Yahoo Tuning Groups Ultimate Backup tuning Fwd: Re: for Dave Keenan

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
--- 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.
===============================================
STEPHEN SZPAK WRITES IN REPONSE::::::::::::::

Hi Dave

Thanks for your encouragement here. I couldn't imagine myself, or anyone else
flowing effortlessly without a color-coded strip.Even I can't just yet, but I think I will
before I hit the 500 hour mark of practicing with it.
I can see it wouldn't work for analysing harmony now. I didn't think about that.
====================================================

> 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.
==============================================
STEPHEN SZPAK RESPONDS:

You, and others, don't know how much I don't know, you know?
First I don't think it's wise to continue trying to explain the rest of what
you've written here. I believe it relates to Sagittal and Blackwood's notation.

If you want to continue you'll be frustrated.

I realize 15 EDO has three interlaced circles of perfect 5ths.
The notes of C and E and G# also exist in 12 EDO. (0 cents 400 cents 800 cents)
What does "we center on D for an odd number and on the DA fifth for
and even number" mean? There is no D in 15 EDO.
======================================================
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.
=====================================================
STEPHEN SZPAK WRITES:
According to Tonalsoft Encyclopaedia of Tuning:

degree:

1) refers to the ordinal "steps" in a diatonic scale
2) refers to the pitches in an equal-tempered scale, one
degree being the basic "step" size in the scale

So, I guess the degree in 15 EDO must be 80 cents. The "best fifth of 15-EDO is
3 degrees". So the "best fifth" is 3 times 80 = 240 cents. 5 times 240 = 1200 cents
which makes a full octave. Even if this is correct I don't see the relevance of it.
======================================================

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.

==================================================
STEPHEN SZPAK RESPONDS:

The notes of 15 EDO are all 80 cents apart one from the other, why would a accidental
of (81/80) 21.5 cents take you up or down one note?

A comma is 21.5 cents. The closest thing that reminds me of that is the perfect 5th,
being off by 20 cents in comparison to 12 EDO or about 18 cents for JI. Are you saying
that by going up by 720 cents in 15 EDO for five times you get back where you started...thereby
causing the comma (actually an approximation of it) to disappear?
=============================================================
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#
--- End forwarded message ---

Stephen Szpak

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

--- In tuning@yahoogroups.com, "Stephen Szpak" <stephen_szpak@h...> wrote:
> You, and others, don't know how much I don't know, you know?
> First I don't think it's wise to continue trying to explain the
rest of
> what
> you've written here. I believe it relates to Sagittal and
Blackwood's
> notation.

Yes. Blackwood's and one of the Sagittals. The other Sagittal notation
notates it as a subset of 60-EDO = 5 * 12-EDO.

> If you want to continue you'll be frustrated.
>
> I realize 15 EDO has three interlaced circles of perfect 5ths.
> The notes of C and E and G# also exist in 12 EDO. (0 cents 400
cents 800
> cents)
> What does "we center on D for an odd number and on the DA fifth for
> and even number" mean? There is no D in 15 EDO.

It isn't very important so don't worry about it. But I meant, if we
don't get to use all 7 letter names in the sequence FCGDAEB before we
close a circle of fifths, then I think it is best to first omit F,
then B. So in 15-EDO we would use only CGDAE.

Dave:
> The best fifth of 15-EDO is 3 degrees which of course closes a circle
> after it is chained five times, CGDAE.

> =====================================================
> STEPHEN SZPAK WRITES:
...Even if this is correct I don't see the
> relevance of it.

It wasn't correct. I screwed up. I was thinking of 5-ET. Of course the
best fifth of 15-EDO is 9 degrees.

> ======================================================
>
>
> 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.
>
> ==================================================
> STEPHEN SZPAK RESPONDS:
>
> The notes of 15 EDO are all 80 cents apart one from the other,
why would
> a accidental
> of (81/80) 21.5 cents take you up or down one note?
>
> A comma is 21.5 cents. The closest thing that reminds me of that
is the
> perfect 5th,
> being off by 20 cents in comparison to 12 EDO or about 18 cents
for JI.
> Are you saying
> that by going up by 720 cents in 15 EDO for five times you get back
> where you started...thereby
> causing the comma (actually an approximation of it) to disappear?

No. 1 degree (step) of 15-EDO corresponds to the 5-comma (syntonic
comma, 80;81) in the sense that it is the difference between an
octave-reduced chain (stack) of four of the best approximations to a
2:3 just fifth and the best approximation to a 4:5 just major third.

After Paul Erlich, we can write the comma ratio with a semicolon
(80;81) to indicate a tempered size, as opposed to writing it with a
colon (80:81) which would represent its size in just intonation (the
21.5 cents you mention).

🔗Stephen Szpak <stephen_szpak@hotmail.com>

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
--- In tuning@yahoogroups.com, "Stephen Szpak" <stephen_szpak@h...> wrote:
> You, and others, don't know how much I don't know, you know?
> First I don't think it's wise to continue trying to explain the
rest of
>what
> you've written here. I believe it relates to Sagittal and
Blackwood's
>notation.

Yes. Blackwood's and one of the Sagittals. The other Sagittal notation
notates it as a subset of 60-EDO = 5 * 12-EDO.

> If you want to continue you'll be frustrated.
>
> I realize 15 EDO has three interlaced circles of perfect 5ths.
> The notes of C and E and G# also exist in 12 EDO. (0 cents 400
cents 800
>cents)
> What does "we center on D for an odd number and on the DA fifth for
> and even number" mean? There is no D in 15 EDO.

Dave:
>The best fifth of 15-EDO is 3 degrees which of course closes a circle
>after it is chained five times, CGDAE.

>=====================================================
>STEPHEN SZPAK WRITES:
...Even if this is correct I don't see the
>relevance of it.

It wasn't correct. I screwed up. I was thinking of 5-ET. Of course the
best fifth of 15-EDO is 9 degrees.

STEPHEN SZPAK WRITES:::::::::: SEE COMMENT BOTTOM OF PAGE
>======================================================
>
>
>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.
>
>==================================================
>STEPHEN SZPAK RESPONDS:
>
> The notes of 15 EDO are all 80 cents apart one from the other,
why would
>a accidental
> of (81/80) 21.5 cents take you up or down one note?
>
> A comma is 21.5 cents. The closest thing that reminds me of that
is the
>perfect 5th,
> being off by 20 cents in comparison to 12 EDO or about 18 cents
for JI.
>Are you saying
> that by going up by 720 cents in 15 EDO for five times you get back >where you started...thereby
> causing the comma (actually an approximation of it) to disappear?

STEPHEN SZPAK WRITES:::::::: SEE COMMENT BOTTOM OF PAGE

COMMENT: I don't understand any of it. We can always come back to this later. I think
it was last week when someone wrote to me about several ways 15 EDO
could be altered to make it a non-EDO scale. It seems that the post was
deleted. I forgot who sent it too.
Do you think, possibly, that the main reason anyone would alter 15 EDO
would be to create some 5 ths that are closer to 700 cents at the expense
of making other 5 ths much farther away, and therefore not useable?

Stephen Szpak

_________________________________________________________________
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