Consonance/Dissonance mapping - yet AGAIN!

Carl Lumma wrote:

>The conclusion was that ratios of small whole numbers are more consonant
>that ratios of large whole numbers, and anything that measures the size of
>the numbers in a ratio will reflect this.

This simplistic conclusion may satisfy those listeners who can only "hear" or
visualise "harmonics" at integer frequency ratios. For the more adventurous who
wish to explore beyond the strict limitations of "Just Idiocy" logic,
see

http://www.harmonics.com/lucy/lsd/scalemak.html

This scalecoding system will enable you to map harmony,
consonance/dissonance and scale patterns plus the beat frequencies which are
generated by the interference between integer frequency ratios.

To summarise:
Intervals of fewer steps of fourths or fifths are more consonant than
intervals of abundant steps of fourths or fifths; which are more dissonant.

BTW I hope that those intending to fret their microtonal guitars to >12tET
systems appreciate that they are "painting themselves into a harmonic corner".

yours disdainfully

lucy

--
~===============================================================~
Charles Lucy - lucy@harmonics.com (LucyScaleDevelopments)
------------ Promoting global harmony through LucyTuning -------
by setting tuning and harmonic standards for the next millennium,
and having fun with them.

for information on LucyTuning
See http://www.ilhawaii.net/~lucy
or http://www.harmonics.com/lucy/

On Wed, 25 Aug 1999, Charles Lucy wrote:
> Intervals of fewer steps of fourths or fifths are more consonant than
> intervals of abundant steps of fourths or fifths; which are more dissonant.

So a major second is more consonant than either kind (major or minor)
of third or sixth? Find me someone whose ears confirm that.

> yours disdainfully

Someone who so forcefully espouses such an obviously flawed theory while
disdaining all others deserves a fair amount of disdain himself, IMO.

--pH <manynote@library.wustl.edu> http://library.wustl.edu/~manynote
O
/\ "Hey--do you think I need to lose some weight?"
-\-\-- o

Charles Lucy wrote,

>> Intervals of fewer steps of fourths or fifths are more consonant than
>> intervals of abundant steps of fourths or fifths; which are more
dissonant.

Paul Hahn wrote,

>So a major second is more consonant than either kind (major or minor)
>of third or sixth? Find me someone whose ears confirm that.

Particularly in Lucy's own tuning, the major and minor thirds and sixths are
extremely consonant, while the major second is very dissonant due to its
ambiguity between two already difficult ratios, 8:9 and 9:10. Another flaw
in Lucy's theory is that after enough Lucy fifths (695.493 cents), you will
get an interval that is closer to a Just fifth, and clearly more consonant
even though it involves far more steps on the chain of Lucy fifths.