Replies - "ghosttones"

Reply to Matt Nathan's comments from Lucy

>You're returning to an ambiguous use of the word "harmonics".
>Please utilize these defined terms instead:

>Partials
>Harmonic Partials
>Inharmonic Partials
>Flageolet tones
>Ghosttones (I can accept this term since you have defined it)
>Complex Tones
>Simple Tones

Please can we get some definitions of these terms for me,
and also for others who might like to use them with minimal
ambiguity.


>Since you wrote **"harmonics" (ghosttones?)**, I'll
>proceed with the assumption that you're talking about
>the tones you get when you lightly touch a string in
>various places and pluck it. I'll also give you the
>benefit of the doubt and assume that you're talking
>about the lowest audible simple tone (sine wave) for
>each ghosttone, and not the complete timbre of each
>ghosttone with its many partials.




>You're saying that the various tones you get by
>lightly touching an open string in various places
>form a continuous series separated by intervals of
>fourths and fifths. I doubt that this is so.

>Please write out this series of fourths and fifths
>(in cents, or Hz, or multiplication factors
>of the original open string frequency) along with
>a corresponding list of places on the string you'll have
>to touch in order to produce each of the pitches
>in that series of fourths and fifths (in inches
>from bridge or nut, or portion of string length, or
>some other measure). Please explain why some positions
>in the series of fourths and fifths are skipped (do
>not have a corresponding touch position), if any. I'm
>assuming the initial pitch at the beginning of the
>series of is the untouched, open string. Please
>explain if this is different.

>I've saved the rest of your message; let's discuss this
>much first.

It is easiest to do this by posting the guitar fretting
positions as a start.
I have also prepared a spreadsheet of integer ratios and difference
beats, which could be used for using beats and a metronome.

I hope that Tony Salinas can also add something about the
piano tuning by beats to this.

(sorry about the "tons" of numbers.)

[ Whole number ratios only used up to 12 limit. ]

LucyTuning beat frequency analysis Reference Freq. A4 440 Hertz

Large Ratio (L)1.116633 small ratio (s)1.073344 Pi3.141593

Position JI Ratio JI (dec.)LT Ratio JI Hertz LT Hertz Beat Hz. Beat
bpm
(A) I 1/1 1.000000 1.000000 440.0000 440.0000 0.0000
0.00
(A#) #I 13/12 1.083333 1.040331 476.6667 457.7455 18.9211
1135.27
(Bb) bII 12/11 1.090909 1.073344 480.0000 472.2714 7.7286
463.72
(Ax) Ix 11/10 1.100000 1.082288 484.0000 476.2068 7.7932
467.59
(B) II 10/9 1.111111 1.116633 488.8889 491.3185 2.4296
145.77
(B) II 9/8 1.125000 1.116633 495.0000 491.3185 3.6815
220.89
(Cb)bbIII 8/7 1.142857 1.152068 502.8571 506.9097 4.0526
243.15
(Cb)bbIII 7/6 1.166667 1.152068 513.3333 506.9097 6.4236
385.42
(B#) #II 7/6 1.166667 1.161668 513.3333 511.1337 2.1996
131.98
13/11 1.181818 520.0000

(C) bIII 6/5 1.200000 1.198531 528.0000 527.3538 0.6462
38.77
11/9 1.222222 537.7778

(C#) III 5/4 1.250000 1.246869 550.0000 548.6224 1.3776
82.66
14/11 1.272727 560.0000

(Db) bIV 9/7 1.285714 1.286436 565.7143 566.0321 0.3178
19.07
13/10 1.300000 572.0000

(D) IV 4/3 1.333333 1.338319 586.6667 588.8606 2.1939
131.63
15/11 1.363636 600.0000

(Ebb) bbV 11/8 1.375000 1.380789 605.0000 607.5472 2.5472
152.83
(D#) #IV 7/5 1.400000 1.392295 616.0000 612.6098 3.3902
203.41
(Eb) bV 7/5 1.400000 1.436477 616.0000 632.0500 16.0500
963.00
17/12 1.416667 623.3333

(Eb) bV 10/7 1.428571 1.436477 628.5714 632.0500 3.4786
208.71
13/9 1.444444 635.5556

16/11 1.454545 640.0000

(E) V 3/2 1.500000 1.494412 660.0000 657.5411 2.4589
147.54
(Fb) bbVI 17/11 1.545455 1.541834 680.0000 678.4071 1.5929
95.57
(E#) #V 14/9 1.555556 1.554682 684.4444 684.0602 0.3842
23.05
(E#) #V 11/7 1.571429 1.554682 691.4286 684.0602 7.3684
442.10
19/12 1.583333 696.6667

(F) bVI 8/5 1.600000 1.604018 704.0000 705.7678 1.7678
106.07
(F) bVI 13/8 1.625000 1.604018 715.0000 705.7678 9.2322
553.93
18/11 1.636364 720.0000

(F#) VI 5/3 1.666667 1.668709 733.3333 734.2320 0.8986
53.92
17/10 1.700000 748.0000

(Gb)bbVII 19/11 1.727273 1.721663 760.0000 757.5317 2.4683
148.10
(Fx) #VI 7/4 1.750000 1.736009 770.0000 763.8441 6.1559
369.35
(G) bVII 7/4 1.750000 1.791099 770.0000 788.0835 18.0835
1085.01
(G) bVII 9/5 1.800000 1.791099 792.0000 788.0835 3.9165
234.99
20/11 1.818182 800.0000

11/6 1.833333 806.6667

(G#) VII 11/6 1.833333 1.863335 806.6667 819.8676 13.2009
792.05
(G#) VII 13/7 1.857143 1.863335 817.1429 819.8676 2.7247
163.48
(G#) VII 15/8 1.875000 1.863335 825.0000 819.8676 5.1324
307.95
17/9 1.888889 831.1111

19/10 1.900000 836.0000

21/11 1.909091 840.0000

(Ab)bVIII 23/12 1.916667 1.922465 843.3333 845.8848 2.5515
153.09




BTW for anyone who can use it this spreadsheet was set up to accept
various
values for the Reference frequencies in Hertz or Ratios for the Large
interval. I can therefore run it on my Amiga for any meantone
(including most equal temperaments, which can be described by the
size of the Large interval as a ratio.)

lucy
Another spreadsheet.....
(ratios and nut to fret distances may be changed to calculate
for various tunings - see previous spreadsheet for frequencies)

"Ghosttones" can be found at frets close in the cycle of forths and
fifths.
i.e. Through fifths E, B, F#, C#, G#, etc.
Through fourths D, G, C, F, Bb, Eb etc.

The volume is lower the further you move away from A.

Fret positions for LucyTuned 19 & 31 frets per octave instruments.
Intervals > Large small
Ratios > 1.116633 1.073344
cents > 190.9858 122.5354

Distance of Nut to Bridge 650 (millimetres)
Fifth
Guitar
String FIRST OCTAVE IntervalSECOND OCTAVE
NoteName Scale Distance Fret Fret (L&s) Distance Fret Fret
Marks@ * Position NutToFret of 19 of 31 from NutToFret of 19 of 31
A ** I 0.0000 0 0 Nut 325.0000 19 31
Bbb bbII 19.9923 - 1 (2s-L) 334.9962 - 32
A# #I 25.1987 1 2 (L-s) 337.5994 20 33
Bb bII 44.4160 2 3 s 347.2080 21 34
Ax xI 49.4205 - 4 (2L-2s) 349.7103 - 35
B II 67.8928 3 5 L 358.9464 22 36
Cb bbIII 85.7970 - 6 2s 367.8985 - 37
B# #II 90.4595 4 7 (2L-s) 370.2298 23 38
C * bIII 107.6696 5 8 (L+s) 378.8348 24 39
Dbb bbIV 124.3503 - 9 3s 387.1751 - 40
C# III 128.6942 6 10 2L 389.3471 25 41
Db bIV 144.7283 7 11 (L+2s) 397.3641 26 42
Cx #III 148.9038 - 12 (3L-s) 399.4519 - 43
D * IV 164.3163 8 13 (2L+s) 407.1581 27 44
Ebb bbV 179.2546 - 14 (L+3s) 414.6273 - 45
D# #IV 183.1449 9 15 3L 416.5724 28 46
Eb bV 197.5042 10 16 (2L+2s) 423.7521 29 47
Dx xIV 201.2436 - 17 (4L-s) 425.6218 - 48
E * V 215.0462 11 18 (3L+s) 432.5231 30 49
Fb bbVI 228.4242 - 19 (2L+3s) 439.2121 - 50
E# #V 231.9081 12 20 4L 440.9541 31 51
F bVI 244.7676 13 21 (3L+2s) 447.3838 32 52
Ex xV 248.1164 - 22 (5L-s) 449.0582 - 53
F# * VI 260.4773 14 23 (4L+s) 455.2387 33 54
Gb bbVII 272.4580 15 24 (3L+3s) 461.2290 34 55
Fx #VI 275.5781 - 25 5L 462.7890 - 56
G bVII 287.0943 16 26 (4L+2s) 468.5472 35 57
Abb bbVIII 298.2564 - 27 (3L+4s) 474.1282 - 58
G# VII 301.1632 17 28 (5L+s) 475.5816 36 59
Ab bVIII 311.8925 18 29 (4L+3s) 480.9462 37 60
Gx #VII 314.6866 - 30 6L 482.3433 - 61
A ** VIII 325.0000 19 31 (5L+2s) 487.5000 38 62




Reply to Gary Morrison:
>Can you show us any specific evidence that this maps to partials of
any
>pitch from any instrument instrument more accurately than integer
>multiples? Or is the closeness of the mapping not your main point?


Yes, I believe it gives a better model of physical reality for
monochords etc. See above tables etc. to try it yourself.
(We are into the partials semantics problem again.)
I am attempting to build tunings on the "ghosttones".
Partials are in this case "red herrings".




> Are you sure that "consonant" is the best choice of words here?
Would
>you for example view a major second (two fifths apart) as more
consonant
>than a major sixth (three fifths apart)?

Yes, in this tuning I have found the IInd (L) to be more "consonant"
than the VIth (4L+s).

reply Tony Salinass:

To list the errors in Wilkinson's book would require another posting
as long as this one.
I found them all once and then left the book with Jonathan Glasier
about five years ago, with corrects written in the book.
Maybe someone has found it.
Wilkinson does give a good explanation of the "problem with JI and
other systems" re. lemmas etc.
lucy

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