Bendeler

Bendeler, as quoted by Toepfer, compiled by A.Sparschuh

Open in Scale Workshop Scala analysis Download scl

Properties

Notes	12
Period	1200.0 ¢
Just	11-limit
Source	Mailing lists
Reference	https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_90063.html#90063
Thread	1 scale

Tone	Tone (¢)	Step	Step (¢)
256/243	90	256/243	90
32768/29403	188	128/121	97
32/27	294	1089/1024	107
4096/3267	391	128/121	97
4/3	498	1089/1024	107
1024/729	588	256/243	90
131072/87846	693	15552/14641	105
128/81	792	14641/13824	99
16384/9801	890	128/121	97
16/9	996	1089/1024	107
2048/1089	1093	128/121	97
2/1	1200	1089/1024	107

Similar scales

File	Notes	Rotation	Max diff (¢)
Sparschuh_proposal_Mietke	12	7	2.8
ForCarl1	12	6	2.8
SpChoirTone456Hz	12	7	3.6
Sp_41_23_bi_epi	12	7	3.8
SpaOldPiano	12	2	3.9
neoSeptenarius	12	7	4.0
Sp7th_part_SC	12	7	4.0
werck3	12	0	4.6
werckmeister3_eb89-l	12	0	4.6
SpUndecanarian	12	7	4.7

Parent scales

File	Notes	Max diff (¢)
schisynch17	17	9.0
dwarf17_5	17	9.2
xen02-wilson-arabic	17	9.2
xen03-wilson-positive-17	17	9.2
xen18-darreg-djami-17	17	9.2
xen18-erlich-passion-13	13	13.6
xen18-erlich-augmented-15	15	12.1
xen07-chalmers-sixth-comma	19	9.1
Yarman24	24	5.9
xen18-erlich-augene-15	15	13.1

Child scales

File	Notes	Max diff (¢)
xen09-wilson-marwa-05-01	7	0.0
xen10-wilson-purvi-01-07	7	0.0
xen18-darreg-djami-busalik	7	0.3
CD14_04_Algeria	6	2.2
xen09-wilson-marwa-11b-01	7	5.2
xen09-wilson-marwa-11b-10	7	5.2
xen09-wilson-marwa-11b-02	7	5.2
xen09-wilson-marwa-11b-03	7	5.2
xen09-wilson-marwa-11b-04	7	5.2
xen09-wilson-marwa-11b-05	7	5.2

Mailing list post

From: Andy (2010-06-09)
Subject: Bendeler

there are also ratios by Bendeler
http://groenewald-berlin.de/text/text_T086.html

in 5ths:
the three Quinten c-g, g-d und b-f# got each  reduced about 
the amount of ~7.820 cents. 

       (f)     4/3     x  3/2               :  2  =      1/1     (c)
       (b)    16/9     x  3/2               :  2  =      4/3     (f)
      (es)    32/27    x  3/2  :                  =     16/9     (b)
      (as)   128/81    x  3/2               :  2  =     32/27    (es)
     (des)   256/243   x  3/2                     =    128/81    (as)
     (ges)  1024/729   x  3/2               :  2  =    256/243   (des)
       (h)  2024/1089  x  3/2  :   243/242  :  2  =   1024/729   (ges)
       (e)  4096/3267  x  3/2                     =   2024/1089  (h)
       (a) 16384/9801  x  3/2               :  2  =   4096/3267  (e) 
       (d) 32768/29403 x  3/2  :                  =  16384/9801  (a)
       (g) 65536/43923 x  3/2  :   243/242  :  2  =  32768/29403 (d)
       (c)     1/1     x  3/2  : 32x114/217         =  65536/43923 (g)

that yiels in chromatically ascending order

c    =     2/1        12.0               2/1         1200.000  Cent
H    =  1089/1024     10.935          2048/1089      1093.454  Cent
B    =     9/8         9.961            16/9          996.090  Cent
A    =  9801/8192      8.895         16384/9801       889.544  Cent
Gs   =    81/64        7.922           128/81         792.180  Cent
G    = 87846/65536     6.928         65536/43923      694.773  Cent
Fs   =   729/512       5.883          1024/729        588.270  Cent
F    =     3/2         4.980             4/3          498.045  Cent
E    =  3267/2048      3.915          4096/3267       391.499  Cent
Ds   =    27/16        2.941            32/27         294.135 Cent    D    = 29403/16384     1.876        32768/29403     187.589Cent       
Cs   =   243/128       0.902           256/243         90.225  Cent
C    =      -          0.0               1/1            0.000  Cent

!Bendeler.scl
Bendeler, as quoted by Toepfer, compiled by A.Sparschuh
12
!
256/243      ! C#
32768/29403  ! D
32/27        ! Eb
4096/3267    ! E 
4/3          ! F
1024/729     ! F#
131072/87846 ! G
128/81       ! G#
16384/9801   ! A
16/9         ! Bb
2048/1089    ! B
2/1
!
!(EOF]

bye
Andy

Full thread (1 messages)

From: Andy (2010-06-09)
Subject: Bendeler

there are also ratios by Bendeler
http://groenewald-berlin.de/text/text_T086.html

in 5ths:
the three Quinten c-g, g-d und b-f# got each  reduced about 
the amount of ~7.820 cents. 

       (f)     4/3     x  3/2               :  2  =      1/1     (c)
       (b)    16/9     x  3/2               :  2  =      4/3     (f)
      (es)    32/27    x  3/2  :                  =     16/9     (b)
      (as)   128/81    x  3/2               :  2  =     32/27    (es)
     (des)   256/243   x  3/2                     =    128/81    (as)
     (ges)  1024/729   x  3/2               :  2  =    256/243   (des)
       (h)  2024/1089  x  3/2  :   243/242  :  2  =   1024/729   (ges)
       (e)  4096/3267  x  3/2                     =   2024/1089  (h)
       (a) 16384/9801  x  3/2               :  2  =   4096/3267  (e) 
       (d) 32768/29403 x  3/2  :                  =  16384/9801  (a)
       (g) 65536/43923 x  3/2  :   243/242  :  2  =  32768/29403 (d)
       (c)     1/1     x  3/2  : 32x114/217         =  65536/43923 (g)

that yiels in chromatically ascending order

c    =     2/1        12.0               2/1         1200.000  Cent
H    =  1089/1024     10.935          2048/1089      1093.454  Cent
B    =     9/8         9.961            16/9          996.090  Cent
A    =  9801/8192      8.895         16384/9801       889.544  Cent
Gs   =    81/64        7.922           128/81         792.180  Cent
G    = 87846/65536     6.928         65536/43923      694.773  Cent
Fs   =   729/512       5.883          1024/729        588.270  Cent
F    =     3/2         4.980             4/3          498.045  Cent
E    =  3267/2048      3.915          4096/3267       391.499  Cent
Ds   =    27/16        2.941            32/27         294.135 Cent    D    = 29403/16384     1.876        32768/29403     187.589Cent       
Cs   =   243/128       0.902           256/243         90.225  Cent
C    =      -          0.0               1/1            0.000  Cent

!Bendeler.scl
Bendeler, as quoted by Toepfer, compiled by A.Sparschuh
12
!
256/243      ! C#
32768/29403  ! D
32/27        ! Eb
4096/3267    ! E 
4/3          ! F
1024/729     ! F#
131072/87846 ! G
128/81       ! G#
16384/9801   ! A
16/9         ! Bb
2048/1089    ! B
2/1
!
!(EOF]

bye
Andy

Raw file

!Bendeler.scl
Bendeler, as quoted by Toepfer, compiled by A.Sparschuh
12
!
256/243      ! C#
32768/29403  ! D
32/27        ! Eb
4096/3267    ! E 
4/3          ! F
1024/729     ! F#
131072/87846 ! G
128/81       ! G#
16384/9801   ! A
16/9         ! Bb
2048/1089    ! B
2/1
!
!(EOF]
!
! https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_90063.html#90063
!
! [info]
! source = Mailing lists
! file = tuning/messages/yahoo_tuning_messages_api_raw_90000-106393.json
! topic_id = 90063
! msg_id = 90063