Topic: Re: [MMM] Re: mixing Equal Temperaments of 11 & 7
1 scales
| File | Description | Notes | Period (ยข) |
|---|---|---|---|
| 7-and-12 | 7-note and 12-note equal temperament, coinciding on Bb | 18 | 1200.0 |
Thread (15 messages)
From: Phil Collins (2007-02-03) Subject: Re: [MMM] Re: mixing Equal Temperaments of 11 & 7 hi monz, Thank you for replying to my posting. Unfortunately, I am very new to the intricacies of tuning jargon and the math end of it is an obstinate impediment. I have become accustomed with some of the just ratios and the cents-o-meter, but not much further than that. I'm not familiar with EDO. When I went to the site you gave me, I found a series of numbers and signs that I don't understand. anyway, I appreciate it. I'm going to NZ to give talk about the matter this week and I've at least got some hands-on experiementation under my belt. Phil monz wrote:Hi Phil, --- In [email protected], "fikolanzo" <pmcomp@...> wrote: > > I am working on ways to combine and integrate 7-tone > Thai Equal Temperament with Western 11-tone Equal Temperament. > I would like advise from anyone who has experience and/or > solutions regarding the possibilities and problems of this > matter. thank you. I am not interested in altering either > system, except to have the Thai instruments tune to > Bb=466.165, according to western equal temperament. > thank you, > Phil It took me about 2 minutes to create a Tonescape .tuning file of this: http://launch.groups.yahoo.com/group/MakeMicroMusic/files/monz/7-and-11-edo-combined_phil_mmm15852.tuning On the Lattice, i have 11-edo on the horizontal axis and 7-edo on the vertical, and each step along a Lattice axis represents one degree of the EDO, with the origin at the center. I wasn't sure if you wanted the origin to be tuned to the Bb 466.165 Hz, so i left it at the default A 440. You can go to "File | Reference Pitch" to change that ... but BE SURE TO TYPE THE KEYBOARD 'ENTER' KEY WHILE THE MOUSE IS POSITIONED OVER THE SLIDER! in order to have Tonescape accept the change. You can download Tonescape from my website homepage. -monz http://tonalsoft.com Tonescape microtonal music software
From: monz (2007-02-03) Subject: [MMM] Re: mixing Equal Temperaments of 11 & 7 Hi Phil, EDO is an acronym for "Equal Division of the Octave". Basically it just means the same thing as "Equal Temperament", but because an equal temperament can be an equal division of some other interval instead of an octave, EDO makes it more definite. I set up your tuning as a Tonescape file in such a simple way that you really don't need to understand anything more than you already do, in order to play around with it and compose some music. So to help avoid the confusion, here's the direct link to the software: http://tonalsoft.com/downloads/redist/Tonescape_Studio_Den_Haag.exe If you have a Windows XP system with the necessary hardware, you can download Tonescape, load your tuning, and start composing! Tonescape has two main windows: . one called Pitch-Height which is similar to the familiar "piano-roll" view found on most MIDI sequencers, except that it's quantized to whatever spacing your tuning has (instead of the standard 12-EDO); and . the Lattice window, which shows the harmonic relationships between the notes of your tuning. From your first post i knew that you're a newbie to all this, so i kept the Lattice of your tuning simple by just putting 11-EDO along one axis and 7-EDO along the other, and using the step-size of each tuning as the axis steps on the Lattice. Hopefully you can get Tonescape working and try it out. PS -- Are you the Phil Collins who was a superstar in the '80s? -monz http://tonalsoft.com Tonescape microtonal music software --- In [email protected], Phil Collins <pmcomp@...> wrote: > > hi monz, > Thank you for replying to my posting. Unfortunately, > I am very new to the intricacies of tuning jargon and > the math end of it is an obstinate impediment. I have > become accustomed with some of the just ratios and > the cents-o-meter, but not much further than that. > I'm not familiar with EDO. When I went to the site > you gave me, I found a series of numbers and signs > that I don't understand. anyway, I appreciate it. > I'm going to NZ to give talk about the matter this > week and I've at least got some hands-on experiementation > under my belt. > > Phil > > > monz wrote:Hi Phil, > > > --- In [email protected], "fikolanzo" <pmcomp@> wrote: > > > > I am working on ways to combine and integrate 7-tone > > Thai Equal Temperament with Western 11-tone Equal Temperament. > > I would like advise from anyone who has experience and/or > > solutions regarding the possibilities and problems of this > > matter. thank you. I am not interested in altering either > > system, except to have the Thai instruments tune to > > Bb=466.165, according to western equal temperament. > > thank you, > > Phil > > > It took me about 2 minutes to create a Tonescape > .tuning file of this: > > http://launch.groups.yahoo.com/group/MakeMicroMusic/files/monz/7-and-11-edo-combined_phil_mmm15852.tuning > > > > On the Lattice, i have 11-edo on the horizontal axis and > 7-edo on the vertical, and each step along a Lattice axis > represents one degree of the EDO, with the origin at the > center. > > I wasn't sure if you wanted the origin to be tuned > to the Bb 466.165 Hz, so i left it at the default > A 440. You can go to "File | Reference Pitch" to > change that ... but BE SURE TO TYPE THE KEYBOARD > 'ENTER' KEY WHILE THE MOUSE IS POSITIONED OVER > THE SLIDER! in order to have Tonescape accept the change. > > > You can download Tonescape from my website homepage.
From: Rick McGowan (2007-02-03) Subject: Re: [MMM] Re: mixing Equal Temperaments of 11 & 7 > I am working on ways to combine and integrate 7-tone > Thai Equal Temperament with Western 11-tone Equal Temperament. Are you all sure the question was really about "11"? And that "11" isn't really a typo for "12"? After all, "11" isn't the ordinary western tuning, and I don't know why someone would be interested in integrating 11 and 7 together, unless they have some orchestra of non-Western instruments in 11 tones/octave. Rick
From: Phil Collins (2007-02-03) Subject: Re: [MMM] Re: mixing Equal Temperaments of 11 & 7 monz, that is very nice to know. One impediment, I'm a Mac-guy. I will be copy your info and take it to NZland, where I surely will be able to avail myself upon a PC person to try it out. If you can recommend a Mac-way to get there, I'd love to know. Thanks for your time and effort. Phil monz wrote: > Hi Phil, > > > EDO is an acronym for "Equal Division of the Octave". > Basically it just means the same thing as "Equal Temperament", > but because an equal temperament can be an equal division > of some other interval instead of an octave, EDO makes > it more definite. > > I set up your tuning as a Tonescape file in such a > simple way that you really don't need to understand > anything more than you already do, in order to play > around with it and compose some music. So to help avoid > the confusion, here's the direct link to the software: > > http://tonalsoft.com/downloads/redist/Tonescape_Studio_Den_Haag.exe > > > If you have a Windows XP system with the necessary > hardware, you can download Tonescape, load your tuning, > and start composing! > > Tonescape has two main windows: > > . one called Pitch-Height which is similar to the > familiar "piano-roll" view found on most MIDI sequencers, > except that it's quantized to whatever spacing your > tuning has (instead of the standard 12-EDO); and > > . the Lattice window, which shows the harmonic > relationships between the notes of your tuning. > > > >From your first post i knew that you're a newbie > to all this, so i kept the Lattice of your tuning > simple by just putting 11-EDO along one axis and > 7-EDO along the other, and using the step-size of > each tuning as the axis steps on the Lattice. > > > Hopefully you can get Tonescape working and try it out. > > > PS -- Are you the Phil Collins who was a superstar > in the '80s? > > > -monz > http://tonalsoft.com > Tonescape microtonal music software > > > > --- In [email protected], Phil Collins <pmcomp@...> > wrote: > > > > hi monz, > > Thank you for replying to my posting. Unfortunately, > > I am very new to the intricacies of tuning jargon and > > the math end of it is an obstinate impediment. I have > > become accustomed with some of the just ratios and > > the cents-o-meter, but not much further than that. > > I'm not familiar with EDO. When I went to the site > > you gave me, I found a series of numbers and signs > > that I don't understand. anyway, I appreciate it. > > I'm going to NZ to give talk about the matter this > > week and I've at least got some hands-on experiementation > > under my belt. > > > > Phil > > > > > > monz wrote:Hi Phil, > > > > > > --- In [email protected], "fikolanzo" <pmcomp@> wrote: > > > > > > I am working on ways to combine and integrate 7-tone > > > Thai Equal Temperament with Western 11-tone Equal Temperament. > > > I would like advise from anyone who has experience and/or > > > solutions regarding the possibilities and problems of this > > > matter. thank you. I am not interested in altering either > > > system, except to have the Thai instruments tune to > > > Bb=466.165, according to western equal temperament. > > > thank you, > > > Phil > > > > > > It took me about 2 minutes to create a Tonescape > > .tuning file of this: > > > > > h > tp://launch.groups.yahoo.com/group/MakeMicroMusic/files/monz/7-and-11-edo-combined_phil_mmm15852.tuning > > > > > > > > > On the Lattice, i have 11-edo on the horizontal axis and > > 7-edo on the vertical, and each step along a Lattice axis > > represents one degree of the EDO, with the origin at the > > center. > > > > I wasn't sure if you wanted the origin to be tuned > > to the Bb 466.165 Hz, so i left it at the default > > A 440. You can go to "File | Reference Pitch" to > > change that ... but BE SURE TO TYPE THE KEYBOARD > > 'ENTER' KEY WHILE THE MOUSE IS POSITIONED OVER > > THE SLIDER! in order to have Tonescape accept the change. > > > > > > You can download Tonescape from my website homepage. > > > > > > >
From: Phil Collins (2007-02-03) Subject: Re: [MMM] Re: mixing Equal Temperaments of 11 & 7 Rick, you are correct, sir! it's a misnomer (number) that evolved over time following a friend's likening my situation to modern conveniance of 7-11 I do indeed mean 12. your mentioning of it is a welcome cautioning before I get too hung up on marketing. Phil Rick McGowan wrote: > I am working on ways to combine and integrate 7-tone > Thai Equal Temperament with Western 11-tone Equal Temperament. Are you all sure the question was really about "11"? And that "11" isn't really a typo for "12"? After all, "11" isn't the ordinary western tuning, and I don't know why someone would be interested in integrating 11 and 7 together, unless they have some orchestra of non-Western instruments in 11 tones/octave. Rick
From: Gene Ward Smith (2007-02-03) Subject: [MMM] Re: mixing Equal Temperaments of 11 & 7 --- In [email protected], "monz" <monz@...> wrote: > EDO is an acronym for "Equal Division of the Octave". > Basically it just means the same thing as "Equal Temperament", > but because an equal temperament can be an equal division > of some other interval instead of an octave, EDO makes > it more definite. EDO does not entail that it is a temperament.
From: monz (2007-02-03) Subject: Re: mixing Equal Temperaments of 11 & 7 Hi Phil, No, sorry -- Tonescape is Windows-only, unless the new Mac-with-Windows will run it, which i'm not sure of. -monz http://tonalsoft.com Tonescape microtonal music software --- In [email protected], Phil Collins <pmcomp@...> wrote: > > monz, > that is very nice to know. One impediment, I'm a Mac-guy. > I will be copy your info and take it to NZland, where I > surely will be able to avail myself upon a PC person to > try it out. If you can recommend a Mac-way to get there, > I'd love to know. > Thanks for your time and effort. > Phil
From: monz (2007-02-03) Subject: [MMM] Re: mixing Equal Temperaments of 11 & 7 --- In [email protected], "Gene Ward Smith" <genewardsmith@...> wrote: > > --- In [email protected], "monz" <monz@> wrote: > > > EDO is an acronym for "Equal Division of the Octave". > > Basically it just means the same thing as "Equal Temperament", > > but because an equal temperament can be an equal division > > of some other interval instead of an octave, EDO makes > > it more definite. > > EDO does not entail that it is a temperament. Yes, of course i should have added that comment myself. -monz
From: monz (2007-02-03) Subject: [MMM] Re: mixing Equal Temperaments of 11 & 7 Hi Phil, Darn, and i thought you were doing something *really* new! OK, it will only take me a couple of minutes to make a new Tonescape .tuning file for you ... voila: http://launch.groups.yahoo.com/group/MakeMicroMusic/files/monz/mixed-7-edo-and-12-edo_2d_degree-space.tuning -monz http://tonalsoft.com Tonescape microtonal music software --- In [email protected], Phil Collins <pmcomp@...> wrote: > > Rick, > you are correct, sir! > it's a misnomer (number) that evolved over time following > a friend's likening my situation to modern conveniance > of 7-11 I do indeed mean 12. > > your mentioning of it is a welcome cautioning before I > get too hung up on marketing. > Phil
From: Rick McGowan (2007-02-03) Subject: Re: [MMM] Re: mixing Equal Temperaments of 11 & 7 Hi Phil, > it's a misnomer (number) that evolved over time following > a friend's likening my situation to modern conveniance of 7-11 Yes, I thought you were probably talking 7 with 12 equal. OK, so what you're trying to do is play some Thai instruments that are tuned to 7 equal, with some ordinary Western instruments that are tuned to 12-equal. Not too hard. The Thai instruments give more-or-less 1200 / 7 = 171.42857 cents per step, resulting in intervals of approximately: 171.42857 * 2 = 342.8 cents 171.42857 * 3 = 514.3 cents 171.42857 * 4 = 685.7 cents 171.42857 * 5 = 857.1 cents 171.42857 * 6 = 1028.5 cents ...and then the octave. So, if you play on the Western instruments in B-flat, you'll sort-of-maybe-a-little-bit sync up at: E-flat: the perfect 4th, or 514 cents Thai, 500 cents Western, F: the perfect 5th, or 685.7 cents Thai, 700 cents Western, A-flat: the minor 7th, or 1028.5 cents Thai, 1000 cents Western That's about the best you can hope for in terms of being pretty close in the unisons. Your Thai 3rd won't match D or D-flat, but you can probably use either of those for "inflections" in the Western instruments and be OK. Pentatonic stuff works pretty well. Let's see how this works in practice. Here is short musical example. A kind of xylphone-like sound in 7-equal coupled with a reed-like thing in 12-equal. First the xylo plays its 7-tone scale, then the reed plays a 7-tone diatonic scale, then they play a bit of so-called music together: http://rm-and-jo.laughingsquid.org/temp/Test-7-12.mp3 This is in "C", but by the same principle, if your Thai instruments are tuned to a B-flat, and you play in B-flat, this is the kind of sound you'll get if you play in a sort of pentatonic way. Your mileage may vary. Rick
From: Kraig Grady (2007-02-03) Subject: Re: [MMM] Re: mixing Equal Temperaments of 11 & 7 the idea that the Thailand used 7 equal was introduced by Europeans in the 19th century. .What the term equal means to them and us , like in many parts of Africa,means different things. Rick McGowan wrote: > Hi Phil, > > >> it's a misnomer (number) that evolved over time following >> a friend's likening my situation to modern conveniance of 7-11 >> > > Yes, I thought you were probably talking 7 with 12 equal. > > OK, so what you're trying to do is play some Thai instruments that are > tuned to 7 equal, with some ordinary Western instruments that are tuned to > 12-equal. Not too hard. > > The Thai instruments give more-or-less 1200 / 7 = 171.42857 cents per > step, resulting in intervals of approximately: > > 171.42857 * 2 = 342.8 cents > 171.42857 * 3 = 514.3 cents > 171.42857 * 4 = 685.7 cents > 171.42857 * 5 = 857.1 cents > 171.42857 * 6 = 1028.5 cents > ...and then the octave. > > So, if you play on the Western instruments in B-flat, you'll > sort-of-maybe-a-little-bit sync up at: > > E-flat: the perfect 4th, or 514 cents Thai, 500 cents Western, > F: the perfect 5th, or 685.7 cents Thai, 700 cents Western, > A-flat: the minor 7th, or 1028.5 cents Thai, 1000 cents Western > > That's about the best you can hope for in terms of being pretty close in > the unisons. Your Thai 3rd won't match D or D-flat, but you can probably > use either of those for "inflections" in the Western instruments and be OK. > Pentatonic stuff works pretty well. > > Let's see how this works in practice. Here is short musical example. A > kind of xylphone-like sound in 7-equal coupled with a reed-like thing in > 12-equal. First the xylo plays its 7-tone scale, then the reed plays a > 7-tone diatonic scale, then they play a bit of so-called music together: > > http://rm-and-jo.laughingsquid.org/temp/Test-7-12.mp3 > > This is in "C", but by the same principle, if your Thai instruments are > tuned to a B-flat, and you play in B-flat, this is the kind of sound you'll > get if you play in a sort of pentatonic way. Your mileage may vary. > > Rick > > > > Yahoo! Groups Links > > > > > > -- Kraig Grady North American Embassy of Anaphoria Island <http://anaphoria.com/index.html> The Wandering Medicine Show KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles
From: Phil Collins (2007-02-03) Subject: Re: [MMM] Re: mixing Equal Temperaments of 11 & 7 hi Rick, Thanks for the information, the mp3 file, and advice. I already have my virginal tuned to Bb, 7-tone ET and am familiar with the comparative ratios on paper as well as by ear. The explorations of late have been more about the special relationships that suggest special musical possibilities/contexts to my ear. I am curious what, if any, musical constructs have occurred. I will try your mp3 in a little bit. The instruments of Thai culture have different ways of elaborating upon the 7-tone ET. I should mention that the Thai and Cambodian music I've encountered is not exactingly true to 171.42 per step; the confluence of Western and other musical sources have had diverse affects on their tuning practices. again, thank you very much, Phil Rick McGowan wrote: Hi Phil, > it's a misnomer (number) that evolved over time following > a friend's likening my situation to modern conveniance of 7-11 Yes, I thought you were probably talking 7 with 12 equal. OK, so what you're trying to do is play some Thai instruments that are tuned to 7 equal, with some ordinary Western instruments that are tuned to 12-equal. Not too hard. The Thai instruments give more-or-less 1200 / 7 = 171.42857 cents per step, resulting in intervals of approximately: 171.42857 * 2 = 342.8 cents 171.42857 * 3 = 514.3 cents 171.42857 * 4 = 685.7 cents 171.42857 * 5 = 857.1 cents 171.42857 * 6 = 1028.5 cents ...and then the octave. So, if you play on the Western instruments in B-flat, you'll sort-of-maybe-a-little-bit sync up at: E-flat: the perfect 4th, or 514 cents Thai, 500 cents Western, F: the perfect 5th, or 685.7 cents Thai, 700 cents Western, A-flat: the minor 7th, or 1028.5 cents Thai, 1000 cents Western That's about the best you can hope for in terms of being pretty close in the unisons. Your Thai 3rd won't match D or D-flat, but you can probably use either of those for "inflections" in the Western instruments and be OK. Pentatonic stuff works pretty well. Let's see how this works in practice. Here is short musical example. A kind of xylphone-like sound in 7-equal coupled with a reed-like thing in 12-equal. First the xylo plays its 7-tone scale, then the reed plays a 7-tone diatonic scale, then they play a bit of so-called music together: http://rm-and-jo.laughingsquid.org/temp/Test-7-12.mp3 This is in "C", but by the same principle, if your Thai instruments are tuned to a B-flat, and you play in B-flat, this is the kind of sound you'll get if you play in a sort of pentatonic way. Your mileage may vary. Rick
From: Phil Collins (2007-02-03) Subject: Re: [MMM] Re: mixing Equal Temperaments of 11 & 7 hi Rick, Thanks for the information, the mp3 file, and advice. I already have my virginal tuned to Bb, 7-tone ET and have been experimenting in complicity with my standard synthesizer. Also, composer Jeff Harrington has been extremely generous by providing me a Bb-based 7-tone ET scale from which to tune from. I am familiar with the comparative ratios between Thai and I on paper as well as by ear. They are sinking in through practice and (rather oddly) my dreams. The explorations of late have been more about the special relationships that suggest special musical possibilities/contexts to my ear. I am curious what, if any, musical constructs have occurred. I will try your mp3 in a little bit. The instruments of Thai culture have different ways of elaborating upon the 7-tone ET. I should mention that the Thai and Cambodian music I've encountered is not exactingly true to 171.42 per step; the confluence of Western and other musical sources have had diverse affects on their tuning practices. again, thank you very much, Phil Rick McGowan wrote: Hi Phil, > it's a misnomer (number) that evolved over time following > a friend's likening my situation to modern conveniance of 7-11 Yes, I thought you were probably talking 7 with 12 equal. OK, so what you're trying to do is play some Thai instruments that are tuned to 7 equal, with some ordinary Western instruments that are tuned to 12-equal. Not too hard. The Thai instruments give more-or-less 1200 / 7 = 171.42857 cents per step, resulting in intervals of approximately: 171.42857 * 2 = 342.8 cents 171.42857 * 3 = 514.3 cents 171.42857 * 4 = 685.7 cents 171.42857 * 5 = 857.1 cents 171.42857 * 6 = 1028.5 cents ...and then the octave. So, if you play on the Western instruments in B-flat, you'll sort-of-maybe-a-little-bit sync up at: E-flat: the perfect 4th, or 514 cents Thai, 500 cents Western, F: the perfect 5th, or 685.7 cents Thai, 700 cents Western, A-flat: the minor 7th, or 1028.5 cents Thai, 1000 cents Western That's about the best you can hope for in terms of being pretty close in the unisons. Your Thai 3rd won't match D or D-flat, but you can probably use either of those for "inflections" in the Western instruments and be OK. Pentatonic stuff works pretty well. Let's see how this works in practice. Here is short musical example. A kind of xylphone-like sound in 7-equal coupled with a reed-like thing in 12-equal. First the xylo plays its 7-tone scale, then the reed plays a 7-tone diatonic scale, then they play a bit of so-called music together: http://rm-and-jo.laughingsquid.org/temp/Test-7-12.mp3 This is in "C", but by the same principle, if your Thai instruments are tuned to a B-flat, and you play in B-flat, this is the kind of sound you'll get if you play in a sort of pentatonic way. Your mileage may vary. Rick
From: monz (2007-02-03) Subject: Re: mixing Equal Temperaments of 11 & 7 Hi Phil and Rick, --- In [email protected], Rick McGowan <rick@...> wrote: > So, if you play on the Western instruments in B-flat, you'll > sort-of-maybe-a-little-bit sync up at: > > E-flat: the perfect 4th, or 514 cents Thai, 500 cents Western, > F: the perfect 5th, or 685.7 cents Thai, 700 cents Western, > A-flat: the minor 7th, or 1028.5 cents Thai, 1000 cents Western > > That's about the best you can hope for in terms of being > pretty close in the unisons. Your Thai 3rd won't match > D or D-flat, but you can probably use either of those > for "inflections" in the Western instruments and be OK. The simplest notation to use to see how they intersect is 84-edo (7*12=84). The pitches of each tuning in ascending order in 84-edo notation are: . 7-edo: 0, 12, 24, 36, 48, 60, 72, 84=0 . 12-edo: 0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84=0 The two close ones are the E-flat and F, which are only one step away in 84-edo. The A-flats are the same distance apart as the Ds: 2 steps of 84-edo. The union of the two is a perfectly symmetrical tuning. In steps of 84-edo, the comparison of close intervals is: E-flat: Thai: 3/7 = 36/84, Western: 5/12 = 35/84 F: Thai: 4/7 = 48/84, Western: 7/12 = 49/84 If you are looking at this in Tonescape, click on the blue Lattice background, "Select Notation" from the pop-up menu, choose "Logarithmic" from the list, leave "Interval Magnitude" set at 2.000, and type "84" into the "Divisions" box, then click the "OK" button. Your Lattice will give all pitches in steps of 84-edo. link to the Tonescape .tuning file: http://launch.groups.yahoo.com/group/MakeMicroMusic/files/monz/mixed-7-edo-and-1\ 2-edo_2d_degree-space.tuning -monz http://tonalsoft.com Tonescape microtonal music software
From: Herman Miller (2007-02-04) Subject: Re: [MMM] Re: mixing Equal Temperaments of 11 & 7 Phil Collins wrote: > monz, > that is very nice to know. One impediment, I'm a Mac-guy. I will be copy > your info and take it to NZland, where I surely will be able to avail > myself upon a PC person to try it out. If you can recommend a Mac-way to > get there, I'd love to know. > Thanks for your time and effort. > Phil Scala is available for Mac, and it's great for figuring out properties of different scales. http://www.xs4all.nl/~huygensf/scala/downloads.html You can start by typing "equal 12" to get a 12-note scale, then add the extra notes of the 7-note scale and sort. ! 7-and-12.scl ! 7-note and 12-note equal temperament, coinciding on Bb 18 ! 100.00000 142.85714 200.00000 300.00000 314.28571 400.00000 485.71429 500.00000 600.00000 657.14286 700.00000 800.00000 828.57143 900.00000 1000.00000 1100.00000 1171.42875 2/1 You can see that there are some very small intervals in this scale, including two small steps of 14.286 cents. There's also a good minor third at 314.286 cents. Scala can show you a complete list of intervals by typing "show intervals".