Yahoo Tuning Groups Ultimate Backup tuning 1/4 comma meantone

Igs said:

<...your temperament is ... something which really isn't all that different than 1/4-comma meantone or the Meantone[12] scale in 31-EDO.>

and...

<it's not true that you've improved on 12-tET--you've simply reinstated Meantone and given it your own personal well-tempered twist>

and...

<Thus, your tuning does not compete with 12-tET, because it does not improve on the features that initially made 12-tET popular>

I need to look into this.

Could someone please post the frequencies (in cents) of both 12 key quarter comma Meantone and the Meantone[12] scale in 31EDO?

The meantone I stumbled across years go started with 1.0 as the tonic and going *up* from 1.0 I multiplied each step by 2.99069756/2 (2.99069756 is the 4th root of 80). I did 8 steps going *up* from 1.0. Next I did 8 steps going *down* from 1.0 (this time each step was divided by 2.99069756/2. A total of 17 keys per octave.

So I'm not sure what regular 12 tone 1/4 comma Meantone is. Is it 1.0 multiplied by 2.99069756/2 12 times?

As I said before my method for building scales has nothing at all to do with commas and tempering them out and if my scale does look a bit like 1/4 comma meantone then it's purely a coincidence. I'd also like to analyze the two Meantones Igs mentioned above and compare them to my Blue Temperament scale to see how many good harmony intervals (an octave or less wide) occur. For me each note should go with the tonic as well. If either of these two Meantone scales turn out better than my Blue Temperament I'll eat my hat.

Again, could someone please post the frequencies (in cents) of both 12 key quarter comma Meantone and the Meantone[12] scale in 31EDO?

John.

🔗Chris Vaisvil <chrisvaisvil@...>

I think this is one

|
12 out of 31-tET, meantone Eb-G#
|
0: 1/1 0.000 unison, perfect prime
1: 77.419 cents 77.419
2: 193.548 cents 193.548
3: 309.677 cents 309.677
4: 387.097 cents 387.097
5: 503.226 cents 503.226
6: 580.645 cents 580.645
7: 696.774 cents 696.774
8: 774.194 cents 774.194
9: 890.323 cents 890.323
10: 1006.452 cents 1006.452
11: 1083.871 cents 1083.871
12: 2/1 1200.000 octave

On Thu, Feb 10, 2011 at 11:55 AM, john777music <jfos777@...> wrote:

>
>
> Igs said:
>
> <...your temperament is ... something which really isn't all that different
> than 1/4-comma meantone or the Meantone[12] scale in 31-EDO.>
>
> and...
>
> <it's not true that you've improved on 12-tET--you've simply reinstated
> Meantone and given it your own personal well-tempered twist>
>
> and...
>
> <Thus, your tuning does not compete with 12-tET, because it does not
> improve on the features that initially made 12-tET popular>
>
> I need to look into this.
>
> Could someone please post the frequencies (in cents) of both 12 key quarter
> comma Meantone and the Meantone[12] scale in 31EDO?
>
> The meantone I stumbled across years go started with 1.0 as the tonic and
> going *up* from 1.0 I multiplied each step by 2.99069756/2 (2.99069756 is
> the 4th root of 80). I did 8 steps going *up* from 1.0. Next I did 8 steps
> going *down* from 1.0 (this time each step was divided by 2.99069756/2. A
> total of 17 keys per octave.
>
> So I'm not sure what regular 12 tone 1/4 comma Meantone is. Is it 1.0
> multiplied by 2.99069756/2 12 times?
>
> As I said before my method for building scales has nothing at all to do
> with commas and tempering them out and if my scale does look a bit like 1/4
> comma meantone then it's purely a coincidence. I'd also like to analyze the
> two Meantones Igs mentioned above and compare them to my Blue Temperament
> scale to see how many good harmony intervals (an octave or less wide) occur.
> For me each note should go with the tonic as well. If either of these two
> Meantone scales turn out better than my Blue Temperament I'll eat my hat.
>
> Again, could someone please post the frequencies (in cents) of both 12 key
> quarter comma Meantone and the Meantone[12] scale in 31EDO?
>
> John.
>
>
>

🔗Chris Vaisvil <chrisvaisvil@...>

and I think this is the other

1/4-comma meantone scale. Pietro Aaron's temp. (1523). 6/5 beats twice 3/2
|
0: 1/1 0.000 unison, perfect prime
1: 76.049 cents 76.049
2: 193.157 cents 193.157
3: 310.265 cents 310.265
4: 386.314 cents 386.314
5: 503.422 cents 503.422
6: 579.471 cents 579.471
7: 696.578 cents 696.578
8: 772.627 cents 772.627
9: 889.735 cents 889.735
10: 1006.843 cents 1006.843
11: 1082.892 cents 1082.892
12: 2/1 1200.000 octave

On Thu, Feb 10, 2011 at 12:06 PM, Chris Vaisvil <chrisvaisvil@...>wrote:

> I think this is one
>
> |
> 12 out of 31-tET, meantone Eb-G#
> |
> 0: 1/1 0.000 unison, perfect prime
> 1: 77.419 cents 77.419
> 2: 193.548 cents 193.548
> 3: 309.677 cents 309.677
> 4: 387.097 cents 387.097
> 5: 503.226 cents 503.226
> 6: 580.645 cents 580.645
> 7: 696.774 cents 696.774
> 8: 774.194 cents 774.194
> 9: 890.323 cents 890.323
> 10: 1006.452 cents 1006.452
> 11: 1083.871 cents 1083.871
> 12: 2/1 1200.000 octave
>
>
> On Thu, Feb 10, 2011 at 11:55 AM, john777music <jfos777@...> wrote:
>
>>
>>
>> Igs said:
>>
>> <...your temperament is ... something which really isn't all that
>> different than 1/4-comma meantone or the Meantone[12] scale in 31-EDO.>
>>
>> and...
>>
>> <it's not true that you've improved on 12-tET--you've simply reinstated
>> Meantone and given it your own personal well-tempered twist>
>>
>> and...
>>
>> <Thus, your tuning does not compete with 12-tET, because it does not
>> improve on the features that initially made 12-tET popular>
>>
>> I need to look into this.
>>
>> Could someone please post the frequencies (in cents) of both 12 key
>> quarter comma Meantone and the Meantone[12] scale in 31EDO?
>>
>> The meantone I stumbled across years go started with 1.0 as the tonic and
>> going *up* from 1.0 I multiplied each step by 2.99069756/2 (2.99069756 is
>> the 4th root of 80). I did 8 steps going *up* from 1.0. Next I did 8 steps
>> going *down* from 1.0 (this time each step was divided by 2.99069756/2. A
>> total of 17 keys per octave.
>>
>> So I'm not sure what regular 12 tone 1/4 comma Meantone is. Is it 1.0
>> multiplied by 2.99069756/2 12 times?
>>
>> As I said before my method for building scales has nothing at all to do
>> with commas and tempering them out and if my scale does look a bit like 1/4
>> comma meantone then it's purely a coincidence. I'd also like to analyze the
>> two Meantones Igs mentioned above and compare them to my Blue Temperament
>> scale to see how many good harmony intervals (an octave or less wide) occur.
>> For me each note should go with the tonic as well. If either of these two
>> Meantone scales turn out better than my Blue Temperament I'll eat my hat.
>>
>> Again, could someone please post the frequencies (in cents) of both 12 key
>> quarter comma Meantone and the Meantone[12] scale in 31EDO?
>>
>> John.
>>
>>
>>
>
>

🔗genewardsmith <genewardsmith@...>

🔗john777music <jfos777@...>

What does Blue JI in 197 equal mean? Does it mean that all the notes in 197 equal are listed and then the 12 notes that are closest to Blue JI are chosen from the list?

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@> wrote:
> >
> > and I think this is the other
>
> And to complete the picture, here is BlueJI in 197 equal:
>
> ! marveldene.scl
> BlueJI in 197et (= Duodene, etc, in 197et)
> 12
> !
> 115.73604
> 201.01523
> 316.75127
> 383.75635
> 499.49239
> 584.77157
> 700.50761
> 816.24365
> 883.24873
> 1017.25888
> 1084.26396
> 1200.00000
>

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, "john777music" <jfos777@...> wrote:
>
> What does Blue JI in 197 equal mean? Does it mean that all the notes in 197 equal are listed and then the 12 notes that are closest to Blue JI are chosen from the list?

Sadly, no. It means 197 times the log base two for each of the primes up to 7 was rounded to the nearest integer, giving the "patent val" mapping of <197 312 457 553|, and then this mapping was applied to each of the intervals of BlueJI and the result converted to cents by multiplying by 1200/197. But I think you'll find the result is much closer to BlueJI that what 31, using the same process, gave you.

🔗john777music <jfos777@...>

Thanks Gene,

I'll take your word for it ;-)

John.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "john777music" <jfos777@> wrote:
> >
> > What does Blue JI in 197 equal mean? Does it mean that all the notes in 197 equal are listed and then the 12 notes that are closest to Blue JI are chosen from the list?
>
> Sadly, no. It means 197 times the log base two for each of the primes up to 7 was rounded to the nearest integer, giving the "patent val" mapping of <197 312 457 553|, and then this mapping was applied to each of the intervals of BlueJI and the result converted to cents by multiplying by 1200/197. But I think you'll find the result is much closer to BlueJI that what 31, using the same process, gave you.
>