Just Intonation Composition
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Just Intonation Composition
I'm currently doing some research and experimentation with justly tuned composition. Is there anyone else on here who has experience with this stuff?
If you don't know who Harry Partch is, you probably don't know what I'm talking about.
If you don't know who Harry Partch is, you probably don't know what I'm talking about.
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Just Intonation Composition
I have experience with it only to the degree that most proficient players of non-keyboard instruments and vocalists use it naturally. So any composition written for them would almost by default be written for just temperament.
If you are referring to writing compositions specifically for fixed-intonation instruments like piano but having them tuned in just temperament, then no, I have never done that.
I suppose that one could write for winds/strings and rather than trusting the players' ears to guide them into acoustic perfection, could use some kind of symbols in the music to suggest pitch alterations that would bring the pitch more into line with just temperament for whatever chord/scale was happening at the time. Seems to me that if your players were good enough to pull that off, they would probably be playing in tune already.....
If you are referring to writing compositions specifically for fixed-intonation instruments like piano but having them tuned in just temperament, then no, I have never done that.
I suppose that one could write for winds/strings and rather than trusting the players' ears to guide them into acoustic perfection, could use some kind of symbols in the music to suggest pitch alterations that would bring the pitch more into line with just temperament for whatever chord/scale was happening at the time. Seems to me that if your players were good enough to pull that off, they would probably be playing in tune already.....
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Just Intonation Composition
The trick is that just temperament allows for a lot more pitches per octave than 12, and there are a couple other issues I've come upon as well.
For example, the ratios 6:5, 7:6, 11:9, and 19:16 all refer to minor thirds of varying types. Traditional notation doesn't really help distinguish these.
And modulating can get thorny, too. There are at least three basic routes to take there: modulate to the new pitch without adusting any of the ratios, like old practice before equal temperament hit it big (the main reason why each key is thought to have it's own character - in an unequal temperament, they literally do), play chords justly but modulate via equal temperament as most instrumentalists do nowadays, or modulate via going to the new pitch, keeping the justly tempered tone and adjust all the ratios to that tone, as a capella choirs tend to do. Each will have it's own unique sound.
. . . so how do you notate all of this?
For example, the ratios 6:5, 7:6, 11:9, and 19:16 all refer to minor thirds of varying types. Traditional notation doesn't really help distinguish these.
And modulating can get thorny, too. There are at least three basic routes to take there: modulate to the new pitch without adusting any of the ratios, like old practice before equal temperament hit it big (the main reason why each key is thought to have it's own character - in an unequal temperament, they literally do), play chords justly but modulate via equal temperament as most instrumentalists do nowadays, or modulate via going to the new pitch, keeping the justly tempered tone and adjust all the ratios to that tone, as a capella choirs tend to do. Each will have it's own unique sound.
. . . so how do you notate all of this?
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Just Intonation Composition
Quote from: Andrew Meronek on Dec 31, 2007, 08:01AM
If you don't know who Harry Partch is, you probably don't know what I'm talking about.
There might have been a few around before Harry hit the scene...
If you don't know who Harry Partch is, you probably don't know what I'm talking about.
There might have been a few around before Harry hit the scene...
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Quote from: SilverSonic on Dec 31, 2007, 11:00AMThere might have been a few around before Harry hit the scene...
LOL
Touche!
LOL
Touche!
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Quote from: Andrew Meronek on Dec 31, 2007, 10:58AMThe trick is that just temperament allows for a lot more pitches per octave than 12, and there are a couple other issues I've come upon as well.......
. . . so how do you notate all of this?
Okay, I see what you are getting at now. You want all the possible permutations of just temperament available on call. The only way I see this happening accurately in a performance situation would be either with tunable instruments (piano, harp, etc.) or electronics. The notation would be to specify the exact tunings in Hz in the score. Then in performance, players would have to switch instruments at the appropriate times. Certain instruments might be able to be re-tuned on the fly.
That's the real world. In theory, you absolutely could come up with a reasonably concise and specific notation system for performance by "ear-tuned" instruments or voice. I'm not sure what that would look like but I'm sure it could be done. But I'm not sure it would ever be able to be performed accurately unless it was very simple stuff musically.
. . . so how do you notate all of this?
Okay, I see what you are getting at now. You want all the possible permutations of just temperament available on call. The only way I see this happening accurately in a performance situation would be either with tunable instruments (piano, harp, etc.) or electronics. The notation would be to specify the exact tunings in Hz in the score. Then in performance, players would have to switch instruments at the appropriate times. Certain instruments might be able to be re-tuned on the fly.
That's the real world. In theory, you absolutely could come up with a reasonably concise and specific notation system for performance by "ear-tuned" instruments or voice. I'm not sure what that would look like but I'm sure it could be done. But I'm not sure it would ever be able to be performed accurately unless it was very simple stuff musically.
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. . . so performances by the Kronos Quartet and the Kepler Quartet don't count?
![Image](http://tromboneforum.org/Smileys/otjf/tongue.gif)
I do know that string quartets are more than capable of handling some just temperament systems having, say, 16 to 20 pitches per octave. As is a certain brass instrument . . .
Oh, and notating the tuning isn't quite as simle an issue. There are two approaches that I've found: pitches based on fequencies, similar to our five-line staff system, or pitches based on their relationship to other pitches.
What little stuff I've been able to find still uses the five line staff, but, depending on the composer, combined the staff with using both ideas: adding more symbols besides sharp signs, flat signs, double sharps, etc. before notes, or literally writing fractions above notes. The former tells you where in your instrument to play a note; the latter tells you what to listen for. The former can get really messy if there are a whole lot of different pitches to deal with; the latter is a lot cleaner with numerous pitches but is completely foreign to most performers and is thus very hard to read.
I've been thinking of a compromise, writing cent adjustments over each note, which makes the fractions much easier to understand in terms of where to play a note on your instrument . . . but you no longer know what to listen for.
![Image](http://tromboneforum.org/Smileys/otjf/tongue.gif)
I do know that string quartets are more than capable of handling some just temperament systems having, say, 16 to 20 pitches per octave. As is a certain brass instrument . . .
Oh, and notating the tuning isn't quite as simle an issue. There are two approaches that I've found: pitches based on fequencies, similar to our five-line staff system, or pitches based on their relationship to other pitches.
What little stuff I've been able to find still uses the five line staff, but, depending on the composer, combined the staff with using both ideas: adding more symbols besides sharp signs, flat signs, double sharps, etc. before notes, or literally writing fractions above notes. The former tells you where in your instrument to play a note; the latter tells you what to listen for. The former can get really messy if there are a whole lot of different pitches to deal with; the latter is a lot cleaner with numerous pitches but is completely foreign to most performers and is thus very hard to read.
I've been thinking of a compromise, writing cent adjustments over each note, which makes the fractions much easier to understand in terms of where to play a note on your instrument . . . but you no longer know what to listen for.
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Just Intonation Composition
Quote from: Andrew Meronek on Jan 01, 2008, 03:08AM . . . so performances by the Kronos Quartet and the Kepler Quartet don't count?
![Image](http://tromboneforum.org/Smileys/otjf/tongue.gif)
Touche.
Okay, apart from very elite small chamber groups that play together constantly, good luck!![Image](http://tromboneforum.org/Smileys/otjf/wink.gif)
QuoteI do know that string quartets are more than capable of handling some just temperament systems having, say, 16 to 20 pitches per octave. As is a certain brass instrument . . .
Which may answer my next question, which is what your intended instrumentation was going to be.
QuoteI've been thinking of a compromise, writing cent adjustments over each note, which makes the fractions much easier to understand in terms of where to play a note on your instrument . . . but you no longer know what to listen for.
Maybe a system of arrows up or down next to the notes, different lengths of arrows indicating how sharp/flat to play the given note. Makes the piece writable in standard notation, which makes it easier to get readings. Then, with practice, the performers can refine the intonations. Might work.![Image](http://tromboneforum.org/Smileys/otjf/dontknow.gif)
![Image](http://tromboneforum.org/Smileys/otjf/tongue.gif)
Touche.
Okay, apart from very elite small chamber groups that play together constantly, good luck!
![Image](http://tromboneforum.org/Smileys/otjf/wink.gif)
QuoteI do know that string quartets are more than capable of handling some just temperament systems having, say, 16 to 20 pitches per octave. As is a certain brass instrument . . .
Which may answer my next question, which is what your intended instrumentation was going to be.
QuoteI've been thinking of a compromise, writing cent adjustments over each note, which makes the fractions much easier to understand in terms of where to play a note on your instrument . . . but you no longer know what to listen for.
Maybe a system of arrows up or down next to the notes, different lengths of arrows indicating how sharp/flat to play the given note. Makes the piece writable in standard notation, which makes it easier to get readings. Then, with practice, the performers can refine the intonations. Might work.
![Image](http://tromboneforum.org/Smileys/otjf/dontknow.gif)
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Just Intonation Composition
Quote from: Dave Tatro on Jan 01, 2008, 10:57AMTouche.
Okay, apart from very elite small chamber groups that play together constantly, good luck!![Image](http://tromboneforum.org/Smileys/otjf/wink.gif)
Which may answer my next question, which is what your intended instrumentation was going to be.
Maybe a system of arrows up or down next to the notes, different lengths of arrows indicating how sharp/flat to play the given note. Makes the piece writable in standard notation, which makes it easier to get readings. Then, with practice, the performers can refine the intonations. Might work.![Image](http://tromboneforum.org/Smileys/otjf/dontknow.gif)
Yeah; I've seen the arrow idea, too. Positively, it's a very straight-foreward, simple tool; negatively, it still doesn't tell the performer what to listen for. And I think it may also be a tool that some composers have tried with some success.
I've even considered using something besides a five line staff; however I know that whatever solution I get, I have to be able to write the music using five line staff notation if I ever want it to be performed, even if it won't be the most ideal way of writing it.
Okay, apart from very elite small chamber groups that play together constantly, good luck!
![Image](http://tromboneforum.org/Smileys/otjf/wink.gif)
Which may answer my next question, which is what your intended instrumentation was going to be.
Maybe a system of arrows up or down next to the notes, different lengths of arrows indicating how sharp/flat to play the given note. Makes the piece writable in standard notation, which makes it easier to get readings. Then, with practice, the performers can refine the intonations. Might work.
![Image](http://tromboneforum.org/Smileys/otjf/dontknow.gif)
Yeah; I've seen the arrow idea, too. Positively, it's a very straight-foreward, simple tool; negatively, it still doesn't tell the performer what to listen for. And I think it may also be a tool that some composers have tried with some success.
I've even considered using something besides a five line staff; however I know that whatever solution I get, I have to be able to write the music using five line staff notation if I ever want it to be performed, even if it won't be the most ideal way of writing it.
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Just Intonation Composition
Pass me down my diamond marimba...
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Quote from: rlb on Jan 01, 2008, 09:01PMPass me down my diamond marimba...
I will, as soon as I dig out my trusty 16 position slide chart!![Image](http://tromboneforum.org/Smileys/otjf/biggrin.gif)
I will, as soon as I dig out my trusty 16 position slide chart!
![Image](http://tromboneforum.org/Smileys/otjf/biggrin.gif)
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Quote from: Andrew Meronek on Jan 01, 2008, 08:33PMYeah; I've seen the arrow idea, too. Positively, it's a very straight-foreward, simple tool; negatively, it still doesn't tell the performer what to listen for. And I think it may also be a tool that some composers have tried with some success.
I've even considered using something besides a five line staff; however I know that whatever solution I get, I have to be able to write the music using five line staff notation if I ever want it to be performed, even if it won't be the most ideal way of writing it.
You might have to create two versions, a "readable" one and a truly specific one. I feel your pain, man!
I'm a little confused about the phrase "negatively, it still doesn't tell the performer what to listen for." What DO you want the performer to listen for? (Sorry if this is a stupid question, but I don't want to erroneously assume the obvious when discussing something nontraditional.
)
I've even considered using something besides a five line staff; however I know that whatever solution I get, I have to be able to write the music using five line staff notation if I ever want it to be performed, even if it won't be the most ideal way of writing it.
You might have to create two versions, a "readable" one and a truly specific one. I feel your pain, man!
I'm a little confused about the phrase "negatively, it still doesn't tell the performer what to listen for." What DO you want the performer to listen for? (Sorry if this is a stupid question, but I don't want to erroneously assume the obvious when discussing something nontraditional.
![Image](http://tromboneforum.org/Smileys/otjf/wink.gif)
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Quote from: Dave Tatro on Jan 02, 2008, 11:48AMYou might have to create two versions, a "readable" one and a truly specific one. I feel your pain, man!
I'm a little confused about the phrase "negatively, it still doesn't tell the performer what to listen for." What DO you want the performer to listen for? (Sorry if this is a stupid question, but I don't want to erroneously assume the obvious when discussing something nontraditional.
)
Five-line staff notation for a single instrument (i.e. you don't see all the notes everyone is playing on your part) cannot tell you what part of the chord you're playing, even with up/down arrows or cent adjustments. I just think it would be neat to be able to tell the performer something like: "your D here is the 5/4 ratio major third." That way, the performer knows what kind of harmonic color to listen for when playing the note. I think that'll ultimately be a more effective way of thinking about controlling tuning and color in ensemble playing than just showing cent adjustments or arrows.
Does that make sense?
I'm a little confused about the phrase "negatively, it still doesn't tell the performer what to listen for." What DO you want the performer to listen for? (Sorry if this is a stupid question, but I don't want to erroneously assume the obvious when discussing something nontraditional.
![Image](http://tromboneforum.org/Smileys/otjf/wink.gif)
Five-line staff notation for a single instrument (i.e. you don't see all the notes everyone is playing on your part) cannot tell you what part of the chord you're playing, even with up/down arrows or cent adjustments. I just think it would be neat to be able to tell the performer something like: "your D here is the 5/4 ratio major third." That way, the performer knows what kind of harmonic color to listen for when playing the note. I think that'll ultimately be a more effective way of thinking about controlling tuning and color in ensemble playing than just showing cent adjustments or arrows.
Does that make sense?
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Quote from: rlb on Jan 01, 2008, 09:01PMPass me down my diamond marimba...
It just so happens that one of the recordings I'm waiting for has as part of the instrumentation a diamond marimba . . .
![Image](http://tromboneforum.org/Smileys/otjf/eek.gif)
It just so happens that one of the recordings I'm waiting for has as part of the instrumentation a diamond marimba . . .
![Image](http://tromboneforum.org/Smileys/otjf/eek.gif)
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Quote from: Andrew Meronek on Jan 02, 2008, 08:18PMFive-line staff notation for a single instrument (i.e. you don't see all the notes everyone is playing on your part) cannot tell you what part of the chord you're playing, even with up/down arrows or cent adjustments. I just think it would be neat to be able to tell the performer something like: "your D here is the 5/4 ratio major third." That way, the performer knows what kind of harmonic color to listen for when playing the note. I think that'll ultimately be a more effective way of thinking about controlling tuning and color in ensemble playing than just showing cent adjustments or arrows.
Does that make sense?
Okay, so it was the obvious after all!![Image](http://tromboneforum.org/Smileys/otjf/redface.gif)
So, how to impart this much info note by note... hmmm... Well, I'm not sure that you should have to with players of the caliber that you would be aiming to write for. When I play music, anything from solo to orchestral to jazz to big band, I am constantly aware of what chord tone I am playing if the music is based on relatively traditional tertiary harmony. So for myself, a small arrow or a 5/4 next to the note would suffice. You don't have to tell me I am playing a major third because I already know that. Maybe I am wrong here, but I have to imagine that most good chamber musicians would share that ability.
Sometimes less is more when it comes to notation. Today, composers tend to micro-manage players a little to much IMHO. In the past, much more was left to the players, who were trusted to understand the stylistic conventions of the music. Of course, you want to write stuff that is NOT conventional, at least in a modern way. Perhaps instead of specific markings on every pitch you might be able to achieve the same effect more simply with some good performance instructions and then very minimal markings on the music itself. I am all for simple, direct, efficient communication from composer to performer!
Don't forget, just because you figure out a way to mark every pitch as you want it down to the cent does not mean anybody will be able to play it to that level of precision....
Does that make sense?
Okay, so it was the obvious after all!
![Image](http://tromboneforum.org/Smileys/otjf/redface.gif)
So, how to impart this much info note by note... hmmm... Well, I'm not sure that you should have to with players of the caliber that you would be aiming to write for. When I play music, anything from solo to orchestral to jazz to big band, I am constantly aware of what chord tone I am playing if the music is based on relatively traditional tertiary harmony. So for myself, a small arrow or a 5/4 next to the note would suffice. You don't have to tell me I am playing a major third because I already know that. Maybe I am wrong here, but I have to imagine that most good chamber musicians would share that ability.
Sometimes less is more when it comes to notation. Today, composers tend to micro-manage players a little to much IMHO. In the past, much more was left to the players, who were trusted to understand the stylistic conventions of the music. Of course, you want to write stuff that is NOT conventional, at least in a modern way. Perhaps instead of specific markings on every pitch you might be able to achieve the same effect more simply with some good performance instructions and then very minimal markings on the music itself. I am all for simple, direct, efficient communication from composer to performer!
Don't forget, just because you figure out a way to mark every pitch as you want it down to the cent does not mean anybody will be able to play it to that level of precision....
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Quote from: Dave Tatro on Jan 03, 2008, 02:59PM. . . if the music is based on relatively traditional tertiary harmony.
Good key point.
Even in traditional tertiary harmony, there are some grey areas.
For example, there are two major thirds, one 14 cents flat and one 35 cents sharp. Arrows might help here.
And there are more than 3 minor thirds, but the most commonly used ones are 6:5 (16 cents sharp), 7:6 (33 cents flat), and 19:16 (2 cents flat). In this case, a downward arrow simply won't do because there are two downward options. And each tuning creates a unique color, so this can be pretty important.
Good key point.
Even in traditional tertiary harmony, there are some grey areas.
For example, there are two major thirds, one 14 cents flat and one 35 cents sharp. Arrows might help here.
And there are more than 3 minor thirds, but the most commonly used ones are 6:5 (16 cents sharp), 7:6 (33 cents flat), and 19:16 (2 cents flat). In this case, a downward arrow simply won't do because there are two downward options. And each tuning creates a unique color, so this can be pretty important.
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Quote from: Andrew Meronek on Jan 01, 2008, 03:08AM
I do know that string quartets are more than capable of handling some just temperament systems having, say, 16 to 20 pitches per octave. As is a certain brass instrument . . .
I do not think this is the case. String quartets, the good ones anyway, will adjust some chords to have simple ratios. You can call those chords just tuning, most people probably would.
But temperament really means adjusting the scale to remove the comma, and I know of no string players who can play a tempered scale.
And part of the reason this even works for stringed instruments is that they are driven rather than struck or plucked, affecting the way the harmonics line up.
A lot of digital pianos have a button for changing temperaments. Have you tried playing some familiar pieces in various ways? If you don't have one, sneak into a music store and use the display models.
I do know that string quartets are more than capable of handling some just temperament systems having, say, 16 to 20 pitches per octave. As is a certain brass instrument . . .
I do not think this is the case. String quartets, the good ones anyway, will adjust some chords to have simple ratios. You can call those chords just tuning, most people probably would.
But temperament really means adjusting the scale to remove the comma, and I know of no string players who can play a tempered scale.
And part of the reason this even works for stringed instruments is that they are driven rather than struck or plucked, affecting the way the harmonics line up.
A lot of digital pianos have a button for changing temperaments. Have you tried playing some familiar pieces in various ways? If you don't have one, sneak into a music store and use the display models.
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since this is a trombone forum, i know that roy nagorcka has written some JI pieces for trombone. when he does he divides each half note into ten equal parts. he writes in regular notes, but with an arrow and a number over each note... the arrow for which way to adjust, and the number for how many cents that way.
ie 3V means 30 cents down.
i think that some of his pieces for trombone are recorded.
clarinet is another instrument which is easy to play micro tones on.
ie 3V means 30 cents down.
i think that some of his pieces for trombone are recorded.
clarinet is another instrument which is easy to play micro tones on.
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Hmmm . . .
I looked up Roy Nagorcka on Google, Amazon, and Wikipedia, and came up with nothing. Is the spelling correct?
FYI, I am using a solution similar to the one you describe, in order to create notation that is easier for performers to interpret. Except I just give cent adjustments, like +18 or -31. My thought is that a performer, once playing through the piece, will start to recognize that +18 is the adjustment for only a couple possible chords and will have a very specific sound, even compared to +16, which would normally be indistinguishable, but which would be used in other chords thus giving the performer an expectation of a different sound.
Oh, and if that is a picture of you, hooray for trombone chicks! We need more of 'em! That, or I've been in the Army way too long.
I looked up Roy Nagorcka on Google, Amazon, and Wikipedia, and came up with nothing. Is the spelling correct?
FYI, I am using a solution similar to the one you describe, in order to create notation that is easier for performers to interpret. Except I just give cent adjustments, like +18 or -31. My thought is that a performer, once playing through the piece, will start to recognize that +18 is the adjustment for only a couple possible chords and will have a very specific sound, even compared to +16, which would normally be indistinguishable, but which would be used in other chords thus giving the performer an expectation of a different sound.
Oh, and if that is a picture of you, hooray for trombone chicks! We need more of 'em! That, or I've been in the Army way too long.
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ooops. ron was the right name yeah ![Image](http://tromboneforum.org/Smileys/otjf/smile.gif)
i've been to a composition class with him once. his a cool guy
and heh no it's not me. it's a norwegian singer called siri gjære :p
![Image](http://tromboneforum.org/Smileys/otjf/smile.gif)
i've been to a composition class with him once. his a cool guy
and heh no it's not me. it's a norwegian singer called siri gjære :p
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Quote from: fluor on Jan 24, 2008, 02:26AMsiri gjære
Wow; I don't think I could pronounce that if I tried.
Wow; I don't think I could pronounce that if I tried.
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Quote from: BFW on Jan 23, 2008, 08:38PMRon Nagorcka, perhaps?
http://www.ronnagorcka.id.au/
Hmmm . . .
At first glance, he seems to take to some of John Cage's ideas. Or perhaps native Japanese music. Reflecting nature and stuff.
http://www.ronnagorcka.id.au/
Hmmm . . .
At first glance, he seems to take to some of John Cage's ideas. Or perhaps native Japanese music. Reflecting nature and stuff.
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Just Intonation Composition
By the way, here are some useful websites I've found concerning just intonation:
http://www.kylegann.com/microtonality.html
The crash course on Mr. Gann's page is excellent. Wikipedia has some good stuff, too:
http://en.wikipedia.org/wiki/Microtonal_music
http://en.wikipedia.org/wiki/Just_intonation
http://en.wikipedia.org/wiki/Tonality_diamond
http://en.wikipedia.org/wiki/Harry_Partch%27s_43-tone_scale
The Microtonal Music article has a huge list of composers at the end, and for many tells what general category of theory they used, whether it was just intonation or some form of equal temperament or something else.
http://www.kylegann.com/microtonality.html
The crash course on Mr. Gann's page is excellent. Wikipedia has some good stuff, too:
http://en.wikipedia.org/wiki/Microtonal_music
http://en.wikipedia.org/wiki/Just_intonation
http://en.wikipedia.org/wiki/Tonality_diamond
http://en.wikipedia.org/wiki/Harry_Partch%27s_43-tone_scale
The Microtonal Music article has a huge list of composers at the end, and for many tells what general category of theory they used, whether it was just intonation or some form of equal temperament or something else.
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Just Intonation Composition
Quote from: Andrew Meronek on Dec 31, 2007, 10:58AM . . . so how do you notate all of this?
I'm late joining this conversation, but the same question came up when I was putting together my little just intonation scale and arpeggio practice book, Breakfast. There I show adjustments in just one place, in a major scale and in a minor scale on page 13, expressed as cent adjustments, like -14, relative to the equal tempered scale. Elsewhere the performer trusts his ear and the accompaniment.
Fine barbershop quartets - for example the Buffalo Bills in the television production of The Music Man a few years ago - certainly don't need notational guidance to sing in just intonation. And surely that is how they sing. So, as Dave T. said up top, trust the performers.
On the computer your music notation program may have a pitch bend function which lets you adjust each note. That function may not print the adjustments on paper, but you can see them on the screen. The program takes care of the documentation and notation for you.
For a thorough discussion of the topic I highly recommend W.A. Mathieu's Harmonic Experience. At the link, select table of contents to see the broad scope of this 576 page book. In an appendix, Glossary of Singable Tones in Just Intonation, Mathieu identifies sixty intervals within the octave by ratios to the tonic!
Good luck, Andrew.
David
I'm late joining this conversation, but the same question came up when I was putting together my little just intonation scale and arpeggio practice book, Breakfast. There I show adjustments in just one place, in a major scale and in a minor scale on page 13, expressed as cent adjustments, like -14, relative to the equal tempered scale. Elsewhere the performer trusts his ear and the accompaniment.
Fine barbershop quartets - for example the Buffalo Bills in the television production of The Music Man a few years ago - certainly don't need notational guidance to sing in just intonation. And surely that is how they sing. So, as Dave T. said up top, trust the performers.
On the computer your music notation program may have a pitch bend function which lets you adjust each note. That function may not print the adjustments on paper, but you can see them on the screen. The program takes care of the documentation and notation for you.
For a thorough discussion of the topic I highly recommend W.A. Mathieu's Harmonic Experience. At the link, select table of contents to see the broad scope of this 576 page book. In an appendix, Glossary of Singable Tones in Just Intonation, Mathieu identifies sixty intervals within the octave by ratios to the tonic!
Good luck, Andrew.
David
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Quote from: David Schwartz on Jan 24, 2008, 04:19AMFor a thorough discussion of the topic I highly recommend W.A. Mathieu's Harmonic Experience. At the link, select table of contents to see the broad scope of this 576 page book. In an appendix, Glossary of Singable Tones in Just Intonation, Mathieu identifies sixty intervals within the octave by ratios to the tonic!
Good luck, Andrew.
David
Well, well. That book looks like exactly what I'm looking for.
Thanks!![Image](http://tromboneforum.org/Smileys/otjf/good.gif)
Good luck, Andrew.
David
Well, well. That book looks like exactly what I'm looking for.
Thanks!
![Image](http://tromboneforum.org/Smileys/otjf/good.gif)
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Here's a slight update:
I received some just-tuning composed music, and some of it is rather awful, and some of it is absolutely awesome. I'll cover the awesome:
The Bells of New Albion by Terry Riley. Riley is known as one of the important minimalists, but he really doesn't deserve the title. This piece is a 2 hour long solo piano work, but it involves a whole lot of improvisation as well as the tune structures which do involve repetitive elements (but not strict like in early Steve Reich or Phillip Glass works) - I really like it a lot. You don't need to listen to the entire two hours at once; he divides the piece into many discernable chunks, and you can listen to each chunk (5-20 minutes) at your leasure. That just-tuned piano is really something else!
And the other masterpiece I found is a set of string quartets written by Ben Johnston and performed by the Kepler Quartet. Man oh man, is this a great album, and man oh man will this album challenge your ears if you're not ready for it! Unlike a piano, in which no matter how creative you get can only really use twelve different pitches, stringed instruments are a lot more flexible in their tuning, and Johnston really exploits that. Not only is the music harmonically and rhythmically challenging, he writes great melodies and gets a huge palette of tone color out of the strings, and the Kepler Quartet really put forth a passionate performance of this stuff; I'd say it's probably the best recorded string quartet performance I've ever heard.
I received some just-tuning composed music, and some of it is rather awful, and some of it is absolutely awesome. I'll cover the awesome:
The Bells of New Albion by Terry Riley. Riley is known as one of the important minimalists, but he really doesn't deserve the title. This piece is a 2 hour long solo piano work, but it involves a whole lot of improvisation as well as the tune structures which do involve repetitive elements (but not strict like in early Steve Reich or Phillip Glass works) - I really like it a lot. You don't need to listen to the entire two hours at once; he divides the piece into many discernable chunks, and you can listen to each chunk (5-20 minutes) at your leasure. That just-tuned piano is really something else!
And the other masterpiece I found is a set of string quartets written by Ben Johnston and performed by the Kepler Quartet. Man oh man, is this a great album, and man oh man will this album challenge your ears if you're not ready for it! Unlike a piano, in which no matter how creative you get can only really use twelve different pitches, stringed instruments are a lot more flexible in their tuning, and Johnston really exploits that. Not only is the music harmonically and rhythmically challenging, he writes great melodies and gets a huge palette of tone color out of the strings, and the Kepler Quartet really put forth a passionate performance of this stuff; I'd say it's probably the best recorded string quartet performance I've ever heard.
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How do you suppose he notated that string quartet music?
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I did get an explanation from Kyle Gann of the notation used in the links below:
QuoteFAC, CEG, and GBD are purely tuned 4:5:6 triads
# = 25/24
b = 24/25
+ = 81/80, adjusting for the syntonic comma
- = 80/81
7 = 35/36
upside-down 7 = 36/35
^ (arrow pointing up) = 33/32
v (arrow pointing down) = 32/33
13 = 65/64
upside-down 13 = 64/65
It's not really possible to do justice to this in typing. The arrows are really arrows, and the sevens are sometimes combined with sharps and flats as a little diagonal line hanging from the top or rising from the bottom. I've been looking around the web for a sample of one of Ben's scores, and all I've found is this one, which doesn't use many of the accidentals:
http://www.smith-publications.com/catalog/samples.pl?id=29
Actually, here's another, which has a little more going on:
http://www.smith-publications.com/catalog/samples.pl?id=11
What people object to are the use of pluses and minuses, which sometimes seem counterintuitive; for instance, C-G, E-B, and F-C are perfect fifths, but D-A is not - the A needs a + or the D a -. There's a competing notation called HEWM using the same symbols but starting with the Pythagorean scale instead of pure triads, which I don't like. And in any case, while the notation makes the relationships perfectly precise, it still doesn't provide much easily digested information for the performer, who has to pretty much memorize where the pitches are anyway.
QuoteFAC, CEG, and GBD are purely tuned 4:5:6 triads
# = 25/24
b = 24/25
+ = 81/80, adjusting for the syntonic comma
- = 80/81
7 = 35/36
upside-down 7 = 36/35
^ (arrow pointing up) = 33/32
v (arrow pointing down) = 32/33
13 = 65/64
upside-down 13 = 64/65
It's not really possible to do justice to this in typing. The arrows are really arrows, and the sevens are sometimes combined with sharps and flats as a little diagonal line hanging from the top or rising from the bottom. I've been looking around the web for a sample of one of Ben's scores, and all I've found is this one, which doesn't use many of the accidentals:
http://www.smith-publications.com/catalog/samples.pl?id=29
Actually, here's another, which has a little more going on:
http://www.smith-publications.com/catalog/samples.pl?id=11
What people object to are the use of pluses and minuses, which sometimes seem counterintuitive; for instance, C-G, E-B, and F-C are perfect fifths, but D-A is not - the A needs a + or the D a -. There's a competing notation called HEWM using the same symbols but starting with the Pythagorean scale instead of pure triads, which I don't like. And in any case, while the notation makes the relationships perfectly precise, it still doesn't provide much easily digested information for the performer, who has to pretty much memorize where the pitches are anyway.
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Just a useless random addition to this whole idea:
I was thinking about how 3/2 is the perfect fifth ratio, which puts a pitch exactly between the octaves, but our ears tell us that the equal tempered tritone is actually right in between, based on how many steps there are to get to the tritone.
So I was thinking this, then I ended up doing some math.
For starters, the equal tempered tritone is simple: starting pitch * square root of 2.
And I was thinking that it's funny how the various just tuned tritone intervals seem to evenly spread around this equal tempered pitch. For example, 7/5 is 17 cents flat, and 10/7 is 17 cents sharp. And then I thought some more, and in fact there are a whole bunch of just tuned pitches that do the same thing, and cents away from the tritone also correspond to cents away from the octave root. For example, that 7/5 tritone, being 17 cents flatter than the equal tempered tritone, is also 583 cents away from the lower octave root, and the 10/7 tritone is 583 cents away from the upper octave. Major thirds are the same way: a major third is 14 cents flatter than the equal tempered third and 386 cents above the lower octave and the minor sixth is 14 cents sharp, 386 cents below the upper octave.
So, I was thinking this, and I was thinking that it might be cool if I could find out why this pattern was happening. I did a bit of basic math remembering (and a little research to fill in the gaps), and I came up with this:
log2(x/y)=1-log2(2y/x)
This is log base 2, and x and y are the numerator and denominator of the pitch ratio in question. It's actually pretty simple; simply multiply both sides by 1200 and each side represents the number of cents toward the octave. And seeing how this example requires the log base to be 2, it becomes easier to see why the pitches also "revolve" around the square root of 2. Oh, and 2y/x is how you get the inverse interval: a major third, being 5/4 has as it's inverse a minor sixth: 4*2/5 or 8/5. Same with the above-mentioned tritone: 7/5 and 5*2/7=10/7
Another way of thinking about this is that our ears hear intervals via multiplication of frequencies, not by addition of frequencies. Multiply the square root of 2 (the E.Q. tritone) by itself, and you get 2, which DOES give you double the starting pitch. Multiple 3/2 (the perfect fifth) by itself and you get 9/4, which does NOT double your starting pitch. Duh.
Hooray for basic algebra!!!
![Image](http://tromboneforum.org/Smileys/otjf/eek.gif)
I was thinking about how 3/2 is the perfect fifth ratio, which puts a pitch exactly between the octaves, but our ears tell us that the equal tempered tritone is actually right in between, based on how many steps there are to get to the tritone.
So I was thinking this, then I ended up doing some math.
For starters, the equal tempered tritone is simple: starting pitch * square root of 2.
And I was thinking that it's funny how the various just tuned tritone intervals seem to evenly spread around this equal tempered pitch. For example, 7/5 is 17 cents flat, and 10/7 is 17 cents sharp. And then I thought some more, and in fact there are a whole bunch of just tuned pitches that do the same thing, and cents away from the tritone also correspond to cents away from the octave root. For example, that 7/5 tritone, being 17 cents flatter than the equal tempered tritone, is also 583 cents away from the lower octave root, and the 10/7 tritone is 583 cents away from the upper octave. Major thirds are the same way: a major third is 14 cents flatter than the equal tempered third and 386 cents above the lower octave and the minor sixth is 14 cents sharp, 386 cents below the upper octave.
So, I was thinking this, and I was thinking that it might be cool if I could find out why this pattern was happening. I did a bit of basic math remembering (and a little research to fill in the gaps), and I came up with this:
log2(x/y)=1-log2(2y/x)
This is log base 2, and x and y are the numerator and denominator of the pitch ratio in question. It's actually pretty simple; simply multiply both sides by 1200 and each side represents the number of cents toward the octave. And seeing how this example requires the log base to be 2, it becomes easier to see why the pitches also "revolve" around the square root of 2. Oh, and 2y/x is how you get the inverse interval: a major third, being 5/4 has as it's inverse a minor sixth: 4*2/5 or 8/5. Same with the above-mentioned tritone: 7/5 and 5*2/7=10/7
Another way of thinking about this is that our ears hear intervals via multiplication of frequencies, not by addition of frequencies. Multiply the square root of 2 (the E.Q. tritone) by itself, and you get 2, which DOES give you double the starting pitch. Multiple 3/2 (the perfect fifth) by itself and you get 9/4, which does NOT double your starting pitch. Duh.
Hooray for basic algebra!!!
![Image](http://tromboneforum.org/Smileys/otjf/idea.gif)
![Image](http://tromboneforum.org/Smileys/otjf/idea.gif)
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Quote from: Andrew Meronek on Feb 27, 2008, 12:19AMAnother way of thinking about this is that our ears hear intervals via multiplication of frequencies, not by addition of frequencies.
Doesn't this result just pop right out of the fact that intervals are ratios?
I think what you've done, interestingly enough, is start from the calculations for equal temperament and derive the octave, rather than the other way around. You've also run into some of the wonderful properties of exponents and logarithms. It's great stuff.
This kind of exercise is why I'd like to teach math someday. I think these results are pure beauty, and I want to help other people see it.
Doesn't this result just pop right out of the fact that intervals are ratios?
I think what you've done, interestingly enough, is start from the calculations for equal temperament and derive the octave, rather than the other way around. You've also run into some of the wonderful properties of exponents and logarithms. It's great stuff.
This kind of exercise is why I'd like to teach math someday. I think these results are pure beauty, and I want to help other people see it.
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Quote from: BFW on Feb 27, 2008, 07:56AMDoesn't this result just pop right out of the fact that intervals are ratios?
Yeah; I suppose that is a pretty good clue.
Yeah; I suppose that is a pretty good clue.
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A piece of software you can use to help experimentation (create a MIDI with performance or notation software) is Scala:
http://www.xs4all.nl/~huygensf/scala/
(I mentioned it before, but I'll explain how I used it to experiment with Just Intonation.)
The feature I liked about it was that it Can retune existing MIDI files. You can convert a standard MIDI file to be in any tuning via pitch bend commands or a MIDI Tuning Standard tuning specification.
This feature makes it a useful tools for sort of quickly previewing simple music using Just Intonation. Basically, you have to export each tonal center as a different MIDI, create 12+ scale files (one for each key), apply appropriate scale files to the appropriate sections, and then find a way to playback the sections consecutively. For complex music, or note perfect music, you would still have to find a way to manually adjust for the different types of intervals (e.g. grave minor seventh versus minor seventh), but at least a bulk of the work could become automated when you're producing simple previews.
- - -
If you're looking for beatless music, Just Intonation won't go that far in all situations. (For example, the ensemble trick is to play a just dominant chord, but to weaken the volume of the dominant seventh to mask the beats produced by the seventh in a just setting.)
To make reading easier, most composers make use of the five-line notation system and create a way to notate deviations to that system. Of course, in the realm of easy-to-play, one could use regular notation with a prepared piano or one could write music playable by computer using any exotic notation that can eventually be read by the computer.
- - -
The math used to calculate this stuff is pretty simple. A spreadsheet I lost did this, but it calculated for any given intonation standard (e.g. 440) and base frequency a list of the cents from root for ET, cents from root for Just (by converting the frequencies to the relative [per]cent notation), and found the exact adjustments through subtraction. This is still all abstraction and is a few steps removed from being able to calculate how to adjust any set of frequencies to be as beatless as possible (or the math--probably simple math considering sound revolves around multiples--needed to describe beatless combinations of frequencies).
http://www.xs4all.nl/~huygensf/scala/
(I mentioned it before, but I'll explain how I used it to experiment with Just Intonation.)
The feature I liked about it was that it Can retune existing MIDI files. You can convert a standard MIDI file to be in any tuning via pitch bend commands or a MIDI Tuning Standard tuning specification.
This feature makes it a useful tools for sort of quickly previewing simple music using Just Intonation. Basically, you have to export each tonal center as a different MIDI, create 12+ scale files (one for each key), apply appropriate scale files to the appropriate sections, and then find a way to playback the sections consecutively. For complex music, or note perfect music, you would still have to find a way to manually adjust for the different types of intervals (e.g. grave minor seventh versus minor seventh), but at least a bulk of the work could become automated when you're producing simple previews.
- - -
If you're looking for beatless music, Just Intonation won't go that far in all situations. (For example, the ensemble trick is to play a just dominant chord, but to weaken the volume of the dominant seventh to mask the beats produced by the seventh in a just setting.)
To make reading easier, most composers make use of the five-line notation system and create a way to notate deviations to that system. Of course, in the realm of easy-to-play, one could use regular notation with a prepared piano or one could write music playable by computer using any exotic notation that can eventually be read by the computer.
- - -
The math used to calculate this stuff is pretty simple. A spreadsheet I lost did this, but it calculated for any given intonation standard (e.g. 440) and base frequency a list of the cents from root for ET, cents from root for Just (by converting the frequencies to the relative [per]cent notation), and found the exact adjustments through subtraction. This is still all abstraction and is a few steps removed from being able to calculate how to adjust any set of frequencies to be as beatless as possible (or the math--probably simple math considering sound revolves around multiples--needed to describe beatless combinations of frequencies).
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Quote from: dwdraw on Mar 02, 2008, 11:20AMIf you're looking for beatless music, Just Intonation won't go that far in all situations.
Actually, no. I'm looking for more direct control over consonance vs. dissonance.
That program does look interesting. I'll have to check it out the next time I have a chance.
Actually, no. I'm looking for more direct control over consonance vs. dissonance.
That program does look interesting. I'll have to check it out the next time I have a chance.
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Just a slight update on my literature search.
As some of you may know, a lot of folk music (not all) is tuned to just intonation. Perhaps the most commonly heard of those is bagpipe music.
My roommate is a big fan of early European music, and he showed me a really interesting CD that uses just intonation:
"Myths from Medieval Iceland," by a group called "Edda Sequentia." Sung in Icelandic, with some traditional instruments; the most identifiable to me being a kind of viol. Some of the voice leadings are very unique; it caught my ear. I thought some of the voice crossing resulting in major second intervals was particularly striking, given that those seconds were still tuned to the original just tuned scale, meaning that each second interval was not necessarily the same.
As some of you may know, a lot of folk music (not all) is tuned to just intonation. Perhaps the most commonly heard of those is bagpipe music.
My roommate is a big fan of early European music, and he showed me a really interesting CD that uses just intonation:
"Myths from Medieval Iceland," by a group called "Edda Sequentia." Sung in Icelandic, with some traditional instruments; the most identifiable to me being a kind of viol. Some of the voice leadings are very unique; it caught my ear. I thought some of the voice crossing resulting in major second intervals was particularly striking, given that those seconds were still tuned to the original just tuned scale, meaning that each second interval was not necessarily the same.
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Quote from: Andrew Meronek on Mar 30, 2008, 07:53AMAs some of you may know, a lot of folk music (not all) is tuned to just intonation. Perhaps the most commonly heard of those is bagpipe music.
Just idly wondering about something.
Inharmonicity.
For example, the piano is not actually tuned to equal temperament. Because of inharmonicity (the stiffness of steel strings causes the overtones to not quite line up) the piano sounds bad if the fundamental of each pitch is tuned to ET, because then the overtones clash. So the piano is stretched, moving the fundamentals away from ET, so that the overtones are close enough that the piano sounds like it is ET even though it is not quite.
The same thing must apply to just intervals (not sure just temperament itself is possible. But intervals are.)
But not all instruments have this problem. An organ wouldn't, for example. The pipes are driven by constant input, therefore the overtones line up. Bowed strings would be the same. Plucked strings would be different.
So, we have folk music with bagpipes or hurdy gurdy, no inharmonicity. But with guitar or hammered dulcimer, large inharmonicity. Accordions with steel reeds, even more.
I'm not asserting any point here, just bringing up something I started wondering about.
Just idly wondering about something.
Inharmonicity.
For example, the piano is not actually tuned to equal temperament. Because of inharmonicity (the stiffness of steel strings causes the overtones to not quite line up) the piano sounds bad if the fundamental of each pitch is tuned to ET, because then the overtones clash. So the piano is stretched, moving the fundamentals away from ET, so that the overtones are close enough that the piano sounds like it is ET even though it is not quite.
The same thing must apply to just intervals (not sure just temperament itself is possible. But intervals are.)
But not all instruments have this problem. An organ wouldn't, for example. The pipes are driven by constant input, therefore the overtones line up. Bowed strings would be the same. Plucked strings would be different.
So, we have folk music with bagpipes or hurdy gurdy, no inharmonicity. But with guitar or hammered dulcimer, large inharmonicity. Accordions with steel reeds, even more.
I'm not asserting any point here, just bringing up something I started wondering about.
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I'm not quite sure you're correct about piano tuning not quite being equal tempered. Obviously, a piano tuned by ear alone will not be. But symthesized pianos definitely are. And pianos tuned with the aid of a tuner should be pretty darn close. And I'm not sure I agree mathematically the reason for adjusting away from equal temperament, either. By definition, nothing besides an octave is in tune in equal temperament, so you're not necessarily making things more "out of tune." Overtones of non-just tuned strings should clash regardless of whether it's equal tempered or not.
Are you talking about a 19th century tuning which was really a refinement of the well temperament that Bach's famous piece was written for? In that temperament, notes aren't quite evenly spaced; in the link below, look for Thomas Young's system:
http://www.kylegann.com/histune.html
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Quote from: Andrew Meronek on Apr 01, 2008, 12:51AM ![Image](http://tromboneforum.org/Smileys/otjf/dontknow.gif)
Obviously, a piano tuned by ear alone will not be.
Pianos tuned by ear are tuned to have a specific number of beats sounding for various intervals.
But you listen for these beats in the upper partials, not in the fundamentals.
Pianos tuned electronically (ETDs, Electronic Tuning Devices) actually mimic the ear. They have software that detects different partials, measures the inharmonicity, and calculates the stretch - which is how far off you have to tune the fundamental. That is, how far off from ET. You can set this software to detect whatever partial you want. TuneLab has a free download if you want to play with it.
![Image](http://tromboneforum.org/Smileys/otjf/dontknow.gif)
Obviously, a piano tuned by ear alone will not be.
Pianos tuned by ear are tuned to have a specific number of beats sounding for various intervals.
But you listen for these beats in the upper partials, not in the fundamentals.
Pianos tuned electronically (ETDs, Electronic Tuning Devices) actually mimic the ear. They have software that detects different partials, measures the inharmonicity, and calculates the stretch - which is how far off you have to tune the fundamental. That is, how far off from ET. You can set this software to detect whatever partial you want. TuneLab has a free download if you want to play with it.
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Just to add something I learned yesterday:
Even octaves are not tuned ET on the piano. Yes, that was a surprise to me.
Octaves are tuned to a compromise between 4:2 and 6:3. That terminology was new to me. An octave has a nominal frequency ration of 2:1, obviously, for the fundamental. But the tuner doesn't listen to the fundamental. He can make the 4th partial of the lower octave correspond to the 2cnd partial of the upper octave, OR he can make the 6th partial of the lower octave correspond to the 3rd partial of the upper octave, but not both. But the articles I read say that the best results come from tuning the octave somewhere between those choices.
Even octaves are not tuned ET on the piano. Yes, that was a surprise to me.
Octaves are tuned to a compromise between 4:2 and 6:3. That terminology was new to me. An octave has a nominal frequency ration of 2:1, obviously, for the fundamental. But the tuner doesn't listen to the fundamental. He can make the 4th partial of the lower octave correspond to the 2cnd partial of the upper octave, OR he can make the 6th partial of the lower octave correspond to the 3rd partial of the upper octave, but not both. But the articles I read say that the best results come from tuning the octave somewhere between those choices.
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Hmmmm . . .
Something tells me that I won't actually understand what's going on until I start doing wave analyses with the sound.
But, upon thinking about what you've told me so far, I am reminded that inharmonicity may make the octave partials not exactly correspond to the whole number ratios. Wierd, given that octaves are pretty much THE simplest interval besides a unison.
Do you know if this is a specific cent or microcent difference between the pitches to tune a proper octave on the piano due to this effect?
This reminds me that on the trombone, the partials aren't exact integer multiples of each other either, primarily because the trombone is not a perfectly cylindrical instrument.
Something tells me that I won't actually understand what's going on until I start doing wave analyses with the sound.
But, upon thinking about what you've told me so far, I am reminded that inharmonicity may make the octave partials not exactly correspond to the whole number ratios. Wierd, given that octaves are pretty much THE simplest interval besides a unison.
Do you know if this is a specific cent or microcent difference between the pitches to tune a proper octave on the piano due to this effect?
This reminds me that on the trombone, the partials aren't exact integer multiples of each other either, primarily because the trombone is not a perfectly cylindrical instrument.
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Quote from: Andrew Meronek on Apr 04, 2008, 02:23AMDo you know if this is a specific cent or microcent difference between the pitches to tune a proper octave on the piano due to this effect?
This reminds me that on the trombone, the partials aren't exact integer multiples of each other either, primarily because the trombone is not a perfectly cylindrical instrument.
Much of this is new to me, and I'm going to find a tuning wrench and play with the old pianos at church. I only have a digital at home. The church has a nice grand which I won't dare touch, but two beater uprights that haven't been tuned in decades, there's no harm I can do. So I don't claim I really know what i'm talking about, but you've intrigued me, and some of this is fascinating. to us geeks anyway.
So here's what I think. I can defend it logically but don't claim 100% certainty here.
The fundamental for an octave on the piano should be 2:1, whether you're ET or most other temperaments, but it won't sound right because the overtones will beat against each other. So you compromise by making the octave a tiny bit wider than 2:1, that's called stretch. There isn't a specific amount that fits all cases, because every piano is slightly different in how much inharmonicity exists. I thought the amount should be relatively stable for any given piano, but a technician told me this morning that humidity affects it. ETD software calculates inharmonicity when you do the tuning and gives you recommended amounts to stretch. Technicians use that recommendation or not, as their ears tell them. They apparently store tuning sets for reference.
It may not be obvious, but this problem exists whether you do ET or any of the historic temperaments.
Now, the trombone. Be careful with terminology. You are correct that the partials are not integer multiples, and you are correct that the reason is the construction of the trombone with cylinders, cones, curves, constrictions, and other c words. However. When playing, the overtones are forced mathematically to be pure integer ratios, unlike the piano. That is why I often say partials are NOT overtones. If you lip slur up a partial series, you do not get integral multiples. But if you play the fundamental and only listen up the partial series, you will.
This reminds me that on the trombone, the partials aren't exact integer multiples of each other either, primarily because the trombone is not a perfectly cylindrical instrument.
Much of this is new to me, and I'm going to find a tuning wrench and play with the old pianos at church. I only have a digital at home. The church has a nice grand which I won't dare touch, but two beater uprights that haven't been tuned in decades, there's no harm I can do. So I don't claim I really know what i'm talking about, but you've intrigued me, and some of this is fascinating. to us geeks anyway.
So here's what I think. I can defend it logically but don't claim 100% certainty here.
The fundamental for an octave on the piano should be 2:1, whether you're ET or most other temperaments, but it won't sound right because the overtones will beat against each other. So you compromise by making the octave a tiny bit wider than 2:1, that's called stretch. There isn't a specific amount that fits all cases, because every piano is slightly different in how much inharmonicity exists. I thought the amount should be relatively stable for any given piano, but a technician told me this morning that humidity affects it. ETD software calculates inharmonicity when you do the tuning and gives you recommended amounts to stretch. Technicians use that recommendation or not, as their ears tell them. They apparently store tuning sets for reference.
It may not be obvious, but this problem exists whether you do ET or any of the historic temperaments.
Now, the trombone. Be careful with terminology. You are correct that the partials are not integer multiples, and you are correct that the reason is the construction of the trombone with cylinders, cones, curves, constrictions, and other c words. However. When playing, the overtones are forced mathematically to be pure integer ratios, unlike the piano. That is why I often say partials are NOT overtones. If you lip slur up a partial series, you do not get integral multiples. But if you play the fundamental and only listen up the partial series, you will.
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Quote from: timothy42b on Apr 04, 2008, 04:46AMMuch of this is new to me, and I'm going to find a tuning wrench and play with the old pianos at church. I only have a digital at home. The church has a nice grand which I won't dare touch, but two beater uprights that haven't been tuned in decades, there's no harm I can do. So I don't claim I really know what i'm talking about, but you've intrigued me, and some of this is fascinating. to us geeks anyway.
So here's what I think. I can defend it logically but don't claim 100% certainty here.
The fundamental for an octave on the piano should be 2:1, whether you're ET or most other temperaments, but it won't sound right because the overtones will beat against each other. So you compromise by making the octave a tiny bit wider than 2:1, that's called stretch. There isn't a specific amount that fits all cases, because every piano is slightly different in how much inharmonicity exists. I thought the amount should be relatively stable for any given piano, but a technician told me this morning that humidity affects it. ETD software calculates inharmonicity when you do the tuning and gives you recommended amounts to stretch. Technicians use that recommendation or not, as their ears tell them. They apparently store tuning sets for reference.
It may not be obvious, but this problem exists whether you do ET or any of the historic temperaments.
Now, the trombone. Be careful with terminology. You are correct that the partials are not integer multiples, and you are correct that the reason is the construction of the trombone with cylinders, cones, curves, constrictions, and other c words. However. When playing, the overtones are forced mathematically to be pure integer ratios, unlike the piano. That is why I often say partials are NOT overtones. If you lip slur up a partial series, you do not get integral multiples. But if you play the fundamental and only listen up the partial series, you will.
Yeah; I realized that about terminology.
And, yes, this problem would obviously exist whatever temperament one uses. It makes me wonder how composers who used really wild just intonation based systems tuned their pianos: Terry Riley on "The Bells of New Albion" and especially LaMonte Young on his masterpiece, "The Well Tuned Piano."
So here's what I think. I can defend it logically but don't claim 100% certainty here.
The fundamental for an octave on the piano should be 2:1, whether you're ET or most other temperaments, but it won't sound right because the overtones will beat against each other. So you compromise by making the octave a tiny bit wider than 2:1, that's called stretch. There isn't a specific amount that fits all cases, because every piano is slightly different in how much inharmonicity exists. I thought the amount should be relatively stable for any given piano, but a technician told me this morning that humidity affects it. ETD software calculates inharmonicity when you do the tuning and gives you recommended amounts to stretch. Technicians use that recommendation or not, as their ears tell them. They apparently store tuning sets for reference.
It may not be obvious, but this problem exists whether you do ET or any of the historic temperaments.
Now, the trombone. Be careful with terminology. You are correct that the partials are not integer multiples, and you are correct that the reason is the construction of the trombone with cylinders, cones, curves, constrictions, and other c words. However. When playing, the overtones are forced mathematically to be pure integer ratios, unlike the piano. That is why I often say partials are NOT overtones. If you lip slur up a partial series, you do not get integral multiples. But if you play the fundamental and only listen up the partial series, you will.
Yeah; I realized that about terminology.
And, yes, this problem would obviously exist whatever temperament one uses. It makes me wonder how composers who used really wild just intonation based systems tuned their pianos: Terry Riley on "The Bells of New Albion" and especially LaMonte Young on his masterpiece, "The Well Tuned Piano."
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Quote from: Andrew Meronek on Apr 04, 2008, 02:23AMThis reminds me that on the trombone, the partials aren't exact integer multiples of each other either, primarily because the trombone is not a perfectly cylindrical instrument.
I confess, I am not following this thread, just came by to see whats up.
No horns are perfect cylindrical or conical.
The saxes are very conical, but necessarily there are some compromises.
The most cylindrical horns are flutes, clarinets and didgeridoos.
The flutes are open in both ends when played, there horns are not.
Clarinets and didgeridoos series of partials looks like this:
8:va basso
locco
b
# ![Image](http://tromboneforum.org/Smileys/otjf/Line5.gif)
But the overtones from any of the partials look like this,
b
you can transpose the series to fit any of the partials.
I confess, I am not following this thread, just came by to see whats up.
No horns are perfect cylindrical or conical.
The saxes are very conical, but necessarily there are some compromises.
The most cylindrical horns are flutes, clarinets and didgeridoos.
The flutes are open in both ends when played, there horns are not.
Clarinets and didgeridoos series of partials looks like this:
![Image](http://tromboneforum.org/Smileys/otjf/BassClef.gif)
![Image](http://tromboneforum.org/Smileys/otjf/Space2.gif)
![Image](http://tromboneforum.org/Smileys/otjf/Space4.gif)
![Image](http://tromboneforum.org/Smileys/otjf/TrebleClef.gif)
![Image](http://tromboneforum.org/Smileys/otjf/Line1.gif)
![Image](http://tromboneforum.org/Smileys/otjf/Line3.gif)
![Image](http://tromboneforum.org/Smileys/otjf/Line4.gif)
![Image](http://tromboneforum.org/Smileys/otjf/Line5.gif)
But the overtones from any of the partials look like this,
![Image](http://tromboneforum.org/Smileys/otjf/BassClef.gif)
![Image](http://tromboneforum.org/Smileys/otjf/Space2.gif)
![Image](http://tromboneforum.org/Smileys/otjf/Space4.gif)
![Image](http://tromboneforum.org/Smileys/otjf/Line6.gif)
![Image](http://tromboneforum.org/Smileys/otjf/TrebleClef.gif)
![Image](http://tromboneforum.org/Smileys/otjf/Line1.gif)
![Image](http://tromboneforum.org/Smileys/otjf/Line2.gif)
![Image](http://tromboneforum.org/Smileys/otjf/Line3.gif)
![Image](http://tromboneforum.org/Smileys/otjf/Space3.gif)
![Image](http://tromboneforum.org/Smileys/otjf/Line4.gif)
![Image](http://tromboneforum.org/Smileys/otjf/Space4.gif)
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Hey there, Sven! ![Image](http://tromboneforum.org/Smileys/otjf/hi.gif)
On a slightly related but different note, I just finished my first little experimentation: a quartet fo trombone quartet entitled "Toccata in Bb" using this just-intonation based system. You can see the music here:
http://www.sibeliusmusic.com/cgi-bin/show_score.pl?scoreid=122086
and although I have that site set to force people to pay for printouts, I'm perfectly okay with sending out some parts so I can get some feedback from some of you here on the forum. I'm particularly focused on making sure that it is clear what I want without having to explain much in the music. That, and whether it sucks or not.![Image](http://tromboneforum.org/Smileys/otjf/biggrin.gif)
![Image](http://tromboneforum.org/Smileys/otjf/hi.gif)
On a slightly related but different note, I just finished my first little experimentation: a quartet fo trombone quartet entitled "Toccata in Bb" using this just-intonation based system. You can see the music here:
http://www.sibeliusmusic.com/cgi-bin/show_score.pl?scoreid=122086
and although I have that site set to force people to pay for printouts, I'm perfectly okay with sending out some parts so I can get some feedback from some of you here on the forum. I'm particularly focused on making sure that it is clear what I want without having to explain much in the music. That, and whether it sucks or not.
![Image](http://tromboneforum.org/Smileys/otjf/biggrin.gif)
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I just uploaded an edited version with MIDI pitch bends, so anyone who wants to can hear the intended tuning. It'll bend your ears!
FYI, I ended up using a grand total of 26 pitches per octave, although a couple of them appear pretty rarely. The most complex one is the -47 cent B-natural at the climax, which is technically a 33/32 above the pitch center Bb.
FYI, I ended up using a grand total of 26 pitches per octave, although a couple of them appear pretty rarely. The most complex one is the -47 cent B-natural at the climax, which is technically a 33/32 above the pitch center Bb.
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Hello Conversation,
I've been using and learning about microtones for a few years, but am by no means an expert. However I have had success using the so-called "Sims-Maneri" system of Equal-temperment and notation, which uses 72 notes to the octave. It was created by Ezra Sims and popularized through Joe Maneri's microtonal class at the New England Conservatory.
Although it's an equal-tempered system, it can be learned and notated quite easily, hundreds of musicians already know it, and the smallest interval (16 2/3 cents or a twelfth-tone) is small enough that the system can be used as an easy approximation of just-tempered systems. Most performers use the Sims-Maneri system in conjunction with cent markings anyway, so if you wanted +15 instead of 16 2/3 you could just use the symbol for 16 2/3 with an asterisk or something. There are fonts for Sibelius and Finale available.
Students of the system have become so familiar with it that they can actually sight-read using it.
You can order the workbook which explains the whole system, along with exercises, here:
http://bostonmicrotonalsociety.org/Pages/Workbook.html
Here in a nutshell is the notation:
I've been using and learning about microtones for a few years, but am by no means an expert. However I have had success using the so-called "Sims-Maneri" system of Equal-temperment and notation, which uses 72 notes to the octave. It was created by Ezra Sims and popularized through Joe Maneri's microtonal class at the New England Conservatory.
Although it's an equal-tempered system, it can be learned and notated quite easily, hundreds of musicians already know it, and the smallest interval (16 2/3 cents or a twelfth-tone) is small enough that the system can be used as an easy approximation of just-tempered systems. Most performers use the Sims-Maneri system in conjunction with cent markings anyway, so if you wanted +15 instead of 16 2/3 you could just use the symbol for 16 2/3 with an asterisk or something. There are fonts for Sibelius and Finale available.
Students of the system have become so familiar with it that they can actually sight-read using it.
You can order the workbook which explains the whole system, along with exercises, here:
http://bostonmicrotonalsociety.org/Pages/Workbook.html
Here in a nutshell is the notation:
![Image](http://bostonmicrotonalsociety.org/Images/Book%20Images/large/p.1_large.jpg)
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Quote from: JacobGarchik on Apr 13, 2008, 02:13PMHello Conversation,
I've been using and learning about microtones for a few years, but am by no means an expert. However I have had success using the so-called "Sims-Maneri" system of Equal-temperment and notation, which uses 72 notes to the octave. It was created by Ezra Sims and popularized through Joe Maneri's microtonal class at the New England Conservatory.
Although it's an equal-tempered system, it can be learned and notated quite easily, hundreds of musicians already know it, and the smallest interval (16 2/3 cents or a twelfth-tone) is small enough that the system can be used as an easy approximation of just-tempered systems. Most performers use the Sims-Maneri system in conjunction with cent markings anyway, so if you wanted +15 instead of 16 2/3 you could just use the symbol for 16 2/3 with an asterisk or something. There are fonts for Sibelius and Finale available.
Those equal temperament systems based on multiples of 12 do tend to be fairly easy to convert to a variant of standard notation. Cool stuff.
FYI, I also found on Wikipedia this excellent little teaser on a turkish classical notation system based on dividing the whole tone into 9 commas, giving 54 pitches per octave:
http://en.wikipedia.org/wiki/Makam
Given how many different notation systems are out there to approximate various just-tuned scales, I still think it's better to just go with a just-tuned scale with just-tuned notation rather than closer and more complex approximations.
I've been using and learning about microtones for a few years, but am by no means an expert. However I have had success using the so-called "Sims-Maneri" system of Equal-temperment and notation, which uses 72 notes to the octave. It was created by Ezra Sims and popularized through Joe Maneri's microtonal class at the New England Conservatory.
Although it's an equal-tempered system, it can be learned and notated quite easily, hundreds of musicians already know it, and the smallest interval (16 2/3 cents or a twelfth-tone) is small enough that the system can be used as an easy approximation of just-tempered systems. Most performers use the Sims-Maneri system in conjunction with cent markings anyway, so if you wanted +15 instead of 16 2/3 you could just use the symbol for 16 2/3 with an asterisk or something. There are fonts for Sibelius and Finale available.
Those equal temperament systems based on multiples of 12 do tend to be fairly easy to convert to a variant of standard notation. Cool stuff.
FYI, I also found on Wikipedia this excellent little teaser on a turkish classical notation system based on dividing the whole tone into 9 commas, giving 54 pitches per octave:
http://en.wikipedia.org/wiki/Makam
Given how many different notation systems are out there to approximate various just-tuned scales, I still think it's better to just go with a just-tuned scale with just-tuned notation rather than closer and more complex approximations.
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Quote from: dwdraw on Mar 02, 2008, 11:20AMA piece of software you can use to help experimentation (create a MIDI with performance or notation software) is Scala:
http://www.xs4all.nl/~huygensf/scala/
(I mentioned it before, but I'll explain how I used it to experiment with Just Intonation.)
The feature I liked about it was that it Can retune existing MIDI files. You can convert a standard MIDI file to be in any tuning via pitch bend commands or a MIDI Tuning Standard tuning specification.
This feature makes it a useful tools for sort of quickly previewing simple music using Just Intonation. Basically, you have to export each tonal center as a different MIDI, create 12+ scale files (one for each key), apply appropriate scale files to the appropriate sections, and then find a way to playback the sections consecutively. For complex music, or note perfect music, you would still have to find a way to manually adjust for the different types of intervals (e.g. grave minor seventh versus minor seventh), but at least a bulk of the work could become automated when you're producing simple previews.
Along these lines, as I said above, I added MIDI pitch bends to my Sibelius file. The best solution I've found so far is to create the most common 12 note scale used in the piece with Scala, re-tune the MIDI file, then go into Sibelius and manually change all the pitches that didn't get correct right. Sibelius apparently uses a standardized MIDI script language; I'm not sure HOW standardized it is.
Does the phrase "~B0,64" mean anything to anyone? This should bend the pitch to the 12-note equal tempered frequency. Different numbers bend it differently, although it's a bit convoluted to figure out how to convert between this and a microcent adjustment.
http://www.xs4all.nl/~huygensf/scala/
(I mentioned it before, but I'll explain how I used it to experiment with Just Intonation.)
The feature I liked about it was that it Can retune existing MIDI files. You can convert a standard MIDI file to be in any tuning via pitch bend commands or a MIDI Tuning Standard tuning specification.
This feature makes it a useful tools for sort of quickly previewing simple music using Just Intonation. Basically, you have to export each tonal center as a different MIDI, create 12+ scale files (one for each key), apply appropriate scale files to the appropriate sections, and then find a way to playback the sections consecutively. For complex music, or note perfect music, you would still have to find a way to manually adjust for the different types of intervals (e.g. grave minor seventh versus minor seventh), but at least a bulk of the work could become automated when you're producing simple previews.
Along these lines, as I said above, I added MIDI pitch bends to my Sibelius file. The best solution I've found so far is to create the most common 12 note scale used in the piece with Scala, re-tune the MIDI file, then go into Sibelius and manually change all the pitches that didn't get correct right. Sibelius apparently uses a standardized MIDI script language; I'm not sure HOW standardized it is.
Does the phrase "~B0,64" mean anything to anyone? This should bend the pitch to the 12-note equal tempered frequency. Different numbers bend it differently, although it's a bit convoluted to figure out how to convert between this and a microcent adjustment.
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Here are some free downloads of just tuned music that I've found on the web. Some of it is good, some of it is not.
http://www.ubu.com/sound/tellus_14.html I like the "Opening Kyrie" and "Tocatta for Violoncello." A lot of it is not that great - an acquired taste, I guess.
http://www.avantgardeproject.org/AGP9/index.htm Some Ben Johnston music. A very large download, and the site features a lot of other avant garde recordings as well.
http://www.youtube.com/results?search_query=michael+harrison+revelation&search_type= Excerpts from a very recent piece for just tuned piano by Michael Harrison. Interesting that I found it on YouTube.
http://www.ubu.com/sound/tellus_14.html I like the "Opening Kyrie" and "Tocatta for Violoncello." A lot of it is not that great - an acquired taste, I guess.
http://www.avantgardeproject.org/AGP9/index.htm Some Ben Johnston music. A very large download, and the site features a lot of other avant garde recordings as well.
http://www.youtube.com/results?search_query=michael+harrison+revelation&search_type= Excerpts from a very recent piece for just tuned piano by Michael Harrison. Interesting that I found it on YouTube.
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A couple of years before he died (2004) Fred Nachbaur posted some utilities and some performances of music in both just intonation and tempered. To listen to his fascinating samples, scroll down to "Demonstrations" and the buttons for Original and Tempered at this link.