Alpha, beta, gamma

As the subject of Wendy Carlos' non-octave Alpha, Beta, and Gamma scales has come up on the MMM list, I decided to get my feet wet and try a little exploration with them.

http://teamouse.googlepages.com/home

http://teamouse.googlepages.com/AlphaBlending.mp3
http://teamouse.googlepages.com/BetaTesting.mp3
http://teamouse.googlepages.com/GammaCorrection.mp3

Nothing much yet, but there's some potentially useful material here. It's a refreshing change from the rank 2 temperaments that I've been working with -- intervals are always the same size as in ETs, but the lack of octaves constrains the way the harmony progresses. I haven't figured out how to notate them yet, but the regularity of the tuning makes it possible to use the piano roll without difficulty.

The third example, in the Carlos Gamma scale, starts with a uniquely microtonal harmonic progression, alternating between major 7th and minor 7th chords, in a kind of interlocked way (with the roots one step apart). This is the sort of thing that's possible in scales like Gamma or 31-ET, but not in 12-ET.

Herman wrote:

> As the subject of Wendy Carlos' non-octave Alpha, Beta, and Gamma scales
> has come up on the MMM list, I decided to get my feet wet and try a
> little exploration with them.

Nice music -- pleasant to my ear.

But I can hear octaves there as well. So where is the "non-octaveness"?

Petr

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
>
> Herman wrote:
>
>
>
> > As the subject of Wendy Carlos' non-octave Alpha, Beta, and Gamma
>scales
> > has come up on the MMM list, I decided to get my feet wet and try
a
> > little exploration with them.
>
>
>
> Nice music -- pleasant to my ear.
>
> But I can hear octaves there as well. So where is the "non-
octaveness"?
>
>
>
> Petr
>

Gamma works out to be the same as 34 equal divisions of a tempered
octave. If you temper an octave by 256/257 and divide it 34-equal you
get the same tuning, within some miniscule amount. It is an excellent
tuning in my opinion.

-Cameron Bobro

Petr Par�zek wrote:
> Herman wrote:
> > > >> As the subject of Wendy Carlos' non-octave Alpha, Beta, and Gamma scales
>> has come up on the MMM list, I decided to get my feet wet and try a
>> little exploration with them.
> > > > Nice music -- pleasant to my ear.
> > But I can hear octaves there as well. So where is the �non-octaveness�?

The actual scale doesn't have any octaves. Some of the voices have octave doublings, though, and the bass part is tuned an octave lower. If this was done with a pipe organ, the melody might use the 8' and 4' ranks, while the pedals would use 16' and 32'.

that is cheating! :)
Is this what people are going to do with all the rest of those stretched and shrunk octaves when they start to cover 5 or 6 octaves?

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Herman Miller wrote:
>
>
> The actual scale doesn't have any octaves. Some of the voices have > octave doublings, though, and the bass part is tuned an octave lower. If > this was done with a pipe organ, the melody might use the 8' and 4' > ranks, while the pedals would use 16' and 32'.
>
>
> --
>
>
>
>

Herman wrote:

> The actual scale doesn't have any octaves. Some of the voices have
> octave doublings, though, and the bass part is tuned an octave lower. If
> this was done with a pipe organ, the melody might use the 8' and 4'
> ranks, while the pedals would use 16' and 32'.

Don't know how much that could be worth it but you might also use 2/1-periodic rank 2 temperaments and temper out the desired commas with them -- these could be called, for example, "alphoct" (meaning "13 5 -9"), "betoct" (meaning "-16 -6 11"), and "gammoct" (meaning "-29 -11 20") or something along those lines.
Another possibility, which is unusable for alpha, is to map the 2/1 to 19 steps in beta and 34 steps in gamma, meaning that beta would have significantly stretched octaves and gamma would have acceptably "compressed" octaves.

Petr