Yahoo Tuning Groups Ultimate Backup tuning Hemipaj and comic

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@> wrote:

> > In 22edo they're also both the same as shrutar.
>
> True, but with shrutar you can no longer say 22 is a good tuning.
>

Yep
that's an really true remark about the 22-edo idea of expaining shruties. But that western-european brainchild
dreams far away from the traditional indian original concept of

http://en.wikipedia.org/wiki/Bharata_Muni

That sounds primordial in terms of

--22-out-of-53---

http://en.wikipedia.org/wiki/Shruti_%28music%29
Quote:
"
The shruti table below shows the mathematical ratios considered to correspond to the system described by Bharata and Dattila, along with the comparable notes in common Western 12-TET tuning, and the names of the 22 shrutis provided by ÅÄrÃ±gadeva. I Append in the table, the comparable notes in 53-TET tuning, of which we can see his amazing accuracy. In 53-TET tuning, the fifth occurs every 31-notes, if we start counting fifths from note 8, we obtain the following series of fifths: 8,39,17,48,26,4,35,13,44, 22,0,31,9,40,18,49,27,5,36,14,45,23,1,..., 8. From here we note that the shruti are progressions of fifths, to be exact are 10 fifths down from note 0, and 11 fifths up!

Indian-Name Ratio Cents Western-Name of Pitch

Ká¹£obhinÄ« 1/1 0 C. unison
TÄ«vrÄ 256/243 90 C# limma
KumudvatÄ« 16/15 112 Db major-semitone
MandÄ 10/9 182 D\ minor-tone
ChandovatÄ« 9/8 203 D. major tone
DayÄvatÄ« 32/27 294 D# Pythagorean minor-3rd
RanjanÄ« 6/5 316 Eb Syntonic minor-3rd
RaktikÄ 5/4 386 E\ major-3rd
RaudrÄ« 81/64 407 E. ditone := (9/8)^2
KrodhÄ 4/3 498 F. 4th
VajrikÄ 27/20 519 F/
PrasÄriá¹Ä« 45/32 590 Gb
PrÄ«ti 729/512 612 F# tritone (9/8)^3
MÄrjanÄ« 3/2 702 G. 5th
Ká¹£iti 128/81 792 Ab
RaktÄ 8/5 814 G#
SandÄ«panÄ« 5/3 884 A\ Syntonic-6th
ÄlÄpinÄ« 27/16 906 A. Pythagorean-6th
MadantÄ« 16/9 996 Bb Pythagorean minor-7th
Rohiá¹Ä« 9/5 1017 A#
RamyÄ 15/8 1088 B\ Syntonic-7th
UgrÄ 243/128 1110 B. Pythagorean-7th
Ká¹£obhinÄ« 2 1200 C.' octave

The 53-TET approximation has an maximum error of 1.5 cents, while the perfect fifths approximation has an maximum error of 2 cents.
"

For the corresponding Scala-File
see again my earlier contribution:

/tuning/topicId_74961.html#74973
"
!Bahratamuni22Shrutis.scl
!
! by Dr. Vidyadhar Gopal Oke's (Univ. Mumbai, India) interpretation
22
!
256/243 ! 2: r1 = 2^8/3^5
16/15 ! 3: r2 = 2^4/5/3
10/9 ! 4: R1 = 5*2/3^2
9/8 ! 5: R2 = 3^2/2^3
32/27 ! 6: g1 = 2^5/3^3
6/5 ! 7: g2 = 3*2/5
5/4 ! 8: G1 = 5/2^2
81/64 ! 9: G2 = 3^4/2^6
4/3 ! 10: M1 = 2^2/3
27/10 ! 11: M2 = 3^3/5/2^2
45/32 ! 12: m1 = 5*3^2/2^5
729/512 ! 13: m2 = 3^6/2^9
3/2 ! 14: p
128/81 ! 15: d1 = 2^7/3^4
8/5 ! 16: d2 = 2^3/5
5/3 ! 17: D1
27/16 ! 18: D2 = 3^3/2^4
16/9 ! 19: n1 = 2^4/3^2
9/5 ! 20: n2 = 3^2/2^3
15/8 ! 21: N2 = 5*3/2^3
243/128 ! 22: N2 = 3^5/2^7
2/1
!
![eof]

Attend, that Dr. Oke's link about just that ratios
has meanwhile moved to the anew updated adress:

http://22shruti.com/research_topic_36.asp
http://22shruti.com/research_topic_38.asp

Beyond all that,
a little shift of the schisma in my own recent 5-limit 53-tone

/tuning-math/message/20593

involves an exact fit of the above 22-shrutis
that meets comletely as subset the full 53-scale,
alike as already Kirnberger's-#1-dodecatonic-tuning (see link)

! Sp53shruti.scl
!
Sparschuh's 53tone generalization of indian 22-shruti ratios (2012)
53
!
! 1/1 ! @ | 0> D. == "S."= @ = Shadja = unison
81/80 ! A | -4 4,-1> D/
43046721/41943040 ! B |-23 16,-1> D+
20480/19683 ! C | 12 -9, 1> EB
256/243 ! D | 8 -5> Eb == "r1" = D
16/15 ! E | 4 -1,-1> D# == "r2" = E
177147/163840 ! F |-15 11,-1> D&
5242880/4782969 ! G | 20 -14, 1> E-
10/9 ! H | 1 -2, 1> E\ == "R1" = H
9/8 ! I | -3 2> E. == "R2" = I
729/640 ! J | -7 6,-1> E/
387420489/335544320 ! K |-26 18,-1> E+=F- in 53-enharmonics
2560/2187 ! L | 9 -7, 1> F\
32/27 ! M | 5 -3> F. == "g1" = M
6/5 ! N | 1 1,-1> F/ == "g2" = N
1594323/1310720 ! O |-18 13,-1> F+
655360/531441 ! P | 17 -12, 1> GB
5/4 ! Q | -2 0, 1> Gb == "G1 = Q
81/64 ! R | -6 4> F# == "G2" = R
6561/5120 ! S |-10 8,-1> F&
167772160/129140163 ! T | 25 -17, 1> G-
320/243 ! U | 6 -5, 1> G\
4/3 ! V | 2 -1> G. == "M1" = V
27/20 ! W | -2 3,-1> G/ == "M2" = W
14348907/10485760 ! X |-21 15,-1> G+
81920/59049 ! Y | 14 -10, 1> AB
45/32 ! Z | -5 2, 1> Ab == "m1" = Z
729/512 ! z | -9 6> G# == "m2" = z
59049/40960 ! y |-13 10,-1> G&
20971520/14348907 ! x | 22 -15, 1> A-
40/27 ! w | 3 -3, 1> A\
3/2 ! v | -1 1> A. == "p." = v
243/160 ! u | -5 5,-1> A/
129140163/83886080 ! t |-24 17,-1> A+
10240/6561 ! s | 11 -8, 1> BB
128/81 ! r | 7 -4> Bb == "d1" = r
8/5 ! q | 3 0,-1> A# == "d2" = q
531441/327680 ! p |-16 12,-1> A&
5242880/4782969 ! o | 19 -13, 1> B-
5/3 ! n | 0 -1, 1> B\ == "D1" = n
27/16 ! m | -4 3> B. == "D2" = m
2187/1280 ! l | -8 7,-1> B/
671088640/387420489 ! k | 27 -18, 1> B+=C- in 53-enharmonics
1280/729 ! j | 8 -6, 1> C\
16/9 ! i | 4 -2> C. == "n1" = i
9/5 ! h | 0 2,-1> C/ == "n2" = h
4782969/2621440 ! g |-19 14,-1> C+
327,680/177,147 ! f | 16 -11, 1> DB
15/8 ! e | -3 1, 1> Db == "N1" = e
243/128 ! d | -7 5> C# == "N2" = d
19683/10240 ! c |-11 9,-1> C&
83886080/43046721 ! b | 24 -16, 1> D-
160/81 ! a | 5 -4,-1> D\
2/1 ! @'| 1> D. == "s." = @' octave
!
![eof]

Conclusion:
The above analysis leads finally to an:
Concise location of the gaps within the '22-out-of-53' concept.

@...DE..HI...MN..QR...VW..Zz...v...rq..nm...ih..ed...@' |22|-out-of-
@ABCDEFGHIJKLMNOPQRSTUVWXYZzyxwvutsrqponmlkjihgfedcba@' full|53|scale

Attend within that the variation in the distances between the 22-Shruties. The span of offset can vary from one to three or even 4 'shrutar'-steps of inter-space range among two neighbouring Shruties.

Consequence:
Hence any modern alleged 22-edo misbelief of explaining the indian Shruties must be considered as far-fetched bare absurd fudge-talk ;-(
but at least as an ahistorically excluded misconception.

bye
Andy

Hemipaj and comic

🔗genewardsmith <genewardsmith@...>

🔗Keenan Pepper <keenanpepper@...>

🔗genewardsmith <genewardsmith@...>

🔗Andy <a_sparschuh@...>