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7/4
Joined: Jan 19, 2004
Posts: 161
Location: ...next stop Mars!
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 Posted: Thu Sep 02, 2004 6:21 am Post subject:
Just Intonation and Temperaments |
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[Editor's note: This topic is split from the Wish List on the Nord Modular forum. We rarely split topics. Maybe we should do more of it. Thanks for the suggestion from Ffransis. --mosc]
| ffransis wrote: | | The ability to adjust the tuning to just intonation (based on a user specified tonic), meantone, Werckmeister, Kirnberger and other temperaments would be useful, as would completely user-defined scales. |
Just Intonation is not a temperament! |
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ffransis
Joined: Jun 24, 2004
Posts: 31
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| Posted: Thu Sep 02, 2004 6:31 am Post subject:
Re: Keyboard temperaments |
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| 7/4 wrote: | | ffransis wrote: | | The ability to adjust the tuning to just intonation (based on a user specified tonic), meantone, Werckmeister, Kirnberger and other temperaments would be useful, as would completely user-defined scales. |
Just Intonation is not a temperament! |
Don't be pedantic! :-) Of course I know JI is not a temperament, but I'll be buggered if I'm going to mind my punctuation to that degree in a short post advocating the setting up of a user-editable tuning table in the G2. Especially as in practice, most musically-minded keyboard players will find non-equal *temperaments* more useful than pure JI. |
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Fozzie
Joined: Jun 04, 2004
Posts: 875
Location: Near Wageningen, the Netherlands
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| Posted: Thu Sep 02, 2004 6:32 am Post subject:
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| ffransis wrote: | ... Hardware is not the problem; this is a software issue. I currently use Scala with my DX7S.
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I am in no way a clavia or G2 expert (no beta-tester either), but what I meant with hardware issues, is the fact that is probably no room / memory to store such scala data. Only way I could imagine this to work is if this data can be used to influence module settings in a patch, and this can be saved normally. In this way only the editor would be needed to open the scl file and 'convert' the information into patch settings, which can be used furthermore without the original scl file. But to me this sounds as some major coding work, and not really 'in line' with the normal clavia strategy of developing modules with new functionality. |
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7/4
Joined: Jan 19, 2004
Posts: 161
Location: ...next stop Mars!
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| Posted: Thu Sep 02, 2004 3:18 pm Post subject:
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| Quote: | Don't be pedantic!  Of course I know JI is not a temperament, but I'll be buggered if I'm going to mind my punctuation to that degree in a short post advocating the setting up of a user-editable tuning table in the G2. |
There’s so much misunderstanding about microtonality, I’d like to see the right terms used. Many years ago I made the same mistake and I accepted it. Use blanket terms like microtonal or alternative tunings and stay out of trouble.
| Quote: | | Especially as in practice, most musically-minded keyboard players will find non-equal *temperaments* more useful than pure JI. |
Composers and other non-keyboard playing musicians use synthesizers too.
“musically-minded”? How insulting. I’ve been doing fine using JI for years and folks find it quite musical. |
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ffransis
Joined: Jun 24, 2004
Posts: 31
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| Posted: Thu Sep 02, 2004 3:32 pm Post subject:
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| I was trying to make light of the situation, but 7/4 clearly missed the point. I use JI often, but not exclusively. Most keyboard players I know of who make use of non-equal temperament scales use meantone, Kirnberger or Werckmeister if they modulate key signatures. As for terminology, I make no "mistake". If you read carefully my original post, I refer to JI and temperaments, but there was no equation of the two unless you specifically look for it. Why should I "stay out of trouble"? I'll sya what I want, and hopefully provoke some intelligent debate. So far I seem to have failed miserably, and for that I apologise to all readers of this forum. |
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7/4
Joined: Jan 19, 2004
Posts: 161
Location: ...next stop Mars!
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| Posted: Thu Sep 02, 2004 3:40 pm Post subject:
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| Whatever... |
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mosc
Site Admin
Joined: Jan 31, 2003
Posts: 18198
Location: Durham, NC
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| Posted: Thu Sep 02, 2004 5:18 pm Post subject:
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I'd sure like everyone to feel comfortable, welcome and appreciated here. Respect is the core value on this site. I don't see anybody violating this value here, but I just wanted to mention it nonetheless...
Anyway, 7/4, I'm not sure I understand the meanings of these words temprament and intonation. Perhaps I should add tunings and microtunings in there too. When you say that Just Intonation is not a temperament, what is it then? I thought a temperament was a formula for adjusting the 12 tones of the scale. I've always thought of JI as one of the many possible formulas one can use. I guess I've ingnorantly been using these words interchangeably.
With all due respect, would you please enlighten me? 
(I'm not asking for an explaination of the different possibilities, only a claification of these terms.) |
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7/4
Joined: Jan 19, 2004
Posts: 161
Location: ...next stop Mars!
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| Posted: Fri Sep 03, 2004 5:25 pm Post subject:
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I'm no authority on Temperaments, but I'll try to compare them to Just Intonation or at least paint the big picture.
Just Intonation is tuning to intervals from the Harmonic series. Intervals are represented as ratios. For example: a 9/8 is the whole tone distance between the 9th harmonic and the fundimental. A 49/48 is the distance between the 49th and 48th harmonics, a microtone, roughly 1/6th of a whole tone.
What's cool about JI are the very consanant beatless intervals like a 9/8 and very small intervals that vibrate (or beat) in a very beautiful way.
But when you try to cram JI into a 12 note tuning for a conventional keyboard, there are problems playing in more than a few keys. This is where temperaments come in. Temperaments are adjustments to the tuning so we can play in more than a few keys. But out of tune.
In the last few hundred years, this lead to 12 tone equal temperament, a solution where folks can play out of tune in any of the 12 keys.
Microtones are small intervals but microtonal is a broad term for any tuning other than 12 tone equal temperament.
- Just Intonation
- Pythagorean (a spiral of Just 5ths, not a temperaments)
- the temperaments
- Gamelan tunings (varies between Gamelans, not Just, not temperament.
- alternative equal temperaments, 19, 22, 31, 24 seem popular.
- and people doing anything they want, measuring points on a map and devising a tuning is one example.
Can you have more than a few key centers in JI? Yep. As many as you want. In fact, JI is not a closed system like the other tuning systems, there are infinte possibilities.
Musicans and composers seem to be scared by this, but you can take a few intervals and work with them.
A recent string qt. I wrote has an 8 note scale, but 3 of them are there to resolve to the other 5.
One guitar piece has only 4 notes, another has 5.
That's enough for now. Any questions folks? |
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Afro88
Joined: Jun 20, 2004
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| Posted: Fri Sep 03, 2004 5:37 pm Post subject:
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| Just intonation sounds like a bit of fun..... ....and the Partial Quantizer module enables me to play around with it . I'm off to do some patching |
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mosc
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| Posted: Fri Sep 03, 2004 6:03 pm Post subject:
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| Hmmm... seems to make sense. So tunings based on the whole number ratios are not tempered, and tunings where one deviates from these whole number ratios are. Is that correct? |
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ffransis
Joined: Jun 24, 2004
Posts: 31
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| Posted: Fri Sep 03, 2004 7:17 pm Post subject:
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| mosc wrote: | | Hmmm... seems to make sense. So tunings based on the whole number ratios are not tempered, and tunings where one deviates from these whole number ratios are. Is that correct? |
Not strictly. It's better to say that tunings based on whole number ratios, where the numbers are small, are just. Any numerical ratio can be expressed as whole numbers if the numbers are large enough.
Temperaments are compromises designed for specific purposes. For example, intervals such as thirds or fifths can be adjusted to beat less. Some temperaments are closer to just intonation, and others to equal temperament. Some scales, e.g., the various gamelan tunings, are simply what they are, and should be appreciated as such. In the end it comes down to the impression on the listener.
Acoustic instrumentalists learn to live with the realities of their instruments, and some push the envelope of what's possible. Fiddlers can play any notes they damn well please (and generally do!). Many folk guitarists, who use open tunings where the open chord (e.g., DADGAD) tends to be tuned just, will avoid fingered chords with problematic intervals such as major thirds, and put up with some notes being slightly out of tune. My main acoustic instrument is a Scandinavian låtmandola - a 6-course octave mandola tuned in fifths, with capos on individual courses on the bottom 3 courses. I tune to open chords, with non-beating fifths, and deal as best I can with deviations in tuning on the upper strings as I move up the fretboard.
Keyboard tunings tend to be more rigid. Some electronic keyboards can be switched between different tuning systems, but many players prefer to avoid doing this while playing, and feel happier using one tuning (e.g., 1/4 comma meantone or Werckmeister) during the course of one particular piece of music, and be able to change key without major problems.
As for the more well-known temperaments, meantone is close(r) to just intonation, and Werckmeister slightly less so. Both tend to be somewhat "bumpy" when shifting between different keys, but that adds character to the music. J.S. Bach's Well-Tempered Clavier was written to illustrate mood changes between key signatures when using tempered scales. It is not, contrary to popular opinion, a case study for equal temperament! Kirnberger temperament is closer to equal temperament, and Valloti and Young, used most often with piano accordions, is little different from equal temperament. |
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mosc
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| Posted: Fri Sep 03, 2004 8:37 pm Post subject:
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Two great posts. Thanks...
I'd love to hear some låtmandola music. Can you post an mp3 or something?
Interesting, what you say about Bach wanting "to illustrate mood changes between key signatures when using tempered scales."
On an equal temperments keyboard one would think the intevals in every key would be tuned the same, so except for the relative transpostion of the tonic center, every key would be equivlant, at least in theory. On a conventional piano or other acoustic keyboard, different keys could certainly have different timbres because of an intrument's physical characteristics. Still, I'm not sure if I understand how D major would have a different mood from D# major on an electronic instrument in equal temperment tuning. |
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ffransis
Joined: Jun 24, 2004
Posts: 31
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| Posted: Sat Sep 04, 2004 4:33 am Post subject:
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| mosc wrote: | | I'd love to hear some låtmandola music. Can you post an mp3 or something? |
I don't have a recording available of my own playing, but in any case I have to refer you to the best known professional player of the instrument. That is Ale Mölller, who is one of Sweden's most famous folk musicians, and plays currently along with the singer Lena Willemark and fiddler Per Gudmundson as Frifot. That site is pretty bare, but if you search for Möller's name on Rootsworld, you'll find some RealAudio and mp3 clips.
If you listen carefully, you'll hear from the mandola some 1/4-tone intervals. The instrument has a few partial frets in order to emulate Scandinavian fiddle styles. The fiddlers don't use precise 1/4 tones, but the placing of the partial frets in those positions gives maximum flexibility.
| mosc wrote: | | Still, I'm not sure if I understand how D major would have a different mood from D# major on an electronic instrument in equal temperment tuning. |
It doesn't give a different mood, save for maybe a slight difference based on pitch differences. Equal temperament was being developed around Bach's time, but few composers are said to have liked the results it gave, including dear old J.S. The mood changes I refer to arise from modulations using (non-equal) tempered scales such as meantone and Werckmeister.
Aside from the tendency for "classical" era composers to display technical flashiness, using way-out key signatures and modulating between them with wild abandon, and the increasing popularity of the piano, I liken the widespread adoption of equal temperament to the adoption of lowest comon denominator technologies such as Microsoft Windows. Everyone knows the technology is crap, but a bit of marketing goes a long way, and before you know it, the inferior product grabs majority market share, so "everyone is using it", and therefore everyone puts up with the grief it causes. Peculiar creatures, homo sapiens.
[Note to Ed.] If this thread is to continue, maybe it should be taken out of the wishlist. |
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mosc
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| Posted: Sat Sep 04, 2004 9:04 am Post subject:
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OK, I split this off to a new topic.
I thought J S Bach was one of the earliest proponents of equal temperament and wrote the WTC to demonstrate the versatility of it.
Well, for whatever reason, ET is here to stay, but it looks like there is a great deal to learn about the other tunings. It seems that in this electronic age, all instruments should at least offer the opportunity to use the tunings of choice.
Perhaps this explains something I've experienced, maybe not. I play the banjo with my wife who plays the guitar. The banjo plays in open G tuning most of the time. I tune it "by ear" and it sounds great until I start playing with Juli who is often in standard guitar tuning. It's usually the banjo's B string that sounds off. Often in the middle of a song, I'll quickly reach up and adjust that sting. You'll see banjo players doing this quite often. After the song is finished, if I test the B, it's out and I retune it - start another song - and the same thing starts up all over again. Is it possible that by tuning an open G tuning by ear I natually tune to just intonation and it sounds bad playing with the guitar that is tuned to equal temperament? |
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ffransis
Joined: Jun 24, 2004
Posts: 31
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| Posted: Sat Sep 04, 2004 10:21 am Post subject:
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| mosc wrote: | | Is it possible that by tuning an open G tuning by ear I natually tune to just intonation and it sounds bad playing with the guitar that is tuned to equal temperament? |
There's a danger here that in attempting to simplify the explanation, and keep it reaonably short, I'll offend some just intonation purist, but whatever, I'll risk it!
You tune your banjo to an open-G chord, so that there's no beating between the notes. How the guitar is tuned is another question. Standard tuning (EADGBE) is a mixture of fourths and thirds. Some players tune every note separately to an electronic tuner, whereas others will take the A (for example) from a reference, and tune the other strings to that A, using either fretted notes or harmonics. Different methods give significantly different results. A guitar could be tuned - say - to an open D chord, or DADGAD (open D, suspended fourth). If that open D chord is just, and your banjo is just, but in G, there's a mismatch, as a just scale is only just with reference to the tonic (and mode) of that scale.
The end result is always going to be a compromise, and that's partly what I meant before about acoustic instrumentalists dealing with the realities of their instruments. Even string quartets can have problems, despite the tunings being all fifths with violins, violas and cellos. The problem there is that the viola C has a harmonic that sounds E. Tune that C slightly sharp of that which would be in tune with the G (CGDA for viola; GDAE violin), and it will resonate nicely with the violin E. However, it's then out of tune with the other three strings.
Tuning in pure fifths (3/2 frequency ratio) is "Pythagorian". If you start at C, and go up in fifths until you reach another C (C-G-D-A-E-B-F#-C#-G#-D#-A#-F-C), the second C vibrates 3/2 to the power 12 (129,7) faster than the first, and therein lies the discrepancy. If it were an even number of octaves the figure would be 128, and all would be well - perfect octaves with no discontinuity.
Even if players tuned all their notes to an electronic standard (in equal temperament), there would still be problems as the instruments behave in different ways. Perhaps that's why so many traditional music sessions sound so dreadfully out of tune. The reason is that players can't hear themselves properly to tune their instruments *to each other*, what with all the noise in the pub, so instead they rely on electronic tuners. |
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7/4
Joined: Jan 19, 2004
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| Posted: Sat Sep 04, 2004 10:54 am Post subject:
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| mosc wrote: |
Perhaps this explains something I've experienced, maybe not. I play the banjo with my wife who plays the guitar. The banjo plays in open G tuning most of the time. I tune it "by ear" and it sounds great until I start playing with Juli who is often in standard guitar tuning. It's usually the banjo's B string that sounds off. Often in the middle of a song, I'll quickly reach up and adjust that sting. You'll see banjo players doing this quite often. After the song is finished, if I test the B, it's out and I retune it - start another song - and the same thing starts up all over again. Is it possible that by tuning an open G tuning by ear I natually tune to just intonation and it sounds bad playing with the guitar that is tuned to equal temperament? |
Maybe.
If you tune by harmonics, the open B is going to be a bit flat. The Just M3rd is 14 cents flat of an 12tet M3rd (where one octave = 1200 cents, a 1/2 tone = 100 cents).
Best to tune by fretted notes. |
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mosc
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| Posted: Sat Sep 04, 2004 12:12 pm Post subject:
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Ha ha... this is a complicated mess - something simple like tuning. 
I never tune the banjo to harmonics because they sound so funky. Tuning by frets is probably the right thing - I've sorta come to that conculsion naturally, but not it actually seems resonable, if only in an over-simplified way.
I bet most musicians don't really know beans about this.
To risk going OT here, have you guys read much about modern string theory, phyics that is? It's quite related to this musical tuning thing it seems to me except that the stings can vibrate in 10 dimensions.  |
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ffransis
Joined: Jun 24, 2004
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| Posted: Sat Sep 04, 2004 12:21 pm Post subject:
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| mosc wrote: | | To risk going OT here, have you guys read much about modern string theory, phyics that is? It's quite related to this musical tuning thing it seems to me except that the stings can vibrate in 10 dimensions. :scratch: |
No. I am a physicist by trade, but am concerned with more mundane (and soluble) problems than the meaning of life, the universe and everything. :-) |
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7/4
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| Posted: Sat Sep 04, 2004 12:25 pm Post subject:
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| Quote: | | I bet most musicians don't really know beans about this. |
Yep!
| Quote: | | To risk going OT here, have you guys read much about modern string theory, phyics that is? It's quite related to this musical tuning thing it seems to me except that the stings can vibrate in 10 dimensions. |
I've heard about it, but never checked it out. I did hear an interview last year on WNYC with someone talking about string theory and harmonics. Pretty cool! |
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bachus
Joined: Feb 29, 2004
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| Posted: Sun Sep 05, 2004 6:19 pm Post subject:
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| mosc wrote: | OK, I split this off to a new topic.
I thought J S Bach was one of the earliest proponents of equal temperament and wrote the WTC to demonstrate the versatility of it. |
No, then, in all seriousness, it would be the ETC and not the WTC. If my doddering memory serves, Bach never used equal temperament; he did use several well-tempered uh... "tunings". If I could get dragged outa the studio and into the library I'd look it up. The rise of equal temperament to dominance over other temperaments and tunings is a surprisingly recent development. (again if memory is not failing me).
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bachus
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| Posted: Sun Sep 05, 2004 6:49 pm Post subject:
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From Tuning by O. H. Jorgensen:
“The fact that no one tuned equal temperament on pianos before the twentieth century needs to be explained since several history books incorrectly state that J. S. Bach invented, proved and introduced equal temperament to the world of music in 1722. …”
I believe this to be correct. As far as I have been able to determine this volume is the most complete and accurate account of the history of tunings and temperaments and the practical methods there of. And it makes for fascinating reading, though I’m sure some would find it a bit dry. For those musicians whose basic material is scale tones this should be considered essential reading. Otherwise it’s like living one’ life inside a house never having recognized that a door there opens into another world. But I say this as one who has consciously accepted the limitations of equal temperament without a great deal of chafing.
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mosc
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| Posted: Sun Sep 05, 2004 7:27 pm Post subject:
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Well, I can see one can spend many hours exploring this topic. Virtually eventhing I compose uses heavily frequency modulated sources, or when notes and scales are used - the notes are improvised that the tunings are arbitrary. However, from now on I'll be much more aware when mistuning my banjo.  |
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bachus
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| Posted: Mon Sep 06, 2004 3:04 am Post subject:
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| mosc wrote: | | Well, I can see one can spend many hours exploring this topic. Virtually eventhing I compose uses heavily frequency modulated sources, or when notes and scales are used - the notes are improvised that the tunings are arbitrary. ... |
Yep, your basic material is not scale tones, so this is only of "academic" interest to you and many others on this list. But alternative tunings are an important point of departure for many "experimentalists."
| mosc wrote: | | However, from now on I'll be much more aware when mistuning my banjo. |
Howard, your banjo always sounded fine to me 
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7/4
Joined: Jan 19, 2004
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| Posted: Mon Sep 06, 2004 3:52 am Post subject:
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| I'm not experimenting. |
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seraph
Editor
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| Posted: Mon Sep 06, 2004 5:43 am Post subject:
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| mosc wrote: | | I thought J S Bach was one of the earliest proponents of equal temperament and wrote the WTC to demonstrate the versatility of it. |
the World Trade Center 
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