Re: note names

Paul said :

> One reasonable proposal along these lines is based on a 31-tET grid:
>
> http://www.uq.net.au/~zzdkeena/Music/IntervalNaming.htm
>
> Of course, if you're using a non-meantone temperament, this scheme will have
> problems.

I adopted what (for me) was a simplified version when I started thinking
in the 31tet world.

All intervals span the range

subminor minor neutral major supermajor

This is aligned with the diatonic major scale in the following manner.

1 :
2 : major
3 : major
4 : minor
5 : major
6 : major
7 : major

In the 31 world, (and perhaps in a miracle world(?)) this
works nicely in that

supermajor and subminor are always "7"-ish
neutral is always "11"-ish
major is the combined "3/5" meantone world (which
departs from Miracle).

George Russell fans will notice that all major intervals is
the lydian mode.

The only points where interval classes cross is in the
fourth/fifth region where
major fourth = subminor fifth
supermajor fourth = minor fifth

I saw a naming for the root as being justifiable either way
and unimpotant regardless.

I guess this was based on my experience in the 12tet world
where augmented and diminished didn't seem to signify so
much that I felt they needed a different modifier.

Bob Valentine

In-Reply-To: <200106141025.NAA25084@...>
We seem to be OT

Bob Valentine wrote:

> 1 :
> 2 : major
> 3 : major
> 4 : minor
> 5 : major
> 6 : major
> 7 : major

That would be

0: unison
5: major second
10: major third
13: minor fourth
18: major fifth
23: major sixth
28: major seventh

>
> In the 31 world, (and perhaps in a miracle world(?)) this
> works nicely in that
>
> supermajor and subminor are always "7"-ish
> neutral is always "11"-ish
> major is the combined "3/5" meantone world (which
> departs from Miracle).

11:7 would be a subminor sixth, I suppose that's still 7-ish. But 7:5 as
a major fourth?

> The only points where interval classes cross is in the
> fourth/fifth region where
> major fourth = subminor fifth
> supermajor fourth = minor fifth

So we can choose the right names if we want to.

As 31 is part of the Miracle world, this would still work, but wouldn't
be such a good fit. I have in fact been thinking about a true Miracle
naming scheme. I settled on all intervals on my decimal nominals as
being either minor or major. So a minor n-step is 3n steps from 31-equal
and a major n-step is 3n+1 steps.

The 10 interval classes are similar to the way I was going in meantone/31
anyway: tritones are a separate class, and tones and semitones are
distinct. But intervals do still fall into different bins. So we could
call the interval classes:

0 unison
1 semitone
2 tone
3 third
4 fourth
5 tritone
6 fifth
7 sixth
8 tone-complement
9 semitone-complement
10 octave

but that might confuse more than it enlightens, so I'll stick with
n-steps.

Minor intervals are more common than major when they're less than a
tritone, and vice versa.

Here are the best approximations to the major and minor decimal interval
classes:

minor 1-step ~ 15:14
major 1-step ~ 12:11
minor 2-step ~ 8:7
major 2-step ~ 7:6
minor 3-step ~ 11:9
major 3-step ~ 5:4
minor 4-step ~ 21:16
major 4-step ~ 4:3
minor 5-step ~ 7:5
major 5-step ~ 10:7
minor 6-step ~ 3:2
major 6-step ~ 32:21
minor 7-step ~ 8:5
major 7-step ~ 18:11
minor 8-step ~ 12:7
major 8-step ~ 7:4
minor 9-step ~ 11:6
major 9-step ~ 15:8
10-step = 2:1

Graham