Re: [tuning] Heathwaite-Smith and the 15 note marvelous dwarf

>(2) The otonal triads are tonic, dominant and subdominant

What does this mean. As defined by consecutive 3:2 approximations?

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >(2) The otonal triads are tonic, dominant and subdominant
>
> What does this mean. As defined by consecutive 3:2 approximations?

Exactly. We have a chain of two fifths, with an otonal pentad at each
of the three nodes--the classic tonic, dominant, subdominant relationship.

>> >(2) The otonal triads are tonic, dominant and subdominant
>>
>> What does this mean. As defined by consecutive 3:2 approximations?
>
>Exactly. We have a chain of two fifths, with an otonal pentad at each
>of the three nodes--the classic tonic, dominant, subdominant
>relationship.

This is your most ambitious generalized diatonic to date. What
subsets would be good to use for motifs?

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> This is your most ambitious generalized diatonic to date. What
> subsets would be good to use for motifs?

I checked for scales contained in the 5-limit dwarf, all of which will
have marvel temperings contained in the marvelous dwarf. How many of
these will actually be distinct is a question which would take some
sorting out, because the list of superset relationships from the Scala
scale list is pretty large.

superset of al-farabi_diat2.scl size: 7
superset of albion.scl size: 12
superset of cluster6a.scl size: 6
superset of cluster6b.scl size: 6
superset of cluster6c.scl size: 6
superset of cluster6d.scl size: 6
superset of cluster8a.scl size: 8
superset of cons8.scl size: 4
superset of cons9.scl size: 5
superset of cons_5.scl size: 8
superset of cross2_5.scl size: 9
superset of didy_chrom.scl size: 7
superset of didy_chrom2.scl size: 7
superset of diff7.scl size: 7
superset of diff7b.scl size: 7
superset of duodene.scl size: 12
dwarf15_5.scl : equal in key 0
superset of dwarf5_5.scl size: 5
superset of dwarf6_5.scl size: 6
superset of dwarf7_5.scl size: 7
superset of dwarf9_5.scl size: 9
superset of efg333.scl size: 4
superset of efg3335.scl size: 8
superset of efg335.scl size: 6
superset of efg3355.scl size: 9
superset of efg355.scl size: 6
superset of euler_diat.scl size: 8
superset of farey3.scl size: 5
superset of fivecrys1.scl size: 7
superset of harrison_5.scl size: 5
superset of harrison_5_4.scl size: 5
superset of harrison_8.scl size: 8
superset of harrison_joy.scl size: 6
superset of harrison_min.scl size: 5
superset of harrison_mix2.scl size: 5
superset of helmholtz.scl size: 7
superset of helmholtz_hd.scl size: 9
superset of hexany10.scl size: 6
superset of hexany15.scl size: 5
superset of hexany16.scl size: 5
superset of hirajoshi2.scl size: 5
superset of indian-raja.scl size: 6
superset of ionic.scl size: 7
superset of korea_5.scl size: 5
superset of kornerup_11.scl size: 11
superset of kring1.scl size: 7
subset of kring1p3.scl size: 35
superset of malcolm.scl size: 12
superset of mersen_l1.scl size: 12
superset of mersen_l2.scl size: 12
superset of mersen_s1.scl size: 12
superset of octony_min.scl size: 8
superset of olympos.scl size: 5
superset of pelog_jc.scl size: 5
superset of pipedum_10a.scl size: 10
superset of prime_5.scl size: 5
superset of ptolemy.scl size: 7
superset of ptolemy_diat.scl size: 7
superset of ptolemy_idiat.scl size: 7
superset of redfield.scl size: 7
superset of solemn.scl size: 6
superset of steltri1.scl size: 6
superset of tartini_7.scl size: 7
superset of tranh.scl size: 5
superset of tri2.scl size: 6
superset of tritriad.scl size: 7
superset of tsjerepnin.scl size: 9
superset of turkish.scl size: 7
superset of verdi2.scl size: 12
superset of yantgen6.scl size: 6
superset of young-lm_guitar.scl size: 12
superset of yves.scl size: 7
superset of zarlino.scl size: 7