miscellaneous new guy questions

Hi...

I have a few questions for y'all, I'm hoping you don't
mind filling me in :-)...

1 - I've begun to order supplies for making my 19-tet
guitar (I've got a half-decent old guitar which
doesn't have much other use, so I'm not too worried
about the quality, just want something to play around
with)... And I was wondering if anyone has any
tips/ideas on tuning such a guitar - can you just tune
it the same way as a 12-tet guitar, or is the 4th/5th
off by too much in 19-tet? I guess I'd be interested
in hearing about tuning a guitar in any n-tet,
n!=12... Just looking at the rationales people have
for what they choose, etc.

2 - There was a thread on neutral thirds here awhile
back, and I wasn't sure exactly what you were
referring to on that point. Are these approximations
of the so called "blue-note" (which correct me if I am
wrong, is halfway between the minor and major
thirds?)...

3 - And speaking of which, just what ratio is the
minor third supposed to be approximating - 6/5 or 7/6?
It seems to fall in between the two in 12-Tet, and is
off by a large amount in both (but 19-tet seems to hit
6/5 pretty squarely on the head)... Perhaps I am
misunderstanding something... Anyone care to
straighten me out?

Thanks for reading,
Brian Szymanski
xbrianskix@yahoo.com

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--- In tuning@y..., <xbrianskix@y...> wrote:
> Hi...
>
> I have a few questions for y'all, I'm hoping you don't
> mind filling me in :-)...

I'm at your service!
>
> 1 - I've begun to order supplies for making my 19-tet
> guitar (I've got a half-decent old guitar which
> doesn't have much other use, so I'm not too worried
> about the quality, just want something to play around
> with)...

Awesome!

And I was wondering if anyone has any
> tips/ideas on tuning such a guitar - can you just tune
> it the same way as a 12-tet guitar, or is the 4th/5th
> off by too much in 19-tet?

Well, it depends on how you tune your 12-tET guitar. Tuning
fourths/fifths by harmonics is not going to work well at all for the
19-tET guitar. But tuning a string to an identical (or octave)
fretted note on an adjacent string, will work perfectly well,
assuming your intonation is set up correctly (this is done the same
way as on a 12-tET guitar, except the octave harmonic and octave
fretted note you'll be comparing, though at the same position as
before will now be at 19th, not 12th, fret).

> I guess I'd be interested
> in hearing about tuning a guitar in any n-tet,
> n!=12... Just looking at the rationales people have
> for what they choose, etc.

I play a 22-tone and a 31-tone equal tempered guitar, and Neil plays
a 19-tone and 34-tone (and sold me his 31-tone in order to get
another one). We have different rationales. Mine focus on simple
scales (with, say, 7 or 10 notes) which allow a great variety
of "higher-limit" harmony (basically, harmonies that go higher up the
harmonic series than just triads) while also being appealing
melodically like the diatonic scale. I'd be happy to go deeper into
this if you wish.

> 2 - There was a thread on neutral thirds here awhile
> back, and I wasn't sure exactly what you were
> referring to on that point. Are these approximations
> of the so called "blue-note" (which correct me if I am
> wrong, is halfway between the minor and major
> thirds?)...

A neutral third is anything about halfway between a major third and a
minor third. I find that to play the blues, the "blue third" (which
is usually somewhere between a major third and a minor third)
shouldn't be played as a single, fixed pitch, but involves a lot of
bending, vibrato, and even microtonal phrasing within that tiny pitch
zone.

> 3 - And speaking of which, just what ratio is the
> minor third supposed to be approximating - 6/5 or 7/6?

It depends what you mean by "supposed to". When the minor third first
became thought of as a consonance, say about 1480, it tended to be
tuned very close to 6/5. After 1800, when 12-tET and similar well-
temperaments became the standard in the West, most theorists thought
of it in terms of 6/5, but a few did mention 7/6 too. Physically, the
12-tET minor third is more than twice as close to 6/5 than to 7/6,
and since 6/5 is also slightly simpler, 6/5 tends to "win out" in
terms of the psychoacoustical effects where ratios are relevant. But
in some situations, especially for loud intervals in a high register,
certain effects will make recognition of more complex ratios
possible. It is there where the closeness of the 12-tET minor third
to 19/16

> It seems to fall in between the two in 12-Tet, and is
> off by a large amount in both (but 19-tet seems to hit
> 6/5 pretty squarely on the head).

That's right! 19-tET and 22-tET give you approximations to both kinds
of minor third, with 31-tET giving both and a neutral third as well.

Let me know if any of this was unclear and please ask any further
questions you'd like to.

Later, Brian!

> --- In tuning@y..., <xbrianskix@y...> wrote:

> > And I was wondering if anyone has any
> > tips/ideas on tuning such a guitar - can you just tune
> > it the same way as a 12-tet guitar, or is the 4th/5th
> > off by too much in 19-tet?

I should clarify something here -- standard Western (diatonic-based)
notation "works" for 19-tET, and therefore you can tune your open
strings to the 19-tET version of E, A, D, G, B, and E, and you'll be
able to play anything that's notated in the standard way, pretty much
the way you are used to playing it. The difference is that C# will
now be different from Db, G# different from Ab, etc.

Standard Western notation doesn't work for certain tunings like 22-
tET -- you'll find many different attempts that all have their own
problems. For 19-tET (and some other ETs), however, there is
essentially unanimous consensus on how to notate it:

19-tET
------

0. C
1. C#
2. Db
3. D
4. D#
5. Eb
6. E
7. E# = Fb
8. F
9. F#
10. Gb
11. G
12. G#
13. Ab
14. A
15. A#
16. Bb
17. B
18. B# = Cb
19. c

Please fire some more questions at me, Brian!

Paul,

Thanks for your responses... I'd actually seen the
notation for 19-tet before, kinda neat that it works
out the way it does.

> I play a 22-tone and a 31-tone equal tempered
> guitar, and Neil plays a 19-tone and 34-tone (and
> sold me his 31-tone in order to get another one). We
> have different rationales. Mine focus on simple
> scales (with, say, 7 or 10 notes) which allow a
> great variety of "higher-limit" harmony (basically,
> harmonies that go higher up the harmonic series than
> just triads) while also being appealing melodically
> like the diatonic scale. I'd be happy to go deeper
> into this if you wish.

Please do... For starters, you mentioned Neil's
approach is different, but you didn't say anything
about it? For seconds, in your approach, are you just
talking about 7th/9th/11th type chords or something
different?

One other question comes to mind, is anyone out there
using scales based not on the octave, but the 5th
above the octave? I'm not sure if I read that idea
somewhere or I thought it up, but either way it seems
like a neat idea. Although I think it might be pretty
hard to get people to stop hearing octaves as being
"the same"... Maybe it could work on an instrument
with a strange series of partials...

In any event, it's good to find there are people
interested in this sort of wackiness besides myself.

Cheers,
Brian Szymanski
bks10@cornell.edu

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--- In tuning@y..., <xbrianskix@y...> wrote:

/tuning/topicId_30285.html#30312

> One other question comes to mind, is anyone out there
> using scales based not on the octave, but the 5th
> above the octave? I'm not sure if I read that idea
> somewhere or I thought it up, but either way it seems
> like a neat idea. Although I think it might be pretty
> hard to get people to stop hearing octaves as being
> "the same"... Maybe it could work on an instrument
> with a strange series of partials...
>

Hi Brian!

It's rare that *I* can actually answer questions here... welcome
aboard! You are speaking of the Bohlen-Pierce scale which uses a 3:1
equivalency rather than the 2:1 octave. The inventor, Heinz Bohlen
actually posts to this very list, so I would refrain from suggesting
that you thought this one up yourself! :)

Here is his website:

http://members.aol.com/bpsite/

Several people have "taken a crack" at writing in this scale, and I
even have an effort myself:

http://artists.mp3s.com/artist_song/1286/1286819.html

The mastermind of alternate scales and their relationship to partials
is Bill Sethares, who *also* posts to this list of late:

http://eceserv0.ece.wisc.edu/~sethares/

> In any event, it's good to find there are people
> interested in this sort of wackiness besides myself.
>

It's wise to keep repeating the following mantra: "all the *other*
people are wacky, all the *other* people are wacky..." :)

Joseph Pehrson

--- In tuning@y..., <xbrianskix@y...> wrote:
> Paul,
>
> Thanks for your responses... I'd actually seen the
> notation for 19-tet before, kinda neat that it works
> out the way it does.
>
> > I play a 22-tone and a 31-tone equal tempered
> > guitar, and Neil plays a 19-tone and 34-tone (and
> > sold me his 31-tone in order to get another one). We
> > have different rationales. Mine focus on simple
> > scales (with, say, 7 or 10 notes) which allow a
> > great variety of "higher-limit" harmony (basically,
> > harmonies that go higher up the harmonic series than
> > just triads) while also being appealing melodically
> > like the diatonic scale. I'd be happy to go deeper
> > into this if you wish.
>
> Please do... For starters, you mentioned Neil's
> approach is different, but you didn't say anything
> about it?

Well, I should let Neil post his thoughts himself. He's less
theoretical than I am and just figures out a way to make music
directly on whatever instrument he's given (that's my impression
anyway). Sometimes he uses the near-just triads that these tunings
offer, but often he uses entirely new harmonies altogether.

> For seconds, in your approach, are you just
> talking about 7th/9th/11th type chords

Of the harmonic series variety.

> or something
> different?

I'm also interested in "Utonal" or "subharmonic" chords, as well
as "asses" (see http://x31eq.com/ass.htm). If a scale can
produce plenty of these, it can also produce plenty of other nice
chords with one or more dissonant interval(s).

Joseph answered you other question well . . . I'll wait and see if
Bill Sethares wants to address the timbre/partials question as his
name was mentioned -- for now I'll just say about the Bohlen-Pierce
scale that Pierce felt the scale should be used with timbres
consisting of only odd partials, while Bohlen does not . . . till
then, any more questions?