Yahoo Tuning Groups Ultimate Backup tuning question for Dave Keenan on 16 tone scale

Hello Dave!
I know we have been talking about 15 EDO but i was curious what the notation of 16 ET would
be. And is it contrary to use yours and George's notation in a way where this notation would be
used for a 16 tone scale that was not Equal. Being a recurrent sequence, the idea of simple ratios
would not apply. So do you two object to the idea of the notation being used asa tabliture when
the tuning involves high number ratios.

>
>
> In a forthcoming paper on the sagittal notation system there are two
> notations proposed for 15-tET. One uses the scale's best approximation
> of a fifth (9/15 oct or 720 c) between the nominals CGDAE, and the
> 5-comma up and down accidentals for one degree either side of these.
>
> C C/ D\ D D/ E\ E E/ G\ G G/ A\ A A/ C\
>
> --------------------------------------

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

--- In tuning@yahoogroups.com, kraig grady <kraiggrady@a...> wrote:
> >
>
> Hello Dave!
> I know we have been talking about 15 EDO but i was curious what
the notation of 16 ET would
> be.

Hi Kraig,

By the way, this -EDO versus -ET versus -tET stuff must be awful for
newbies. I'm not even sure which one to use myself! :-) Any newbies
reading, you can safely assume they all mean the same thing (equal
division of the octave) maybe until you get into some very fine
points, or maybe forever.

Regarding 16-ET: Its best fifths are so far from just that there is no
sensible "native-fifth" notation for it. But a notation based on the
pelogic temperament (as generated by the 675 cent interval), could be
devised for it, with 7 nominals. However I would not want to use the
letters FCGDAEB for these since in that case the EF and BC intervals
would be 50% _wider_ than the CD GA etc. intervals (225c versus 150c).

Instead we recommended that 16-ET be notated as every 3rd note of
48-ET, which is of course a multiple of (or perhaps I should say, a
further subdivision of) 12-ET into eighth-tones, which looks like this.

48-ET Sagittal mixed notation (ASCII shorthand)
A to G, #, b as for 12-ET
^ quarter-tone up (11-M-diesis up)
~ eighth-tone up (23-comma up)
z eighth-tone down (23-comma down)
v quarter-tone down (11-M-diesis down)

Here's 16-ET as every 3rd note of 48-ET (aligned with D natural to
minimize accidentals).

Cz C^ C#~ D Ebz Ev E~ F F#z Gv G~ G#(or Ab) Az A^ Bb~ B

It isn't pretty, but it's simpler than, for example, the 72-ET-based
notation for blackjack.

> And is it contrary to use yours and George's notation in a way where
this notation would be
> used for a 16 tone scale that was not Equal.

Not necessarily. If it was nearly equal this would be fine.

> Being a recurrent sequence, the idea of simple ratios
> would not apply.

Can you tell us what the scale is (cents or ratios), or what the
generator(s) is/are? We may be able to come up with a better notation
for your unequal 16 as an approximate subset of some larger ET other
than 48-ET.

If it's a pelog superset, then maybe it's closer to being 16 out of
23-ET or 39-ET.

The first question to ask when looking for a sagittal notation for
some scale is, does it contain any chain(s) of fifths (between 4/7 and
3/5 octave in size), and if so, what size are they?

> So do you two object to the idea of the notation being used asa
tabliture when
> the tuning involves high number ratios.

I'm not sure what you mean by "tablature" here. I understand tablature
to be notation that indicates in a fairly direct and pictorial manner
where the performer should put their fingers. This does not involve
directly represent pitches and so sagittal notation is not relevant here.

Perhaps you are using the term loosely, as I have noticed others
doing, to also include scordatura notations? I understand scordatura
to be indirectly telling the performer where to put their fingers by
directly indicating the pitch that this _would_ produce _if_ the
instrument were in its standard tuning. Standard tunings don't usually
require accidentals other than # and b, so sagittal would usually not
be relevant here either.

But I understand you want to let the performer think of the instrument
as being in 16-ET and play it accordingly, even though it is really in
an unequal 16 note per octave scale.

In general I'd say yes, we would object to sagittal being used in this
way. This is because the overiding principle of the whole sagittal
system is that the accidentals represent specific commas, so no matter
what the tuning, if you see, for example, C E\ you know that this is
the tuning's best approximation of a just major third from C. i.e. You
know roughly what it will _sound_ like. This is analogous to what
happens in different human languages that use the same character set.

In general scordatura severely violates this connection between
notation and sound, and would defeat sagittal's whole raison detre.

However, what you're proposing may actually be close enough in sound
to 16-ET that it isn't really a scordatura. And if this is not the
case, then we'd certainly like to be given a chance to come up with a
better direct-pitch sagittal notation for your scale before you resort
to scordatura.

-- Dave Keenan

question for Dave Keenan on 16 tone scale

🔗kraig grady <kraiggrady@anaphoria.com>

🔗Dave Keenan <d.keenan@bigpond.net.au>

🔗Herman Miller <hmiller@IO.COM>