Hi,
Maybe this is the approach you are looking for?
For other divisions than 12 steps to an octave you would replace the
twelfth root with the N-th root

2016-02-10 8:40 GMT+01:00 Zohar Argaman :
> Hi
> my work involved some frequency response measurements which i implemented
> using csound.
> choosing how to traverse the spectrum, i came up with this formula:
> startFreq*2^[(log2(endFreq)-log2(startFreq))*(i/NumOfNotes)]
>
> where in the specific case im interested in, endFreq=2*startFreq
> and where num of notes is number of notes on the scale, i is an iterator -
> note stepper
>
> i investigated because the sounds of a 7 note scale reminded a major scale
> and a 4 note scale reminded pentatonic, an 11 note scale reminded chromatic.
> i thought it would be interesting to listen to different scales and maybe
> get inspiration of some microtonal ideas. [actually i've been anxious to
> generalise a voice leading technique from the traditional 11 note scale,
> inspired  by Einstein's General Relativity]
> so the scales sound interesting, but they don't sound RIGHT yet.
> in this case, the 5th degree sounds more like a tritone.
>
> i've uploaded the scales for anyone to listen:
> https://soundcloud.com/fuckuwifi
>
> any ideas on whats going on?
> Csound mailing list Csound@listserv.heanet.ie
> https://listserv.heanet.ie/cgi-bin/wa?A0=CSOUND Send bugs reports to
> https://github.com/csound/csound/issues Discussions of bugs and features can
> be posted here

Hi Zohar,

At least your formula is correct.
Maybe you should also try out intervals: two simultaneous notes:
startFreq + iterFreq.

Best,
Wolf

Am 10.02.2016 um 08:40 schrieb Zohar Argaman:
> Hi
> my work involved some frequency response measurements which i implemented
> using csound.
> choosing how to traverse the spectrum, i came up with this formula:
> startFreq*2^[(log2(endFreq)-log2(startFreq))*(i/NumOfNotes)]
>
> where in the specific case im interested in, endFreq=2*startFreq
> and where num of notes is number of notes on the scale, i is an iterator -
> note stepper
>
> i investigated because the sounds of a 7 note scale reminded a major scale
> and a 4 note scale reminded pentatonic, an 11 note scale reminded chromatic.
> i thought it would be interesting to listen to different scales and maybe
> get inspiration of some microtonal ideas. [actually i've been anxious to
> generalise a voice leading technique from the traditional 11 note scale,
> inspired  by Einstein's General Relativity]
> so the scales sound interesting, but they don't sound RIGHT yet.
> in this case, the 5th degree sounds more like a tritone.
>
> i've uploaded the scales for anyone to listen:
> https://soundcloud.com/fuckuwifi
>
> any ideas on whats going on?
>
> Csound mailing list
> Csound@listserv.heanet.ie
> https://listserv.heanet.ie/cgi-bin/wa?A0=CSOUND
> Send bugs reports to
>         https://github.com/csound/csound/issues
> Discussions of bugs and features can be posted here
>

Csound mailing list
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hi zohar -

if i understand correctly, you divide an octave (the relation between 
startFreq and endFreq) in N equal parts (4, 7, 11, ...).

this is one method of working with intervals.  on a usual piano or 
keyboard we have 12 divisions; it can be extended to 24 (quarter tones) 
or whatever.

a completely different method is an integer relation between two 
frequencies: a fifth consists of two frequencies in the proportion 3/2, 
a fourth 4/3, a major third is 5/4, and so on.

both methods are not compatible.  even a fifth on the piano is not a 
pure fifth in the acoustical sense, not to speak from major and minor 
thirds.  only, the difference is not too large to recognize the 
acoustically correct interval, and if you hear this tuning all your 
life, you will consider it as correct (although musicians who are used 
to ancient music really suffer from an equal tempered piano, in 
particular the major third).

so, when you write: "the scales sound interesting, but they don't sound 
RIGHT yet", i am wondering whether you expect an acoustically correct / 
pure tuning from an equal division of the octave, which cannot be.

best -
	joachim



On 10/02/16 08:40, Zohar Argaman wrote:
> Hi
> my work involved some frequency response measurements which i
> implemented using csound.
> choosing how to traverse the spectrum, i came up with this formula:
> startFreq*2^[(log2(endFreq)-log2(startFreq))*(i/NumOfNotes)]
>
> where in the specific case im interested in, endFreq=2*startFreq
> and where num of notes is number of notes on the scale, i is an iterator
> - note stepper
>
> i investigated because the sounds of a 7 note scale reminded a major
> scale and a 4 note scale reminded pentatonic, an 11 note scale reminded
> chromatic.
> i thought it would be interesting to listen to different scales and
> maybe get inspiration of some microtonal ideas. [actually i've been
> anxious to generalise a voice leading technique from the traditional 11
> note scale, inspired  by Einstein's General Relativity]
> so the scales sound interesting, but they don't sound RIGHT yet.
> in this case, the 5th degree sounds more like a tritone.
>
> i've uploaded the scales for anyone to listen:
> https://soundcloud.com/fuckuwifi
>
> any ideas on whats going on?
> Csound mailing list Csound@listserv.heanet.ie
> 
> https://listserv.heanet.ie/cgi-bin/wa?A0=CSOUND Send bugs reports to
> https://github.com/csound/csound/issues Discussions of bugs and features
> can be posted here

Csound mailing list
Csound@listserv.heanet.ie
https://listserv.heanet.ie/cgi-bin/wa?A0=CSOUND
Send bugs reports to
        https://github.com/csound/csound/issues
Discussions of bugs and features can be posted here