Interval Calculator

To all,

I have uploaded a program to the "Files" section which I wrote that calculates the consonance of an interval. One version is for older Macs (OS9) and another version for PCs. I don't know yet whether the latter runs because I can compile PC programs on my Mac but can't run them. The program is only relevant to instruments whose timbres are close to the 'ideal' (i.e. the frequencies of the harmonics are exactly x, 2x, 3x, 4x etc. and the amplitudes are y, y/2, y/3, y/4 etc).
I hope to have a version for OSX Macs soon.
Check it out.

Michael, did you read my last post? (message #87516, subject: Harmonic Series coincidence).

John.

John,

Interesting. The bizarre thing is that intervals like 11/9 (IE 1.2222) comes out as so low (about -2) while it's nearby neighbor 5/4 comes out as 2. Try playing the two intervals and see if you think there really is such a huge consonance difference. Your formula doesn't seem to like x/11 type intervals or x/9 ones...even the ones that sound perfectly fine to my ear (maybe a bit too much weight on simply having a low denominator)?

The calculator does a fairly good job with super-particular ratios around 11/10-17/16 (10/9 comes out as around -2.3, 17/16 more like -4....which sounds about right so far as comparing the two in relative consonance). Although I disagree that 12/13 is somehow -3.3 while the not-so-different 10/9 is -2.3 (IMVHO something more like 2.7 would make sense in comparison).

Also......around 7/6 the consonance is around -.5, at 6/5 it is at about .5, and at 5/4 it is around 2...and 2/1 gives a bizarrely higher value of 21! The increases in consonance starting around 6/5 and simpler seem a bit unrealistic. 5/3 has a value slightly better than 4/3 despite 4/3 having lower numbers....good call (here critical band dissonance makes the bit of difference, IMVHO)!
If I were to rate those ratios myself...7/6 may have about 1.05, 6/5 could have about 1.1 while 5/4 would have about 1.18, 4/3 would have 1.25, and 3/2 would have 1.35 and the octave would be somewhat of a max at about 1.4....notice the values would level out beyond a certain point rather than having the consonance grow exponentially (almost infinitely!) as it approaches 1/1.

________________________________
From: john777music <jfos777@...>
To: tuning@yahoogroups.com
Sent: Sun, April 18, 2010 4:15:42 PM
Subject: [tuning] Interval Calculator

To all,

I have uploaded a program to the "Files" section which I wrote that calculates the consonance of an interval. One version is for older Macs (OS9) and another version for PCs. I don't know yet whether the latter runs because I can compile PC programs on my Mac but can't run them. The program is only relevant to instruments whose timbres are close to the 'ideal' (i.e. the frequencies of the harmonics are exactly x, 2x, 3x, 4x etc. and the amplitudes are y, y/2, y/3, y/4 etc).
I hope to have a version for OSX Macs soon.
Check it out.

Michael, did you read my last post? (message #87516, subject: Harmonic Series coincidence) .

John.

Michael,

thanks for your comments which I have found very enlightening over the last few weeks.

I've been testing my program and it definitely needs to take complex intervals that are close to simple intervals into account. The 56/45 interval gave a value of -4.34 but it clearly sounds sweet (it's only 7.7 cents away from 5/4). So my idea of 'perfection or bust' was wrong.

This led me to investigate the threshold for deviation from the 'true' interval and I came up with 13.578 cents (128/127). Perhaps the threshold might be wider for stronger intervals and vice versa.
I'll have to incorporate this idea into the program when pairing the 'elements' of two notes.

BTW, did you check to see how many symmetries turned up using my NPT scale?

John.

Wanted to let you know, John, that I moved your files to your
own folder

/tuning/files/JohnOSullivan/

per group policy. Sorry for any inconvenience.

-Carl

>"This led me to investigate the threshold for deviation from the 'true'
interval and I came up with 13.578 cents (128/127)."
Sounds about right to me...I'd put it at about 14-15 cents, but I'm known to be a bit liberal so far as dissonance and 13.5 isn't far off from that at all anyhow. Yes, you can hear some slight beating vs. "perfect JI"...but you really have to "stare" at the sound to notice any difference at all.

Here's your chance though...using this knowledge I'm pretty sure you can make your scale sure that no dyad/combination within 2 octaves is more than about 13 cents impure...thus not perfect but at least (just about perfect enough to be confused with perfect to the ear). Try it! :-)

Then your challenge becomes (I figure) "what chords can I make that are not possible in 12TET?" especially since 12TET generally follows the "everything is within 13 cents of perfect" principle and as such does a fairly good job at "faking perfect" in many cases.

>"BTW, did you check to see how many symmetries turned up using my NPT
scale?"
I will...once I get done cleaning up my own scale. For example I've found that the 6/5 in my scale conflicts with the 5/3 (IE not within 13 cents of a pure interval) and tempering the 6/5 to about 1.208 makes it sound "close enough" in terms of that...making the ratio generated between those two extremely close to 11/8 while making the new 6/5 still very close to the original 6/5). Ah the wonderful "cheat" of tempering from JI. ;-)

Here again is my list of good intervals (an octave or less wide) arranged in descending order of strength. The values are from my Interval Calculator program. Intervals with a negative value are, IMO, dissonant. The values are *relative* to a zero point I chose myself according to my own taste. Others might choose a different cut off point but the hierarchy should always be the same. For *absolute* values a constant value z should be added to each result but I haven't worked out what z is yet.

1/1...93.8291
2/1...67.2094
3/2...32.2295
4/3...19.1148
5/3...16.6687
5/4...12.1248
7/4....9.4285
6/5....7.8115
7/5....6.6618
8/5....5.8094
9/5....5.1963
7/6....4.8043
8/7....2.6135
11/6....2.4169
9/7....2.1161
10/7....1.5793
11/7....1.2044
9/8....0.9203
12/7....0.8705
13/7....0.4260
11/8....0.1951
--------------
10/9...-0.4096
13/8...-0.4326
11/9...-0.6216
13/9...-1.1591
11/10..-1.4959
13/10..-1.8168
12/11..-2.4098
13/11..-2.4418
13/12..-3.1892

The calculator program (I spent a long time testing it and it seems accurate) should be useful for quickly identifying *all* the good intervals that occur on, say, a grand piano which has a span of more than 7 octaves. So very wide good intervals (e.g. wider than 16/1) can quickly be identified. The idea then is to use only the good intervals in chords. An interval is good if it within 6.776 cents (256/255) of any interval that the calculator says should be good.

If anyone wants to try my Interval Calculator, the latest revised version can be found in the JohnOSullivan folder in the Files section.

www.johnsmusic7.com

John.

Most of these agree quite well with what I hear as well.  In general, great
job!

   My only gripes

1) Is it seems some of the 13-limit dyads are rated too highly...IE to me 12/11 sounds better than 13/9.  So anything with a 13 or higher prime in its fraction (note 15 would not count as a prime, since it can be reduced to 3 * 5), IMVHO, should get an extra penalty for dissonance.

2)  Meanwhile 18/11, which is nowhere on your list...sounds better to me than either...than again I think 18/11 should get the same value as it's inverse, octave / (18/11) =
11/9...plus a bit of advantage for being farther apart and having less critical band dissonance. 

3) Same goes for 22/15...which would be calculated as (octave AKA 2) / (22/15) = 15/11 (and thus given a much better rating).  22/15 sounds less dissonant to me than either of the above.

  How come?  My guess is that giving extra consonance for ratios near very major fractions AKA the ones identified as best in
Harmonic Entropy (IE near 3/2 and its inverse 4/3...plus  5/4 and it's inverse 8/5, and 4/3) would fix this.  Try 22/15 for yourself vs. 11/9...and I think you'll be surprised how 22/15 managed to sound smoother.

  In general, I think you should
A1) Calculate a dyad's dissonance (without taking critical band into account)
A2) Take closeness to very simple fractions IE 3/2,4/3, 5/4, and 8/5 into account to boost consonance if near those fractions.
A3) Figure critical band into the value for that dyad
----------------
B) Calculate 2 over the dyad in A IE the octave inverse of that dyad
B2) Take closeness of that dyad to very simple fractions IE 3/2,4/3, 5/4, and 8/5 into account to boost consonance if near those fractions.
B3) Figure critical band into the value for that dyad

C) take the LOWER DISSONANCE VALUE of the two dyads IE whichever is lower between the dyad and its octave inverse

--- On Sat, 2/12/11, john777music <jfos777@...> wrote:

From: john777music <jfos777@...>
Subject: [tuning] Interval Calculator
To: tuning@yahoogroups.com
Date: Saturday, February 12, 2011, 9:40 AM

Here again is my list of good intervals (an octave or less wide) arranged in descending order of strength. The values are from my Interval Calculator program. Intervals with a negative value are, IMO, dissonant. The values are *relative* to a zero point I chose myself according to my own taste. Others might choose a different cut off point but the hierarchy should always be the same. For *absolute* values a constant value z should be added to each result but I haven't worked out what z is yet.

1/1...93.8291

2/1...67.2094

3/2...32.2295

4/3...19.1148

5/3...16.6687

5/4...12.1248

7/4....9.4285

6/5....7.8115

7/5....6.6618

8/5....5.8094

9/5....5.1963

7/6....4.8043

8/7....2.6135

11/6....2.4169

9/7....2.1161

10/7....1.5793

11/7....1.2044

9/8....0.9203

12/7....0.8705

13/7....0.4260

11/8....0.1951

--------------

10/9...-0.4096

13/8...-0.4326

11/9...-0.6216

13/9...-1.1591

11/10..-1.4959

13/10..-1.8168

12/11..-2.4098

13/11..-2.4418

13/12..-3.1892

The calculator program (I spent a long time testing it and it seems accurate) should be useful for quickly identifying *all* the good intervals that occur on, say, a grand piano which has a span of more than 7 octaves. So very wide good intervals (e.g. wider than 16/1) can quickly be identified. The idea then is to use only the good intervals in chords. An interval is good if it within 6.776 cents (256/255) of any interval that the calculator says should be good.

If anyone wants to try my Interval Calculator, the latest revised version can be found in the JohnOSullivan folder in the Files section.

www.johnsmusic7.com

John.

Ok,

I put them in ascending order and popped them into scala

0: 1/1 0.000 unison, perfect prime
1: 9/8 203.910 major whole tone
2: 8/7 231.174 septimal whole tone
3: 7/6 266.871 septimal minor third
4: 6/5 315.641 minor third
5: 5/4 386.314 major third
6: 9/7 435.084 septimal major third, BP third
7: 4/3 498.045 perfect fourth
8: 11/8 551.318 undecimal semi-augmented fourth
9: 7/5 582.512 septimal or Huygens' tritone, BP
fourth
10: 10/7 617.488 Euler's tritone
11: 3/2 701.955 perfect fifth
12: 11/7 782.492 undecimal augmented fifth
13: 8/5 813.686 minor sixth
14: 5/3 884.359 major sixth, BP sixth
15: 12/7 933.129 septimal major sixth
16: 7/4 968.826 harmonic seventh
17: 9/5 1017.596 just minor seventh, BP seventh
18: 11/6 1049.363 21/4-tone, undecimal neutral seventh
19: 13/7 1071.702 16/3-tone
20: 2/1 1200.000 octave

and here is the scala formatted version

! E:\Cakewalk\scales\john20110212.scl
!
john 2011 02 12 best
20
!
9/8
8/7
7/6
6/5
5/4
9/7
4/3
11/8
7/5
10/7
3/2
11/7
8/5
5/3
12/7
7/4
9/5
11/6
13/7
2/1

Hi Chris,

wanna try composing something in the scale below?

John.

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Ok,
>
> I put them in ascending order and popped them into scala
>
> 0: 1/1 0.000 unison, perfect prime
> 1: 9/8 203.910 major whole tone
> 2: 8/7 231.174 septimal whole tone
> 3: 7/6 266.871 septimal minor third
> 4: 6/5 315.641 minor third
> 5: 5/4 386.314 major third
> 6: 9/7 435.084 septimal major third, BP third
> 7: 4/3 498.045 perfect fourth
> 8: 11/8 551.318 undecimal semi-augmented fourth
> 9: 7/5 582.512 septimal or Huygens' tritone, BP
> fourth
> 10: 10/7 617.488 Euler's tritone
> 11: 3/2 701.955 perfect fifth
> 12: 11/7 782.492 undecimal augmented fifth
> 13: 8/5 813.686 minor sixth
> 14: 5/3 884.359 major sixth, BP sixth
> 15: 12/7 933.129 septimal major sixth
> 16: 7/4 968.826 harmonic seventh
> 17: 9/5 1017.596 just minor seventh, BP seventh
> 18: 11/6 1049.363 21/4-tone, undecimal neutral seventh
> 19: 13/7 1071.702 16/3-tone
> 20: 2/1 1200.000 octave
>
> and here is the scala formatted version
>
> ! E:\Cakewalk\scales\john20110212.scl
> !
> john 2011 02 12 best
> 20
> !
> 9/8
> 8/7
> 7/6
> 6/5
> 5/4
> 9/7
> 4/3
> 11/8
> 7/5
> 10/7
> 3/2
> 11/7
> 8/5
> 5/3
> 12/7
> 7/4
> 9/5
> 11/6
> 13/7
> 2/1
>

Actually - that is exactly what I had in mind.

:-)

Chris

On Sat, Feb 12, 2011 at 1:26 PM, john777music <jfos777@...> wrote:

>
>
> Hi Chris,
>
> wanna try composing something in the scale below?
>
> John.
>
>
> --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
> >
> > Ok,
> >
> > I put them in ascending order and popped them into scala
> >
> > 0: 1/1 0.000 unison, perfect prime
> > 1: 9/8 203.910 major whole tone
> > 2: 8/7 231.174 septimal whole tone
> > 3: 7/6 266.871 septimal minor third
> > 4: 6/5 315.641 minor third
> > 5: 5/4 386.314 major third
> > 6: 9/7 435.084 septimal major third, BP third
> > 7: 4/3 498.045 perfect fourth
> > 8: 11/8 551.318 undecimal semi-augmented fourth
> > 9: 7/5 582.512 septimal or Huygens' tritone, BP
> > fourth
> > 10: 10/7 617.488 Euler's tritone
> > 11: 3/2 701.955 perfect fifth
> > 12: 11/7 782.492 undecimal augmented fifth
> > 13: 8/5 813.686 minor sixth
> > 14: 5/3 884.359 major sixth, BP sixth
> > 15: 12/7 933.129 septimal major sixth
> > 16: 7/4 968.826 harmonic seventh
> > 17: 9/5 1017.596 just minor seventh, BP seventh
> > 18: 11/6 1049.363 21/4-tone, undecimal neutral seventh
> > 19: 13/7 1071.702 16/3-tone
> > 20: 2/1 1200.000 octave
> >
> > and here is the scala formatted version
> >
> > ! E:\Cakewalk\scales\john20110212.scl
> > !
> > john 2011 02 12 best
> > 20
> > !
> > 9/8
> > 8/7
> > 7/6
> > 6/5
> > 5/4
> > 9/7
> > 4/3
> > 11/8
> > 7/5
> > 10/7
> > 3/2
> > 11/7
> > 8/5
> > 5/3
> > 12/7
> > 7/4
> > 9/5
> > 11/6
> > 13/7
> > 2/1
> >
>
>
>

Michael,

I tested 22/15 and it seems quite dissonant to me and is not very near a *good* interval.

The calculator works out the consonance value (based on periodicity) of an interval (using the first 1024 partials of each note) and also works out the dissonance value (based on beating/beats) and then the dissonance value is subtracted from the consonance value to get the result.

Prime limits are not a factor in the program.

John.

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> Most of these agree quite well with what I hear as well.  In general, great
> job!
>
>    My only gripes
>
> 1) Is it seems some of the 13-limit dyads are rated too highly...IE to me 12/11 sounds better than 13/9.  So anything with a 13 or higher prime in its fraction (note 15 would not count as a prime, since it can be reduced to 3 * 5), IMVHO, should get an extra penalty for dissonance.
>
> 2)  Meanwhile 18/11, which is nowhere on your list...sounds better to me than either...than again I think 18/11 should get the same value as it's inverse, octave / (18/11) =
> 11/9...plus a bit of advantage for being farther apart and having less critical band dissonance. 
>
> 3) Same goes for 22/15...which would be calculated as (octave AKA 2) / (22/15) = 15/11 (and thus given a much better rating).  22/15 sounds less dissonant to me than either of the above.
>
>   How come?  My guess is that giving extra consonance for ratios near very major fractions AKA the ones identified as best in
> Harmonic Entropy (IE near 3/2 and its inverse 4/3...plus  5/4 and it's inverse 8/5, and 4/3) would fix this.  Try 22/15 for yourself vs. 11/9...and I think you'll be surprised how 22/15 managed to sound smoother.
>
>
>   In general, I think you should
> A1) Calculate a dyad's dissonance (without taking critical band into account)
> A2) Take closeness to very simple fractions IE 3/2,4/3, 5/4, and 8/5 into account to boost consonance if near those fractions.
> A3) Figure critical band into the value for that dyad
> ----------------
> B) Calculate 2 over the dyad in A IE the octave inverse of that dyad
> B2) Take closeness of that dyad to very simple fractions IE 3/2,4/3, 5/4, and 8/5 into account to boost consonance if near those fractions.
> B3) Figure critical band into the value for that dyad
>
>
> C) take the LOWER DISSONANCE VALUE of the two dyads IE whichever is lower between the dyad and its octave inverse
>
>
> --- On Sat, 2/12/11, john777music <jfos777@...> wrote:
>
> From: john777music <jfos777@...>
> Subject: [tuning] Interval Calculator
> To: tuning@yahoogroups.com
> Date: Saturday, February 12, 2011, 9:40 AM
>
>
>
>
>
>
>
>  
>
>
>
>
>
>
>
>
>
> Here again is my list of good intervals (an octave or less wide) arranged in descending order of strength. The values are from my Interval Calculator program. Intervals with a negative value are, IMO, dissonant. The values are *relative* to a zero point I chose myself according to my own taste. Others might choose a different cut off point but the hierarchy should always be the same. For *absolute* values a constant value z should be added to each result but I haven't worked out what z is yet.
>
>
>
> 1/1...93.8291
>
> 2/1...67.2094
>
> 3/2...32.2295
>
> 4/3...19.1148
>
> 5/3...16.6687
>
> 5/4...12.1248
>
> 7/4....9.4285
>
> 6/5....7.8115
>
> 7/5....6.6618
>
> 8/5....5.8094
>
> 9/5....5.1963
>
> 7/6....4.8043
>
> 8/7....2.6135
>
> 11/6....2.4169
>
> 9/7....2.1161
>
> 10/7....1.5793
>
> 11/7....1.2044
>
> 9/8....0.9203
>
> 12/7....0.8705
>
> 13/7....0.4260
>
> 11/8....0.1951
>
> --------------
>
> 10/9...-0.4096
>
> 13/8...-0.4326
>
> 11/9...-0.6216
>
> 13/9...-1.1591
>
> 11/10..-1.4959
>
> 13/10..-1.8168
>
> 12/11..-2.4098
>
> 13/11..-2.4418
>
> 13/12..-3.1892
>
>
>
> The calculator program (I spent a long time testing it and it seems accurate) should be useful for quickly identifying *all* the good intervals that occur on, say, a grand piano which has a span of more than 7 octaves. So very wide good intervals (e.g. wider than 16/1) can quickly be identified. The idea then is to use only the good intervals in chords. An interval is good if it within 6.776 cents (256/255) of any interval that the calculator says should be good.
>
>
>
> If anyone wants to try my Interval Calculator, the latest revised version can be found in the JohnOSullivan folder in the Files section.
>
>
>
> www.johnsmusic7.com
>
>
>
> John.
>

Here you go.

http://micro.soonlabel.com/just/john20110212/daily201012-john-revised-mubaraks-dilemma.mp3

online play

http://improvfriday.ning.com/xn/detail/4162021:Comment:24752

Chris

On Sat, Feb 12, 2011 at 1:26 PM, john777music <jfos777@...> wrote:

>
>
> Hi Chris,
>
> wanna try composing something in the scale below?
>
> John.
>
>
> --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
> >
> > Ok,
> >
> > I put them in ascending order and popped them into scala
> >
> > 0: 1/1 0.000 unison, perfect prime
> > 1: 9/8 203.910 major whole tone
> > 2: 8/7 231.174 septimal whole tone
> > 3: 7/6 266.871 septimal minor third
> > 4: 6/5 315.641 minor third
> > 5: 5/4 386.314 major third
> > 6: 9/7 435.084 septimal major third, BP third
> > 7: 4/3 498.045 perfect fourth
> > 8: 11/8 551.318 undecimal semi-augmented fourth
> > 9: 7/5 582.512 septimal or Huygens' tritone, BP
> > fourth
> > 10: 10/7 617.488 Euler's tritone
> > 11: 3/2 701.955 perfect fifth
> > 12: 11/7 782.492 undecimal augmented fifth
> > 13: 8/5 813.686 minor sixth
> > 14: 5/3 884.359 major sixth, BP sixth
> > 15: 12/7 933.129 septimal major sixth
> > 16: 7/4 968.826 harmonic seventh
> > 17: 9/5 1017.596 just minor seventh, BP seventh
> > 18: 11/6 1049.363 21/4-tone, undecimal neutral seventh
> > 19: 13/7 1071.702 16/3-tone
> > 20: 2/1 1200.000 octave
> >
> > and here is the scala formatted version
> >
> > ! E:\Cakewalk\scales\john20110212.scl
> > !
> > john 2011 02 12 best
> > 20
> > !
> > 9/8
> > 8/7
> > 7/6
> > 6/5
> > 5/4
> > 9/7
> > 4/3
> > 11/8
> > 7/5
> > 10/7
> > 3/2
> > 11/7
> > 8/5
> > 5/3
> > 12/7
> > 7/4
> > 9/5
> > 11/6
> > 13/7
> > 2/1
> >
>
>
>

Chris, does the piece use all 20 notes or just a subset?

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Here you go.
>
> http://micro.soonlabel.com/just/john20110212/daily201012-john-revised-mubaraks-dilemma.mp3
>
> online play
>
> http://improvfriday.ning.com/xn/detail/4162021:Comment:24752
>
>
> Chris
>
> On Sat, Feb 12, 2011 at 1:26 PM, john777music <jfos777@...> wrote:
>
> >
> >
> > Hi Chris,
> >
> > wanna try composing something in the scale below?
> >
> > John.
> >
> >
> > --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@> wrote:
> > >
> > > Ok,
> > >
> > > I put them in ascending order and popped them into scala
> > >
> > > 0: 1/1 0.000 unison, perfect prime
> > > 1: 9/8 203.910 major whole tone
> > > 2: 8/7 231.174 septimal whole tone
> > > 3: 7/6 266.871 septimal minor third
> > > 4: 6/5 315.641 minor third
> > > 5: 5/4 386.314 major third
> > > 6: 9/7 435.084 septimal major third, BP third
> > > 7: 4/3 498.045 perfect fourth
> > > 8: 11/8 551.318 undecimal semi-augmented fourth
> > > 9: 7/5 582.512 septimal or Huygens' tritone, BP
> > > fourth
> > > 10: 10/7 617.488 Euler's tritone
> > > 11: 3/2 701.955 perfect fifth
> > > 12: 11/7 782.492 undecimal augmented fifth
> > > 13: 8/5 813.686 minor sixth
> > > 14: 5/3 884.359 major sixth, BP sixth
> > > 15: 12/7 933.129 septimal major sixth
> > > 16: 7/4 968.826 harmonic seventh
> > > 17: 9/5 1017.596 just minor seventh, BP seventh
> > > 18: 11/6 1049.363 21/4-tone, undecimal neutral seventh
> > > 19: 13/7 1071.702 16/3-tone
> > > 20: 2/1 1200.000 octave
> > >
> > > and here is the scala formatted version
> > >
> > > ! E:\Cakewalk\scales\john20110212.scl
> > > !
> > > john 2011 02 12 best
> > > 20
> > > !
> > > 9/8
> > > 8/7
> > > 7/6
> > > 6/5
> > > 5/4
> > > 9/7
> > > 4/3
> > > 11/8
> > > 7/5
> > > 10/7
> > > 3/2
> > > 11/7
> > > 8/5
> > > 5/3
> > > 12/7
> > > 7/4
> > > 9/5
> > > 11/6
> > > 13/7
> > > 2/1
> > >
> >
> >
> >
>

John,

It was an improvisation with a little bit of edits. I had 15 minutes before leaving to visit a fish store with my wife. (Aquarium). Right now I'm in a laundry mat drinking a diet coke. I say all that as explanation as to why don't know the answer with certainty. I doubt I used all 20 notes in an octave span but I'm sure I came close. Reasonable Chords were achievable by constructing extended augmented triads. Playing a diatonic type scale worked if a major or minor third was included as needed in the run.

I will be glad to provide a piano roll view later and that would let you visually see the note usage.

Chis
-----Original Message-----
From: "john777music" <jfos777@yahoo.com>
Sender: tuning@yahoogroups.com
Date: Sat, 12 Feb 2011 19:30:50
To: <tuning@yahoogroups.com>
Reply-To: tuning@yahoogroups.com
Subject: [tuning] Re: Interval Calculator

Chris, does the piece use all 20 notes or just a subset?

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Here you go.
>
> http://micro.soonlabel.com/just/john20110212/daily201012-john-revised-mubaraks-dilemma.mp3
>
> online play
>
> http://improvfriday.ning.com/xn/detail/4162021:Comment:24752
>
>
> Chris
>
> On Sat, Feb 12, 2011 at 1:26 PM, john777music <jfos777@...> wrote:
>
> >
> >
> > Hi Chris,
> >
> > wanna try composing something in the scale below?
> >
> > John.
> >
> >
> > --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@> wrote:
> > >
> > > Ok,
> > >
> > > I put them in ascending order and popped them into scala
> > >
> > > 0: 1/1 0.000 unison, perfect prime
> > > 1: 9/8 203.910 major whole tone
> > > 2: 8/7 231.174 septimal whole tone
> > > 3: 7/6 266.871 septimal minor third
> > > 4: 6/5 315.641 minor third
> > > 5: 5/4 386.314 major third
> > > 6: 9/7 435.084 septimal major third, BP third
> > > 7: 4/3 498.045 perfect fourth
> > > 8: 11/8 551.318 undecimal semi-augmented fourth
> > > 9: 7/5 582.512 septimal or Huygens' tritone, BP
> > > fourth
> > > 10: 10/7 617.488 Euler's tritone
> > > 11: 3/2 701.955 perfect fifth
> > > 12: 11/7 782.492 undecimal augmented fifth
> > > 13: 8/5 813.686 minor sixth
> > > 14: 5/3 884.359 major sixth, BP sixth
> > > 15: 12/7 933.129 septimal major sixth
> > > 16: 7/4 968.826 harmonic seventh
> > > 17: 9/5 1017.596 just minor seventh, BP seventh
> > > 18: 11/6 1049.363 21/4-tone, undecimal neutral seventh
> > > 19: 13/7 1071.702 16/3-tone
> > > 20: 2/1 1200.000 octave
> > >
> > > and here is the scala formatted version
> > >
> > > ! E:\Cakewalk\scales\john20110212.scl
> > > !
> > > john 2011 02 12 best
> > > 20
> > > !
> > > 9/8
> > > 8/7
> > > 7/6
> > > 6/5
> > > 5/4
> > > 9/7
> > > 4/3
> > > 11/8
> > > 7/5
> > > 10/7
> > > 3/2
> > > 11/7
> > > 8/5
> > > 5/3
> > > 12/7
> > > 7/4
> > > 9/5
> > > 11/6
> > > 13/7
> > > 2/1
> > >
> >
> >
> >
>

Ok, my memory was off on those chords - BUT - you can see for yourself what
I did.

The improvisation was the 3rd try at doing something with the tuning - as I
said time was short.

The piano roll view is here:

http://micro.soonlabel.com/just/john20110212/john-revised-score.jpg

Chris

On Sat, Feb 12, 2011 at 4:30 PM, <chrisvaisvil@...> wrote:

> John,
>
> It was an improvisation with a little bit of edits. I had 15 minutes before
> leaving to visit a fish store with my wife. (Aquarium). Right now I'm in a
> laundry mat drinking a diet coke. I say all that as explanation as to why
> don't know the answer with certainty. I doubt I used all 20 notes in an
> octave span but I'm sure I came close. Reasonable Chords were achievable by
> constructing extended augmented triads. Playing a diatonic type scale worked
> if a major or minor third was included as needed in the run.
>
> I will be glad to provide a piano roll view later and that would let you
> visually see the note usage.
>
> Chis
> ------------------------------
> *From: * "john777music" <jfos777@...>
> *Sender: * tuning@yahoogroups.com
> *Date: *Sat, 12 Feb 2011 19:30:50 -0000
> *To: *<tuning@yahoogroups.com>
> *ReplyTo: * tuning@yahoogroups.com
> *Subject: *[tuning] Re: Interval Calculator
>
>
>
> Chris, does the piece use all 20 notes or just a subset?
>
> --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
> >
> > Here you go.
> >
> >
> http://micro.soonlabel.com/just/john20110212/daily201012-john-revised-mubaraks-dilemma.mp3
> >
> > online play
> >
> > http://improvfriday.ning.com/xn/detail/4162021:Comment:24752
> >
> >
> > Chris
> >
> > On Sat, Feb 12, 2011 at 1:26 PM, john777music <jfos777@...> wrote:
> >
> > >
> > >
> > > Hi Chris,
> > >
> > > wanna try composing something in the scale below?
> > >
> > > John.
> > >
> > >
> > > --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@> wrote:
> > > >
> > > > Ok,
> > > >
> > > > I put them in ascending order and popped them into scala
> > > >
> > > > 0: 1/1 0.000 unison, perfect prime
> > > > 1: 9/8 203.910 major whole tone
> > > > 2: 8/7 231.174 septimal whole tone
> > > > 3: 7/6 266.871 septimal minor third
> > > > 4: 6/5 315.641 minor third
> > > > 5: 5/4 386.314 major third
> > > > 6: 9/7 435.084 septimal major third, BP third
> > > > 7: 4/3 498.045 perfect fourth
> > > > 8: 11/8 551.318 undecimal semi-augmented fourth
> > > > 9: 7/5 582.512 septimal or Huygens' tritone, BP
> > > > fourth
> > > > 10: 10/7 617.488 Euler's tritone
> > > > 11: 3/2 701.955 perfect fifth
> > > > 12: 11/7 782.492 undecimal augmented fifth
> > > > 13: 8/5 813.686 minor sixth
> > > > 14: 5/3 884.359 major sixth, BP sixth
> > > > 15: 12/7 933.129 septimal major sixth
> > > > 16: 7/4 968.826 harmonic seventh
> > > > 17: 9/5 1017.596 just minor seventh, BP seventh
> > > > 18: 11/6 1049.363 21/4-tone, undecimal neutral seventh
> > > > 19: 13/7 1071.702 16/3-tone
> > > > 20: 2/1 1200.000 octave
> > > >
> > > > and here is the scala formatted version
> > > >
> > > > ! E:\Cakewalk\scales\john20110212.scl
> > > > !
> > > > john 2011 02 12 best
> > > > 20
> > > > !
> > > > 9/8
> > > > 8/7
> > > > 7/6
> > > > 6/5
> > > > 5/4
> > > > 9/7
> > > > 4/3
> > > > 11/8
> > > > 7/5
> > > > 10/7
> > > > 3/2
> > > > 11/7
> > > > 8/5
> > > > 5/3
> > > > 12/7
> > > > 7/4
> > > > 9/5
> > > > 11/6
> > > > 13/7
> > > > 2/1
> > > >
> > >
> > >
> > >
> >
>
>
>

Thanks Chris,

I asked because the scale has 20 notes and a keyboard has only 12 per octave. How would you work with 20 keys per octave?

Here's another scale for you if you're interested...

1/1
15/14
8/7
7/6
9/7
21/16
7/5
10/7
14/9
12/7
7/4
27/14
2/1

I call it Seventh Heaven.

John.

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Ok, my memory was off on those chords - BUT - you can see for yourself what
> I did.
>
> The improvisation was the 3rd try at doing something with the tuning - as I
> said time was short.
>
> The piano roll view is here:
>
> http://micro.soonlabel.com/just/john20110212/john-revised-score.jpg
>
> Chris
>
> On Sat, Feb 12, 2011 at 4:30 PM, <chrisvaisvil@...> wrote:
>
> > John,
> >
> > It was an improvisation with a little bit of edits. I had 15 minutes before
> > leaving to visit a fish store with my wife. (Aquarium). Right now I'm in a
> > laundry mat drinking a diet coke. I say all that as explanation as to why
> > don't know the answer with certainty. I doubt I used all 20 notes in an
> > octave span but I'm sure I came close. Reasonable Chords were achievable by
> > constructing extended augmented triads. Playing a diatonic type scale worked
> > if a major or minor third was included as needed in the run.
> >
> > I will be glad to provide a piano roll view later and that would let you
> > visually see the note usage.
> >
> > Chis
> > ------------------------------
> > *From: * "john777music" <jfos777@...>
> > *Sender: * tuning@yahoogroups.com
> > *Date: *Sat, 12 Feb 2011 19:30:50 -0000
> > *To: *<tuning@yahoogroups.com>
> > *ReplyTo: * tuning@yahoogroups.com
> > *Subject: *[tuning] Re: Interval Calculator
> >
> >
> >
> > Chris, does the piece use all 20 notes or just a subset?
> >
> > --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@> wrote:
> > >
> > > Here you go.
> > >
> > >
> > http://micro.soonlabel.com/just/john20110212/daily201012-john-revised-mubaraks-dilemma.mp3
> > >
> > > online play
> > >
> > > http://improvfriday.ning.com/xn/detail/4162021:Comment:24752
> > >
> > >
> > > Chris
> > >
> > > On Sat, Feb 12, 2011 at 1:26 PM, john777music <jfos777@> wrote:
> > >
> > > >
> > > >
> > > > Hi Chris,
> > > >
> > > > wanna try composing something in the scale below?
> > > >
> > > > John.
> > > >
> > > >
> > > > --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@> wrote:
> > > > >
> > > > > Ok,
> > > > >
> > > > > I put them in ascending order and popped them into scala
> > > > >
> > > > > 0: 1/1 0.000 unison, perfect prime
> > > > > 1: 9/8 203.910 major whole tone
> > > > > 2: 8/7 231.174 septimal whole tone
> > > > > 3: 7/6 266.871 septimal minor third
> > > > > 4: 6/5 315.641 minor third
> > > > > 5: 5/4 386.314 major third
> > > > > 6: 9/7 435.084 septimal major third, BP third
> > > > > 7: 4/3 498.045 perfect fourth
> > > > > 8: 11/8 551.318 undecimal semi-augmented fourth
> > > > > 9: 7/5 582.512 septimal or Huygens' tritone, BP
> > > > > fourth
> > > > > 10: 10/7 617.488 Euler's tritone
> > > > > 11: 3/2 701.955 perfect fifth
> > > > > 12: 11/7 782.492 undecimal augmented fifth
> > > > > 13: 8/5 813.686 minor sixth
> > > > > 14: 5/3 884.359 major sixth, BP sixth
> > > > > 15: 12/7 933.129 septimal major sixth
> > > > > 16: 7/4 968.826 harmonic seventh
> > > > > 17: 9/5 1017.596 just minor seventh, BP seventh
> > > > > 18: 11/6 1049.363 21/4-tone, undecimal neutral seventh
> > > > > 19: 13/7 1071.702 16/3-tone
> > > > > 20: 2/1 1200.000 octave
> > > > >
> > > > > and here is the scala formatted version
> > > > >
> > > > > ! E:\Cakewalk\scales\john20110212.scl
> > > > > !
> > > > > john 2011 02 12 best
> > > > > 20
> > > > > !
> > > > > 9/8
> > > > > 8/7
> > > > > 7/6
> > > > > 6/5
> > > > > 5/4
> > > > > 9/7
> > > > > 4/3
> > > > > 11/8
> > > > > 7/5
> > > > > 10/7
> > > > > 3/2
> > > > > 11/7
> > > > > 8/5
> > > > > 5/3
> > > > > 12/7
> > > > > 7/4
> > > > > 9/5
> > > > > 11/6
> > > > > 13/7
> > > > > 2/1
> > > > >
> > > >
> > > >
> > > >
> > >
> >
> >
> >
>

Hi John,

It is very easy to understand how its mapped and hard to play on a regular
keyboard.

Pianoteq (and most any software synthesizer) simply does a linear mapping of
pitch to midi note number. (there are other options - but this is for later)
For instance C4 = midi note number 60
look at this chart
http://tomscarff.110mb.com/midi_analyser/midi_note_numbers_for_octaves.htm

So then, lets say pianoteq started where 1/1 was midi note 60 it would then
assign a consecutive midi note number for the next higher note in your
tuning. So for instance using your tuning below 15/14 = midi note 61, 8/7 =
midi note 62, and so on until all of the notes were mapped. Then the process
repeats itself, usually at the octave.

So, now we have a scale with 20 consecutive notes - and the octave is 20
steps, not 12 steps apart - for example the Mubarak piece I wrote in your 20
note tuning the C and minor 13th (A flat + octave above) was the interval
played to sound like an octave. One (simplified) approach I take in
improvising alternate tunings is to mentally map a few intervals as ones I
can use as stable resting points and then I move from one stable point to
another. Of course, you have to find the appropriate melodic path, and
chordal voice leading comes into play as well. And things can get even more
detailed if you push for greater amounts of counterpoint - especially when I
score a piece. You will notice that *usually* my piano improvisations, while
still decidedly polyphonic, are *often* two melodic lines divided between my
hands. Its a fairly natural thing to do I'd think. And as my skill as a
keyboard player increases I'm able to do more of what I hear in my mind's
ear.

Chris

On Sun, Feb 13, 2011 at 12:11 PM, john777music <jfos777@...> wrote:

>
>
> Thanks Chris,
>
> I asked because the scale has 20 notes and a keyboard has only 12 per
> octave. How would you work with 20 keys per octave?
>
> Here's another scale for you if you're interested...
>
> 1/1
> 15/14
> 8/7
> 7/6
> 9/7
> 21/16
> 7/5
> 10/7
> 14/9
> 12/7
> 7/4
> 27/14
> 2/1
>
> I call it Seventh Heaven.
>
>
> John.
>
> --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
> >
> > Ok, my memory was off on those chords - BUT - you can see for yourself
> what
> > I did.
> >
> > The improvisation was the 3rd try at doing something with the tuning - as
> I
> > said time was short.
> >
> > The piano roll view is here:
> >
> > http://micro.soonlabel.com/just/john20110212/john-revised-score.jpg
> >
> > Chris
> >
> > On Sat, Feb 12, 2011 at 4:30 PM, <chrisvaisvil@...> wrote:
> >
> > > John,
> > >
> > > It was an improvisation with a little bit of edits. I had 15 minutes
> before
> > > leaving to visit a fish store with my wife. (Aquarium). Right now I'm
> in a
> > > laundry mat drinking a diet coke. I say all that as explanation as to
> why
> > > don't know the answer with certainty. I doubt I used all 20 notes in an
> > > octave span but I'm sure I came close. Reasonable Chords were
> achievable by
> > > constructing extended augmented triads. Playing a diatonic type scale
> worked
> > > if a major or minor third was included as needed in the run.
> > >
> > > I will be glad to provide a piano roll view later and that would let
> you
> > > visually see the note usage.
> > >
> > > Chis
> > > ------------------------------
> > > *From: * "john777music" <jfos777@...>
> > > *Sender: * tuning@yahoogroups.com
>
> > > *Date: *Sat, 12 Feb 2011 19:30:50 -0000
> > > *To: *<tuning@...m>
> > > *ReplyTo: * tuning@yahoogroups.com
> > > *Subject: *[tuning] Re: Interval Calculator
> > >
> > >
> > >
> > > Chris, does the piece use all 20 notes or just a subset?
> > >
> > > --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@> wrote:
> > > >
> > > > Here you go.
> > > >
> > > >
> > >
> http://micro.soonlabel.com/just/john20110212/daily201012-john-revised-mubaraks-dilemma.mp3
> > > >
> > > > online play
> > > >
> > > > http://improvfriday.ning.com/xn/detail/4162021:Comment:24752
> > > >
> > > >
> > > > Chris
> > > >
> > > > On Sat, Feb 12, 2011 at 1:26 PM, john777music <jfos777@> wrote:
> > > >
> > > > >
> > > > >
> > > > > Hi Chris,
> > > > >
> > > > > wanna try composing something in the scale below?
> > > > >
> > > > > John.
> > > > >
> > > > >
> > > > > --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@>
> wrote:
> > > > > >
> > > > > > Ok,
> > > > > >
> > > > > > I put them in ascending order and popped them into scala
> > > > > >
> > > > > > 0: 1/1 0.000 unison, perfect prime
> > > > > > 1: 9/8 203.910 major whole tone
> > > > > > 2: 8/7 231.174 septimal whole tone
> > > > > > 3: 7/6 266.871 septimal minor third
> > > > > > 4: 6/5 315.641 minor third
> > > > > > 5: 5/4 386.314 major third
> > > > > > 6: 9/7 435.084 septimal major third, BP third
> > > > > > 7: 4/3 498.045 perfect fourth
> > > > > > 8: 11/8 551.318 undecimal semi-augmented fourth
> > > > > > 9: 7/5 582.512 septimal or Huygens' tritone, BP
> > > > > > fourth
> > > > > > 10: 10/7 617.488 Euler's tritone
> > > > > > 11: 3/2 701.955 perfect fifth
> > > > > > 12: 11/7 782.492 undecimal augmented fifth
> > > > > > 13: 8/5 813.686 minor sixth
> > > > > > 14: 5/3 884.359 major sixth, BP sixth
> > > > > > 15: 12/7 933.129 septimal major sixth
> > > > > > 16: 7/4 968.826 harmonic seventh
> > > > > > 17: 9/5 1017.596 just minor seventh, BP seventh
> > > > > > 18: 11/6 1049.363 21/4-tone, undecimal neutral seventh
> > > > > > 19: 13/7 1071.702 16/3-tone
> > > > > > 20: 2/1 1200.000 octave
> > > > > >
> > > > > > and here is the scala formatted version
> > > > > >
> > > > > > ! E:\Cakewalk\scales\john20110212.scl
> > > > > > !
> > > > > > john 2011 02 12 best
> > > > > > 20
> > > > > > !
> > > > > > 9/8
> > > > > > 8/7
> > > > > > 7/6
> > > > > > 6/5
> > > > > > 5/4
> > > > > > 9/7
> > > > > > 4/3
> > > > > > 11/8
> > > > > > 7/5
> > > > > > 10/7
> > > > > > 3/2
> > > > > > 11/7
> > > > > > 8/5
> > > > > > 5/3
> > > > > > 12/7
> > > > > > 7/4
> > > > > > 9/5
> > > > > > 11/6
> > > > > > 13/7
> > > > > > 2/1
> > > > > >
> > > > >
> > > > >
> > > > >
> > > >
> > >
> > >
> > >
> >
>
>
>