for Dave Keenan

> Over time (50 years?) I would think one or two standards for 15 EDO >(and all other EDO's) would emerge on their own just because some are >logical and most aren't.

Two _have_ emerged. Chain-of-best-fifths with additional accidentals
for one degree up or down, and notation relative to 12-ET with either
cents or additional accidentals for fifth-tones and tenth-tones.
--- End forwarded message ---

You have stated that these two standards have emerged for 15 EDO notaton. I have
my own idea that simply uses 15 lines with two visual aids so the musician knows where
he/she is in the octave. Notes can only go on the lines and never in between them. There
are never any accidentals used. Each note has its own name. Every note is a color and every
color is a note. A color-coded strip is placed across the keyboard as a reference. This also
allows the performer to improvise if he/she is not playing a specific piece of notated music.
I doubt if this would ever become a "standard" , but do you think it has merit in
its simplicity ? Or any other way? This is what I practice using, so I won't be changing
what I do, but I was wondering about the idea for anyone else. I sort of assume that people
playing in 19EDO , 17 EDO and perhaps other divisions of the octave must use a color-coded
strip right? How do they improvise on the spot without one?

Also, I didn't fully understand what you wrote above (accidentals were included in both
references, so since I knew what I had in mind didn't have accidentals, I included my idea
above) . Is there a website besides sonic-arts.org that explains microtonal terms? What's
really sad is I'm not sure "chain of best fifths" is a microtonal term or not. Thanks.

Stephen Szpak

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--- In tuning@yahoogroups.com, "Stephen Szpak" <stephen_szpak@h...> wrote:
>
> > Over time (50 years?) I would think one or two standards for
15 EDO
> >(and all other EDO's) would emerge on their own just because some
are
> >logical and most aren't.
>
> Two _have_ emerged. Chain-of-best-fifths with additional accidentals
> for one degree up or down, and notation relative to 12-ET with either
> cents or additional accidentals for fifth-tones and tenth-tones.
> --- End forwarded message ---
>
> You have stated that these two standards have emerged for 15 EDO
notaton.
> I have
> my own idea that simply uses 15 lines with two visual aids so the
> musician knows where
> he/she is in the octave. Notes can only go on the lines and never in
> between them. There
> are never any accidentals used. Each note has its own name. Every
note is
> a color and every
> color is a note. A color-coded strip is placed across the
keyboard as a
> reference. This also
> allows the performer to improvise if he/she is not playing a
specific
> piece of notated music.
> I doubt if this would ever become a "standard" , but do
you think
> it has merit in
> its simplicity ?

Absolutely. If it works for you and your instrument, go for it.

I suppose that could be considered a form of keyboard tablature (a
notation that tells you directly where to put your fingers) as much as
an encoding of pitch.

But of course it wouldn't necessarily be the best format for other
purposes such as for playing other instruments or for analysing harmony.

> Or any other way? This is what I practice using, so I
> won't be changing
> what I do, but I was wondering about the idea for anyone else. I
sort of
> assume that people
> playing in 19EDO , 17 EDO and perhaps other divisions of the
octave must
> use a color-coded
> strip right? How do they improvise on the spot without one?

I'll leave that for others to comment on.

> Also, I didn't fully understand what you wrote above
(accidentals were
> included in both
> references, so since I knew what I had in mind didn't have
accidentals,
> I included my idea
> above) . Is there a website besides sonic-arts.org that explains
> microtonal terms? What's
> really sad is I'm not sure "chain of best fifths" is a
microtonal term
> or not. Thanks.

In this case what I mean by "chain of best fifths" notation is to find
the closest approximation to a 2:3 frequency ratio in the equal
temperament and notate a chain of 7 of these as FCGDAE, unless the
circle closes before 7, as it does in the case of 15-EDO, in which
case we center on D for an odd number and on the DA fifth for an even
number.

The number of degrees making the best fifth in n-EDO is given by
Round(n*ln(3/2)/ln(2)).

The best fifth of 15-EDO is 3 degrees which of course closes a circle
after it is chained five times, CGDAE. Then we need accidentals which
take us up and down by one degree to get us to the other two parallel
closed chains. In Sagittal we suggest using the accidental that
represents the 5-comma (81/80). Then, for example, the closest
approximation to a just major triad on C is notated C E\ G, as it is
in just about every other tuning where the 5-comma doesn't vanish.

Blackwood's notation works this way too but rather than limit the
nominals to CGDAE he allows B as a synonym for C and F as a synonym
for E, and goes further to allow sharps and flats so that the
following notes above each other are synonyms.
Dd Ab Eb Bb F
C G D A E
B F# C# G# D#