Comma Pumps

I'm sure this has been beaten to death, but has there ever been any
consensus on how to best tune something like the vi-ii-V-I comma pump?
Especially extended variants, like vi m9 - ii m9 - V9 - I, like
Debussy uses in his Reverie, which I've been trying to retune to
11-limit just (with occasional use of metastable ratios, since I love
them).

I've tried tuning the vi chord a comma sharp, so that the minor third
of the vi chord is a comma sharp of the root of the I chord - that
gives a very very interesting sound that isn't all that bad. Making
the comma jump exist between the ii and V sort of works too, although
it isn't quite as smooth... I've been also experimenting with making
the iim9 chord use pythagorean minor thirds instead of 6/5 ones, so
that the next V9 chord can have the pythagorean minor third between
the fifth and the seventh (using a 16/9 seventh), the sound of which I
do tend to like a lot.

Is there some ingenious solution worked out?

-Mike

I don't see a great point in playing comma pumps in strict JI. You can try it with the first phrase of God Save The King and you soon realize that either you'll have to temper out the syntonic comma or you just won't make it.

The problem is that there is not even any one particular way of tuning chords like CEADG which we could call "the correct one" so if you want to tune chords like this to JI, you'll never find one solution which would be in any way significantly better than any other of many possible solutions. And every one of these will have some serious disadvantages, no matter that these don't need to be always the same.

Petr

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> I'm sure this has been beaten to death, but has there ever been
> any consensus on how to best tune something like the vi-ii-V-I
> comma pump?

Short answer: some consensus, yes. But let's focus on the
Lassus for now, and then come back to this. OK?

-Carl

Just out of curiosity, I have put LucyTuned (all black notes are
flats) and 12edo versions of said piece into this folder:

http://www.lucytune.com/godsaveourqueen/

Yes, I had a problem with the chromatic run up, so I settled on Bb - B
- C after trying lotsa other possibilities.

On 13 Feb 2009, at 19:02, Petr Parízek wrote:

>
> I don't see a great point in playing comma pumps in strict JI. You
> can try it with the first phrase of God Save The King and you soon
> realize that either you'll have to temper out the syntonic comma or
> you just won't make it.
>
> The problem is that there is not even any one particular way of
> tuning chords like CEADG which we could call "the correct one" so if
> you want to tune chords like this to JI, you'll never find one
> solution which would be in any way significantly better than any
> other of many possible solutions. And every one of these will have
> some serious disadvantages, no matter that these don't need to be
> always the same.
>
> Petr
>
>
>
>
>

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

95% of it sounds exactly the same to me between both versions.

    HOWEVER...at certain points, like at the chord between 4.6 and 5.3 seconds, the 12TET chord just sounds sour while the Lucy Tuned version sounds dead-on.

   Charles, could you give a technical explanation for what is happening with that chord in Lucy Tuning vs. 12TET?  Because whatever is going on...seems to show that, at least in some special chord cases, Lucy Tuning can make a huge difference.

-Michael

--- On Fri, 2/13/09, Charles Lucy <lucy@...> wrote:

From: Charles Lucy <lucy@...>
Subject: Re: [tuning] Comma Pumps - GodSaveQueen curiosity;-)
To: tuning@yahoogroups.com
Date: Friday, February 13, 2009, 12:51 PM

Just out of curiosity, I have put LucyTuned (all black notes are flats) and 12edo versions of said piece into this folder:
http://www.lucytune .com/godsaveourq ueen/
Yes, I had a problem with the chromatic run up, so I settled on Bb - B - C after trying lotsa other possibilities.

On 13 Feb 2009, at 19:02, Petr Parízek wrote:

I don't see a great point in playing comma pumps in strict JI. You can try it with the first phrase of God Save The King and you soon realize that either you'll have to temper out the syntonic comma or you just won't make it. The problem is that there is not even any one particular way of tuning chords like CEADG which we could call "the correct one" so if you want to tune chords like this to JI, you'll never find one solution which would be in any way significantly better than any other of many possible solutions. And every one of these will have some serious disadvantages, no matter that these don't need to be always the same. Petr  
 

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

I'll put the score into the same folder as a .pdf and let you know
when it's up there.

On 13 Feb 2009, at 21:10, Michael Sheiman wrote:

>
> 95% of it sounds exactly the same to me between both versions.
>
> HOWEVER...at certain points, like at the chord between 4.6 and
> 5.3 seconds, the 12TET chord just sounds sour while the Lucy Tuned
> version sounds dead-on.
>
> Charles, could you give a technical explanation for what is
> happening with that chord in Lucy Tuning vs. 12TET? Because
> whatever is going on...seems to show that, at least in some special
> chord cases, Lucy Tuning can make a huge difference.
>
> -Michael
>
> --- On Fri, 2/13/09, Charles Lucy <lucy@...> wrote:
>
> From: Charles Lucy <lucy@harmonics.com>
> Subject: Re: [tuning] Comma Pumps - GodSaveQueen curiosity;-)
> To: tuning@yahoogroups.com
> Date: Friday, February 13, 2009, 12:51 PM
>
> Just out of curiosity, I have put LucyTuned (all black notes are
> flats) and 12edo versions of said piece into this folder:
>
>
> http://www.lucytune .com/godsaveourq ueen/
>
> Yes, I had a problem with the chromatic run up, so I settled on Bb -
> B - C after trying lotsa other possibilities.
>
>
>
>
> On 13 Feb 2009, at 19:02, Petr Parízek wrote:
>
>>
>> I don't see a great point in playing comma pumps in strict JI. You
>> can try it with the first phrase of God Save The King and you soon
>> realize that either you'll have to temper out the syntonic comma or
>> you just won't make it.
>>
>> The problem is that there is not even any one particular way of
>> tuning chords like CEADG which we could call "the correct one" so
>> if you want to tune chords like this to JI, you'll never find one
>> solution which would be in any way significantly better than any
>> other of many possible solutions. And every one of these will have
>> some serious disadvantages, no matter that these don't need to be
>> always the same.
>>
>> Petr
>>
>>
>>
>>
>
> 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

The Score is now here:

http://www.lucytune.com/godsaveourqueen/GodSaveQueenScore.pdf

the differences in cents between the tunings can be found in the
coloured lower part of this page:

http://www.lucytune.com/midi_and_keyboard/pitch_bend.html

Notes used are:

(Gb) Db-Ab-Eb-Bb-F-C-G-D-A-E-B

On 13 Feb 2009, at 21:10, Michael Sheiman wrote:

>
> 95% of it sounds exactly the same to me between both versions.
>
> HOWEVER...at certain points, like at the chord between 4.6 and
> 5.3 seconds, the 12TET chord just sounds sour while the Lucy Tuned
> version sounds dead-on.
>
> Charles, could you give a technical explanation for what is
> happening with that chord in Lucy Tuning vs. 12TET? Because
> whatever is going on...seems to show that, at least in some special
> chord cases, Lucy Tuning can make a huge difference.
>
> -Michael
>
> --- On Fri, 2/13/09, Charles Lucy <lucy@...> wrote:
>
> From: Charles Lucy <lucy@...>
> Subject: Re: [tuning] Comma Pumps - GodSaveQueen curiosity;-)
> To: tuning@yahoogroups.com
> Date: Friday, February 13, 2009, 12:51 PM
>
> Just out of curiosity, I have put LucyTuned (all black notes are
> flats) and 12edo versions of said piece into this folder:
>
>
> http://www.lucytune .com/godsaveourq ueen/
>
> Yes, I had a problem with the chromatic run up, so I settled on Bb -
> B - C after trying lotsa other possibilities.
>
>
>
>
> On 13 Feb 2009, at 19:02, Petr Parízek wrote:
>
>>
>> I don't see a great point in playing comma pumps in strict JI. You
>> can try it with the first phrase of God Save The King and you soon
>> realize that either you'll have to temper out the syntonic comma or
>> you just won't make it.
>>
>> The problem is that there is not even any one particular way of
>> tuning chords like CEADG which we could call "the correct one" so
>> if you want to tune chords like this to JI, you'll never find one
>> solution which would be in any way significantly better than any
>> other of many possible solutions. And every one of these will have
>> some serious disadvantages, no matter that these don't need to be
>> always the same.
>>
>> Petr
>>
>>
>>
>>
>
> 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

Well of course, _any_ strongly 'unequal' meantone makes a big
difference with respect to 12-ET.
GSTQ(K) wasn't ever meant to be 12-equal in any case: being a
17th-century English tune, its players probably required/used meantone
anyway.

The RELEVANT test of 'Lucy' would be comparing it to something ancient
and historical with similar musical properties like 2/7-comma
meantone. Charles, could you put a 50EDO version up there too?
~~~T~~~

--- In tuning@yahoogroups.com, Michael Sheiman <djtrancendance@...> wrote:
>
> 95% of it sounds exactly the same to me between both versions.
>
> HOWEVER...at certain points, like at the chord between 4.6 and
5.3 seconds, the 12TET chord just sounds sour while the Lucy Tuned
version sounds dead-on.
>
> Charles, could you give a technical explanation for what is
happening with that chord in Lucy Tuning vs. 12TET? Because whatever
is going on...seems to show that, at least in some special chord
cases, Lucy Tuning can make a huge difference.
>
> -Michael
>
> --- On Fri, 2/13/09, Charles Lucy <lucy@...> wrote:
>
>
> Just out of curiosity, I have put LucyTuned (all black
notes are flats) and 12edo versions of said piece into this folder:
> http://www.lucytune .com/godsaveourq ueen/
> Yes, I had a problem with the chromatic run up, so I settled on Bb -
B - C after trying lotsa other possibilities.
>
>
>

Hi Mike,

I'm sure this has been beaten to death, but has there ever been any
> consensus on how to best tune something like the vi-ii-V-I comma pump?
> Especially extended variants, like vi m9 - ii m9 - V9 - I, like
> Debussy uses in his Reverie, which I've been trying to retune to
> 11-limit just (with occasional use of metastable ratios, since I love
> them).
>
> I've tried tuning the vi chord a comma sharp, so that the minor third
> of the vi chord is a comma sharp of the root of the I chord - that
> gives a very very interesting sound that isn't all that bad. Making
> the comma jump exist between the ii and V sort of works too, although
> it isn't quite as smooth... I've been also experimenting with making
> the iim9 chord use pythagorean minor thirds instead of 6/5 ones, so
> that the next V9 chord can have the pythagorean minor third between
> the fifth and the seventh (using a 16/9 seventh), the sound of which I
> do tend to like a lot.
>
> Is there some ingenious solution worked out?
>

Ah yes this is the single most annoying problem there is!
Since normal music theory / harmony states so clearly you should be able to
do this in major mode.
But this is one of the things that's most wrong about normal music theory.
This progression is usually not inside the major mode but involves a
modulation.

Below are the base JI major modes:
C D E F G A B C
1/1 9/8 5/4 4/3 3/2 5/3 15/8 2/1 mode 1.1
1/1 10/9 5/4 4/3 3/2 5/3 15/8 2/1 mode 2.3
1/1 9/8 5/4 27/20 3/2 27/16 15/8 2/1 mode 3.4
1/1 10/9 5/4 4/3 40/27 5/3 50/27 2/1 mode 4.7

You can indeed do any 3 of the chords in one of the major modes. (after the
point is mode degree starting at 1, the modes I posted in another thread
earlyer)
I, IV, V in mode 1.1
I, II, IV in mode 2.3
I, II, V in mode 3.4
II, IV, V in mode 4.7

But you can't do all 4 chords I, II, IV, V in the same base mode.
I guess the above modes are in normal music theory all seen as one and the
same major mode, and since there are indeed 3 chords possible in each they
concluded you can do it with all 4 in the same mode which is wrong.

You can do it several ways with the simplest modulation of 3/2 in extended
modes.

1/1 5/4 3/2 -> 1/1 4/3 5/3 -> 10/9 4/3 5/3 -> 9/8 3/2 15/8 -> 1/1 5/4 3/2
2/1

1/1 5/4 3/2 -> 1/1 4/3 5/3 -> 9/8 27/20 27/16 -> 9/8 3/2 15/8 -> 1/1 5/4 3/2
2/1

1/1 5/4 3/2 -> 1/1 4/3 5/3 -> 10/9 4/3 5/3 -> 10/9 40/27 50/27 -> 1/1 5/4
3/2 2/1

1/1 5/4 3/2 -> 81/80 27/20 27/16 -> 9/8 27/20 27/16 -> 9/8 3/2 15/8 -> 1/1
5/4 3/2 2/1

You can also do it in an extended mode without akward 81/80 like this:
1/1 5/4 3/2 -> 1/1 4/3 27/16 -> 9/8 4/3 27/16 -> 9/8 3/2 15/8 -> 1/1 5/4 3/2
2/1
this makes one major triad of 1/1 81/64 3/2 and one minor triad of 1/1 32/27
3/2.

Which one of the above is used in actual music depends on the composition
and context.

Marcel

If you tell me the offsets that you require for each of the 12 notes in cents, I can produce any tuning (up to 12 notes per octave) that you might want by resetting the values in Logic.

For 50edo, you would have to decide which steps each of the 12 notes would be selected to play.

On 13 Feb 2009, at 21:51, Tom Dent wrote:

>
> Well of course, _any_ strongly 'unequal' meantone makes a big
> difference with respect to 12-ET.
> GSTQ(K) wasn't ever meant to be 12-equal in any case: being a
> 17th-century English tune, its players probably required/used meantone
> anyway.
>
> The RELEVANT test of 'Lucy' would be comparing it to something ancient
> and historical with similar musical properties like 2/7-comma
> meantone. Charles, could you put a 50EDO version up there too?
> ~~~T~~~
>
> --- In tuning@yahoogroups.com, Michael Sheiman <djtrancendance@...> > wrote:
> >
> > 95% of it sounds exactly the same to me between both versions.
> >
> > HOWEVER...at certain points, like at the chord between 4.6 and
> 5.3 seconds, the 12TET chord just sounds sour while the Lucy Tuned
> version sounds dead-on.
> >
> > Charles, could you give a technical explanation for what is
> happening with that chord in Lucy Tuning vs. 12TET? Because whatever
> is going on...seems to show that, at least in some special chord
> cases, Lucy Tuning can make a huge difference.
> >
> > -Michael
> >
> > --- On Fri, 2/13/09, Charles Lucy <lucy@...> wrote:
> >
> >
> > Just out of curiosity, I have put LucyTuned (all black
> notes are flats) and 12edo versions of said piece into this folder:
> > http://www.lucytune .com/godsaveourq ueen/
> > Yes, I had a problem with the chromatic run up, so I settled on Bb -
> B - C after trying lotsa other possibilities.
> >
> >
> >
>
>
>
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

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
> The RELEVANT test of 'Lucy' would be comparing it to something
> ancient and historical with similar musical properties like
> 2/7-comma meantone.

An even more relevant test would be to put it up against
an optimal meantone, such as quarter-comma (sum-abs optimal),
7/26-comma (RMS-optimal), or TOP meantone (limit-weighted
optimal). Here is TOP meantone (5-limit)...

!
TOP meantone.
12
!
76.16
193.43
310.70
386.86
504.13
580.29
697.56
773.72
890.99
1008.27
1084.42
1201.70
!

-Carl

OK Carl;

You have seen the score, and know that it is in Eb. Which cent values do you wish to assign to which note?

I am I right in assuming that C should be + 1.7
Db be - 23.8
D be - 6.6
Eb be +10.7

etc. etc. ?

or is it easier for me to just make a meantone in which the fifth is (697.56 - 1.70) = 695.86 cents

The adjusted values that I had used to LucyTune GodSaveQueen were:

C = + 13.5
Db = + 36.1
D = + 4.5
Eb = + 27.0
E = - 4.5
F = +18.0
Gb = +40.6
G = + 9.0
Ab = +31.5
A = 0.0
Bb = +22.5
B = - 9.0

so for yours it would be:

C = + 12.4
Db = + 33.1
D = + 4.1
Eb = + 24.8
E = - 4.1
F = +16.6
Gb = +37.3
G = + 8.3
Ab = +29.0
A = 0.0
Bb = +20.7
B = - 8.3

Agreed?

or maybe I should just put up the .lso for Logic Pro 8 and let you adjust the microtuned cent values on your system?

On 14 Feb 2009, at 00:02, Carl Lumma wrote:

> --- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
> >
> > The RELEVANT test of 'Lucy' would be comparing it to something
> > ancient and historical with similar musical properties like
> > 2/7-comma meantone.
>
> An even more relevant test would be to put it up against
> an optimal meantone, such as quarter-comma (sum-abs optimal),
> 7/26-comma (RMS-optimal), or TOP meantone (limit-weighted
> optimal). Here is TOP meantone (5-limit)...
>
> !
> TOP meantone.
> 12
> !
> 76.16
> 193.43
> 310.70
> 386.86
> 504.13
> 580.29
> 697.56
> 773.72
> 890.99
> 1008.27
> 1084.42
> 1201.70
> !
>
> -Carl
>
>
>
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

If the music is centered in Eb, why A is on zero? I ask because when I did some let's say tonal or extended tonal microtuned works with clear centre (tonic), I set root note to zero shift. Here that means to make offset -27 Cents for your first example. Then Eb will be zero, A -27.

Yet another general question: when music modulates to different keys, always new root note should be zeroed, and the other notes retuned, if not, all relations will be damaged. Or do you have different solution?

Daniel Forro

On 14 Feb 2009, at 10:01 AM, Charles Lucy wrote:

> OK Carl;
>
>
> You have seen the score, and know that it is in Eb. Which cent > values do you wish to assign to which note?
>
> I am I right in assuming that C should be + 1.7
> Db be - 23.8
> D be - 6.6
> Eb be +10.7
>
> etc. etc. ?
>
> or is it easier for me to just make a meantone in which the fifth > is (697.56 - 1.7 0) = 695.86 cents
>
> The adjusted values that I had used to LucyTune GodSaveQueen were:
>
> C = + 13.5
> Db = + 36.1
> D = + 4.5
> Eb = + 27.0
> E = - 4.5
> F = +18.0
> Gb = +40.6
> G = + 9.0
> Ab = +31.5
> A = 0.0
> Bb = +22.5
> B = - 9.0
>
> so for yours it would be:
>
> C = + 12.4
> Db = + 33.1
> D = + 4.1
> Eb = + 24.8
> E = - 4.1
> F = +16.6
> Gb = +37.3
> G = + 8.3
> Ab = +29.0
> A = 0.0
> Bb = +20.7
> B = - 8.3
>
>
> Agreed?
>
>
> or maybe I should just put up the .lso for Logic Pro 8 and let you > adjust the microtuned cent values on your system?
>
>
>
> On 14 Feb 2009, at 00:02, Carl Lumma wrote:
>
>> --- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>> >
>> > The RELEVANT test of 'Lucy' would be comparing it to something
>> > ancient and historical with similar musical properties like
>> > 2/7-comma meantone.
>>
>> An even more relevant test would be to put it up against
>> an optimal meantone, such as quarter-comma (sum-abs optimal),
>> 7/26-comma (RMS-optimal), or TOP meantone (limit-weighted
>> optimal). Here is TOP meantone (5-limit)...
>>
>> !
>> TOP meantone.
>> 12
>> !
>> 76.16
>> 193.43
>> 310.70
>> 386.86
>> 504.13
>> 580.29
>> 697.56
>> 773.72
>> 890.99
>> 1008.27
>> 1084.42
>> 1201.70
>> !
>>
>> -Carl
>>
>>
>
> Charles Lucy
> lucy@...

--Yet another general question: when music modulates to different keys,
--always new root note should be zeroed, and the other notes retuned,
--if not, all relations will be damaged. Or do you have different
--solution?
      Not necessarily.  It could be that the harmonic relationships are just shifted.  For example the first two notes in a minor triad becoming the first two notes in a major triad when the key is shifted up.  Different intervals, yes...but still ones that are "in tune".
    Either that or...if the lack of a shift only results in around a 6 or less cents difference from a perfectly tuned ratio..the difference likely wouldn't be enough to make the human ear tell the difference.

   Would their likely be more of an error if the other notes weren't shifted along with the root?  Most likely... Would that error be enough (IE greater than 6 cents) off the perfect interval to confuse the human mind into thinking it is wrong?  Not necessarily...

     BTW, I've noticed with my own scales under PHI tuning...the ratios seems to just "rotate" between keys...there is no audible change I can hear in the overall purity of the scales (or which chords can/can't work best) after transposing them...unlike in non-adaptive JI.

-Michael
--- On Fri, 2/13/09, Daniel Forro <dan.for@...> wrote:

From: Daniel Forro <dan.for@...>
Subject: Re: [tuning] Re: Comma Pumps - GodSaveQueen curiosity;-)
To: tuning@yahoogroups.com
Date: Friday, February 13, 2009, 6:44 PM

If the music is centered in Eb, why A is on zero? I ask because when

I did some let's say tonal or extended tonal microtuned works with

clear centre (tonic), I set root note to zero shift. Here that means

to make offset -27 Cents for your first example. Then Eb will be

zero, A -27.

Yet another general question: when music modulates to different keys,

always new root note should be zeroed, and the other notes retuned,

if not, all relations will be damaged. Or do you have different

solution?

Daniel Forro

On 14 Feb 2009, at 10:01 AM, Charles Lucy wrote:

> OK Carl;

>

>

> You have seen the score, and know that it is in Eb. Which cent

> values do you wish to assign to which note?

>

> I am I right in assuming that C should be + 1.7

> Db be - 23.8

> D be - 6.6

> Eb be +10.7

>

> etc. etc. ?

>

> or is it easier for me to just make a meantone in which the fifth

> is (697.56 - 1.7 0) = 695.86 cents

>

> The adjusted values that I had used to LucyTune GodSaveQueen were:

>

> C = + 13.5

> Db = + 36.1

> D = + 4.5

> Eb = + 27.0

> E = - 4.5

> F = +18.0

> Gb = +40.6

> G = + 9.0

> Ab = +31.5

> A = 0.0

> Bb = +22.5

> B = - 9.0

>

> so for yours it would be:

>

> C = + 12.4

> Db = + 33.1

> D = + 4.1

> Eb = + 24.8

> E = - 4.1

> F = +16.6

> Gb = +37.3

> G = + 8.3

> Ab = +29.0

> A = 0.0

> Bb = +20.7

> B = - 8.3

>

>

> Agreed?

>

>

> or maybe I should just put up the .lso for Logic Pro 8 and let you

> adjust the microtuned cent values on your system?

>

>

>

> On 14 Feb 2009, at 00:02, Carl Lumma wrote:

>

>> --- In tuning@yahoogroups. com, "Tom Dent" <stringph@.. .> wrote:

>> >

>> > The RELEVANT test of 'Lucy' would be comparing it to something

>> > ancient and historical with similar musical properties like

>> > 2/7-comma meantone.

>>

>> An even more relevant test would be to put it up against

>> an optimal meantone, such as quarter-comma (sum-abs optimal),

>> 7/26-comma (RMS-optimal) , or TOP meantone (limit-weighted

>> optimal). Here is TOP meantone (5-limit)...

>>

>> !

>> TOP meantone.

>> 12

>> !

>> 76.16

>> 193.43

>> 310.70

>> 386.86

>> 504.13

>> 580.29

>> 697.56

>> 773.72

>> 890.99

>> 1008.27

>> 1084.42

>> 1201.70

>> !

>>

>> -Carl

>>

>>

>

> Charles Lucy

> lucy@lucytune. com

The reason that I have zeroed on A is so that all LucyTuned instruments are set to A=440, 880 etc. so that they can play together with eachother in a consistent tuning.

Since A4=440 Hz is the generally agreed stand pitch for musical note naming according to the DIN BSI etc. It seems reasonable to use the standard.

There are many arguments for other values to be used e.g. C = 256 etc, but I accept that A=440 is most widely used, so I have made all LucyTuned instruments and software to conform to that value.

On 14 Feb 2009, at 02:44, Daniel Forro wrote:

> If the music is centered in Eb, why A is on zero? I ask because when
> I did some let's say tonal or extended tonal microtuned works with
> clear centre (tonic), I set root note to zero shift. Here that means
> to make offset -27 Cents for your first example. Then Eb will be
> zero, A -27.
>
> Yet another general question: when music modulates to different keys,
> always new root note should be zeroed, and the other notes retuned,
> if not, all relations will be damaged. Or do you have different
> solution?
>
> Daniel Forro
>
> On 14 Feb 2009, at 10:01 AM, Charles Lucy wrote:
>
> > OK Carl;
> >
> >
> > You have seen the score, and know that it is in Eb. Which cent
> > values do you wish to assign to which note?
> >
> > I am I right in assuming that C should be + 1.7
> > Db be - 23.8
> > D be - 6.6
> > Eb be +10.7
> >
> > etc. etc. ?
> >
> > or is it easier for me to just make a meantone in which the fifth
> > is (697.56 - 1.7 0) = 695.86 cents
> >
> > The adjusted values that I had used to LucyTune GodSaveQueen were:
> >
> > C = + 13.5
> > Db = + 36.1
> > D = + 4.5
> > Eb = + 27.0
> > E = - 4.5
> > F = +18.0
> > Gb = +40.6
> > G = + 9.0
> > Ab = +31.5
> > A = 0.0
> > Bb = +22.5
> > B = - 9.0
> >
> > so for yours it would be:
> >
> > C = + 12.4
> > Db = + 33.1
> > D = + 4.1
> > Eb = + 24.8
> > E = - 4.1
> > F = +16.6
> > Gb = +37.3
> > G = + 8.3
> > Ab = +29.0
> > A = 0.0
> > Bb = +20.7
> > B = - 8.3
> >
> >
> > Agreed?
> >
> >
> > or maybe I should just put up the .lso for Logic Pro 8 and let you
> > adjust the microtuned cent values on your system?
> >
> >
> >
> > On 14 Feb 2009, at 00:02, Carl Lumma wrote:
> >
> >> --- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
> >> >
> >> > The RELEVANT test of 'Lucy' would be comparing it to something
> >> > ancient and historical with similar musical properties like
> >> > 2/7-comma meantone.
> >>
> >> An even more relevant test would be to put it up against
> >> an optimal meantone, such as quarter-comma (sum-abs optimal),
> >> 7/26-comma (RMS-optimal), or TOP meantone (limit-weighted
> >> optimal). Here is TOP meantone (5-limit)...
> >>
> >> !
> >> TOP meantone.
> >> 12
> >> !
> >> 76.16
> >> 193.43
> >> 310.70
> >> 386.86
> >> 504.13
> >> 580.29
> >> 697.56
> >> 773.72
> >> 890.99
> >> 1008.27
> >> 1084.42
> >> 1201.70
> >> !
> >>
> >> -Carl
> >>
> >>
> >
> > Charles Lucy
> > lucy@...
>
>
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

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
> OK Carl;
>
> You have seen the score, and know that it is in Eb. Which cent
> values do you wish to assign to which note?

Sorry, I haven't had a chance to look at this yet; I will do
so when I get back.

> The adjusted values that I had used to LucyTune GodSaveQueen were:
>
> C = + 13.5
> Db = + 36.1
> D = + 4.5
> Eb = + 27.0
> E = - 4.5
> F = +18.0
> Gb = +40.6
> G = + 9.0
> Ab = +31.5
> A = 0.0
> Bb = +22.5
> B = - 9.0
>
> so for yours it would be:
>
> C = + 12.4
> Db = + 33.1
> D = + 4.1
> Eb = + 24.8
> E = - 4.1
> F = +16.6
> Gb = +37.3
> G = + 8.3
> Ab = +29.0
> A = 0.0
> Bb = +20.7
> B = - 8.3
>
> Agreed?

I haven't checked this, but if you're doing this in Logic,
I doubt it'll work, since TOP meantone is a nonoctave tuning
and I don't think Logic can do those.

I would recommend just using 1/4 comma, or 7/26 comma
meantone for the comparison, since they are octave-based
and easy to do in Logic and many other instruments.

-Carl

I've been giving it some more thought and listened on the piano and this one
seems most logical / natural to me. (in this context without any other
music, a different context will change it offcourse)1/1 5/4 3/2 -> 4/3 5/3
2/1 -> 9/8 27/20 27/16 -> 3/2 15/8 9/4 -> 1/1 5/4 3/2 and on and on..

Sounds perfect to me. Commas don't bother me at all, they only make it
clearer what's beeing played.

To do this with a V7 going to I for instance:
1/1 5/4 3/2 -> 1/1 4/3 5/3 -> 9/8 27/20 27/16 -> 9/8 3/2 2/1 8/3 -> 1/1 3/2
2/1 5/2

You can play the same with a major chord on ii which sounds nicer:
1/1 5/4 3/2 -> 4/3 5/3 2/1 -> 9/8 45/32 27/16 -> 3/2 15/8 9/4 -> 1/1 5/4 3/2

In all cases no matter where you play it on the keyboard in what ever
inversion, my guess is that in the underlying structure not one note shifts
by a comma, the notes go 1/1 then up by 4/3 then down by 32/27 then up by
4/3 then down by 3/2.
And the thirds go 1/1 then up by 4/3 down by 100/81 (result of modulation,
not a stepsize in any of the base modes) then up by 25/18 then down by 3/2.
The modulation is from IV to ii.
The modulation back is wherever you want to put it or not really there.
Which is perhaps why it wants to go round and round.
I don't know if the above is a good way to look at it, just playing with
ideas. I have a lot of things worked out allready but this way of looking
not so much.

Marcel

On Fri, Feb 13, 2009 at 11:04 PM, Marcel de Velde <m.develde@...>wrote:

> Hi Mike,
>
> I'm sure this has been beaten to death, but has there ever been any
>> consensus on how to best tune something like the vi-ii-V-I comma pump?
>> Especially extended variants, like vi m9 - ii m9 - V9 - I, like
>> Debussy uses in his Reverie, which I've been trying to retune to
>> 11-limit just (with occasional use of metastable ratios, since I love
>> them).
>>
>> I've tried tuning the vi chord a comma sharp, so that the minor third
>> of the vi chord is a comma sharp of the root of the I chord - that
>> gives a very very interesting sound that isn't all that bad. Making
>> the comma jump exist between the ii and V sort of works too, although
>> it isn't quite as smooth... I've been also experimenting with making
>> the iim9 chord use pythagorean minor thirds instead of 6/5 ones, so
>> that the next V9 chord can have the pythagorean minor third between
>> the fifth and the seventh (using a 16/9 seventh), the sound of which I
>> do tend to like a lot.
>>
>> Is there some ingenious solution worked out?
>>
>
> Ah yes this is the single most annoying problem there is!
> Since normal music theory / harmony states so clearly you should be able to
> do this in major mode.
> But this is one of the things that's most wrong about normal music theory.
> This progression is usually not inside the major mode but involves a
> modulation.
>
> Below are the base JI major modes:
> C D E F G A B C
> 1/1 9/8 5/4 4/3 3/2 5/3 15/8 2/1 mode 1.1
> 1/1 10/9 5/4 4/3 3/2 5/3 15/8 2/1 mode 2.3
> 1/1 9/8 5/4 27/20 3/2 27/16 15/8 2/1 mode 3.4
> 1/1 10/9 5/4 4/3 40/27 5/3 50/27 2/1 mode 4.7
>
> You can indeed do any 3 of the chords in one of the major modes. (after the
> point is mode degree starting at 1, the modes I posted in another thread
> earlyer)
> I, IV, V in mode 1.1
> I, II, IV in mode 2.3
> I, II, V in mode 3.4
> II, IV, V in mode 4.7
>
> But you can't do all 4 chords I, II, IV, V in the same base mode.
> I guess the above modes are in normal music theory all seen as one and the
> same major mode, and since there are indeed 3 chords possible in each they
> concluded you can do it with all 4 in the same mode which is wrong.
>
> You can do it several ways with the simplest modulation of 3/2 in extended
> modes.
>
> 1/1 5/4 3/2 -> 1/1 4/3 5/3 -> 10/9 4/3 5/3 -> 9/8 3/2 15/8 -> 1/1 5/4 3/2
> 2/1
>
> 1/1 5/4 3/2 -> 1/1 4/3 5/3 -> 9/8 27/20 27/16 -> 9/8 3/2 15/8 -> 1/1 5/4
> 3/2 2/1
>
> 1/1 5/4 3/2 -> 1/1 4/3 5/3 -> 10/9 4/3 5/3 -> 10/9 40/27 50/27 -> 1/1 5/4
> 3/2 2/1
>
> 1/1 5/4 3/2 -> 81/80 27/20 27/16 -> 9/8 27/20 27/16 -> 9/8 3/2 15/8 -> 1/1
> 5/4 3/2 2/1
>
> You can also do it in an extended mode without akward 81/80 like this:
> 1/1 5/4 3/2 -> 1/1 4/3 27/16 -> 9/8 4/3 27/16 -> 9/8 3/2 15/8 -> 1/1 5/4
> 3/2 2/1
> this makes one major triad of 1/1 81/64 3/2 and one minor triad of 1/1
> 32/27 3/2.
>
> Which one of the above is used in actual music depends on the composition
> and context.
>
> Marcel
>
>

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
> If you tell me the offsets that you require for each of the 12 notes
> in cents, I can produce any tuning (up to 12 notes per octave) that
> you might want by resetting the values in Logic.
>
> For 50edo, you would have to decide which steps each of the 12 notes
> would be selected to play.
>

There is no 'decision' to be made, I am referring to the standard
meantone mapping. If C is step 0, G is step 29, D is step 8, etc.
etc., all diatonic semitones are 5 steps and all chromatic 3.
To save Charles the labour of calculation, here is the 50edo meantone
in cents:
(0)
72 (C#) or 120 (Db)
192
312 (Eb)
384
504
576 (F# - the score has no Gb)
696
768 (G#) or 816 (Ab)
888
1008
1080
1200

looking forward to the result!

By the way, GSTQ is perfectly well performable on a normal harpsichord
in JI: as I will show!
~~~T~~~

> On 13 Feb 2009, at 21:51, Tom Dent wrote:
>
> >
> > Well of course, _any_ strongly 'unequal' meantone makes a big
> > difference with respect to 12-ET.
> > GSTQ(K) wasn't ever meant to be 12-equal in any case: being a
> > 17th-century English tune, its players probably required/used meantone
> > anyway.
> >
> > The RELEVANT test of 'Lucy' would be comparing it to something ancient
> > and historical with similar musical properties like 2/7-comma
> > meantone. Charles, could you put a 50EDO version up there too?
> > ~~~T~~~
> >

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "Tom Dent" <stringph@> wrote:
> >
> > The RELEVANT test of 'Lucy' would be comparing it to something
> > ancient and historical with similar musical properties like
> > 2/7-comma meantone.
>
> An even more relevant test would be to put it up against
> an optimal meantone, such as quarter-comma (sum-abs optimal),
> 7/26-comma (RMS-optimal), or TOP meantone (limit-weighted
> optimal). Here is TOP meantone (5-limit)...
>
> !
> TOP meantone.
> 12
> !
> 76.16
> 193.43
> 310.70
> 386.86
> 504.13
> 580.29
> 697.56
> 773.72
> 890.99
> 1008.27
> 1084.42
> 1201.70
> !
>
> -Carl

The problem I see is that you can't do a 'fine-tooth' comparison of
Lucy to meantones where the minor 3rd is more mistuned than the major,
since the musical effects will clearly be different. Someone able to
hear the difference might then chalk it up to the magical pi-based
properties or whatever, rather than specifically the sizes of thirds.
~~~T~~~

Tom Dent wrote:

> The problem I see is that you can't do a 'fine-tooth' comparison of
> Lucy to meantones where the minor 3rd is more mistuned than the major,
> since the musical effects will clearly be different. Someone able to
> hear the difference might then chalk it up to the magical pi-based
> properties or whatever, rather than specifically the sizes of thirds.

Agreed completely. Anyway, I think there may be three very good ideas to try. One is 2/7-comma meantone, another is the one whose octave is 1/9th of the synt. comma wider than pure and whose fifth is 2/9 of the synt. comma narrower than pure, and the third version is the one whose octave is 1/12 of the synt. comma wider than pure and whose fifth is 1/4 of the comma narrower than pure. Personally, I'm not sure which of these could be the best solution there, because the minor third in 2/7-comma is more away from JI than in the other two, and the other two have fourths 1/3-comma wider than pure, which may seem too wide for someone.

Petr

It would also be nice if the test was blind, so that personal biases
(which seem to be pretty large around here lately) don't make as much
of an impact.

-Mike

On Sun, Feb 15, 2009 at 2:26 PM, Petr Parízek <p.parizek@chello.cz> wrote:
> Tom Dent wrote:
>
>> The problem I see is that you can't do a 'fine-tooth' comparison of
>> Lucy to meantones where the minor 3rd is more mistuned than the major,
>> since the musical effects will clearly be different. Someone able to
>> hear the difference might then chalk it up to the magical pi-based
>> properties or whatever, rather than specifically the sizes of thirds.
>
> Agreed completely. Anyway, I think there may be three very good ideas to
> try. One is 2/7-comma meantone, another is the one whose octave is 1/9th of
> the synt. comma wider than pure and whose fifth is 2/9 of the synt. comma
> narrower than pure, and the third version is the one whose octave is 1/12 of
> the synt. comma wider than pure and whose fifth is 1/4 of the comma narrower
> than pure. Personally, I'm not sure which of these could be the best
> solution there, because the minor third in 2/7-comma is more away from JI
> than in the other two, and the other two have fourths 1/3-comma wider than
> pure, which may seem too wide for someone.
>
> Petr
>
>
>
>
>
>

OK Tom;
I'll shift everything up by 12 cents, so that A=440 Hz to conform with the other three eversions.
and put it up when completed.

On 15 Feb 2009, at 17:37, Tom Dent wrote:

> --- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
> >
> > If you tell me the offsets that you require for each of the 12 notes
> > in cents, I can produce any tuning (up to 12 notes per octave) that
> > you might want by resetting the values in Logic.
> >
> > For 50edo, you would have to decide which steps each of the 12 notes
> > would be selected to play.
> >
>
> There is no 'decision' to be made, I am referring to the standard
> meantone mapping. If C is step 0, G is step 29, D is step 8, etc.
> etc., all diatonic semitones are 5 steps and all chromatic 3.
> To save Charles the labour of calculation, here is the 50edo meantone
> in cents:
> (0)
> 72 (C#) or 120 (Db)
> 192
> 312 (Eb)
> 384
> 504
> 576 (F# - the score has no Gb)
> 696
> 768 (G#) or 816 (Ab)
> 888
> 1008
> 1080
> 1200
>
> looking forward to the result!
>
> By the way, GSTQ is perfectly well performable on a normal harpsichord
> in JI: as I will show!
> ~~~T~~~
>
> > On 13 Feb 2009, at 21:51, Tom Dent wrote:
> >
> > >
> > > Well of course, _any_ strongly 'unequal' meantone makes a big
> > > difference with respect to 12-ET.
> > > GSTQ(K) wasn't ever meant to be 12-equal in any case: being a
> > > 17th-century English tune, its players probably required/used > meantone
> > > anyway.
> > >
> > > The RELEVANT test of 'Lucy' would be comparing it to something > ancient
> > > and historical with similar musical properties like 2/7-comma
> > > meantone. Charles, could you put a 50EDO version up there too?
> > > ~~~T~~~
> > >
>
>
>
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

If you can let me have what you calculate as the values for the + or -
cents for each of the notes, assuming A=0 i.e.440Hz, I'll reset and
bounce all five new tunings (Your three + Tom's two) as mp3's and up
and put them up.

On 15 Feb 2009, at 19:26, Petr Parízek wrote:

>
> Tom Dent wrote:
>
> > The problem I see is that you can't do a 'fine-tooth' comparison of
> > Lucy to meantones where the minor 3rd is more mistuned than the
> major,
> > since the musical effects will clearly be different. Someone able to
> > hear the difference might then chalk it up to the magical pi-based
> > properties or whatever, rather than specifically the sizes of
> thirds.
>
> Agreed completely. Anyway, I think there may be three very good
> ideas to try. One is 2/7-comma meantone, another is the one whose
> octave is 1/9th of the synt. comma wider than pure and whose fifth
> is 2/9 of the synt. comma narrower than pure, and the third version
> is the one whose octave is 1/12 of the synt. comma wider than pure
> and whose fifth is 1/4 of the comma narrower than pure. Personally,
> I'm not sure which of these could be the best solution there,
> because the minor third in 2/7-comma is more away from JI than in
> the other two, and the other two have fourths 1/3-comma wider than
> pure, which may seem too wide for someone.
>
> Petr
>
>
>
>
>
>
>

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 wrote:

> If you can let me have what you calculate as the values for the + or - cents for each of the
> notes, assuming A=0 i.e.440Hz, I'll reset and bounce all five new tunings (Your three +
> Tom's two) as mp3's and up and put them up.

Maybe I should warn you that two of the tunings which I suggested have octaves wider than 1200 cents and one of the tunings Carl suggested also has wider octaves, so you would have to use, for example, multiple MIDI channels or whatever.

Petr

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
> If you can let me have what you calculate as the values for the + or -
> cents for each of the notes, assuming A=0 i.e.440Hz, I'll reset and
> bounce all five new tunings (Your three + Tom's two) as mp3's and up
> and put them up.
>
>

Hang on one c-p minute! When did I ever suggest TWO meantones for you
to synthesize? All I said was 50-EDO (which is almost exactly the same
as 2/7 comma) with standard meantone mapping.

Since you've written the piece in Eb, obviously you should choose the
flats from the meantone sequence (though F#/Gb is irrelevant in the
piece). I just put some of the sharps in as well to make up the
'standard' Eb-G# meantone range.

If you're considering choosing the G# from a meantone sequence to be
the subdominant in Eb major, something is already seriously wrong...
~~~T~~~

No I haven't used G#, I set the original tuning to Lucy 5b0s i.e. 5 flats no sharps, and the others in a similar way.

i.e. assuming A=0, black notes which are flats will have positive changes in cents; and black notes which are sharps would be negative changes.

I appreciate that not everyone uses A = 440 as a reference, but that is just an arbitrary rule that I have used for the past 20 years, so that the notenames used in all LucyTuned pieces will match the same pitches.

Since it works (for me), I continue to use it, as do all the people that I usually collaborate with professionally.

On 15 Feb 2009, at 20:27, Tom Dent wrote:

> --- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
> >
> > If you can let me have what you calculate as the values for the + > or -
> > cents for each of the notes, assuming A=0 i.e.440Hz, I'll reset and
> > bounce all five new tunings (Your three + Tom's two) as mp3's and up
> > and put them up.
> >
> >
>
> Hang on one c-p minute! When did I ever suggest TWO meantones for you
> to synthesize? All I said was 50-EDO (which is almost exactly the same
> as 2/7 comma) with standard meantone mapping.
>
> Since you've written the piece in Eb, obviously you should choose the
> flats from the meantone sequence (though F#/Gb is irrelevant in the
> piece). I just put some of the sharps in as well to make up the
> 'standard' Eb-G# meantone range.
>
> If you're considering choosing the G# from a meantone sequence to be
> the subdominant in Eb major, something is already seriously wrong...
> ~~~T~~~
>
>
>
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

Ah OK, I don't mind about the pitch reference. It's only a couple of
Hz either way...
Relative to A we have simply
(+12 +32 +4 +24 -4 +16 -12 +8 +28 0 +20 -8)
for 4 flats and 1 sharp.

However, you seem to have a problem with the sequencer: namely, the
bass clarinet notes don't sound. It should for example provide a big
downward scale near the end and give the major third in the final
chord, but it's completely absent. It would be worth checking whether
each part does actually function - I'm not too sure about the
clarinets either.

Conclusion: with harpsichords, you're directly in contact with
whatever wrong notes there may be!
~~~T~~~

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
> No I haven't used G#, I set the original tuning to Lucy 5b0s i.e. 5
> flats no sharps, and the others in a similar way.
>
> i.e. assuming A=0, black notes which are flats will have positive
> changes in cents; and black notes which are sharps would be negative
> changes.
>
> I appreciate that not everyone uses A = 440 as a reference, but that
> is just an arbitrary rule that I have used for the past 20 years, so
> that the notenames used in all LucyTuned pieces will match the same
> pitches.
>
>

OK Tom, I'll check that.
I had just grabbed a midifile and chopped it to remove the further arrangements, after it had played the main section once.

I wish Logic had a more sophisticated microtuning system. I have asked the techies at Apple to improve it but .........
I also asked them to enable microtuning in GarageBand, and have yet to discover whether the new version includes it.

On 15 Feb 2009, at 20:51, Tom Dent wrote:

>
> Ah OK, I don't mind about the pitch reference. It's only a couple of
> Hz either way...
> Relative to A we have simply
> (+12 +32 +4 +24 -4 +16 -12 +8 +28 0 +20 -8)
> for 4 flats and 1 sharp.
>
> However, you seem to have a problem with the sequencer: namely, the
> bass clarinet notes don't sound. It should for example provide a big
> downward scale near the end and give the major third in the final
> chord, but it's completely absent. It would be worth checking whether
> each part does actually function - I'm not too sure about the
> clarinets either.
>
> Conclusion: with harpsichords, you're directly in contact with
> whatever wrong notes there may be!
> ~~~T~~~
>
> --- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
> >
> > No I haven't used G#, I set the original tuning to Lucy 5b0s i.e. 5
> > flats no sharps, and the others in a similar way.
> >
> > i.e. assuming A=0, black notes which are flats will have positive
> > changes in cents; and black notes which are sharps would be negative
> > changes.
> >
> > I appreciate that not everyone uses A = 440 as a reference, but that
> > is just an arbitrary rule that I have used for the past 20 years, so
> > that the notenames used in all LucyTuned pieces will match the same
> > pitches.
> >
> >
>
>
>
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

OK Tom;

I have put your example tuning as specified in this email quote up in this folder (names contain tom)

http://www.lucytune.com/godsaveourqueen/

On 15 Feb 2009, at 20:51, Tom Dent wrote:

>
> Ah OK, I don't mind about the pitch reference. It's only a couple of
> Hz either way...
> Relative to A we have simply
> (+12 +32 +4 +24 -4 +16 -12 +8 +28 0 +20 -8)
> for 4 flats and 1 sharp.
>
> However, you seem to have a problem with the sequencer: namely, the
> bass clarinet notes don't sound. It should for example provide a big
> downward scale near the end and give the major third in the final
> chord, but it's completely absent. It would be worth checking whether
> each part does actually function - I'm not too sure about the
> clarinets either.
>
> Conclusion: with harpsichords, you're directly in contact with
> whatever wrong notes there may be!
> ~~~T~~~
>
> --- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
> >
> > No I haven't used G#, I set the original tuning to Lucy 5b0s i.e. 5
> > flats no sharps, and the others in a similar way.
> >
> > i.e. assuming A=0, black notes which are flats will have positive
> > changes in cents; and black notes which are sharps would be negative
> > changes.
> >
> > I appreciate that not everyone uses A = 440 as a reference, but that
> > is just an arbitrary rule that I have used for the past 20 years, so
> > that the notenames used in all LucyTuned pieces will match the same
> > pitches.
> >
> >
>
>
>
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

I am not sure how you would like to handle the greater than an octave
values using Logic.
If I see the values, I shall have to decide which notes fall into
higher octaves, and make a separate track for them with a different
set of tuning codes,
turn then into audio and then bounce their audios and the remainder
together using a different set of midi tunings for the others.

On 15 Feb 2009, at 20:23, Petr Parízek wrote:

>
> Charles wrote:
>
> > If you can let me have what you calculate as the values for the +
> or - cents for each of the
> > notes, assuming A=0 i.e.440Hz, I'll reset and bounce all five new
> tunings (Your three +
> > Tom's two) as mp3's and up and put them up.
>
> Maybe I should warn you that two of the tunings which I suggested
> have octaves wider than 1200 cents and one of the tunings Carl
> suggested also has wider octaves, so you would have to use, for
> example, multiple MIDI channels or whatever.
>
> Petr
>
>
>
>
>
>
>

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

The test was wrong then, for Carl's TOP meantone proposal.
(see if you can fix it, for Petr's stretched octaves as well) -

Up to now, at least both meantone versions are much better than the
12 edo one, by far...
(to my ears) - quite impressive how it changes the timbres for the 3
samples -
But, according to Tom harpsichord performance, my prefered version,
no tempering is needed for this GSTQ part !
Would not music where comma problem really occurs would be better for
such a meantone test ?

And at slow down tempo if possible...

Thanks for the effort anyway !

- - - - - - - - - - - - - - - - - - - - - - -
Jacques

Le 15 févr. 09 à 23:14, Charles Lucy a écrit :

> I am not sure how you would like to handle the greater than an
> octave values using Logic.
>
> If I see the values, I shall have to decide which notes fall into
> higher octaves, and make a separate track for them with a different
> set of tuning codes,
> turn then into audio and then bounce their audios and the remainder
> together using a different set of midi tunings for the others.
>
>
> On 15 Feb 2009, at 20:23, Petr Parízek wrote:
>
>>
>> Charles wrote:
>>
>> > If you can let me have what you calculate as the values for the
>> + or - cents for each of the
>> > notes, assuming A=0 i.e.440Hz, I'll reset and bounce all five
>> new tunings (Your three +
>> > Tom's two) as mp3's and up and put them up.
>>
>> Maybe I should warn you that two of the tunings which I suggested
>> have octaves wider than 1200 cents and one of the tunings Carl
>> suggested also has wider octaves, so you would have to use, for
>> example, multiple MIDI channels or whatever.
>>
>> Petr
>>
>
>
>
>

Charles wrote:

> If I see the values, I shall have to decide which notes fall into higher octaves, and make
> a separate track for them with a different set of tuning codes,

Okay, as Tom has already listed 50-equal, I'll go on to the two of my suggested tunings with stretched octaves -- hope that these won't be a problem for you to tune and that the values will be helpful. For the 1/12-comma stretched octave tuning, the major second is ~191.364666 cents and the minor second is ~122.484430 cents. For the 1/9-comma stretched octave tuning, the major second is ~191.962063 cents and the minor second is ~121.289636 cents.

Petr

Yes Jacques;

It looks as though I misinterpreted Carl's specs.

If the octave is to be stretched. I need to know exactly what ptiches
are intended for each of the various notes in each octave.

Yes, a slowed down version of the debatable section could easily be
produced by reducing the tempo, if we can agree on the notes/bars
required and the exact tunings needed.

On 15 Feb 2009, at 22:59, Jacques Dudon wrote:

> The test was wrong then, for Carl's TOP meantone proposal.
>
> (see if you can fix it, for Petr's stretched octaves as well) -
>
> Up to now, at least both meantone versions are much better than the
> 12 edo one, by far...
> (to my ears) - quite impressive how it changes the timbres for the 3
> samples -
> But, according to Tom harpsichord performance, my prefered version,
> no tempering is needed for this GSTQ part !
> Would not music where comma problem really occurs would be better
> for such a meantone test ?
>
> And at slow down tempo if possible...
>
> Thanks for the effort anyway !
>
> - - - - - - - - - - - - - - - - - - - - - - -
> Jacques
>
>
>
>
>
> Le 15 févr. 09 à 23:14, Charles Lucy a écrit :
>
>> I am not sure how you would like to handle the greater than an
>> octave values using Logic.
>>
>> If I see the values, I shall have to decide which notes fall into
>> higher octaves, and make a separate track for them with a different
>> set of tuning codes,
>> turn then into audio and then bounce their audios and the remainder
>> together using a different set of midi tunings for the others.
>>
>>
>> On 15 Feb 2009, at 20:23, Petr Parízek wrote:
>>
>>>
>>> Charles wrote:
>>>
>>> > If you can let me have what you calculate as the values for the
>>> + or - cents for each of the
>>> > notes, assuming A=0 i.e.440Hz, I'll reset and bounce all five
>>> new tunings (Your three +
>>> > Tom's two) as mp3's and up and put them up.
>>>
>>> Maybe I should warn you that two of the tunings which I suggested
>>> have octaves wider than 1200 cents and one of the tunings Carl
>>> suggested also has wider octaves, so you would have to use, for
>>> example, multiple MIDI channels or whatever.
>>>
>>> Petr
>>>
>>
>>
>>
>
>
>

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

OK I understand that the Large interval is 191.4 and the small
interval is 122.5,

so (191.364666*5) + (122.484430*2) = 1201.792

So keeping the GSTQ in the key of Eb, do I add and subtract Large and
small intervals from the lowest(?) Eb to arrive at the pitch values
for each of the others?

On 15 Feb 2009, at 23:04, Petr Parízek wrote:

>
> Charles wrote:
>
> > If I see the values, I shall have to decide which notes fall into
> higher octaves, and make
> > a separate track for them with a different set of tuning codes,
>
> Okay, as Tom has already listed 50-equal, I’ll go on to the two of
> my suggested tunings with stretched octaves -- hope that these won’t
> be a problem for you to tune and that the values will be helpful.
> For the 1/12-comma stretched octave tuning, the major second is
> ~191.364666 cents and the minor second is ~122.484430 cents. For the
> 1/9-comma stretched octave tuning, the major second is ~191.962063
> cents and the minor second is ~121.289636 cents.
>
> Petr
>
>
>
>
>
>
>

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 wrote:

> So keeping the GSTQ in the key of Eb, do I add and subtract Large and small intervals from
> the lowest(?) Eb to arrive at the pitch values for each of the others?

I’m not 100% sure if we both mean the same thing but most probably yes.

Petr

I wrote:

> For the 1/12-comma stretched octave tuning, the major second is ~191.364666 cents and the
> minor second is ~122.484430 cents. For the 1/9-comma stretched octave tuning, the major
> second is ~191.962063 cents and the minor second is ~121.289636 cents.

Actually, I wouldn't be surprised if the latter sounded a bit more "in tune" than the former -- for various reasons -- but that's another story.

Petr

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> It would also be nice if the test was blind, so that personal
> biases (which seem to be pretty large around here lately) don't
> make as much of an impact.
>
> -Mike

Let's be clear: I never said these meantones would sound
better than LucyTuning. I said they would make a good
comparison, since they are the next-most-promoted meantones
after LucyTuning. What I did say was that the difference
would be small, which is really the main point -- that
there is nothing special about LucyTuning, other than the
fact that it is a meantone.

-Carl

That is what I was hoping to demonstrate with a blind test, so that we
don't have people's biases in the way.
-Mike

On Mon, Feb 16, 2009 at 3:52 AM, Carl Lumma <carl@...> wrote:
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>>
>> It would also be nice if the test was blind, so that personal
>> biases (which seem to be pretty large around here lately) don't
>> make as much of an impact.
>>
>> -Mike
>
> Let's be clear: I never said these meantones would sound
> better than LucyTuning. I said they would make a good
> comparison, since they are the next-most-promoted meantones
> after LucyTuning. What I did say was that the difference
> would be small, which is really the main point -- that
> there is nothing special about LucyTuning, other than the
> fact that it is a meantone.
>
> -Carl
>
>

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
> I am not sure how you would like to handle the greater than an
> octave values using Logic.
> If I see the values, I shall have to decide which notes fall
> into higher octaves, and make a separate track for them with
> a different set of tuning codes, turn then into audio and then
> bounce their audios and the remainder together using a
> different set of midi tunings for the others.

As I already said, don't worry about it. It is too hard to do
in Logic. I will provide you with corrected scales for this
comparison.

-Carl

Agreed...next time let's not name the scales used and just give names like
one.mp3
two.mp3
three.mp3
. :-)

--- On Mon, 2/16/09, Mike Battaglia <battaglia01@...> wrote:

From: Mike Battaglia <battaglia01@...>
Subject: Re: [tuning] Re: Comma Pumps - GodSaveQueen curiosity;-)
To: tuning@yahoogroups.com
Date: Monday, February 16, 2009, 12:55 AM

That is what I was hoping to demonstrate with a blind test, so that we

don't have people's biases in the way.

-Mike

On Mon, Feb 16, 2009 at 3:52 AM, Carl Lumma <carl@...> wrote:

> --- In tuning@yahoogroups. com, Mike Battaglia <battaglia01@ ...> wrote:

>>

>> It would also be nice if the test was blind, so that personal

>> biases (which seem to be pretty large around here lately) don't

>> make as much of an impact.

>>

>> -Mike

>

> Let's be clear: I never said these meantones would sound

> better than LucyTuning. I said they would make a good

> comparison, since they are the next-most-promoted meantones

> after LucyTuning. What I did say was that the difference

> would be small, which is really the main point -- that

> there is nothing special about LucyTuning, other than the

> fact that it is a meantone.

>

> -Carl

>

>

--What I did say was that the difference
--would be small, which is really the main point -- that
--there is nothing special about LucyTuning, other than the
--fact that it is a meantone.

In general, I find this "small difference" an issue not just in this comparison, but in the art of tuning as a whole.
Not just between mean-tone and Lucy Tuning, but between
1. 5-limit JI (diatonic)
2. Mean-tone
3. Lucy Tuning
4. 12TET
5. Any type of scale configurations`in 19TET, 22TET, 36TET...meant to basically emulate intervals and chords seen in said above tunings

   To me all of these sound very alike for the most part (and considering they are for the most part no more than 8 cents or so off from each other that makes sense).

   There are some things that bug me a bit, like the sour third in 12TET or the wolf notes in mean-tone...but there's really nothing so different between any of those that makes me think of them as truly different scales far as their overall emotional effects.

   Just as a side-note: it still amazes me how much fuss goes on about tunings that are so closely related.  It's almost tempting to say just one of those tunings should replace all the others...then again, that's kind of what happened with 12TET.   Far as Lucy Tuning...yes I think it should replace 12TET as a small step forward...but I don't think that would be a revolution in music by any means, just a "slight purification".

-Michael

--- On Mon, 2/16/09, Carl Lumma <carl@...> wrote:

From: Carl Lumma <carl@...>
Subject: [tuning] Re: Comma Pumps - GodSaveQueen curiosity;-)
To: tuning@yahoogroups.com
Date: Monday, February 16, 2009, 12:52 AM

--- In tuning@yahoogroups. com, Mike Battaglia <battaglia01@ ...> wrote:

>

> It would also be nice if the test was blind, so that personal

> biases (which seem to be pretty large around here lately) don't

> make as much of an impact.

>

> -Mike

Let's be clear: I never said these meantones would sound

better than LucyTuning. I said they would make a good

comparison, since they are the next-most-promoted meantones

after LucyTuning. What I did say was that the difference

would be small, which is really the main point -- that

there is nothing special about LucyTuning, other than the

fact that it is a meantone.

-Carl

I wrote:
> I would recommend just using 1/4 comma, or 7/26 comma
> meantone for the comparison, since they are octave-based
> and easy to do in Logic and many other instruments.

OK, I'll go ahead show my work for those following along
at home.

The syntonic comma is 81/80, which is 21.506290 cents.
7/26 of that is 5.790155 cents, so the 7/26-comma meantone
fifth is 701.955001 - 5.790155 = 696.164846 cents. Recall
from my previous message that this is the meantone fifth
which minimizes the RMS error of 5-limit triads. For those
of you who are allergic to history, I won't mention that
Woolhouse was apparently the first to compute this result,
in 1835.

I will point out that it's within a gnat's breath of the
LucyTuned fifth of 695.492966 cents. However, once we
start chaining fifths, this difference will compound.
Recall that in meantone, major triads are always 0 4 1
fifths, so

LucyTuned: 0 382.0 695.5
Woolhouse: 0 384.7 696.2

If anyone would care to synthesize these, it would be a
more direct comparison than rendering a piece of music.

But let's go ahead with GSTQ. Charles said it's it's in
Eb, so we'll put the wolf fifth as far away as possible:
between A and E. To do this, I'll go into Scala, type
"pythag", tell it size 12, accept 2/1 octaves and monotonic
scale, enter the Woolhouse fifth, and a count downwards
of 8 to get the wolf between A and E. That gives:

!
Woolhouse meantone, Eb-centered
12
!
119.17577
192.32969
311.50546
430.68123
503.83515
623.01092
696.16485
815.34062
888.49454
1007.67031
1126.84608
2/1
!

Doing the same thing for the Lucy fifth gives:

!
LucyTuning, Eb-centered
12
!
122.53517
190.98593
313.52110
436.05627
504.50703
627.04220
695.49297
818.02814
886.47890
1009.01407
1131.54924
2/1
!

Now, for Logic, we'll want to convert these to deviations
from 12-ET. And to make the comparison fair, we'll want
to 'tare' Eb's deviation to zero...

Woolhouse:
7.7 C#
-19.2 D
0.00 D#
19.2 E
-7.7 F
11.5 F#
-15.3 G
3.8 G#
-23.0 A
-3.8 A#
15.3 B
-11.5 C

Lucy:
9.0 C#
-22.5 D
0.0 D#
22.5 E
-9.0 F
13.5 F#
-18.0 G
4.5 G#
-27.0 A
-4.5 A#
18.0 B
-13.5 C

You can also see that here:
http://spreadsheets.google.com/pub?key=pJ81Jwm6ARUdaXNucgQ2VQw

-Carl

>    Just as a side-note: it still amazes me how much fuss goes
> on about tunings that are so closely related.  It's almost
> tempting to say just one of those tunings should replace all
> the others...then again, that's kind of what happened with
> 12TET.   Far as Lucy Tuning...yes I think it should replace
> 12TET as a small step forward...but I don't think that would
> be a revolution in music by any means, just a "slight
> purification".
>
> -Michael

LucyTuning taken out to 31 would probably be the biggest
revolution in 500 years.

-Carl

Still, I believe this anthem is not the perfect example for that
comparison, because of its absence of comma dlilemna.
What we are doing here is only testing how different temperaments are
"not doing so bad" in the interpretation of a JI piece.
No suggestion, anybody, even of a diatonic composition with fourth
successions of both major and minor chords or whatever,
for example with a "D minor " (in a C major key) type of stuff, where
Tom's beautiful harpsichord would be a little more in trouble ? ;-)
at this point, I believe his harpsichord version wins the test.

In the meantime, since many different types of meantones are not
represented here,
I would submit at least two more, without octave stretching :

Mezzo meta-meantone
classic quarter-syntonic comma but very sligthly improved in order to
achieve equal-beating,
(tone interval 193.1652187, diatonic semitone 117.0869532 cents)

!
Mezzo
12
!
76.07826556
193.1652187
310.2521719
386.3304375
503.4173906
579.4956562
696.5826094
772.6608749
889.7478281
1006.834781
1082.913047
1200
!

Skisni meta-meantone (sent prviously on this list)
highly convergent, differentially coherent and equal-beating meantone
close to a 1/5 of pythagorean comma-type
(tone interval 194.5568098, diatonic semitone 113.6079755 cents)

!
Skisni
12
!
80.94883432
194.5568098
308.1647853
389.1136196
502.7215951
583.6704294
697.2784049
778.2272392
891.8352147
1005.44319
1086.392025
1200
!

If I had the value in Hz of the concluding major triad tonic I could
give you the equal-beating periods,
in order to tune the tempo for each one, but I don't want to take
advantage over others here !
Neither I want to take your time for that -

Thanks,
- - - - - - -
Jacques

Le 16 févr. 09 à 00:11, Charles Lucy a écrit :

> Yes Jacques
>
> It looks as though I misinterpreted Carl's specs.
>
> If the octave is to be stretched. I need to know exactly what
> ptiches are intended for each of the various notes in each octave.
>
> Yes, a slowed down version of the debatable section could easily be
> produced by reducing the tempo, if we can agree on the notes/bars
> required and the exact tunings needed.
>
> On 15 Feb 2009, at 22:59, Jacques Dudon wrote:
>
>> The test was wrong then, for Carl's TOP meantone proposal.
>>
>> (see if you can fix it, for Petr's stretched octaves as well) -
>>
>> Up to now, at least both meantone versions are much better than
>> the 12 edo one, by far...
>> (to my ears) - quite impressive how it changes the timbres for the
>> 3 samples -
>> But, according to Tom harpsichord performance, my prefered
>> version, no tempering is needed for this GSTQ part !
>> Would not music where comma problem really occurs would be better
>> for such a meantone test ?
>>
>> And at slow down tempo if possible...
>>
>> Thanks for the effort anyway !
>>
>> - - - - - - - - - - - - - - - - - - - - - - -
>> Jacques

You are only experiencing the familiar (simple) harmonies in the pieces that you have heard.
Once you start moving beyond 12 steps of fourths and fifths, "interesting" things start to happen musically.

On 16 Feb 2009, at 09:45, Michael Sheiman wrote:

>
> --What I did say was that the difference
> --would be small, which is really the main point -- that
> --there is nothing special about LucyTuning, other than the
> --fact that it is a meantone.
>
> In general, I find this "small difference" an issue not just in this > comparison, but in the art of tuning as a whole.
> Not just between mean-tone and Lucy Tuning, but between
> 1. 5-limit JI (diatonic)
> 2. Mean-tone
> 3. Lucy Tuning
> 4. 12TET
> 5. Any type of scale configurations`in 19TET, 22TET, 36TET...meant > to basically emulate intervals and chords seen in said above tunings
>
> To me all of these sound very alike for the most part (and > considering they are for the most part no more than 8 cents or so > off from each other that makes sense).
>
> There are some things that bug me a bit, like the sour third in > 12TET or the wolf notes in mean-tone...but there's really nothing so > different between any of those that makes me think of them as truly > different scales far as their overall emotional effects.
>
> Just as a side-note: it still amazes me how much fuss goes on > about tunings that are so closely related. It's almost tempting to > say just one of those tunings should replace all the others...then > again, that's kind of what happened with 12TET. Far as Lucy > Tuning...yes I think it should replace 12TET as a small step > forward...but I don't think that would be a revolution in music by > any means, just a "slight purification".
>
> -Michael
>
> --- On Mon, 2/16/09, Carl Lumma <carl@...> wrote:
>
> From: Carl Lumma <carl@...>
> Subject: [tuning] Re: Comma Pumps - GodSaveQueen curiosity;-)
> To: tuning@yahoogroups.com
> Date: Monday, February 16, 2009, 12:52 AM
>
> --- In tuning@yahoogroups. com, Mike Battaglia <battaglia01@ ...> > wrote:
> >
> > It would also be nice if the test was blind, so that personal
> > biases (which seem to be pretty large around here lately) don't
> > make as much of an impact.
> >
> > -Mike
>
> Let's be clear: I never said these meantones would sound
> better than LucyTuning. I said they would make a good
> comparison, since they are the next-most-promoted meantones
> after LucyTuning. What I did say was that the difference
> would be small, which is really the main point -- that
> there is nothing special about LucyTuning, other than the
> fact that it is a meantone.
>
> -Carl
>
>
>
>
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

Thanks Carl;

I shall attempt to get to them in the next coupla days; as soon as I can get the time.

On 16 Feb 2009, at 10:27, Carl Lumma wrote:

> I wrote:
> > I would recommend just using 1/4 comma, or 7/26 comma
> > meantone for the comparison, since they are octave-based
> > and easy to do in Logic and many other instruments.
>
> OK, I'll go ahead show my work for those following along
> at home.
>
> The syntonic comma is 81/80, which is 21.506290 cents.
> 7/26 of that is 5.790155 cents, so the 7/26-comma meantone
> fifth is 701.955001 - 5.790155 = 696.164846 cents. Recall
> from my previous message that this is the meantone fifth
> which minimizes the RMS error of 5-limit triads. For those
> of you who are allergic to history, I won't mention that
> Woolhouse was apparently the first to compute this result,
> in 1835.
>
> I will point out that it's within a gnat's breath of the
> LucyTuned fifth of 695.492966 cents. However, once we
> start chaining fifths, this difference will compound.
> Recall that in meantone, major triads are always 0 4 1
> fifths, so
>
> LucyTuned: 0 382.0 695.5
> Woolhouse: 0 384.7 696.2
>
> If anyone would care to synthesize these, it would be a
> more direct comparison than rendering a piece of music.
>
> But let's go ahead with GSTQ. Charles said it's it's in
> Eb, so we'll put the wolf fifth as far away as possible:
> between A and E. To do this, I'll go into Scala, type
> "pythag", tell it size 12, accept 2/1 octaves and monotonic
> scale, enter the Woolhouse fifth, and a count downwards
> of 8 to get the wolf between A and E. That gives:
>
> !
> Woolhouse meantone, Eb-centered
> 12
> !
> 119.17577
> 192.32969
> 311.50546
> 430.68123
> 503.83515
> 623.01092
> 696.16485
> 815.34062
> 888.49454
> 1007.67031
> 1126.84608
> 2/1
> !
>
> Doing the same thing for the Lucy fifth gives:
>
> !
> LucyTuning, Eb-centered
> 12
> !
> 122.53517
> 190.98593
> 313.52110
> 436.05627
> 504.50703
> 627.04220
> 695.49297
> 818.02814
> 886.47890
> 1009.01407
> 1131.54924
> 2/1
> !
>
> Now, for Logic, we'll want to convert these to deviations
> from 12-ET. And to make the comparison fair, we'll want
> to 'tare' Eb's deviation to zero...
>
> Woolhouse:
> 7.7 C#
> -19.2 D
> 0.00 D#
> 19.2 E
> -7.7 F
> 11.5 F#
> -15.3 G
> 3.8 G#
> -23.0 A
> -3.8 A#
> 15.3 B
> -11.5 C
>
> Lucy:
> 9.0 C#
> -22.5 D
> 0.0 D#
> 22.5 E
> -9.0 F
> 13.5 F#
> -18.0 G
> 4.5 G#
> -27.0 A
> -4.5 A#
> 18.0 B
> -13.5 C
>
> You can also see that here:
> http://spreadsheets.google.com/pub?key=pJ81Jwm6ARUdaXNucgQ2VQw
>
> -Carl
>
>
>
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

By the way, I think I know why people are having such a hard time
distinguishing the Lucy-synthesized anthems one from another: because
of the instrumentation!

Basically the clarinets and flute all have quite overtone-poor
timbres, so particularly when the inner parts are provided by
clarinets, the beating or clash of tempered intervals is hard to
discern. Much more so than, for example, if the ensemble were oboes
and bassoons, or solo strings. So the listener is left with the
melodic properties of the tuning, which are quite hard to discern in
four-part harmony.

Now Jacques says, hearing my version, that there is no comma problem
in the piece. I don't want to take too much advantage of secrecy (you
didn't see how I prepared the harpsichord), but this is quite funny!
Because there is absolutely a comma-problem, right there in the first
two bars and at other points.

How did I fix it? - the instrument has 12 keys per octave, whereas the
piece only uses 9 notes (C,C#,D,Eb,E,F,G,A,Bb). Therefore, I can tune
the G to 9/10 above F and the G# to 9/8...

C major is played as C-E-G#, whereas G minor is G-Bb-D as usual. In
the little left-hand break before the second half, I (should have) played
A-f c-g# f-a g-bb
using the two different G's in successive beats.

Basically you don't even notice the comma shift if it occurs between
the melody and some other part. If the melody were F-F-G/G-F-E instead
of F-F-G/E-F-G I might be in trouble.
The mistake you hear halfway through is where I hit the lower G by
mistake in a C major chord: result, horrible flat fifth. I thought
that would alert somebody.

Full ratios relative to F:
C=3/2 G=10/9 'G#'=9/8 D=5/3 A=5/4 E=15/16 Bb=4/3
now the septimals:
Eb = A*5/7 = 25/28
C# = G*7/5 = 14/9 (=Bb*7/6 =A*)

At first I tried tuning 'B' as an extra Bb to E*10/7 = 75/56 to use in
the C7 chords, but somehow it sounded too high in the melody (225/224
sharp to F) - or perhaps 25/14 above the root C is not comprehensible
enough compared to either 16/9 or 9/5.

However the septimal Eb and C# sound fine to me in their harmonic
context.

For D minor I would tune C# up to A*5/4, otherwise I don't see
additional problems (assuming a real G# doesn't come up!). Perhaps one
would need two B naturals too, or more practicably two E naturals
(using Eb and E keys).
~~~T~~~

--- In tuning@yahoogroups.com, Jacques Dudon <fotosonix@...> wrote:
>
> Still, I believe this anthem is not the perfect example for that
> comparison, because of its absence of comma dlilemna.
> What we are doing here is only testing how different temperaments are
> "not doing so bad" in the interpretation of a JI piece.
> No suggestion, anybody, even of a diatonic composition with fourth
> successions of both major and minor chords or whatever,
> for example with a "D minor " (in a C major key) type of stuff, where
> Tom's beautiful harpsichord would be a little more in trouble ? ;-)
> at this point, I believe his harpsichord version wins the test.
>

I noticed that comma mistake in the middle, and I thougth you were
using some kind of a more-than-12 keys keyboard, since you were
playing the correct 9/8 right after !
But I missed the comma shift in the beginnning (now I know it, of
course !), well done. And quite pleasant to hear.

So I retract my complain of "absence of comma resolution" ! I was
charmed by the sound - however I am sure there must be more probant
pieces for that kind of little problems that would need meantoning
badly. They would be abundant in Celtic music.
Also, as I already suggested, a lower speed would be much better to
hear the different tunings. Not faster than for one that has to
choose his comma options, right ? ;-)

- - - - - -
Jacques

Le 16 févr. 09 à 16:34, Tom Dent a écrit
>
> Now Jacques says, hearing my version, that there is no comma problem
> in the piece. I don't want to take too much advantage of secrecy (you
> didn't see how I prepared the harpsichord), but this is quite funny!
> Because there is absolutely a comma-problem, right there in the first
> two bars and at other points.
>
> How did I fix it? - the instrument has 12 keys per octave, whereas the
> piece only uses 9 notes (C,C#,D,Eb,E,F,G,A,Bb). Therefore, I can tune
> the G to 9/10 above F and the G# to 9/8...
>
> C major is played as C-E-G#, whereas G minor is G-Bb-D as usual. In
> the little left-hand break before the second half, I (should have)
> played
> A-f c-g# f-a g-bb
> using the two different G's in successive beats.
>
> Basically you don't even notice the comma shift if it occurs between
> the melody and some other part. If the melody were F-F-G/G-F-E instead
> of F-F-G/E-F-G I might be in trouble.
> The mistake you hear halfway through is where I hit the lower G by
> mistake in a C major chord: result, horrible flat fifth. I thought
> that would alert somebody.
>
> ~~~T~~~
>
> --- In tuning@yahoogroups.com, Jacques Dudon <fotosonix@...> wrote:
> >
> > Still, I believe this anthem is not the perfect example for that
> > comparison, because of its absence of comma dilemna.
> > What we are doing here is only testing how different temperaments
> are
> > "not doing so bad" in the interpretation of a JI piece.
> > No suggestion, anybody, even of a diatonic composition with fourth
> > successions of both major and minor chords or whatever,
> > for example with a "D minor " (in a C major key) type of stuff,
> where
> > Tom's beautiful harpsichord would be a little more in trouble ? ;-)
> > at this point, I believe his harpsichord version wins the test.
> >

Hi Carl,
I am not sure what's a gnat breath, but for the case I would'nt say
it is that small then...
Anyway I would be interested to understand what is meant by RMS (root
mean square ?) error applied to meantone, and why would Woolhouse
fifth would minimize it, if you could resume that or give a link some
time.
Thanks !
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Jacques

Le 16 févr. 09 à 11:27, Carl Lumma a écrit :

> I wrote:
> > I would recommend just using 1/4 comma, or 7/26 comma
> > meantone for the comparison, since they are octave-based
> > and easy to do in Logic and many other instruments.
>
> OK, I'll go ahead show my work for those following along
> at home.
>
> The syntonic comma is 81/80, which is 21.506290 cents.
> 7/26 of that is 5.790155 cents, so the 7/26-comma meantone
> fifth is 701.955001 - 5.790155 = 696.164846 cents. Recall
> from my previous message that this is the meantone fifth
> which minimizes the RMS error of 5-limit triads. For those
> of you who are allergic to history, I won't mention that
> Woolhouse was apparently the first to compute this result,
> in 1835.
>
> I will point out that it's within a gnat's breath of the
> LucyTuned fifth of 695.492966 cents. However, once we
> start chaining fifths, this difference will compound.
> Recall that in meantone, major triads are always 0 4 1
> fifths, so
>
> LucyTuned: 0 382.0 695.5
> Woolhouse: 0 384.7 696.2
>
> If anyone would care to synthesize these, it would be a
> more direct comparison than rendering a piece of music.
>
> But let's go ahead with GSTQ. Charles said it's it's in
> Eb, so we'll put the wolf fifth as far away as possible:
> between A and E. To do this, I'll go into Scala, type
> "pythag", tell it size 12, accept 2/1 octaves and monotonic
> scale, enter the Woolhouse fifth, and a count downwards
> of 8 to get the wolf between A and E. That gives:
>
> !
> Woolhouse meantone, Eb-centered
> 12
> !
> 119.17577
> 192.32969
> 311.50546
> 430.68123
> 503.83515
> 623.01092
> 696.16485
> 815.34062
> 888.49454
> 1007.67031
> 1126.84608
> 2/1
> !
>
> Doing the same thing for the Lucy fifth gives:
>
> !
> LucyTuning, Eb-centered
> 12
> !
> 122.53517
> 190.98593
> 313.52110
> 436.05627
> 504.50703
> 627.04220
> 695.49297
> 818.02814
> 886.47890
> 1009.01407
> 1131.54924
> 2/1
> !
>
> Now, for Logic, we'll want to convert these to deviations
> from 12-ET. And to make the comparison fair, we'll want
> to 'tare' Eb's deviation to zero...
>
> Woolhouse:
> 7.7 C#
> -19.2 D
> 0.00 D#
> 19.2 E
> -7.7 F
> 11.5 F#
> -15.3 G
> 3.8 G#
> -23.0 A
> -3.8 A#
> 15.3 B
> -11.5 C
>
> Lucy:
> 9.0 C#
> -22.5 D
> 0.0 D#
> 22.5 E
> -9.0 F
> 13.5 F#
> -18.0 G
> 4.5 G#
> -27.0 A
> -4.5 A#
> 18.0 B
> -13.5 C
>
> You can also see that here:
> http://spreadsheets.google.com/pub?key=pJ81Jwm6ARUdaXNucgQ2VQw
>
> -Carl
>
>
>

--- In tuning@yahoogroups.com, Jacques Dudon <fotosonix@...> wrote:
>
> Still, I believe this anthem is not the perfect example for that
> comparison, because of its absence of comma dlilemna.

Hi, Jacques.

I'm not sure why the comma dilemma is important for this
comparison. Since both tunings are meantones they would both
handle the dilemma the same way if it were present.

>I believe his harpsichord version wins the test.

Of course. But the comparison was originally suggested to
prove or disprove claims that LucyTuning is a special tuning.
I am claiming it is just a meantone, and that it makes no
sense to pick a particular fifth on the continuum of meantone
fifths and claim it is vastly different than its neighbors.

-Carl

Thanks! I look forward to hearing them. Let me know if
you hit any snags. -Carl

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
> Thanks Carl;
>
> I shall attempt to get to them in the next coupla days; as
> soon as I can get the time.
>
> On 16 Feb 2009, at 10:27, Carl Lumma wrote:
>
> > OK, I'll go ahead show my work for those following along
> > at home.
> >
> > The syntonic comma is 81/80, which is 21.506290 cents.
> > 7/26 of that is 5.790155 cents, so the 7/26-comma meantone
> > fifth is 701.955001 - 5.790155 = 696.164846 cents. Recall
> > from my previous message that this is the meantone fifth
> > which minimizes the RMS error of 5-limit triads. For those
> > of you who are allergic to history, I won't mention that
> > Woolhouse was apparently the first to compute this result,
> > in 1835.
> >
> > I will point out that it's within a gnat's breath of the
> > LucyTuned fifth of 695.492966 cents. However, once we
> > start chaining fifths, this difference will compound.
> > Recall that in meantone, major triads are always 0 4 1
> > fifths, so
> >
> > LucyTuned: 0 382.0 695.5
> > Woolhouse: 0 384.7 696.2
> >
> > If anyone would care to synthesize these, it would be a
> > more direct comparison than rendering a piece of music.
> >
> > But let's go ahead with GSTQ. Charles said it's it's in
> > Eb, so we'll put the wolf fifth as far away as possible:
> > between A and E. To do this, I'll go into Scala, type
> > "pythag", tell it size 12, accept 2/1 octaves and monotonic
> > scale, enter the Woolhouse fifth, and a count downwards
> > of 8 to get the wolf between A and E. That gives:
> >
> > !
> > Woolhouse meantone, Eb-centered
> > 12
> > !
> > 119.17577
> > 192.32969
> > 311.50546
> > 430.68123
> > 503.83515
> > 623.01092
> > 696.16485
> > 815.34062
> > 888.49454
> > 1007.67031
> > 1126.84608
> > 2/1
> > !
> >
> > Doing the same thing for the Lucy fifth gives:
> >
> > !
> > LucyTuning, Eb-centered
> > 12
> > !
> > 122.53517
> > 190.98593
> > 313.52110
> > 436.05627
> > 504.50703
> > 627.04220
> > 695.49297
> > 818.02814
> > 886.47890
> > 1009.01407
> > 1131.54924
> > 2/1
> > !
> >
> > Now, for Logic, we'll want to convert these to deviations
> > from 12-ET. And to make the comparison fair, we'll want
> > to 'tare' Eb's deviation to zero...
> >
> > Woolhouse:
> > 7.7 C#
> > -19.2 D
> > 0.00 D#
> > 19.2 E
> > -7.7 F
> > 11.5 F#
> > -15.3 G
> > 3.8 G#
> > -23.0 A
> > -3.8 A#
> > 15.3 B
> > -11.5 C
> >
> > Lucy:
> > 9.0 C#
> > -22.5 D
> > 0.0 D#
> > 22.5 E
> > -9.0 F
> > 13.5 F#
> > -18.0 G
> > 4.5 G#
> > -27.0 A
> > -4.5 A#
> > 18.0 B
> > -13.5 C
> >
> > You can also see that here:
> > http://spreadsheets.google.com/pub?key=pJ81Jwm6ARUdaXNucgQ2VQw
> >
> > -Carl
>

--- In tuning@yahoogroups.com, Jacques Dudon <fotosonix@...> wrote:
>
> Hi Carl,
> I am not sure what's a gnat breath, but for the case I wouldn't
> say it is that small then...
> Anyway I would be interested to understand what is meant by RMS
> (root mean square ?) error applied to meantone, and why would
> Woolhouse fifth would minimize it, if you could resume that or
> give a link some time.
> Thanks !

Sure Jacques.

A gnat is a tiny insect, so yes, a way of saying "small".
The difference in fifths is small, but as they are chained
together the differences add up.

Yes, root mean squared. One lists the 5-limit intervals

3/2
5/4
6/5
(inversions aren't necessary to study for meantones which
have perfect octaves)

and finds the error in of each, squares it, and then sums
these three squared errors. You can read all about
Woolhouse's approach here:

http://tonalsoft.com/monzo/woolhouse/essay.aspx

-Carl

Interesting concept Charles...do you have any recommended examples of these "un-familiar harmonies" you seem to be indirectly suggesting show the hidden potential of these on-the-surface "near-JI-sounding" scales?

--- On Mon, 2/16/09, Charles Lucy <lucy@...> wrote:

From: Charles Lucy <lucy@...>
Subject: Re: [tuning] Re: Comma Pumps - GodSaveQueen curiosity;-)
To: tuning@yahoogroups.com
Date: Monday, February 16, 2009, 5:51 AM

You are only experiencing the familiar (simple) harmonies in the pieces that you have heard.Once you start moving beyond 12 steps of fourths and fifths, "interesting" things start to happen musically.
On 16 Feb 2009, at 09:45, Michael Sheiman wrote:

--What I did say was that the difference
--would be small, which is really the main point -- that
--there is nothing special about LucyTuning, other than the
--fact that it is a meantone.

In general, I find this "small difference" an issue not just in this comparison, but in the art of tuning as a whole.
Not just between mean-tone and Lucy Tuning, but between
1. 5-limit JI (diatonic)
2. Mean-tone
3. Lucy Tuning
4. 12TET
5. Any type of scale configurations` in 19TET, 22TET, 36TET...meant to basically emulate intervals and chords seen in said above tunings

   To me all of these sound very alike for the most part (and considering they are for the most part no more than 8 cents or so off from each other that makes sense).

   There are some things that bug me a bit, like the sour third in 12TET or the wolf notes in mean-tone... but there's really nothing so different between any of those that makes me think of them as truly different scales far as their overall emotional effects.

   Just as a side-note: it still amazes me how much fuss goes on about tunings that are so closely related.  It's almost tempting to say just one of those tunings should replace all the others...then again, that's kind of what happened with 12TET.   Far as Lucy Tuning...yes I think it should replace 12TET as a small step forward...but I don't think that would be a revolution in music by any means, just a "slight purification" .

-Michael 

--- On Mon, 2/16/09, Carl Lumma <carl@...> wrote:

From: Carl Lumma <carl@...>
Subject: [tuning] Re: Comma Pumps - GodSaveQueen curiosity;-)
To: tuning@yahoogroups. com
Date: Monday, February 16, 2009, 12:52 AM

--- In tuning@yahoogroups. com, Mike Battaglia <battaglia01@ ...> wrote:
>
> It would also be nice if the test was blind, so that personal
> biases (which seem to be pretty large around here lately) don't
> make as much of an impact.
> 
> -Mike

Let's be clear: I never said these meantones would sound
better than LucyTuning. I said they would make a good
comparison, since they are the next-most-promoted meantones
after LucyTuning. What I did say was that the difference
would be small, which is really the main point -- that
there is nothing special about LucyTuning, other than the
fact that it is a meantone.

-Carl

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

Michael Sheiman wrote:
> --What I did say was that the difference
> --would be small, which is really the main point -- that
> --there is nothing special about LucyTuning, other than the
> --fact that it is a meantone.
> > In general, I find this "small difference" an issue not just in this > comparison, but in the art of tuning as a whole.
> Not just between mean-tone and Lucy Tuning, but between
> 1. 5-limit JI (diatonic)
> 2. Mean-tone
> 3. Lucy Tuning
> 4. 12TET
> 5. Any type of scale configurations`in 19TET, 22TET, 36TET...meant to > basically emulate intervals and chords seen in said above tunings
> > To me all of these sound very alike for the most part (and > considering they are for the most part no more than 8 cents or so off > from each other that makes sense).
> > There are some things that bug me a bit, like the sour third in 12TET > or the wolf notes in mean-tone...but there's really nothing so different > between any of those that makes me think of them as truly different > scales far as their overall emotional effects.

The "wolf" intervals in meantone really are different intervals -- e.g. G#-Eb is a diminished sixth. 12-ET does count as a sort of meantone, but the 12-ET thirds are quite jarring in comparison with the milder thirds of more typical meantones like 1/5-comma or 1/4-comma. But yes, a diatonic scale is a diatonic scale, although I'd make a distinction between the meantone-type diatonic scales (with a single size of tone) and the less symmetrical scales of JI and 22-ET (with major and minor tones). You can even have a sort of diatonic scale in 21-ET, although the major and minor tones are in opposite places compared with 22-ET.

Even such a dissonant interval as G#-Eb has some potential uses. Try playing Bb-F-G#-Eb in meantone and resolving the Eb down to a D.

these three squared errors. You can read all about
Woolhouse's approach here:
http://tonalsoft. <http://tonalsoft.com/monzo/woolhouse/essay.aspx>
com/monzo/woolhouse/essay.aspx

Thanks Carl for sending us to that interesting and scarcely known source!

The issue with Woolhouse is that, if I understand his mathematics right, he
puts the three errors at the same level.
Since antiquity musicians-including man of the stature of Rameau-have agreed
that the more consonant an interval is, the greater should be its purity in
a temperament. This, after all, was the main argument for 1/5 and even 1/6
S.c. meantone against 1/4 S.c. (which was much easier to tune).

(Extant historical discussions on the matter, as many of the readers in the
list surely know, would fill libraries.
The ones in mid-18th France are fully discussed in
Barbieri, Patrizio. "Il ‘migliore’ sistema musicale temperato: ‘querelles’
fra Estève, Romieu e altri accademici francesi (c.1740-60)”, L’Organo XXVII
(1991-92) pp. 31-81.)

Kind regards,
Claudio

BARBIERI Patrizio. Il 'migliore' sistema musicale temperato : Querelles fra
Estève, Romieu e altri
Accadelmici Francesi (c.1740-60), 1989
BARBIERI Patrizio. Il 'migliore' sistema musicale temperato : Querelles fra
Estève, Romieu e altri
Accadelmici Francesi (c.1740-60), 1989

<http://geo.yahoo.com/serv?s=97359714/grpId=70605/grpspId=1705897753/msgId=8
1359/stime=1234812149/nc1=1/nc2=2/nc3=3>

--- In tuning@yahoogroups.com, "Claudio Di Veroli" <dvc@...> wrote:

> Thanks Carl for sending us to that interesting and scarcely
> known source!

Thank Joe Monzo for his excellently-researched article.

> The issue with Woolhouse is that, if I understand his
> mathematics right, he puts the three errors at the same level.
> Since antiquity musicians-including man of the stature of
> Rameau-have agreed that the more consonant an interval is, the
> greater should be its purity in a temperament.

Indeed. And this argument, carried to its full extent, leads
to TOP meantone (which I gave earlier), which even tempers the
octave in proportion to its consonance.

If we restrict ourselves to pure octaves, Erlich gives
175/634-comma meantone as RMS optimal.

-Carl