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Author Topic: Just Intonation Composition  (Read 57181 times)
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timothy42b
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« Reply #40 on: Apr 04, 2008, 04:46AM »

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.

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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« Reply #41 on: Apr 04, 2008, 07:35AM »

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. 

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."
« Last Edit: Apr 04, 2008, 12:27PM by Andrew Meronek » Logged

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« Reply #42 on: Apr 04, 2008, 12:11PM »

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.
I confess, I am not following this thread, just came by to see what’s 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 didgeridoo’s.
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 #
But the overtones from any of the partials look like this,    you can transpose the series to fit any of the partials.

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« Reply #43 on: Apr 04, 2008, 09:05PM »

Hey there, Sven! Hi

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. :D
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« Reply #44 on: Apr 13, 2008, 01:21PM »

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.
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« Reply #45 on: Apr 13, 2008, 02:13PM »

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:

 
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« Reply #46 on: Apr 13, 2008, 10:28PM »

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.

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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Andrew Meronek

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« Reply #47 on: Apr 16, 2008, 05:37AM »

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.


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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« Reply #48 on: Apr 23, 2008, 11:43AM »

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.

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« Reply #49 on: Apr 23, 2008, 08:51PM »

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.
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« Reply #50 on: Apr 27, 2008, 12:13AM »

Wow, great website, David!

Yesterday, I was pondering some other odd ways of constructing scales, and I decided to try to build a scale that defines an octave as being 3:1 instead of 2:1, that is, I triple the starting pitch. Thus, if I start this scale on a piano's C and ascend, the next octave of the scale starts on a piano's G, a twelveth above. I got the idea from this: http://en.wikipedia.org/wiki/Bohlen-Pierce_scale

Although, unlike the example given in the website, I deliberately made a scale that maps onto a standard piano keyboard, and I used a lot of 5-limit intervals. Therefore, it's still a very consonant, pretty scale with lots of thirds - but chord inversions get pretty interesting, and the way I ended up structuring it makes for creating a lot of "jazz" chords that all fall within one octave. Cool stuff.
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« Reply #51 on: Apr 27, 2008, 04:54AM »

A little serendipity this weekend:

I was reading Benade, trying to find the explanation for strange results in one of my kids physics lab writeups:  a cylindrical tube resonating far below predicted frequency based on length.

I came across an interesting comment he offhandedly threw away:  talking about why violin strings don't produce beats when wind instruments do (has to do with the uneven stick and slide bowing mechanism), he mentioned that because of these factors string partials end up 20 cents wide, causing string quartets and wind quartets to have totally different intonation characteristics.  Winds can produce both purer consonances and purer dissonances.  Strings cannot but can vary color more.

If so, there would surely be some implications for composing just interval music for different groups. 

Oh, the physics lab:  Benade didn't cover it, my analysis suggests the kids shortened the tube enough to get a Helmholtz resonator effect. 
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« Reply #52 on: Apr 27, 2008, 06:59AM »

Benade who?
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« Reply #53 on: Apr 27, 2008, 10:34PM »

While there are many texts on musical acoustics, THE classic work is Fundamentals of Musical Acoustics by Benade.  The paperback edition is about $12 on Amazon, every musician should have a copy of this work. 

He did his research before computers and some of the modern measurement technology, stuff like RTA equipment.  He deleted the math in order to make the text more accessible to lay readers.  So there are some limitations, and other authors to read.  But this is still the one to start with. 
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« Reply #54 on: Apr 28, 2008, 12:48AM »

Ah, cool. I'll check him out. Good!
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« Reply #55 on: May 16, 2008, 10:33AM »


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.


Well, I just got the recording, and this is a real gem. He tuned his piano to have both consonant and dissonant intervals, and his dissonant intervals, what he refers to as "commas," create specific interference patterns, i.e., beats and he uses these patterns as rhythmic devices. This makes for a really interesting, unique sound. I highly recommend checking this out! Good!
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« Reply #56 on: May 17, 2008, 11:03AM »

I know someone has maked an organ to play the way we do. Make the major 3rd lower and minor 3rd higher.
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« Reply #57 on: Jun 04, 2008, 07:46AM »

One more literature update:

I managed to my hands on a relatively rare CD: Ben Johnston Microtonal Piano. I'm listening to it right now, and boy is it something! Amazed

The two microtonal pieces on it are a suite and a sonata; the suite is tonal, although complex, and is tuned entirely in the 5th octave harmonic series pitches, and the sonata is completely atonal, with each key on the piano tuned almost arbitrarily accoring to relationships to other notes, but ends up having very few consonant octaves. Both approaches result in a really, really unusual, colorful sound - although I think I like the overtone-based Suite better, at least upon my first listenings.
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« Reply #58 on: Jun 22, 2008, 11:20AM »

Hello,

I just got done playing a Maneri piece a few months ago, and I have to say that the Sims-Maneri system works very very well for microtonal writing. Lots of musicians know it, and there's even the Boston Microtonal Society, which plays mostly 72 note ET music, but uses other systems as well depending on the composer.

I also took a class from Michael Harrison this year where he explained how he tuned the piano for Revelations. Michael tended to do a lot of tunings by ear, and he was heavily influenced by Indian Raga music and the alternate tuning systems found there.

Hope this helps, and if you ever have a solo trombone work, please let me know!

William Lang
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« Reply #59 on: Oct 23, 2008, 06:34AM »

Upon doing some fresh googling of just intonation, I came across this excellent site:

http://tonalsoft.com/enc/encyclopedia.aspx

And includes:

A Microtonal Analysis of Robert Johnston's "Drunken Hearted Man"
HEWM Notation

and of course lots of other really useful articles. Good!
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