Mailing list post
From: genewardsmith (2010-05-13)
Subject: Nonoctave meantone
If you are looking to break out of the octave rut but aren't ready for Bohlen-Pierce or Carlos Beta, you might consider using something other than octaves or subdivisions of octaves in standard temperaments. Below I give 1/4-comma meantone in a scale with period 1/4 of the "quintave" (5, to the rest of us)and generator a tone. It's not only meantone, it's also a bit like what Carlos Beta would be if it was in tune. Beta can be seen as a massively stretched version of 19et, in what you might call Over The TOP tuning, making 3/2 pure. The meantone scale has the usual flat fifth and while it divides it into 11 parts, it uses two step sizes to do it.
! quart.scl
1/4-comma meantone with a period of 5^(1/4) and a tone generator
44
!
76.048999263460931020
152.09799852692186216
193.15685693241740887
269.20585619587833989
345.25485545933927107
386.31371386483481774
462.36271312829574874
538.41171239175667988
579.47057079725222662
655.51957006071315760
696.57842846620870436
772.62742772966963536
848.67642699313056655
889.73528539862611321
965.78428466208704432
1041.8332839255479755
1082.8921423310435221
1158.9411415945044531
1234.9901408579653842
1276.0489992634609309
1352.0979985269218620
1393.1568569324174088
1469.2058561958783398
1545.2548554593392710
1586.3137138648348176
1662.3627131282957486
1738.4117123917566798
1779.4705707972522264
1855.5195700607131576
1931.5685693241740886
1972.6274277296696353
2048.6764269931305662
2089.7352853986261131
2165.7842846620870441
2241.8332839255479752
2282.8921423310435220
2358.9411415945044529
2434.9901408579653842
2476.0489992634609308
2552.0979985269218618
2628.1469977903827929
2669.2058561958783397
2745.2548554593392708
5
Full thread (3 messages)
From: genewardsmith (2010-05-13)
Subject: Nonoctave meantone
If you are looking to break out of the octave rut but aren't ready for Bohlen-Pierce or Carlos Beta, you might consider using something other than octaves or subdivisions of octaves in standard temperaments. Below I give 1/4-comma meantone in a scale with period 1/4 of the "quintave" (5, to the rest of us)and generator a tone. It's not only meantone, it's also a bit like what Carlos Beta would be if it was in tune. Beta can be seen as a massively stretched version of 19et, in what you might call Over The TOP tuning, making 3/2 pure. The meantone scale has the usual flat fifth and while it divides it into 11 parts, it uses two step sizes to do it.
! quart.scl
1/4-comma meantone with a period of 5^(1/4) and a tone generator
44
!
76.048999263460931020
152.09799852692186216
193.15685693241740887
269.20585619587833989
345.25485545933927107
386.31371386483481774
462.36271312829574874
538.41171239175667988
579.47057079725222662
655.51957006071315760
696.57842846620870436
772.62742772966963536
848.67642699313056655
889.73528539862611321
965.78428466208704432
1041.8332839255479755
1082.8921423310435221
1158.9411415945044531
1234.9901408579653842
1276.0489992634609309
1352.0979985269218620
1393.1568569324174088
1469.2058561958783398
1545.2548554593392710
1586.3137138648348176
1662.3627131282957486
1738.4117123917566798
1779.4705707972522264
1855.5195700607131576
1931.5685693241740886
1972.6274277296696353
2048.6764269931305662
2089.7352853986261131
2165.7842846620870441
2241.8332839255479752
2282.8921423310435220
2358.9411415945044529
2434.9901408579653842
2476.0489992634609308
2552.0979985269218618
2628.1469977903827929
2669.2058561958783397
2745.2548554593392708
5
From: Chris Vaisvil (2010-05-13)
Subject: Re: [tuning] Nonoctave meantone
Thank you Gene - I'll run that through my GR-20 tonight!
Chris
On Thu, May 13, 2010 at 5:14 PM, genewardsmith
<genewardsmith@...>wrote:
>
>
> If you are looking to break out of the octave rut but aren't ready for
> Bohlen-Pierce or Carlos Beta, you might consider using something other than
> octaves or subdivisions of octaves in standard temperaments. Below I give
> 1/4-comma meantone in a scale with period 1/4 of the "quintave" (5, to the
> rest of us)and generator a tone. It's not only meantone, it's also a bit
> like what Carlos Beta would be if it was in tune. Beta can be seen as a
> massively stretched version of 19et, in what you might call Over The TOP
> tuning, making 3/2 pure. The meantone scale has the usual flat fifth and
> while it divides it into 11 parts, it uses two step sizes to do it.
>
> ! quart.scl
> 1/4-comma meantone with a period of 5^(1/4) and a tone generator
> 44
> !
> 76.048999263460931020
> 152.09799852692186216
> 193.15685693241740887
> 269.20585619587833989
> 345.25485545933927107
> 386.31371386483481774
> 462.36271312829574874
> 538.41171239175667988
> 579.47057079725222662
> 655.51957006071315760
> 696.57842846620870436
> 772.62742772966963536
> 848.67642699313056655
> 889.73528539862611321
> 965.78428466208704432
> 1041.8332839255479755
> 1082.8921423310435221
> 1158.9411415945044531
> 1234.9901408579653842
> 1276.0489992634609309
> 1352.0979985269218620
> 1393.1568569324174088
> 1469.2058561958783398
> 1545.2548554593392710
> 1586.3137138648348176
> 1662.3627131282957486
> 1738.4117123917566798
> 1779.4705707972522264
> 1855.5195700607131576
> 1931.5685693241740886
> 1972.6274277296696353
> 2048.6764269931305662
> 2089.7352853986261131
> 2165.7842846620870441
> 2241.8332839255479752
> 2282.8921423310435220
> 2358.9411415945044529
> 2434.9901408579653842
> 2476.0489992634609308
> 2552.0979985269218618
> 2628.1469977903827929
> 2669.2058561958783397
> 2745.2548554593392708
> 5
>
>
>
From: Chris Vaisvil (2010-05-14)
Subject: Re: [tuning] Nonoctave meantone
Here is the piece I put together tonight.
http://www.notonlymusic.com/board/download/file.php?id=222
Of course this is a re-post of sorts.
On Thu, May 13, 2010 at 5:14 PM, genewardsmith
<genewardsmith@...>wrote:
>
>
> If you are looking to break out of the octave rut but aren't ready for
> Bohlen-Pierce or Carlos Beta, you might consider using something other than
> octaves or subdivisions of octaves in standard temperaments. Below I give
> 1/4-comma meantone in a scale with period 1/4 of the "quintave" (5, to the
> rest of us)and generator a tone. It's not only meantone, it's also a bit
> like what Carlos Beta would be if it was in tune. Beta can be seen as a
> massively stretched version of 19et, in what you might call Over The TOP
> tuning, making 3/2 pure. The meantone scale has the usual flat fifth and
> while it divides it into 11 parts, it uses two step sizes to do it.
>
> ! quart.scl
> 1/4-comma meantone with a period of 5^(1/4) and a tone generator
> 44
> !
> 76.048999263460931020
> 152.09799852692186216
> 193.15685693241740887
> 269.20585619587833989
> 345.25485545933927107
> 386.31371386483481774
> 462.36271312829574874
> 538.41171239175667988
> 579.47057079725222662
> 655.51957006071315760
> 696.57842846620870436
> 772.62742772966963536
> 848.67642699313056655
> 889.73528539862611321
> 965.78428466208704432
> 1041.8332839255479755
> 1082.8921423310435221
> 1158.9411415945044531
> 1234.9901408579653842
> 1276.0489992634609309
> 1352.0979985269218620
> 1393.1568569324174088
> 1469.2058561958783398
> 1545.2548554593392710
> 1586.3137138648348176
> 1662.3627131282957486
> 1738.4117123917566798
> 1779.4705707972522264
> 1855.5195700607131576
> 1931.5685693241740886
> 1972.6274277296696353
> 2048.6764269931305662
> 2089.7352853986261131
> 2165.7842846620870441
> 2241.8332839255479752
> 2282.8921423310435220
> 2358.9411415945044529
> 2434.9901408579653842
> 2476.0489992634609308
> 2552.0979985269218618
> 2628.1469977903827929
> 2669.2058561958783397
> 2745.2548554593392708
> 5
>
>
>