Yahoo Tuning Groups Ultimate Backup tuning New JI scale

Hi Michael,

your construction, as many others seen here, shows interesting mathematical
aspects.
Which being a mathematician I certainly find interesting.

I am also a musician however, and here I find something puzzling in your
(and many other) JI proposal.
E.g., I understand that you find 7/5 consonant.
However, in any keyboard with a good complement of partials (e.g. a
harpsichord or even a MIDI stock sampling such as the one provided with
Creative PC sound cards) I distinctly hear as dissonant any rational
interval with numbers greater than 5.
It is not me: I am in good company as you certainly know from the musical
acoustics writings of the last five centuries where the fenomenon was first
reported and then explained.

On behalf of the "non-JI-tterati" in the list, I would be grateful to have
an explanation about the rationale for constructing scales using ratios that
centuries of musicians - and most present-day ones -l do not perceive as
consonant.

Thanks and kind regards,

Claudio
http://harps.braybaroque.ie/

_____

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of
djtrancendance
Sent: 17 March 2009 04:42
To: tuning@yahoogroups.com
Subject: [tuning] New JI scale

In an order to test myself, I came up with a JI tuning that seems to have
properties somewhat competitive with my PHI scale (tons of possible chords,
9 tones per 2/1 octave...) and some very similar ratios, yet all it is
comprised of rational numbers.

Here is the (9-tone) scale
1) 1/1
2) 17/16
3) 9/8
4) 13/11
5) 5/4
6) 7/5
7) 25/16
8) 18/11
9) 15/8
2/1 (octave)

I found a lot of it by ears and the rest by otonal/utonal relationships. Why
the 7/5 works, though, is a mystery to me...I found it by ear alone.

It can in many ways be viewed as a rational estimate of my PHI scale
(1.636363 sounds/feels like a 5th in this scale and 1.5 is omitted
altogether!). Since it's rational number based hopefully even a few of those
who thought a was a bit crazy using irrational numbers can make some sense
of it. :-)

-Michael

🔗Marcel de Velde <m.develde@...>

>
> I am also a musician however, and here I find something puzzling in your
> (and many other) JI proposal.
> E.g., I understand that you find 7/5 consonant.
> However, in any keyboard with a good complement of partials (e.g. a
> harpsichord or even a MIDI stock sampling such as the one provided with
> Creative PC sound cards) I distinctly hear as dissonant any rational
> interval with numbers greater than 5.
> It is not me: I am in good company as you certainly know from the musical
> acoustics writings of the last five centuries where the fenomenon was first
> reported and then explained.
>

Hi Claudio,

Yes 7/5 sounds fairly dissonant to me too.
Though any other ratio between the fourth and the fifth sounds even more
dissonant.
So I do beleive it's the least dissonant ratio for that location.
Also try 7/3. The septimal minor third an octave higher. It sounds fairly
consonant to me.
The difficulty I think is not in finding a consonant interval for any
location, but the difficulty is in understanding the underlying theory of
music so that you know how and when to use these intervals.

Marcel

🔗Mike Battaglia <battaglia01@...>

You don't hear 7/4 as consonant?
-Mike

On Tue, Mar 17, 2009 at 8:04 AM, Claudio Di Veroli <dvc@...> wrote:
> Hi Michael,
>
> your construction, as many others seen here, shows interesting mathematical
> aspects.
> Which being a mathematician I certainly find interesting.
>
> I am also a musician however, and here I find something puzzling in your
> (and many other) JI proposal.
> E.g., I understand that you find 7/5 consonant.
> However, in any keyboard with a good complement of partials (e.g. a
> harpsichord or even a MIDI stock sampling such as the one provided with
> Creative PC sound cards) I distinctly hear as dissonant any rational
> interval with numbers greater than 5.
> It is not me: I am in good company as you certainly know from the musical
> acoustics writings of the last five centuries where the fenomenon was first
> reported and then explained.
>
> On behalf of the "non-JI-tterati" in the list, I would be grateful to have
> an explanation about the rationale for constructing scales using ratios that
> centuries of musicians - and most present-day ones -l do not perceive as
> consonant.
>
> Thanks and kind regards,
>
> Claudio
> http://harps.braybaroque.ie/
>
>
>
> ________________________________
> From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of
> djtrancendance
> Sent: 17 March 2009 04:42
> To: tuning@yahoogroups.com
> Subject: [tuning] New JI scale
>
> In an order to test myself, I came up with a JI tuning that seems to have
> properties somewhat competitive with my PHI scale (tons of possible chords,
> 9 tones per 2/1 octave...) and some very similar ratios, yet all it is
> comprised of rational numbers.
>
> Here is the (9-tone) scale
> 1) 1/1
> 2) 17/16
> 3) 9/8
> 4) 13/11
> 5) 5/4
> 6) 7/5
> 7) 25/16
> 8) 18/11
> 9) 15/8
> 2/1 (octave)
>
> I found a lot of it by ears and the rest by otonal/utonal relationships. Why
> the 7/5 works, though, is a mystery to me...I found it by ear alone.
>
> It can in many ways be viewed as a rational estimate of my PHI scale
> (1.636363 sounds/feels like a 5th in this scale and 1.5 is omitted
> altogether!). Since it's rational number based hopefully even a few of those
> who thought a was a bit crazy using irrational numbers can make some sense
> of it. :-)
>
> -Michael
>
>

🔗Claudio Di Veroli <dvc@...>

Mike wrote:

_____

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of
Mike Battaglia
Sent: 18 March 2009 22:29
To: tuning@yahoogroups.com
Subject: Re: [tuning] New JI scale

You don't hear 7/4 as consonant?
-Mike

On Tue, Mar 17, 2009 at 8:04 AM, Claudio Di Veroli <dvc@braybaroque.
<mailto:dvc%40braybaroque.ie> ie> wrote:
> Hi Michael,
>
> your construction, as many others seen here, shows interesting
mathematical
> aspects.
> Which being a mathematician I certainly find interesting.
>
> I am also a musician however, and here I find something puzzling in your
> (and many other) JI proposal.
> E.g., I understand that you find 7/5 consonant.
> However, in any keyboard with a good complement of partials (e.g. a
> harpsichord or even a MIDI stock sampling such as the one provided with
> Creative PC sound cards) I distinctly hear as dissonant any rational
> interval with numbers greater than 5.
> It is not me: I am in good company as you certainly know from the musical
> acoustics writings of the last five centuries where the fenomenon was
first
> reported and then explained.
>
> On behalf of the "non-JI-tterati" in the list, I would be grateful to have
> an explanation about the rationale for constructing scales using ratios
that
> centuries of musicians - and most present-day ones -l do not perceive as
> consonant.
>
> Thanks and kind regards,
>
> Claudio
> http://harps. <http://harps.braybaroque.ie/> braybaroque.ie/
>
>
>
> ________________________________
> From: tuning@yahoogroups. <mailto:tuning%40yahoogroups.com> com
[mailto:tuning@yahoogroups. <mailto:tuning%40yahoogroups.com> com] On Behalf
Of
> djtrancendance
> Sent: 17 March 2009 04:42
> To: tuning@yahoogroups. <mailto:tuning%40yahoogroups.com> com
> Subject: [tuning] New JI scale
>
> In an order to test myself, I came up with a JI tuning that seems to have
> properties somewhat competitive with my PHI scale (tons of possible
chords,
> 9 tones per 2/1 octave...) and some very similar ratios, yet all it is
> comprised of rational numbers.
>
> Here is the (9-tone) scale
> 1) 1/1
> 2) 17/16
> 3) 9/8
> 4) 13/11
> 5) 5/4
> 6) 7/5
> 7) 25/16
> 8) 18/11
> 9) 15/8
> 2/1 (octave)
>
> I found a lot of it by ears and the rest by otonal/utonal relationships.
Why
> the 7/5 works, though, is a mystery to me...I found it by ear alone.
>
> It can in many ways be viewed as a rational estimate of my PHI scale
> (1.636363 sounds/feels like a 5th in this scale and 1.5 is omitted
> altogether!). Since it's rational number based hopefully even a few of
those
> who thought a was a bit crazy using irrational numbers can make some sense
> of it. :-)
>
> -Michael
>
>

🔗Claudio Di Veroli <dvc@...>

🔗Aaron Krister Johnson <aaron@...>

Claudio,

You are confusing 7/4 with 7/5.

7/4 is a harmonic minor 7th. 7/5 is a tritone, but not the only size available (another quick example might be 45/32). Both 7/4 and 7/5 are consonant sounding, but since dissonance in music is largely contextual, 7/5 can be considered a dissonance or a consonance.

In any event, most would agree that outside of stylistic context, either 7/4 or 7/5 are quite pleasant and concordant.

-Aaron.

--- In tuning@yahoogroups.com, "Claudio Di Veroli" <dvc@...> wrote:
>
> Mike wrote:
> You don't hear 7/4 as consonant?
>
> We harpsichordists have used the 7/4 (tritone) for centuries as an example
> of dissonance, even if tuned pure.
> The tritone (not only the wolf intervals) was called "devil in music" even
> when pure (it is almost pure in 1/4 s.c. meantone).
> Just for a check I went to the Wikipedia, where there are some further
> details.
> http://temper.braybaroque.ie/
>
> Regards
>
> Claudio
>

🔗Graham Breed <gbreed@...>

Claudio Di Veroli wrote (corrected):

> We harpsichordists have used the 7/5 (tritone) for centuries as an example of > dissonance, even if tuned pure.

The 4/3 (fourth) has also been an example of dissonance, even when tuned pure, for centuries. Do you hear it as consonant? Thirds and sixths were examples of dissonance for centuries, and we don't know if they were tuned pure. Do you hear them as consonant?

> The tritone (not only the wolf intervals) was called "devil in music" even when > pure (it is almost pure in 1/4 s.c. meantone).

Tritones (and enharmonies) are the only middle-sized intervals outside the 5-limit in a diatonic scale, hence the warning.

I hope we all agree that tritones (and intervals of 7/4) are not 5-limit consonances. But the original context was a 9 note scale. Can *you* find 9 notes that can be played together without dissonance? Michael is doing his best.

> Just for a check I went to the Wikipedia, where there are some further details.

Okay, I'll get back to you when I've finished reading Wikipedia.

But for now ... how about this?

http://en.wikipedia.org/wiki/Barbershop_(musical_style)

"Gage Averill writes that `Barbershoppers have become partisans of this acoustic phenomenon' and that `the more experienced singers of the barbershop revival (at least after the 1940s) have self-consciously tuned their dominant seventh and tonic chords in just intonation to maximize the overlap of common overtones.'"
[Averill, Gage (2003). Four Parts, No Waiting: A Social History of American Barbershop Harmony. Oxford University Press. ISBN 0195116720.]

Maybe you should be contacting the barbershop community to correct their terrible mistake.

Graham

🔗Daniel Forro <dan.for@...>

Yes, Claudio, 6 halftones must be definitely satanic for sure :-) What about this tri-tritone 666 Scriabinesque chord

C-F#-Bb-E-Ab-D

It doesn't sound as a hell. Probably because we hear rather its third structure

C-E-G#-Bb-D-F#

(C11+/5+)

and whole tone scale base.

Nice spring equinox to the all!

Daniel Forro

On 19 Mar 2009, at 7:50 AM, Claudio Di Veroli wrote:

>
> Mike wrote:
> You don't hear 7/4 as consonant?
> We harpsichordists have used the 7/4 (tritone) for centuries as an > example of dissonance, even if tuned pure.
> The tritone (not only the wolf intervals) was called "devil in > music" even when pure (it is almost pure in 1/4 s.c. meantone).
> Just for a check I went to the Wikipedia, where there are some > further details.
> http://temper.braybaroque.ie/
>
> Regards
>
> Claudio

🔗Claudio Di Veroli <dvc@...>

Thanks Aron!

> Claudio, You are confusing 7/4 with 7/5. 7/4 is a harmonic minor 7th.

Indeed, I stand corrected!!

> 7/5 is a tritone, but not the only size available (another quick example
might be 45/32). Both 7/4 and 7/5 are consonant sounding, but since
dissonance in music is largely contextual, 7/5 can be considered a
dissonance or a consonance.
In any event, most would agree that outside of stylistic context, either 7/4
or 7/5 are quite pleasant and concordant.
You are on your own on this one!
I side with centuries of musicians' opinions and my own tuning+hearing
tests:
7/4 is "just a little less dissonant" than 7/5 on instruments rich on
harmonics such as harpsichord and bowed string instruments.
Of course, in an instrument poor in 7th harmonics (such as some pianos and
organ pipes) both intervals will be OK, for lack of the harmonics that could
produce dissonance.

Regards,

Claudio

🔗Claudio Di Veroli <dvc@...>

Daniel wrote:
Yes, Claudio, 6 halftones must be definitely satanic for sure :-)
What about this tri-tritone 666 Scriabinesque chord
C-F#-Bb-E-Ab-D
It doesn't sound as a hell. Probably because we hear rather its third
structure C-E-G#-Bb-D-F# (C11+/5+)
and whole tone scale base.
Nice spring equinox to the all!
_____________________________________

Thanks Daniel!

It is a real pity that we cannot meet and discuss with instruments, both
traditional and MIDI, tuning, playing music, both classical and modern, in a
non-symposium environment!
I mean, we tune a MIDI harpsichord/violin with different intervals: try,
hear, hear again, temper, retune, play something, discuss: one always finds
something!
E.g., when I was preparing sound examples for my recent work, I was
surprised at how intervals below Zarlino's 6-limit (3/2, 4/3, 5/3, 5/4) are
so consonant and then 6/5, 7/6, 7/4, 7/5, 8/5 become suddenly and
progressively dissonant, especially on a harpsichord.
Since one is progressing by small integer steps, it is not apparent why this
happens. Of course the explanation is found writing down the partials as
notes and analysing pairs of partials and beats: the situation changes
dramatically due to the structure of the harmonic series. Yet it depends
strongly on the type of instruments also, and there is sure an element of
personal taste as well.

Unfortunately the "web magic" disguises the sad fact that we members of this
list are dispersed in all corners of the Globe. HOWEVER; if anybody feels
like meeting in a small group somewhere in Europe for a couple of days,
computers and tuning hammers at hand, I will be just very happy to play host
in our home in Bray, just South of Dublin, Ireland, with views of the
Wicklow mountaints (well hills actually) and decent musical equipment.

Best,

Claudio

🔗Daniel Forro <dan.for@...>

Yes, Claudio, general image of harpsichord is that it has very well pronunciated, concrete, rich and sharp sound full of higher harmonics, beats from detuned unison, octave coupling, and there's also strong inharmonic transient caused by plucking, so harpsichord tuning is very important and dissonances are to hear easily. But there's possible to get out a simple sound, too.

Your idea to invite colleagues is great, but difficult to realize... Anyway thanks for kind invitation, who knows, maybe one day, as rich pensioners living from our royalties for microtonal works :-)

Daniel Forro

On 19 Mar 2009, at 11:32 AM, Claudio Di Veroli wrote:

> Thanks Daniel!
>
> It is a real pity that we cannot meet and discuss with instruments, > both traditional and MIDI, tuning, playing music, both classical > and modern, in a non-symposium environment!
> I mean, we tune a MIDI harpsichord/violin with different intervals: > try, hear, hear again, temper, retune, play something, discuss: one > always finds something!
> E.g., when I was preparing sound examples for my recent work, I was > surprised at how intervals below Zarlino's 6-limit (3/2, 4/3, 5/3, > 5/4) are so consonant and then 6/5, 7/6, 7/4, 7/5, 8/5 become > suddenly and progressively dissonant, especially on a harpsichord.
> Since one is progressing by small integer steps, it is not apparent > why this happens. Of course the explanation is found writing down > the partials as notes and analysing pairs of partials and beats: > the situation changes dramatically due to the structure of the > harmonic series. Yet it depends strongly on the type of instruments > also, and there is sure an element of personal taste as well.
>
> Unfortunately the "web magic" disguises the sad fact that we > members of this list are dispersed in all corners of the Globe. > HOWEVER; if anybody feels like meeting in a small group somewhere > in Europe for a couple of days, computers and tuning hammers at > hand, I will be just very happy to play host in our home in Bray, > just South of Dublin, Ireland, with views of the Wicklow mountaints > (well hills actually) and decent musical equipment.
>
> Best,
>
> Claudio
>

🔗Michael Sheiman <djtrancendance@...>

--Can *you* find 9 notes that can be played
--together without dissonance? Michael is doing his best.

Thank you! :-) And, for the record, I don't think the "JI imitating PHI" type scale I posted is by any means perfect...heck, my ears seem to tell me my PHI scale is better.

Nonetheless, I wanted to be fair to "JI theory" and open-minded to the fact permutations of it may be able to beat my own efforts (based on PHI) on making a consonant 9-note-per-2/1-octave scale. Here's the challenging new and odd theories with older, more well researched ones in a quest for a good balance! :-)

--- On Wed, 3/18/09, Graham Breed <gbreed@gmail.com> wrote:

From: Graham Breed <gbreed@...>
Subject: Re: [tuning] New JI scale
To: tuning@yahoogroups.com
Date: Wednesday, March 18, 2009, 5:45 PM

Claudio Di Veroli wrote (corrected):

> We harpsichordists have used the 7/5 (tritone) for centuries as an example of
> dissonance, even if tuned pure.

The 4/3 (fourth) has also been an example of dissonance,
even when tuned pure, for centuries. Do you hear it as
consonant? Thirds and sixths were examples of dissonance
for centuries, and we don't know if they were tuned pure.
Do you hear them as consonant?

> The tritone (not only the wolf intervals) was called "devil in music" even when
> pure (it is almost pure in 1/4 s.c. meantone).

Tritones (and enharmonies) are the only middle-sized
intervals outside the 5-limit in a diatonic scale, hence the
warning.

I hope we all agree that tritones (and intervals of 7/4) are
not 5-limit consonances. But the original context was a 9
note scale. Can *you* find 9 notes that can be played
together without dissonance? Michael is doing his best.

> Just for a check I went to the Wikipedia, where there are some further details.

Okay, I'll get back to you when I've finished reading Wikipedia.

But for now ... how about this?

http://en.wikipedia .org/wiki/ Barbershop_(musical_style)

"Gage Averill writes that `Barbershoppers have become
partisans of this acoustic phenomenon' and that `the more
experienced singers of the barbershop revival (at least
after the 1940s) have self-consciously tuned their dominant
seventh and tonic chords in just intonation to maximize the
overlap of common overtones.'"
[Averill, Gage (2003). Four Parts, No Waiting: A Social
History of American Barbershop Harmony. Oxford University
Press. ISBN 0195116720.]

Maybe you should be contacting the barbershop community to
correct their terrible mistake.

Graham

🔗Carl Lumma <carl@...>

🔗Daniel Forro <dan.for@...>

🔗Carl Lumma <carl@...>

🔗Charles Lucy <lucy@...>

I don't know why yet for some reason all Claudio's postings display as miniscule light blue text on my OSX Mail application, making them very difficult to read.
Does anyone else have this problem with his, and his alone, postings?
On 19 Mar 2009, at 02:32, Claudio Di Veroli wrote:

>
> Daniel wrote:
> Yes, Claudio, 6 halftones must be definitely satanic for sure :-)
> What about this tri-tritone 666 Scriabinesque chord
> C-F#-Bb-E-Ab-D
> It doesn't sound as a hell. Probably because we hear rather its third
> structure C-E-G#-Bb-D-F# (C11+/5+)
> and whole tone scale base.
> Nice spring equinox to the all!
> _____________________________________
>
> Thanks Daniel!
>
> It is a real pity that we cannot meet and discuss with instruments, > both traditional and MIDI, tuning, playing music, both classical and > modern, in a non-symposium environment!
> I mean, we tune a MIDI harpsichord/violin with different intervals: > try, hear, hear again, temper, retune, play something, discuss: one > always finds something!
> E.g., when I was preparing sound examples for my recent work, I was > surprised at how intervals below Zarlino's 6-limit (3/2, 4/3, 5/3, > 5/4) are so consonant and then 6/5, 7/6, 7/4, 7/5, 8/5 become > suddenly and progressively dissonant, especially on a harpsichord.
> Since one is progressing by small integer steps, it is not apparent > why this happens. Of course the explanation is found writing down > the partials as notes and analysing pairs of partials and beats: the > situation changes dramatically due to the structure of the harmonic > series. Yet it depends strongly on the type of instruments also, and > there is sure an element of personal taste as well.
>
> Unfortunately the "web magic" disguises the sad fact that we members > of this list are dispersed in all corners of the Globe. HOWEVER; if > anybody feels like meeting in a small group somewhere in Europe for > a couple of days, computers and tuning hammers at hand, I will be > just very happy to play host in our home in Bray, just South of > Dublin, Ireland, with views of the Wicklow mountaints (well hills > actually) and decent musical equipment.
>
> Best,
>
> Claudio
>
>
>
Charles Lucy
lucy@...

- 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

🔗Charles Lucy <lucy@...>

According to my claims, any nine contiguous LucyTuned notes on the chain of fourths and fifths, should give you the result that you are seeking.

What instrument would you like be to use to demonstrate this for you in an audio file?

or you could try it yourself;-)

On 19 Mar 2009, at 03:10, Michael Sheiman wrote:

> --Can *you* find 9 notes that can be played
> --together without dissonance? Michael is doing his best.
>
> Thank you! :-) And, for the record, I don't think the "JI > imitating PHI" type scale I posted is by any means perfect...heck, > my ears seem to tell me my PHI scale is better.
>
> Nonetheless, I wanted to be fair to "JI theory" and open-minded > to the fact permutations of it may be able to beat my own efforts > (based on PHI) on making a consonant 9-note-per-2/1-octave scale. > Here's the challenging new and odd theories with older, more well > researched ones in a quest for a good balance! :-)
>
>
>
> --- On Wed, 3/18/09, Graham Breed <gbreed@...> wrote:
>
> From: Graham Breed <gbreed@...>
> Subject: Re: [tuning] New JI scale
> To: tuning@yahoogroups.com
> Date: Wednesday, March 18, 2009, 5:45 PM
>
> Claudio Di Veroli wrote (corrected):
>
> > We harpsichordists have used the 7/5 (tritone) for centuries as an > example of
> > dissonance, even if tuned pure.
>
> The 4/3 (fourth) has also been an example of dissonance,
> even when tuned pure, for centuries. Do you hear it as
> consonant? Thirds and sixths were examples of dissonance
> for centuries, and we don't know if they were tuned pure.
> Do you hear them as consonant?
>
> > The tritone (not only the wolf intervals) was called "devil in > music" even when
> > pure (it is almost pure in 1/4 s.c. meantone).
>
> Tritones (and enharmonies) are the only middle-sized
> intervals outside the 5-limit in a diatonic scale, hence the
> warning.
>
> I hope we all agree that tritones (and intervals of 7/4) are
> not 5-limit consonances. But the original context was a 9
> note scale. Can *you* find 9 notes that can be played
> together without dissonance? Michael is doing his best.
>
> > Just for a check I went to the Wikipedia, where there are some > further details.
>
> Okay, I'll get back to you when I've finished reading Wikipedia.
>
> But for now ... how about this?
>
> http://en.wikipedia .org/wiki/ Barbershop_(musical_style)
>
> "Gage Averill writes that `Barbershoppers have become
> partisans of this acoustic phenomenon' and that `the more
> experienced singers of the barbershop revival (at least
> after the 1940s) have self-consciously tuned their dominant
> seventh and tonic chords in just intonation to maximize the
> overlap of common overtones.'"
> [Averill, Gage (2003). Four Parts, No Waiting: A Social
> History of American Barbershop Harmony. Oxford University
> Press. ISBN 0195116720.]
>
> Maybe you should be contacting the barbershop community to
> correct their terrible mistake.
>
> Graham
>
>
>
Charles Lucy
lucy@...

- 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

🔗Claudio Di Veroli <dvc@...>

🔗Charles Lucy <lucy@...>

🔗Michael Sheiman <djtrancendance@...>

Charles,

--According to my claims, any nine contiguous LucyTuned notes on the
chain of fourths and --fifths, should give you the result that you are
seeking.
Well then, go for it! :-) The tricky thing is you have to
A) play all 9 notes within a 'tiny' 2/1 octave interval (and no more than that)
B) have all notes played together at once within that interval (IE as a 9-note chord) and still sound consonant

Personal note: this is a huge reason why I often use intervals other than the standard perfect 3rd, 2nd, etc. ...because I've found all of those lead to chords that can only fit about 5 notes in a consonant chord within an octave. Maybe the Lucy Tuned circle of 4ths and 5ths can somehow slip by this problem?...we'll have to see.

And that, of course, implies people have to learn some pretty complex music theory to learn all the chords and avoid dissonance...which presents a steep learning curve (which may well explain why common musicians have been scared to adopt many of even the best non-7-tone micro-tonal scales).

---What instrument would you like be to use to demonstrate this for you in an audio file?
The harpsichord. :-) It appears to be the most demanding one so far as dissonance...and also the once I used to test my "rational numbered ratios approximating/'tempering' the circle of PI scale".
If you can Lucy-Tuning it to work smoothly with the harpsichord in the above extreme conditions, you're the man. :-)

--- On Thu, 3/19/09, Charles Lucy <lucy@...> wrote:

From: Charles Lucy <lucy@...>
Subject: [tuning] 9 contiguous notes
To: tuning@yahoogroups.com
Date: Thursday, March 19, 2009, 12:31 AM

According to my claims, any nine contiguous LucyTuned notes on the chain of fourths and fifths, should give you the result that you are seeking.
What instrument would you like be to use to demonstrate this for you in an audio file?
or you could try it yourself;-)
On 19 Mar 2009, at 03:10, Michael Sheiman wrote:
--Can *you* find 9 notes that can be played
--together without dissonance? Michael is doing his best. Thank you! :-) And, for the record, I don't think the "JI imitating PHI" type scale I posted is by any means perfect...heck, my ears seem to tell me my PHI scale is better. Nonetheless, I wanted to be fair to "JI theory" and open-minded to the fact permutations of it may be able to beat my own efforts (based on PHI) on making a consonant 9-note-per-2/ 1-octave scale. Here's the challenging new and odd theories with older, more well researched ones in a quest for a good balance! :-)

--- On Wed, 3/18/09, Graham Breed <gbreed@gmail. com> wrote:

From: Graham Breed <gbreed@gmail. com>
Subject: Re: [tuning] New JI scale
To: tuning@yahoogroups. com
Date: Wednesday, March 18, 2009, 5:45 PM

Claudio Di Veroli wrote (corrected):

> We harpsichordists have used the 7/5 (tritone) for centuries as an example of
> dissonance, even if tuned pure.

The 4/3 (fourth) has also been an example of dissonance,
even when tuned pure, for centuries. Do you hear it as
consonant? Thirds and sixths were examples of dissonance
for centuries, and we don't know if they were tuned pure.
Do you hear them as consonant?

> The tritone (not only the wolf intervals) was called "devil in music" even when
> pure (it is almost pure in 1/4 s.c. meantone).

Tritones (and enharmonies) are the only middle-sized
intervals outside the 5-limit in a diatonic scale, hence the
warning.

I hope we all agree that tritones (and intervals of 7/4) are
not 5-limit consonances. But the original context was a 9
note scale. Can *you* find 9 notes that can be played
together without dissonance? Michael is doing his best.

> Just for a check I went to the Wikipedia, where there are some further details.

Okay, I'll get back to you when I've finished reading Wikipedia.

But for now ... how about this?

http://en.wikipedia .org/wiki/ Barbershop_(musical_style)

"Gage Averill writes that `Barbershoppers have become
partisans of this acoustic phenomenon' and that `the more
experienced singers of the barbershop revival (at least
after the 1940s) have self-consciously tuned their dominant
seventh and tonic chords in just intonation to maximize the
overlap of common overtones.'"
[Averill, Gage (2003). Four Parts, No Waiting: A Social
History of American Barbershop Harmony. Oxford University
Press. ISBN 0195116720.]

Maybe you should be contacting the barbershop community to
correct their terrible mistake.

Graham

Charles Lucylucy@lucytune. com
- Promoting global harmony through LucyTuning -
for information on LucyTuning go to:http://www.lucytune .com
For LucyTuned Lullabies go to:http://www.lullabie s.co.uk

🔗Charles Lucy <lucy@...>

I have attempted this but used an arco cello instrument as it would give sustain.
Have a listen to what I have done so far.
The results are in this folder with info on the tunings etc.

http://www.lucytune.com/9contig/

I could try it with harpsichord if I can find one.

On 19 Mar 2009, at 14:30, Michael Sheiman wrote:

> Charles,
>
> --According to my claims, any nine contiguous LucyTuned notes on the > chain of fourths and --fifths, should give you the result that you > are seeking.
> Well then, go for it! :-) The tricky thing is you have to
> A) play all 9 notes within a 'tiny' 2/1 octave interval (and no more > than that)
> B) have all notes played together at once within that interval (IE > as a 9-note chord) and still sound consonant
>
> Personal note: this is a huge reason why I often use intervals > other than the standard perfect 3rd, 2nd, etc. ...because I've found > all of those lead to chords that can only fit about 5 notes in a > consonant chord within an octave. Maybe the Lucy Tuned circle of > 4ths and 5ths can somehow slip by this problem?...we'll have to see.
>
> And that, of course, implies people have to learn some pretty > complex music theory to learn all the chords and avoid > dissonance...which presents a steep learning curve (which may well > explain why common musicians have been scared to adopt many of even > the best non-7-tone micro-tonal scales).
>
> ---What instrument would you like be to use to demonstrate this for > you in an audio file?
> The harpsichord. :-) It appears to be the most demanding one so > far as dissonance...and also the once I used to test my "rational > numbered ratios approximating/'tempering' the circle of PI scale".
> If you can Lucy-Tuning it to work smoothly with the harpsichord > in the above extreme conditions, you're the man. :-)
>
>
>
> --- On Thu, 3/19/09, Charles Lucy <lucy@...> wrote:
>
> From: Charles Lucy <lucy@...>
> Subject: [tuning] 9 contiguous notes
> To: tuning@yahoogroups.com
> Date: Thursday, March 19, 2009, 12:31 AM
>
> According to my claims, any nine contiguous LucyTuned notes on the > chain of fourths and fifths, should give you the result that you are > seeking.
>
>
> What instrument would you like be to use to demonstrate this for you > in an audio file?
>
> or you could try it yourself;-)
>
> On 19 Mar 2009, at 03:10, Michael Sheiman wrote:
>
>> --Can *you* find 9 notes that can be played
>> --together without dissonance? Michael is doing his best.
>>
>> Thank you! :-) And, for the record, I don't think the "JI >> imitating PHI" type scale I posted is by any means perfect...heck, >> my ears seem to tell me my PHI scale is better.
>>
>> Nonetheless, I wanted to be fair to "JI theory" and open-minded >> to the fact permutations of it may be able to beat my own efforts >> (based on PHI) on making a consonant 9-note-per-2/ 1-octave scale. >> Here's the challenging new and odd theories with older, more well >> researched ones in a quest for a good balance! :-)
>>
>>
>>
>> --- On Wed, 3/18/09, Graham Breed <gbreed@gmail. com> wrote:
>>
>> From: Graham Breed <gbreed@gmail. com>
>> Subject: Re: [tuning] New JI scale
>> To: tuning@yahoogroups. com
>> Date: Wednesday, March 18, 2009, 5:45 PM
>>
>> Claudio Di Veroli wrote (corrected):
>>
>> > We harpsichordists have used the 7/5 (tritone) for centuries as >> an example of
>> > dissonance, even if tuned pure.
>>
>> The 4/3 (fourth) has also been an example of dissonance,
>> even when tuned pure, for centuries. Do you hear it as
>> consonant? Thirds and sixths were examples of dissonance
>> for centuries, and we don't know if they were tuned pure.
>> Do you hear them as consonant?
>>
>> > The tritone (not only the wolf intervals) was called "devil in >> music" even when
>> > pure (it is almost pure in 1/4 s.c. meantone).
>>
>> Tritones (and enharmonies) are the only middle-sized
>> intervals outside the 5-limit in a diatonic scale, hence the
>> warning.
>>
>> I hope we all agree that tritones (and intervals of 7/4) are
>> not 5-limit consonances. But the original context was a 9
>> note scale. Can *you* find 9 notes that can be played
>> together without dissonance? Michael is doing his best.
>>
>> > Just for a check I went to the Wikipedia, where there are some >> further details.
>>
>> Okay, I'll get back to you when I've finished reading Wikipedia.
>>
>> But for now ... how about this?
>>
>> http://en.wikipedia .org/wiki/ Barbershop_(musical_style)
>>
>> "Gage Averill writes that `Barbershoppers have become
>> partisans of this acoustic phenomenon' and that `the more
>> experienced singers of the barbershop revival (at least
>> after the 1940s) have self-consciously tuned their dominant
>> seventh and tonic chords in just intonation to maximize the
>> overlap of common overtones.'"
>> [Averill, Gage (2003). Four Parts, No Waiting: A Social
>> History of American Barbershop Harmony. Oxford University
>> Press. ISBN 0195116720.]
>>
>> Maybe you should be contacting the barbershop community to
>> correct their terrible mistake.
>>
>> Graham
>>
>>
>
> 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.lullabie s.co.uk
>
>
>
>
>
Charles Lucy
lucy@...

- 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

🔗Claudio Di Veroli <dvc@...>

Dear friends,

I strongly recommend a recent work by one of the most respected
international scholars in tuning history and musical acoustics, Prof.
Patrizio Barbieri. He has recently published a treatise "Enharmonic
Instruments 1470-1900", specialising in historical instruments and music
with more than 12 notes per octave. The full "Chapter D-Beyond the Senario:
the Septimal and Undecimal harmonies" is devoted to intervals with ratios
involving numbers greater than 6. It runs from page 179 to page 219 and
over its 40 pages gives lots of insights on historical writings and the use
of those intervals in the history of Western Classical music and acoustical
theory.

Kind regards

Claudio
http://temper.braybaroque.ie/

::::::::::::::::::::::::::::::::::::::
>Now doubt about consonancy, but how this beautiful natural 7th is
>used practically? I see disproportion between JI fourth in the scale
>and this seventh if used on dominant chord (or between other grades
>of scale and respective seventh chords which will use these tones as
>seventh).
>Daniel Forro

9 Mar 2009, at 2:36 PM, Carl Lumma wrote:
> Claudio, do you speak from personal experience? Tartini
> found the 7th harmonic consonant, and our own Tom Dent has
> posted 7-limit harpsichord examples here. Psychoacoustic
> experiments have confirmed that naive listeners report
> most 7-limit intervals (with the exception of 10/7) to
> be consonant, and I've never heard anyone complain about
> Barbershop being dissonant.
> -Carl

🔗Michael Sheiman <djtrancendance@...>

🔗Charles Lucy <lucy@...>

Look a little further in the folder and you will find from the pdf and the jpg images the exact tunings that I have used and from the score you can see exactly what notations have been used:

http://www.lucytune.com/9contig/

Every file in this folder is associated with this experiment, so that you can get the complete picture.

On 19 Mar 2009, at 19:00, Michael Sheiman wrote:

> Hmm.....
>
> The second chord (out of 3) in ALL examples (including plain old > 12TET) sounds by far the best...but still the 6th and 8th notes > sound a bit "off" in 12TET and the 6th and 7th sound a bit off to me > in Lucy Tuning. Still, this sounds much better than any of the > attempts I've tried before with straight-JI or 12TET (meaning, using > approximations of perfect intervals).
>
> What notes/intervals are you using for that chord?
>
> The other odd thing is...my ears couldn't tell much difference > between Lucy Tuning and 12TET on that second chord when hearing the > entire chord...though they could when you played the scale ascending/> leading up to the chord.
> ----------------------------------------------------------------------------------------------------------------
> -Michael
>
>
Charles Lucy
lucy@...

- 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

🔗Charles Lucy <lucy@...>

Hi Michael;

I have tried using the same midi file in Logic with harpsichord as the instrument, (instead of cello).

I chose cello because it would be possible to hear all the notes individually and then together as the cello could be sustained.

This would then expose the beating clearly for the listeners to judge for themselves how the various tunings worked for nine note chords.

With harpsichord, the duration of the notes is so short that the overlapping pitches are missing, which you could hear with the arco cello.

Maybe you should just send me a midi file of what you wish to test and then I can experiment with different instruments and tunings from your midi file for you and others to compare how they sound.

On 19 Mar 2009, at 19:00, Michael Sheiman wrote:

- 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

🔗Andreas Sparschuh <a_sparschuh@...>

--- In tuning@yahoogroups.com, "djtrancendance" <djtrancendance@...> wrote:
>
Hi Michael,
attend that
http://www.microtonal-synthesis.com/scale_53tet.html
contains almost your's 'new'-9tone scale invention:
when compared compared to the degrees of 53

1, ~6, 10, 14, 18, 27, ~35,

Attend the only 2 approximative deviations at degrees ~6 and ~35:

> Here is the (9-tone) scale
> 1) 1/1 =1
> 2) 17/16 ~6 113.208c 16/15 +1.4763c minor diatonic semitone
> 3) 9/8 =10 203.774c 9/8 -0.1364c major whole tone
> 4) 13/11 =14 294.340c 13/11 +5.1299c tridecimal minor third
> 5) 5/4 =18 384.906c 5/4 -1.4081c major third
> 6) 7/5 =27 588.679c 7/5 +6.1671c septimal or Huygens' tritone..
> 7) 25/16 ~35 769.811c 14/9 +4.8954c septimal minor sixth
> 8) 18/11 =39 860.377c 18/11 +7.7853c undecimal neutral sixth
> 9) 15/8 =49 1086.792 15/8 -1.4763c classic major seventh
>1') 2/1 =53 (octave)
>
>
> I found a lot of it by ears and the rest by otonal/utonal
> relationships.
When extending your's scale to 53 there are much more such relations.

> Why the 7/5 works,
> though, is a mystery to me...I
http://www.xs4all.nl/~huygensf/doc/diezen.html
Quote:
"Dit punt roert Huygens aan in de vorm van de vraag, of de verhouding zeven tot vijf (gezwegen van vier, of zes) een consonant interval betekent of een dissonant. Huygens acht het consonant, al heeft het een afwijkend karakter van de in zijn tijd gebruikelijke intervallen. Het is iets kleiner dan het interval fa-si in het do-re-mi geslacht, dat drie tonen bevat en als diatonische tritonus (45/32) onderscheiden kan worden van de harmonische tritonus (7/5). Huygens vindt in de harmonische tritonus een eigen schoonheid. Hij herinnert aan de vergissing der antieken, die de terts als dissonant verwierpen, terwijl deze later zo vanzelfsprekend genoten werd. Hij waarschuwt dat men ten aanzien van de zevende harmonische niet in dezelfde fout moet vervallen. Geen wonder dat hij het een voordeel acht van zijn diëzenstemming, als deze blijkt ook de intervallen met het getal zeven tot hun recht te doen komen. Dat dit zo is rekent men als volgt vlug na. De harmonische tritonus 7/5 is bijna de helft van een oktaaf. Zijn supplement is 10/7. Het verschil tussen de harmonische tritonus en zijn supplement is 50/49, iets kleiner dan de enharmonische diëze 128/125 - goed beschouwd 0,9 normale diëze. "

> found it by ear alone.
as already Huygens discoverded that in
http://diapason.xentonic.org/ttl/ttl06.html

bye
A.S

New JI scale

🔗djtrancendance <djtrancendance@...>

🔗Claudio Di Veroli <dvc@...>

🔗Marcel de Velde <m.develde@...>

🔗Mike Battaglia <battaglia01@...>

🔗Claudio Di Veroli <dvc@...>

🔗Claudio Di Veroli <dvc@...>

🔗Aaron Krister Johnson <aaron@...>

🔗Graham Breed <gbreed@...>

🔗Daniel Forro <dan.for@...>

🔗Claudio Di Veroli <dvc@...>

🔗Claudio Di Veroli <dvc@...>

🔗Daniel Forro <dan.for@...>

🔗Michael Sheiman <djtrancendance@...>

🔗Michael Sheiman <djtrancendance@...>

🔗Carl Lumma <carl@...>

🔗Daniel Forro <dan.for@...>

🔗Carl Lumma <carl@...>

🔗Charles Lucy <lucy@...>

🔗Charles Lucy <lucy@...>

🔗Claudio Di Veroli <dvc@...>

🔗Claudio Di Veroli <dvc@...>

🔗Charles Lucy <lucy@...>

🔗Michael Sheiman <djtrancendance@...>

🔗Charles Lucy <lucy@...>

🔗Claudio Di Veroli <dvc@...>

🔗Michael Sheiman <djtrancendance@...>

🔗Charles Lucy <lucy@...>

🔗Charles Lucy <lucy@...>

🔗Andreas Sparschuh <a_sparschuh@...>