What is the blues flat five?

Greetings. No time to introduce myself. I've been a
member of the list for a little while now. I have a
pretty good understanding of almost all the common
just intonation intervals, but I have never gotten a
clear understanding of one thing: the flat five.

I understand that the Pythagorean 729/512 is not
really a flat five at all and doesn't appear in the
most basic structures.

The five limit 64/45 is obviously a useful note as an
upper leading tone to 4/3, but is it the note used in
a flat five chord?

I'd assume that 10/7 is a better flat five for
something that would really be heard as a chord and
also since blues and jazz which use flat five chords
tend to have more 7-limit notes.

If that is correct, does that mean that 15/14 would be
needed for a flat five chord on the dominant?

Is the flat five of a jazz flat five chord the same
note as the added flat five in the blues scale?

Anyway, I'd like thoughts and comments on this.
Also, How come all the information I've seen out there
references 7/4 and 7/6 in blues but no mention of the
flat five? Essentially, I wouldn't be sending this if
I could find the information elsewhere. Why isn't it
out there?

Thanks,

Aaron Wolf

www.ozmusic.com/aaron
mp3.com/aaronwolf

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hi Aaron,

> From: "Aaron Wolf" <backfromthesilo@yahoo.com>
> To: <tuning@yahoogroups.com>
> Sent: Saturday, May 31, 2003 8:01 PM
> Subject: [tuning] What is the blues flat five?
>
>
> Greetings. No time to introduce myself. I've been a
> member of the list for a little while now. I have a
> pretty good understanding of almost all the common
> just intonation intervals, but I have never gotten a
> clear understanding of one thing: the flat five.
>
> I understand that the Pythagorean 729/512 is not
> really a flat five at all and doesn't appear in the
> most basic structures.
>
> The five limit 64/45 is obviously a useful note as an
> upper leading tone to 4/3, but is it the note used in
> a flat five chord?
>
> I'd assume that 10/7 is a better flat five for
> something that would really be heard as a chord and
> also since blues and jazz which use flat five chords
> tend to have more 7-limit notes.
>
> If that is correct, does that mean that 15/14 would be
> needed for a flat five chord on the dominant?
>
> Is the flat five of a jazz flat five chord the same
> note as the added flat five in the blues scale?
>
> Anyway, I'd like thoughts and comments on this.
> Also, How come all the information I've seen out there
> references 7/4 and 7/6 in blues but no mention of the
> flat five? Essentially, I wouldn't be sending this if
> I could find the information elsewhere. Why isn't it
> out there?
>
> Thanks,
>
> Aaron Wolf

no votes from me on which tuning is the "best"
"flat five" ... which i'd most likely call a
"diminished-5th". as always, it depends for me
on a particular musical context, and the particular
thing i'm trying to express at that point.

but i have examined the matter in some detail,
and present a pretty exhaustive list of 13-limit
JI diminished-5ths on my "tritone" dictionary entry:

http://sonic-arts.org/dict/tritone.htm

at the bottom, there's also a tabulation and
graph of a bunch of meantone tritones as well.
(the graphic is brand new and is a better version
of the one i had there before.)

and at the beginning i examine the history
of tritone tuning to some extent.

i tend to really like the sound of both 7- and
11-limit intervals in blues. another alternative
for the "diminished-5th" which i don't examine on
my webpage is the ratio 23:16 (= ~628.2743473 cents),
which i've used in some JI blues.

in general, for piano performance, whether blues
or jazz, all intervals will be in 12edo.

hope you find that helpful.

-monz

--- In tuning@yahoogroups.com, Aaron Wolf <backfromthesilo@y...> wrote:

> The five limit 64/45 is obviously a useful note as an
> upper leading tone to 4/3, but is it the note used in
> a flat five chord?

If you are in a system where 225/224 is tempered out, then 64/45 and
10/7 are the same. Otherwise, I guess it is up to you to play whatever
note suits you.

--- In tuning@yahoogroups.com, Aaron Wolf <backfromthesilo@y...>
wrote:
> Greetings. No time to introduce myself. I've been a
> member of the list for a little while now. I have a
> pretty good understanding of almost all the common
> just intonation intervals, but I have never gotten a
> clear understanding of one thing: the flat five.

how much blues is actually played in just intonation? i actually
missed an awesome opportunity to witness such a rarity in new york
last friday :( but basically, we're in fairly speculative territory
here, with few clear guidelines beyond experience and personal taste.

> I understand that the Pythagorean 729/512 is not
> really a flat five at all

hmm . . . how about 1024/729?

> and doesn't appear in the
> most basic structures.

how do you define "most basic structures"? this could be a topic for
the tuning-math list . . .

> The five limit 64/45 is obviously a useful note as an
> upper leading tone to 4/3, but is it the note used in
> a flat five chord?

this is a strange question. i play both blues and jazz. can you
clarify which chord exactly you mean? dizzy gillespie and others used
the term "flat five chord" for certain sounds now commonly referred to
by terms such as "lydian dominant scale" . . . and this is certainly a
corner of jazz quite distant from the blues aspect . . .

> I'd assume that 10/7 is a better flat five for
> something that would really be heard as a chord

i guess i need to know what all the notes are in this "something" you
have in mind . . .

> and
> also since blues and jazz which use flat five chords
> tend to have more 7-limit notes.

hmm . . .

> If that is correct, does that mean that 15/14 would be
> needed for a flat five chord on the dominant?

this seems like a very odd choice. either 21/20 or 33/32 would sound
more consonant if your dominant is 3/2-15/8-9/8-21/16 (is it? you
mentioned 7-limit above), and would resolve more incisively to the
tonic to boot.

> Is the flat five of a jazz flat five chord the same
> note as the added flat five in the blues scale?

i don't think so, unless 12-equal is being used.

> Anyway, I'd like thoughts and comments on this.
> Also, How come all the information I've seen out there
> references 7/4 and 7/6 in blues but no mention of the
> flat five?

if you're really using 7/4 and 7/6 a lot, then 7/5 would be the
natural choice for a flat five. but really the more common "blue
notes" are more like 11/9 and 11/6, if you have to put ratios relative
to the tonic on them.

> Essentially, I wouldn't be sending this if
> I could find the information elsewhere. Why isn't it
> out there?

looks like what is out there is largely *mis*information.

Thanks so far for the comments, but they really aren't answering
my question. I truly have explored the resources I've seen online
and elsewhere.

Basically, I understand the value of 64/45 in a 5-limit style.
I also understand the complexities of relating to temperament
and of the various possibilities for "tritone"

But while there are various interesting notes that can be bluesy,
pretty much everything I've seen agrees on calling 7/6 the blues
third. And 7/4 is generally seen as the note for the blues 7th.
And that sounds right to my ear. I have less of a sense of the
blues flat five both intellectually and aurally.

I have not used flat five chords too extensively, though I am
familiar with the blues scale within temperament.

I also know that the tuning is subtle and this is a subtle point.

So to phrase the question more simply:
Is there any consensus on 10/7 and its use in various styles?
Does anyone claim that to be the blues flat five?

I'm also wondering if anyone could give me specific situations
that arise in music outside of the theoretical tuning-math circle
which would call for or not call for 10/7. Some musical phrase
written in equal temperament that would translate best to JI by
use of 10/7...

And I don't need to be convinced of the value of tempering things
or of the other tritones, etc. etc. I'm not disregarding all
possibilities, I just want to learn where 10/7 really fits in to things.

Aaron

--- In tuning@yahoogroups.com, "Gene Ward Smith"
<gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, Aaron Wolf
<backfromthesilo@y...> wrote:
>
> > The five limit 64/45 is obviously a useful note as an
> > upper leading tone to 4/3, but is it the note used in
> > a flat five chord?
>
> If you are in a system where 225/224 is tempered out, then
64/45 and
> 10/7 are the same. Otherwise, I guess it is up to you to play
whatever
> note suits you.

--- In tuning@yahoogroups.com, "backfromthesilo"
<backfromthesilo@y...> wrote:

> I'm also wondering if anyone could give me specific situations
> that arise in music outside of the theoretical tuning-math circle
> which would call for or not call for 10/7. Some musical phrase
> written in equal temperament that would translate best to JI by
> use of 10/7...

one example would be a chord like 1/1:8/7:10/7:12/7, which might be
your preferred rendition of the middle chord in a I-II/I-I
progression, depending on the voicings used. on the utonal side of
things, which harry partch rather liked, you have chords like
1/1:5/4:10/7:5/3, which in 12-equal is a chord traditionally used to
set up a modulation to the iii. note that, if tuned to 5/4, the root
of iii is then a common overtone of all four notes in the chord used
to set up the modulation to it . . .

--- In tuning@yahoogroups.com, "backfromthesilo"
<backfromthesilo@y...> wrote:

> But while there are various interesting notes that can be bluesy,
> pretty much everything I've seen agrees on calling 7/6 the blues
> third. And 7/4 is generally seen as the note for the blues 7th.
> And that sounds right to my ear. I have less of a sense of the
> blues flat five both intellectually and aurally.

A 7-limit JI scale containing 7/4 and 7/6 is normally better off using
7/5, not 10/7, if it needs to choose between them. Having started down
the path of 7's in the numerator, you keep at it in order to maximize
consonance; in the same way, you are likely to want a 21/20 rather
than a 15/14.

backfromthesilo wrote:

> But while there are various interesting notes that can be bluesy, > pretty much everything I've seen agrees on calling 7/6 the blues > third. And 7/4 is generally seen as the note for the blues 7th. > And that sounds right to my ear. I have less of a sense of the > blues flat five both intellectually and aurally.

Not that I have an answer; this is just to loosen up the other convictions: there are as many or more sources that place the blues third and seventh _between_ their major and minor 5-limit counterparts and not below them.
I used the 7-limit intonation, and i made the flat fifth a 7/5. Also, my practice has no bearing whatsoever on actual blues practice. I hope it was rightfully informed from many jazz horn players. And this is possibly a modern conception, and the inbetweenies are older (note e.g. the singing of Jelly Roll Morton or the many many guitarists bending up the minor intervals for blue notes).

klaus

Love the 49/48 comma 'twixt 7/4 and 12/7
1/1:8/7:10/7:12/7 and 4:5:6:7

>Message: 12
> Date: Sun, 01 Jun 2003 07:46:32 -0000
> From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
>Subject: Re: What is the blues flat five?
>
>--- In tuning@yahoogroups.com, "backfromthesilo"
<backfromthesilo@y...> wrote:
>
> I'm also wondering if anyone could give me specific situations
> that arise in music outside of the theoretical tuning-math circle
> which would call for or not call for 10/7. Some musical phrase
> written in equal temperament that would translate best to JI by
> use of 10/7...
>
>one example would be a chord like 1/1:8/7:10/7:12/7, which might be
>your preferred rendition of the middle chord in a I-II/I-I
>progression, depending on the voicings used. on the utonal side of
>things, which harry partch rather liked, you have chords like
>1/1:5/4:10/7:5/3, which in 12-equal is a chord traditionally used to
>set up a modulation to the iii. note that, if tuned to 5/4, the root
>of iii is then a common overtone of all four notes in the chord used
>to set up the modulation to it . . .
>

***From: Christopher Bailey******************

http://music.columbia.edu/~chris

**********************************************

----- Original Message -----
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>

> how much blues is actually played in just intonation? i actually
> missed an awesome opportunity to witness such a rarity in new york
> last friday :( but basically, we're in fairly speculative territory
> here, with few clear guidelines beyond experience and personal taste.

How would you know it was an awesome opportunity if you
were not there?

* David Beardsley
* microtonal guitar
* http://biink.com/db

----- Original Message -----
From: "David Beardsley" <db@biink.com>

> ----- Original Message -----
> From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
>
> > how much blues is actually played in just intonation? i actually
> > missed an awesome opportunity to witness such a rarity in new york
> > last friday :( but basically, we're in fairly speculative territory
> > here, with few clear guidelines beyond experience and personal taste.
>
> How would you know it was an awesome opportunity if you
> were not there?

Never mind. I see you already answered my question.

* David Beardsley
* microtonal guitar
* http://biink.com/db

This interval is at least theoretically unstateable as a whole number
integer fraction; it is the middle of the octave towards which
integer ratios build.
Clearly there can be no whole number integer ratio such that (N1/N2)
(N1/N2)= 2, as the square root of 2 is irrational.
Don't know what this has to do with intervals in the Blues, but I
thought you might be interested.

All the best
John S

--- In tuning@yahoogroups.com, David Beardsley <db@b...> wrote:
> ----- Original Message -----
> From: "wallyesterpaulrus" <wallyesterpaulrus@y...>
>
> > how much blues is actually played in just intonation? i actually
> > missed an awesome opportunity to witness such a rarity in new
york
> > last friday :( but basically, we're in fairly speculative
territory
> > here, with few clear guidelines beyond experience and personal
taste.
>
> How would you know it was an awesome opportunity if you
> were not there?

because jon catler was involved. should i have said "i missed a rare
opportunity to witness such an awesomeness"?

jsnelsonone a �crit :

> This interval is at least theoretically unstateable as a whole number
> integer fraction; it is the middle of the octave towards which
> integer ratios build.
> Clearly there can be no whole number integer ratio such that (N1/N2)
> (N1/N2)= 2, as the square root of 2 is irrational.
> Don't know what this has to do with intervals in the Blues, but I
> thought you might be interested.

Do you mean it gives you the blues because you're half way between
the beginning and the end ?
And another metaphysical question, when you play two tones, the second
of frequency (square root of 2) times the first, where do you place the tonic ?

--- In tuning@yahoogroups.com, jacques dudon <aeh@f...> wrote:

> And another metaphysical question, when you play two tones, the
second
> of frequency (square root of 2) times the first, where do you place
the tonic ?

in many if not most situations, i find the most likely tonic is about
a major third below the lower tone. in unusually sensitive
situations, such as where combinational tones are produced, i'll hear
the tonic more at a fifth below the lower tone. but there is always
some ambiguity. observations such as these led me to develop harmonic
entropy theory:

http://sonic-arts.org/dict/harmentr.htm

/harmonic_entropy/

> --- In tuning@yahoogroups.com, Aaron Wolf <backfromthesilo@y...>
> wrote:

> > I'd assume that 10/7 is a better flat five for
> > something that would really be heard as a chord

I do not have extensive musical practice, but in my mind, 10/7 suggest
strongly a JI 7th dominant chord in simplest possible ratio
7:(8):10:(12), in fact an inversion of (4):5:(6):7. This form
is not uncommon (i think) in western music when a smooth JI dominant
7th chord is aimed at (even though classical western music seems to
have a problem with the 7th harmonic)

> Anyway, I'd like thoughts and comments on this.
> Also, How come all the information I've seen out there
> references 7/4 and 7/6 in blues but no mention of the
> flat five?

In my mind 7/4 (inversion of 8/7) and 7/6 are more suggestive of some
african scales where basic chord 6:7:8 is based on the superparticular
division of the forth instead of the western 4:5:6 which is based on
the superparticular division of the fifth. Those interval are more
foreing to western tradition

yours truly

François Laferrière

Harmonic Entropy is a new concept to me but seems very useful.
Unfortunately the Dictionary link page appears to be missing a chart.

Thanks for the info

John S

Try this http://sonic-arts.org/td/entropy.htm. A graph speaks a
thousend numbers.
John S

Try this http://sonic-arts.org/td/entropy.htm
A graph paints a thousend numbers.
John S

--- In tuning@yahoogroups.com, "francois_laferriere"
<francois.laferriere@o...> wrote:
> > --- In tuning@yahoogroups.com, Aaron Wolf <backfromthesilo@y...>
> > wrote:
>
> > > I'd assume that 10/7 is a better flat five for
> > > something that would really be heard as a chord
>
> I do not have extensive musical practice, but in my mind, 10/7
suggest
> strongly a JI 7th dominant chord in simplest possible ratio
> 7:(8):10:(12), in fact an inversion of (4):5:(6):7.

this isn't clear. aaron was asking about the *pitch* 10/7 as part of
a scale rooted on 1/1. so do you mean 10/7 as part of a
1/1:8/7:10/7:12/7 chord? or what?

wallyesterpaulrus a �crit :

> --- In tuning@yahoogroups.com, jacques dudon <aeh@f...> wrote:
>
> > And another metaphysical question, when you play two tones, the second
> > of frequency (square root of 2) times the first, where do you place the tonic ?
>
> in many if not most situations, i find the most likely tonic is about
> a major third below the lower tone. in unusually sensitive
> situations, such as where combinational tones are produced, i'll hear
> the tonic more at a fifth below the lower tone.

I hear 1/1 *and* square root of 2 myself. This was rather a joke in my sense,
because whatever you hear, you might be able to hear as well
in the transposition by square root of 2, so always two solutions.
But your answer is very interesting, a major third below the lower tone
it seems that 7/5 is not far, while the fifth below sounds more like 17/12,
closer to the half octave, which generates a 5/12 that suggests a 1/6...
while 17/12's second order difference tone generates a very coherent 7/24
that also suggests the same harmony... good subject of study for harmonic
entropy ??

> but there is always
> some ambiguity. observations such as these led me to develop harmonic
> entropy theory:
>
> http://sonic-arts.org/dict/harmentr.htm
> /harmonic_entropy/

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:
> --- In tuning@yahoogroups.com, "francois_laferriere"
> <francois.laferriere@o...> wrote:
> > > --- In tuning@yahoogroups.com, Aaron Wolf <backfromthesilo@y...>
> > > wrote:
> >
> > > > I'd assume that 10/7 is a better flat five for
> > > > something that would really be heard as a chord
> >
> > I do not have extensive musical practice, but in my mind, 10/7
> suggest
> > strongly a JI 7th dominant chord in simplest possible ratio
> > 7:(8):10:(12), in fact an inversion of (4):5:(6):7.
>
> this isn't clear. aaron was asking about the *pitch* 10/7 as part of
> a scale rooted on 1/1.

ohhhh! I missed the point that Aaron was taking about 10/7 as part of
a scale (in melodic context?)... you are right, that is different

> so do you mean 10/7 as part of a
> 1/1:8/7:10/7:12/7 chord? or what?

Yes that is what I meant (the number in parenthesis are the "missing"
notes suggested by the 10/7 dyad). My problem is that I am grossly
ignorant of the function of the flat fifth interval in blues.
Otherwise would have suggested something more clever (or even more
cleverly, I would have remained silent :-))

yours truly

François Laferrière