pure tritones in 1/6 comma

Tom Dent wrote:
> > I could argue with equal validity that the tritone of 31-edo is an
> > audibly pure 7/5 - which is much clearer to the ear than whatever
> > definition of 'pure tritone' Brad wants to use (can 45/32 be
> > meaningfully called 'pure'?).
> >

And Paul Poletti continued:
> I, too, wonder what Brad is smoking when he talks about "pure"
> tritones in 1/6 mean. If I play c-f# in 1/6, I instantly hear the
> beating, and when I "fix" it, i.e. tune it "pure" (beatless), I find
> my ear goes to either 7/5 or 10/7, both of which sound far more
> "pure", though quite different in feel.

Not smoking anything. When I hear the pure tritones of 1/6 comma on my harpsichords, played in isolation, my ear takes them apart immediately to a pure 9:8 plus a pure 5:4. That is, if I hear C-F#, my ear fills in a phantom D by implication and I "hear" all three notes making a seventh chord in 4-2 position.

That pure relationship is also a quick and simple way to install one of these 1/6 comma tritones. Start from C, tune a pure G to it (temporary note), tune a pure D to that (another temporary note), and then a pure 5:4 F# from the D.

The resulting C-F# rings out strongly, however pointlessly anyone may argue against it ON PAPER that 45/32 isn't "meaningfully pure". We've all written about this before, several rounds, and on my harpsichords I continue to hear a 45/32 as pure. Some people apparently hear things differently. There's no need to insult me as a non-smoker or belittle my perceptions. All three of 7/5, 10/7, and 45/32 sound pure...to me.

And once the tritone endpoints are laid down accurately, the rest of the regular 1/6 comma installation is merely a matter of fitting in 5ths that all sound similar to one another (C-G-D-A-E-B-F#, six 5ths in sequence absorbing the one syntonic comma across their span), and continuing to check all the pure 45/32 tritones as they become available. The tritones are a nifty way to check the continued accuracy of each 5th/4th outward.

Brad Lehman

Why are you all making such a meal of this dim7th thing?

From C there is no F# in a diminished; it uses Gb and Bbb

Think about it in diatonic or meantone perspective.

Forget about integer frequency ratios;
they are only landmarks and about beat rates,
They have little else to do with tuning, and even less with harmony ;-)

C = Tonic I
Eb = bIIIrd = b3
Gb = bVth = b5
Bbb = bbVIIth = bb7

Each interval is a bIIIrd = b3

In 12edo bIIIrd is 3 semitones
four steps of three semitones = one octave

On Feb 15, 2008, at 1:55 PM, Brad Lehman wrote:

> Tom Dent wrote:
> > > I could argue with equal validity that the tritone of 31-edo is an
> > > audibly pure 7/5 - which is much clearer to the ear than whatever
> > > definition of 'pure tritone' Brad wants to use (can 45/32 be
> > > meaningfully called 'pure'?).
> > >
>
> And Paul Poletti continued:
> > I, too, wonder what Brad is smoking when he talks about "pure"
> > tritones in 1/6 mean. If I play c-f# in 1/6, I instantly hear the
> > beating, and when I "fix" it, i.e. tune it "pure" (beatless), I find
> > my ear goes to either 7/5 or 10/7, both of which sound far more
> > "pure", though quite different in feel.
>
> Not smoking anything. When I hear the pure tritones of 1/6 comma on my
> harpsichords, played in isolation, my ear takes them apart immediately
> to a pure 9:8 plus a pure 5:4. That is, if I hear C-F#, my ear fills > in
> a phantom D by implication and I "hear" all three notes making a > seventh
> chord in 4-2 position.
>
> That pure relationship is also a quick and simple way to install one > of
> these 1/6 comma tritones. Start from C, tune a pure G to it (temporary
> note), tune a pure D to that (another temporary note), and then a pure
> 5:4 F# from the D.
>
> The resulting C-F# rings out strongly, however pointlessly anyone may
> argue against it ON PAPER that 45/32 isn't "meaningfully pure". We've
> all written about this before, several rounds, and on my > harpsichords I
> continue to hear a 45/32 as pure. Some people apparently hear things
> differently. There's no need to insult me as a non-smoker or belittle
> my perceptions. All three of 7/5, 10/7, and 45/32 sound pure...to me.
>
> And once the tritone endpoints are laid down accurately, the rest of > the
> regular 1/6 comma installation is merely a matter of fitting in 5ths
> that all sound similar to one another (C-G-D-A-E-B-F#, six 5ths in
> sequence absorbing the one syntonic comma across their span), and
> continuing to check all the pure 45/32 tritones as they become
> available. The tritones are a nifty way to check the continued > accuracy
> of each 5th/4th outward.
>
> Brad Lehman
>
>
Charles Lucy
lucy@lucytune.com

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

Brad Lehman wrote:

> That pure relationship is also a quick and simple way to install one of
> these 1/6 comma tritones. Start from C, tune a pure G to it (temporary
> note), tune a pure D to that (another temporary note), and then a pure
> 5:4 F# from the D.

Is it so hard to tune a 9/8 by ear and then a 5/4 from that? Epimoric intervals are quite well distinguishable, as far as I can hear them.

> And once the tritone endpoints are laid down accurately, the rest of the
> regular 1/6 comma installation is merely a matter of fitting in 5ths
> that all sound similar to one another (C-G-D-A-E-B-F#, six 5ths in
> sequence absorbing the one syntonic comma across their span), and
> continuing to check all the pure 45/32 tritones as they become
> available. The tritones are a nifty way to check the continued accuracy
> of each 5th/4th outward.

That is, as long as you know how fast they should beat.

Petr

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
> Why are you all making such a meal of this dim7th thing?
>
> From C there is no F# in a diminished; it uses Gb and Bbb
>
> Think about it in diatonic or meantone perspective.
>
> Forget about integer frequency ratios;
> they are only landmarks and about beat rates,
> They have little else to do with tuning, and even less with harmony ;-)
>
>
> C = Tonic I
> Eb = bIIIrd = b3
> Gb = bVth = b5
> Bbb = bbVIIth = bb7
>
Um, er, well, correct me if I'm wrong, 'cause I'm too lazy to go back
to find Brad's original message, but I believe he made some glowing
praise of dim7 chords in 1/6 comma mean because, as he claimed, they
are composed of two interlocked "pure tritones".

Now, be that the case, last time I checked, a perfectly legal dim7
chord in reg. mean. of any flavor is F#-A-C-Eb, hence my grab at C-F#
to test Brad's "pure" tritone theory.

Anyway, it now appears that Brad is indeed operating with an
alternative definition of the word "pure", which seems to mean ANY
interval which is arrived at by summing up a series of other (truly)
pure intervals. You know, like the pure major third C-E in
Pythagorean, fur example.

Ciao,

P

Yes that makes sense (i.e. subtracting flat thirds) and working the other direction around the spiral from how I usually would think about it, or starting from the F# and adding flat thirds.

Got it!

On Feb 15, 2008, at 10:17 PM, Paul Poletti wrote:

> --- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
> >
> > Why are you all making such a meal of this dim7th thing?
> >
> > From C there is no F# in a diminished; it uses Gb and Bbb
> >
> > Think about it in diatonic or meantone perspective.
> >
> > Forget about integer frequency ratios;
> > they are only landmarks and about beat rates,
> > They have little else to do with tuning, and even less with > harmony ;-)
> >
> >
> > C = Tonic I
> > Eb = bIIIrd = b3
> > Gb = bVth = b5
> > Bbb = bbVIIth = bb7
> >
> Um, er, well, correct me if I'm wrong, 'cause I'm too lazy to go back
> to find Brad's original message, but I believe he made some glowing
> praise of dim7 chords in 1/6 comma mean because, as he claimed, they
> are composed of two interlocked "pure tritones".
>
> Now, be that the case, last time I checked, a perfectly legal dim7
> chord in reg. mean. of any flavor is F#-A-C-Eb, hence my grab at C-F#
> to test Brad's "pure" tritone theory.
>
> Anyway, it now appears that Brad is indeed operating with an
> alternative definition of the word "pure", which seems to mean ANY
> interval which is arrived at by summing up a series of other (truly)
> pure intervals. You know, like the pure major third C-E in
> Pythagorean, fur example.
>
> Ciao,
>
> P
>
>
>
Charles Lucy
lucy@lucytune.com

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk