 53?

I really like what you're doing with your music. I will point
out something you probably already know -- that 53 is not the
best choice for a lot of existing music, since it does not
temper out the syntonic comma. Something like 31 is about
optimal among tunings that do (and its errors can in principle
be corrected all the way to JI with a fairly straightforward
"adaptive tuning" algorithm that inserts sub-step shifts).

I think realtime feedback for the composer about roughness
(sensory dissonance) would be quite useful in exploring
new tunings. Normally the way I have thought about tunings
is to first choose a set of chords I know are consonant
(e.g. major and minor triads, etc) and then find scales that
contain these chords aplenty (e.g. diatonic scale), and then
to constrain the notation (piano roll, lines and spaces on a
staff, etc.) to the steps of this scale. Then the composer
only needs to remember the scale step patterns of the chords
(e.g. 1-3-5), and melodies appear linearly. The missing
notes to be accessed with accidentals or key signatures.
In other words, a straightforward generalization of common-
practice notation.

But I think the absolute pitch scale has value too, so I
encourage your efforts fully (and indeed, would like to
try an applet).

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> Thanks for posting. Your app is one of a few piano roll -style microtonal sequencers demonstrated recently, which is incredibly
> exciting for folks like me who have watched microtonal music
> slowly become more popular over the years. And, who have been
> incredibly lazy, waiting for someone like you to create such a
> thing. I presume you're familiar with the Rationale sequencer
> by Chuckk Hubbard?
> http://www.badmuthahubbard.com/cgi-bin/rationaleinfo.py

Now, I am not, thanks for the link. I am quite new to tuning theory. My interest was for a long time mostly in 1920s and '30s jazz music, '40s swing, gypsy swing, some klezmer. No place for theories there, yet tones are constantly bent and adjusted for higher or lower tension, and surely not in any 12-tone prison. The notation is only a rough guide, both in time and in pitch.

My intent was not to make a sequencer, but that is what I got, as I needed it for my experiments with consonance calculations and also to make a transcript of electroacoustic music recordings for a research project.

> It looks like yours is a Java application. Have you thought
> about sharing it as an applet?

Yes, it is in Java. I thought of making it an applet, but applets run in a sandbox and I did not want to get into security policies. So it is a regular Java application.

> One question. You say, "can be constrained to any number
> of steps: namely twelve, forty eight, or fifty three". Do
> you really mean any number of steps, or just 12, 48 and 53?

Yes, I mean any number. It works internally with frequencies. The GUI currently has the option of none, 12, 48, 53, just because that's what I needed.

> you probably already know ... 53 ... does not
> temper out the syntonic comma.

I know now :)

> I think realtime feedback for the composer about roughness
> (sensory dissonance) would be quite useful ...
> ... the absolute pitch scale has value too, so I
> encourage your efforts fully (and indeed, would like to
> try an applet).

Thank you. I will upload it to the Files section shortly. Please remember that it is a experimental application and therefore the controls and features are lacking a lot. For sound you will need a running copy of SuperCollider.

Ian

--- In tuning@yahoogroups.com, "igb.33143" <ian.burleigh@...> wrote:

>My interest was for a long time mostly in 1920s and '30s jazz
>music, '40s swing, gypsy swing, some klezmer. No place for
>theories there, yet tones are constantly bent and adjusted
>for higher or lower tension, and surely not in any 12-tone
>prison. The notation is only a rough guide, both in time and
>in pitch.

This is true of all musical styles. Interpretation is
revered even in classical music. Nevertheless, I think what
one starts with as the rough guide matters! I can't imagine
microtonal musicians will forego embellishments.

> It works internally with frequencies.
> The GUI currently has the option of none, 12, 48, 53, just
> because that's what I needed.

Perhaps the user could just type the desired number into a
field.

> > I think realtime feedback for the composer about roughness
> > (sensory dissonance) would be quite useful ...
> > ... the absolute pitch scale has value too, so I
> > encourage your efforts fully (and indeed, would like to
> > try an applet).
>
> Thank you. I will upload it to the Files section shortly.
> Please remember that it is a experimental application and
> therefore the controls and features are lacking a lot.
> For sound you will need a running copy of SuperCollider.

Ah, I didn't realize you were using SuperCollider. I'm
downloading it now.

-Carl