question about scale degrees in patterns

classic Classic list List threaded Threaded
9 messages Options
Reply | Threaded
Open this post in threaded view
|

question about scale degrees in patterns

shiihs
As I found out recently, to my surprise, a scale degree behaves counterintuitive in patterns.
By adding +/- 0.1, you add/subtract a semitone.

What is the rationale for not making 0.5 the note that sounds exactly half-way 0 and 1 (which can be different depending on the scale, octave, tuning, ...)?

Reply | Threaded
Open this post in threaded view
|

Re: question about scale degrees in patterns

ddw_music
shiihs wrote
As I found out recently, to my surprise, a scale degree behaves counterintuitive in patterns.
By adding +/- 0.1, you add/subtract a semitone.

What is the rationale for not making 0.5 the note that sounds exactly half-way 0 and 1 (which can be different depending on the scale, octave, tuning, ...)?
Because you can't assume that 2 will always be the largest number of chromatic divisions between scale degrees. For instance, in C harmonic minor, there's Ab (degree 5 in SC) and B-natural (degree 6). What would 5.5 be in this case?

It's really necessary to be able to distinguish between "up a chromatic unit" and "down a chromatic unit."

hjh
Reply | Threaded
Open this post in threaded view
|

Re: question about scale degrees in patterns

shiihs
What I'd intuitively expect is something microtonal in between Ab and B then:

Between Ab (5) and B (6) you have 3 semitones, so 5.5 would be halfway: 3/2=1.5 semitone above Ab, or
A quarter sharp.

Similar in C ionian scale: between 2 (E) and 3 (F), 2.5 would be E quarter sharp.




Reply | Threaded
Open this post in threaded view
|

Re: question about scale degrees in patterns

shiihs
... although indeed it's less straightforward then to ask the system to raise something with a semitone. The convention of adding .1 still seems a bit random but if I understand correctly there are workarounds by first converting degrees to midi note numbers and then raising or lowering those with fractions to get the behavior I expected (I will have to try that out this evening).



Reply | Threaded
Open this post in threaded view
|

Re: question about scale degrees in patterns

Tim Walters
There is an accidental system:

1s // 1.1, up 1 chromatic degree from 1
1b // 0.9, down 1 chromatic degree from 1
1s150 // 1.15, up 1.50 chromatic degrees from 1
1b050 // 0.95, down 50 chromatic degrees from 1

Currently, these values are actually in absolute semitones, and so will
only be correct (in terms of chromatic degrees) for 12ET-based scales.
There is an active pull request that would update this for non-12ET and
other tunings.

On 1/4/17 4:47 AM, shiihs wrote:

> ... although indeed it's less straightforward then to ask the system to raise
> something with a semitone. The convention of adding .1 still seems a bit
> random but if I understand correctly there are workarounds by first
> converting degrees to midi note numbers and then raising or lowering those
> with fractions to get the behavior I expected (I will have to try that out
> this evening).
>
>
>
>
>
>
>
> --
> View this message in context: http://new-supercollider-mailing-lists-forums-use-these.2681727.n2.nabble.com/question-about-scale-degrees-in-patterns-tp7629974p7629981.html
> Sent from the SuperCollider Users New (Use this!!!!) mailing list archive at Nabble.com.
>
> _______________________________________________
> sc-users mailing list
>
> info (subscription, etc.): http://www.birmingham.ac.uk/facilities/ea-studios/research/supercollider/mailinglist.aspx
> archive: http://www.listarc.bham.ac.uk/marchives/sc-users/
> search: http://www.listarc.bham.ac.uk/lists/sc-users/search/


_______________________________________________
sc-users mailing list

info (subscription, etc.): http://www.birmingham.ac.uk/facilities/ea-studios/research/supercollider/mailinglist.aspx
archive: http://www.listarc.bham.ac.uk/marchives/sc-users/
search: http://www.listarc.bham.ac.uk/lists/sc-users/search/
Reply | Threaded
Open this post in threaded view
|

Re: question about scale degrees in patterns

ddw_music
In reply to this post by shiihs
shiihs wrote
What I'd intuitively expect is something microtonal in between Ab and B then:

Between Ab (5) and B (6) you have 3 semitones, so 5.5 would be halfway: 3/2=1.5 semitone above Ab, or
A quarter sharp.
But then, with this suggestion, to get chromatic semitones, you need to add a different fraction depending on the size of the scale interval... half step is +0.5 sometimes, +0.3333333 elsewhere. That complicates math on scale degrees.

This is one of those where, no matter how it's implemented, somebody isn't going to like it.

You might look at my ModalSpec (ddwCommon quark) -- it handles the notes in between scale degrees as you prefer. I'm still using ModalSpec in my work, but one side effect of this is that I don't use accidentals in my work very often, and I have to avoid gapped scales because a chromatic offset of 0.5 doesn't work everywhere. So, be careful what you wish for ;)

hjh
Reply | Threaded
Open this post in threaded view
|

Re: question about scale degrees in patterns

shiihs
In reply to this post by ddw_music
ddw_music wrote

>
> shiihs wrote
>> As I found out recently, to my surprise, a scale degree behaves
>> counterintuitive in patterns.
>> By adding +/- 0.1, you add/subtract a semitone.
>> What is the rationale for not making 0.5 the note that sounds exactly
>> half-way 0 and 1 (which can be different depending on the scale, octave,
>> tuning, ...)?
> Because you can't assume that 2 will always be the largest number of
> chromatic divisions between scale degrees. For instance, in C harmonic
> minor, there's Ab (degree 5 in SC) and B-natural (degree 6). What would
> 5.5 be in this case?
>
> It's really necessary to be able to distinguish between "up a chromatic
> unit" and "down a chromatic unit."

The more I think about this, the less it makes sense to me. Scale degrees in
my understanding live in a very different universe (level of abstraction)
than semitones. When working with scale degrees, to me it has no physical
meaning to "raise something a semitone". Raising a semitone is something
that makes sense only when working in a MIDI number-like chromatic space.

Scale degree, in my interpretation, says something about the index of an
element in an ordered list of notes, also known as a scale. Scales in
general needn't contain 12 divisions per octave, needn't have equal
divisions, needn't repeat at the octave (may span multiple octaves), may
consist of  different notes when rising versus when descending etc.

E.g. in a hypothetical scale consisting of only notes "c e f a b" and
repeating at the octave, c could be assigned degree 0, e : degree 1, f :
degree 2, a : degree 3 and b : degree 4). Scale degree in combination with
octave number here unambiguously identifies a note belonging to that scale.
(Octave or other period numbers only make sense for repeating scales. If you
had a collection of notes spanning multiple octaves generated from a
stochastic process, you'd have to give each note a new degree number.).

In a very strict approach, one could argue that notes like g or e-flat
cannot be assigned a degree as they do not exist in the scale "c e f a b".

In a looser interpretation, one could indirectly address such notes by
introducing fractional degrees. Fractional degree 3.5 would be halfway
between 3 and 4, so after conversion to a midi number space (at an octave of
choice) (3->a=69, 4->b=71) it could correspond to a note halfway 69 and 71,
or in other words 70=a-sharp/b-flat. In this proposal the fraction is
preserved through the mapping from scale degree space to midi number space
(mostly because I couldn't think of anything else to do with it that would
make sense).

Similarly, fractional degree 1.5 would be halfway between 1 and 2, or after
conversion to MIDI number space (1->e=64, 2->f=65), halfway e and f = 64.5
which corresponds to e quarter sharp. Fractions in scale degrees in my
interpretation therefore have no direct relation to chromatic distance.
Chromatic distances only have a meaning in a MIDI number like space.

I've converted these ideas in a (somewhat pretentiously named) TheoryQuark
https://github.com/shimpe/theoryquark.





--
Sent from: http://new-supercollider-mailing-lists-forums-use-these.2681727.n2.nabble.com/SuperCollider-Users-New-Use-this-f2676391.html

_______________________________________________
sc-users mailing list

info (subscription, etc.): http://www.birmingham.ac.uk/facilities/ea-studios/research/supercollider/mailinglist.aspx
archive: http://www.listarc.bham.ac.uk/marchives/sc-users/
search: http://www.listarc.bham.ac.uk/lists/sc-users/search/
Reply | Threaded
Open this post in threaded view
|

Re: question about scale degrees in patterns

julian.rohrhuber

> On 30.12.2017, at 12:32, [hidden email] wrote:
>
> ddw_music wrote
>>
>> shiihs wrote
>>> As I found out recently, to my surprise, a scale degree behaves
>>> counterintuitive in patterns.
>>> By adding +/- 0.1, you add/subtract a semitone.
>>> What is the rationale for not making 0.5 the note that sounds exactly
>>> half-way 0 and 1 (which can be different depending on the scale, octave,
>>> tuning, ...)?
>> Because you can't assume that 2 will always be the largest number of
>> chromatic divisions between scale degrees. For instance, in C harmonic
>> minor, there's Ab (degree 5 in SC) and B-natural (degree 6). What would
>> 5.5 be in this case?
>>
>> It's really necessary to be able to distinguish between "up a chromatic
>> unit" and "down a chromatic unit.”
In sclang, by convention, fractional degrees represent accidentals which are measured by semitones. This is just a convenient way to express deviations from a given scale. It is really just a way to be able to implement notation like 3b or 7s.

signature.asc (849 bytes) Download Attachment
Reply | Threaded
Open this post in threaded view
|

Re: question about scale degrees in patterns

ddw_music
In reply to this post by shiihs
shiihs wrote
> What is the rationale for not making 0.5 the note that sounds exactly
> half-way 0 and 1 (which can be different depending on the scale, octave,
> tuning, ...)?

FWIW, my ModalSpec class *does* divide the space between scale degrees
equally. Using a C harmonic minor scale, a chromatic scale would be

C = 0
C# = 0.5
D = 1
Eb = 2
E = 2.5
F = 3
F# = 3.5
G = 4
Ab = 5
A = 5 + (1/3)
Bb = 5 + (2/3)
B = 6
C' = 7

Well, you can guess the problem: If you start with a diatonic degree and you
only want to raise or lower it by a semitone, you have to add/subtract
either 1 or 1/2 or 1/3 depending on the starting degree. Transposition of
chromatically inflected materials is not arithmetically transparent.

At the time, I thought the equal division was better, but in hindsight, I
think I was wrong.

hjh



--
Sent from: http://new-supercollider-mailing-lists-forums-use-these.2681727.n2.nabble.com/SuperCollider-Users-New-Use-this-f2676391.html

_______________________________________________
sc-users mailing list

info (subscription, etc.): http://www.birmingham.ac.uk/facilities/ea-studios/research/supercollider/mailinglist.aspx
archive: http://www.listarc.bham.ac.uk/marchives/sc-users/
search: http://www.listarc.bham.ac.uk/lists/sc-users/search/