Hi Everyone.

Recently I have become interested in pentatonic scales. This interest came about after modifying one of my 2-stringer CBGs so it would become a chromatically fretted instruments. The original frets were white tie-wraps, and for the new frets (for all the accidental notes (i.e. sharps& flats)) I used black tie-wraps, producing an instrument with color coded frets (white for naturals and black for accidentals, just like piano keys). I did this because I wanted to learn the chromatic fretboard better. But, in experimenting with the instrument, I found that playing just the black frets produced tunes that sounded very oriental. This effect was also due in part to my use of nylon strings (actually Aquilla Nylgut) instead of steal strings and metal frets.  

Recognizing that the Chinese also had several pentatonic scales of their own, I thought that making a CBG with a Chinese pentatonic scale might be something that Chinese people would be interested in. So, I have been researching the topic on the Internet and came across this very interesting site entitled "The Theory Behind Chinese Music". This seems like a pretty appropriate topic for this discussion group, so let's explore this together.

 

-Rand.

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hey Rand.

this is a really interesting idea, good one.  If you havent cut your fret slots yet, I have a fret calculator that can do pythagorean and just temperament.  I think you can only approximate the sounds you are looking for with 12 tone equal temperament, which is all any online claculator will give you.  Just shoot me a scale length if you like.

 

  ** the reason Dianne is looking at split frets is because she is taking care to carry the scale over to the second string, which is tuned to a perfect fifth.  There will always be a one note differential, to account for the difference between these two keys.  McNally (and most dulci makers) address is with the "6 1/2" fret.  Otherwise the scale generated from the middle string will be different. eg in a C tuned strummer the middle string is G.  If the frets for the middle string are the same ones as layed out for the root note string (ionian mode) there will be a F#, not a F on that string.  Hopefully that makes sense.  This pentatonic you are looking at here is exactly what we call a 'major pentatonic' here in the west, 1,2,3,5,6,1  I think Freddie King, the hideaway, the stumble, that kinda thing straight away.  The oriental sound will have to come from your approach to temperament, imho.

Hi Jef:

I was pretty disappointed with the result of my Major Pentatonic Fretboard. It turned out to sound just like my Diatonic fretboard less a couple of notes (which is why it sounded so familiar). Another source says it's the intervals that make it sound "oriental", but I think that is only part of the answer. As you say, the other part is how the Chinese scales are calculated, and not having a convenient calculator, I thought I'd test the "different intervals" idea separately with the odd intervals of the Oriental Scale. But, yes, I'd like to see how much a difference in "scale calculations" (or how the temperament is handled) would sound. So, maybe I'll make two fretboards so I can test these 2 factors separately. I'll actually have to make a second instrument "test-bed" so I can hear them at (nearly) the same time. The current series of fretboards are being designed with a scale length of 500mm (50cm). The Pythagorean method is what I have seen repeatedly when Googling the Internet about Chinese pentatonic scales. You can post your results here to share with everyone. Thanks.

-Rand.


Jef Long said:

hey Rand.

this is a really interesting idea, good one.  If you havent cut your fret slots yet, I have a fret calculator that can do pythagorean and just temperament.  I think you can only approximate the sounds you are looking for with 12 tone equal temperament, which is all any online claculator will give you.  Just shoot me a scale length if you like.

 

  ** the reason Dianne is looking at split frets is because she is taking care to carry the scale over to the second string, which is tuned to a perfect fifth.  There will always be a one note differential, to account for the difference between these two keys.  McNally (and most dulci makers) address is with the "6 1/2" fret.  Otherwise the scale generated from the middle string will be different. eg in a C tuned strummer the middle string is G.  If the frets for the middle string are the same ones as layed out for the root note string (ionian mode) there will be a F#, not a F on that string.  Hopefully that makes sense.  This pentatonic you are looking at here is exactly what we call a 'major pentatonic' here in the west, 1,2,3,5,6,1  I think Freddie King, the hideaway, the stumble, that kinda thing straight away.  The oriental sound will have to come from your approach to temperament, imho.

2011-01-25 07:23:19.028 JeFretGui 1[50659:207] Calculate a 500mm scale length Pythagorean Tempered fingerboard to 24 frets
2011-01-25 07:23:19.030 JeFretGui 1[50659:207] fret # 0 is at 500 mm or 19.69 inches
2011-01-25 07:23:19.031 JeFretGui 1[50659:207] fret # 1 is at 475 mm or 18.69 inches
2011-01-25 07:23:19.031 JeFretGui 1[50659:207] fret # 2 is at 444 mm or 17.50 inches
2011-01-25 07:23:19.032 JeFretGui 1[50659:207] fret # 3 is at 422 mm or 16.61 inches
2011-01-25 07:23:19.032 JeFretGui 1[50659:207] fret # 4 is at 395 mm or 15.55 inches
2011-01-25 07:23:19.033 JeFretGui 1[50659:207] fret # 5 is at 375 mm or 14.76 inches
2011-01-25 07:23:19.033 JeFretGui 1[50659:207] fret # 6 is at 356 mm or 14.01 inches
2011-01-25 07:23:19.035 JeFretGui 1[50659:207] fret # 7 is at 333 mm or 13.12 inches
2011-01-25 07:23:19.036 JeFretGui 1[50659:207] fret # 8 is at 316 mm or 12.46 inches
2011-01-25 07:23:19.040 JeFretGui 1[50659:207] fret # 9 is at 296 mm or 11.67 inches
2011-01-25 07:23:19.041 JeFretGui 1[50659:207] fret # 10 is at 281 mm or 11.07 inches
2011-01-25 07:23:19.042 JeFretGui 1[50659:207] fret # 11 is at 263 mm or 10.37 inches
2011-01-25 07:23:19.042 JeFretGui 1[50659:207] fret # 12 is at 250 mm or 9.84 inches
2011-01-25 07:23:19.043 JeFretGui 1[50659:207] fret # 13 is at 237 mm or 9.34 inches
2011-01-25 07:23:19.043 JeFretGui 1[50659:207] fret # 14 is at 222 mm or 8.75 inches
2011-01-25 07:23:19.044 JeFretGui 1[50659:207] fret # 15 is at 211 mm or 8.30 inches
2011-01-25 07:23:19.045 JeFretGui 1[50659:207] fret # 16 is at 198 mm or 7.78 inches
2011-01-25 07:23:19.045 JeFretGui 1[50659:207] fret # 17 is at 188 mm or 7.38 inches
2011-01-25 07:23:19.050 JeFretGui 1[50659:207] fret # 18 is at 178 mm or 7.01 inches
2011-01-25 07:23:19.052 JeFretGui 1[50659:207] fret # 19 is at 167 mm or 6.56 inches
2011-01-25 07:23:19.052 JeFretGui 1[50659:207] fret # 20 is at 158 mm or 6.23 inches
2011-01-25 07:23:19.053 JeFretGui 1[50659:207] fret # 21 is at 148 mm or 5.83 inches
2011-01-25 07:23:19.054 JeFretGui 1[50659:207] fret # 22 is at 141 mm or 5.54 inches
2011-01-25 07:23:19.054 JeFretGui 1[50659:207] fret # 23 is at 132 mm or 5.18 inches
2011-01-25 07:23:19.056 JeFretGui 1[50659:207] fret # 24 is at 125 mm or 4.92 inches
2011-01-25 07:23:19.059 JeFretGui 1[50659:207] fretboard ends at 119 mm or 4.67 inches


Rand Moore said:

Hi Jef:

I was pretty disappointed with the result of my Major Pentatonic Fretboard. It turned out to sound just like my Diatonic fretboard less a couple of notes (which is why it sounded so familiar). Another source says it's the intervals that make it sound "oriental", but I think that is only part of the answer. As you say, the other part is how the Chinese scales are calculated, and not having a convenient calculator, I thought I'd test the "different intervals" idea separately with the odd intervals of the Oriental Scale. But, yes, I'd like to see how much a difference in "scale calculations" (or how the temperament is handled) would sound. So, maybe I'll make two fretboards so I can test these 2 factors separately. I'll actually have to make a second instrument "test-bed" so I can hear them at (nearly) the same time. The current series of fretboards are being designed with a scale length of 500mm (50cm). The Pythagorean method is what I have seen repeatedly when Googling the Internet about Chinese pentatonic scales. You can post your results here to share with everyone. Thanks.

-Rand.

Sorry, i used an earlier build that delivers the inch value with a decimal, doh!

 

2011-01-25 07:30:34.901 JeFret Util[50728:207] fret # 0 is at 500 mm or 19 11/16 inches
2011-01-25 07:30:34.902 JeFret Util[50728:207] fret # 1 is at 475 mm or 18 11/16 inches
2011-01-25 07:30:34.902 JeFret Util[50728:207] fret # 2 is at 444 mm or 17 1/2 inches
2011-01-25 07:30:34.903 JeFret Util[50728:207] fret # 3 is at 422 mm or 16 19/32 inches
2011-01-25 07:30:34.903 JeFret Util[50728:207] fret # 4 is at 395 mm or 15 9/16 inches
2011-01-25 07:30:34.904 JeFret Util[50728:207] fret # 5 is at 375 mm or 14 3/4 inches
2011-01-25 07:30:34.904 JeFret Util[50728:207] fret # 6 is at 356 mm or 14   -   inches
2011-01-25 07:30:34.905 JeFret Util[50728:207] fret # 7 is at 333 mm or 13 1/8 inches
2011-01-25 07:30:34.905 JeFret Util[50728:207] fret # 8 is at 316 mm or 12 15/32 inches
2011-01-25 07:30:34.905 JeFret Util[50728:207] fret # 9 is at 296 mm or 11 21/32 inches
2011-01-25 07:30:34.906 JeFret Util[50728:207] fret # 10 is at 281 mm or 11 1/16 inches
2011-01-25 07:30:34.907 JeFret Util[50728:207] fret # 11 is at 263 mm or 10 3/8 inches
2011-01-25 07:30:34.907 JeFret Util[50728:207] fret # 12 is at 250 mm or 9 27/32 inches
2011-01-25 07:30:34.907 JeFret Util[50728:207] fret # 13 is at 237 mm or 9 11/32 inches
2011-01-25 07:30:34.908 JeFret Util[50728:207] fret # 14 is at 222 mm or 8 3/4 inches
2011-01-25 07:30:34.908 JeFret Util[50728:207] fret # 15 is at 211 mm or 8 5/16 inches
2011-01-25 07:30:34.909 JeFret Util[50728:207] fret # 16 is at 198 mm or 7 25/32 inches
2011-01-25 07:30:34.909 JeFret Util[50728:207] fret # 17 is at 188 mm or 7 3/8 inches
2011-01-25 07:30:34.910 JeFret Util[50728:207] fret # 18 is at 178 mm or 7   -   inches
2011-01-25 07:30:34.910 JeFret Util[50728:207] fret # 19 is at 167 mm or 6 9/16 inches
2011-01-25 07:30:34.911 JeFret Util[50728:207] fret # 20 is at 158 mm or 6 7/32 inches
2011-01-25 07:30:34.911 JeFret Util[50728:207] fret # 21 is at 148 mm or 5 27/32 inches
2011-01-25 07:30:34.912 JeFret Util[50728:207] fret # 22 is at 141 mm or 5 17/32 inches
2011-01-25 07:30:34.912 JeFret Util[50728:207] fret # 23 is at 132 mm or 5 3/16 inches
2011-01-25 07:30:34.913 JeFret Util[50728:207] fret # 24 is at 125 mm or 4 29/32 inches
2011-01-25 07:30:34.913 JeFret Util[50728:207] fretboard ends at 119 mm or 4 21/32 inches

Thanks for the data, Jef. I'll let you know when I have some results.

-Rand.


Hi Jef.

I saw that the numbers you gave me were "as measured from the bridge" and I'm used to seeing them "as measured from the nut", so I edited out everything except the important numbers into a tabbed-separated table using Notepad and then cut and pasted them into Excel to have it do the math to convert your numbers to "as measured from the nut" by subtracting the numbers from 500. I also converted them from "mm" to "cm" which is what I normally use to do a fretboard. Then I got to thinking I should compare them to what the Stew-Mac (12EQT) Fret Calculator gave me. What I noticed was that except for one fret position, there was only a small difference in the fret placement numbers. The differences were "insignificant". But there was the one anomaly: fret position #1 which I haven't been able to explain away. The numbers are:

Stew-Mac (12EQT): 2.81 cm
Pythagorean: 2.50 cm
Difference: 0.31 cm // (2.81-2.5)
Diff as a %: 10.91 % // (2.81-2.5) / 2.81 * 100 = 11.032028469750889679715302491103

Ai-Yah! Even the MS Calculator program gives a different answer.
But a 10 or 11% difference is significant.

Maybe you can double check the numbers you gave me?

 

I can email you the excel spreadsheet if you like. The anomaly troubles me.

 

-Rand

the numbers are spot on mate.  Pythagorean and just temperament are calculated on ratios and usually expressed from the bridge.  just subtract the scale length first then multiply by -0.1 for cm

 

i can practically guarantee you my calculator is at least as accurate as stew macs, it uses objective C double long floats, should be good to 16 or so decimal places.

 

Yes, the diminished second is by far the most obvious difference, but every fret but the octave is in a slightly different spot.  The thirds, both major and minor, are both quite different too.

my calculator can synthesize sounds and apply the ratios to the frequency as well, so i can actually hear the difference ;)  believe me, the human ear can detect a 1 cent (100 cents = 1 equal tempered semitone) so all the differences are of significance

Rand Moore said:

Hi Jef.

I saw that the numbers you gave me were "as measured from the bridge" and I'm used to seeing them "as measured from the nut", so I edited out everything except the important numbers into a tabbed-separated table using Notepad and then cut and pasted them into Excel to have it do the math to convert your numbers to "as measured from the nut" by subtracting the numbers from 500. I also converted them from "mm" to "cm" which is what I normally use to do a fretboard. Then I got to thinking I should compare them to what the Stew-Mac (12EQT) Fret Calculator gave me. What I noticed was that except for one fret position, there was only a small difference in the fret placement numbers. The differences were "insignificant". But there was the one anomaly: fret position #1 which I haven't been able to explain away. The numbers are:

Stew-Mac (12EQT): 2.81 cm
Pythagorean: 2.50 cm
Difference: 0.31 cm // (2.81-2.5)
Diff as a %: 10.91 % // (2.81-2.5) / 2.81 * 100 = 11.032028469750889679715302491103

Ai-Yah! Even the MS Calculator program gives a different answer.
But a 10 or 11% difference is significant.

Maybe you can double check the numbers you gave me?

 

I can email you the excel spreadsheet if you like. The anomaly troubles me.

 

-Rand

Okay, Jef. I just didn't know what to expect. Sounds like a cool program. I'll build a fretboard using the Oriental Scale and your Pythagorean numbers and another using the Stew-Mac 12EQT numbers and I'll let you what I think. I'll put my other projects on hold while I get these built so we don't have to wait to long for results.

 

-Rand.

here is a screen grab from my calculator beta with a pythagorean fingerboard on left (with white dot markers) and 12tet fingerboard on the right (black dots)  please note this is rendered to only 400 pixels so there is some rounding.  I stuck it in photoshop and dropped *'s down the right hand side by the equal temperament fingerboard, showing the most obvious differences between the two temperaments, and I dropped x's on the left by the pythagorean neck to indicate the frets you need for your scale.

.. wait til you see a just tempered neck btw..

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