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Is the tempered scale overrated?

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Thomas the Rhymer 19 Oct 02 - 12:51 PM
treewind 19 Oct 02 - 01:44 PM
Clinton Hammond 19 Oct 02 - 01:44 PM
pavane 19 Oct 02 - 02:07 PM
belfast 19 Oct 02 - 02:30 PM
JohnInKansas 19 Oct 02 - 02:34 PM
Thomas the Rhymer 19 Oct 02 - 03:39 PM
BanjoRay 19 Oct 02 - 07:01 PM
Thomas the Rhymer 19 Oct 02 - 08:04 PM
Peter K (Fionn) 19 Oct 02 - 08:37 PM
Helen 19 Oct 02 - 08:48 PM
Thomas the Rhymer 19 Oct 02 - 09:35 PM
JohnInKansas 20 Oct 02 - 02:13 AM
BlueSage 20 Oct 02 - 02:57 AM
pavane 20 Oct 02 - 03:47 AM
JohnInKansas 20 Oct 02 - 05:59 AM
BlueSage 20 Oct 02 - 03:14 PM
Thomas the Rhymer 20 Oct 02 - 04:41 PM
GUEST,Arne Langsetmo 20 Oct 02 - 08:27 PM
GUEST,Arne Langsetmo 20 Oct 02 - 08:37 PM
GUEST,Arne Langsetmo 20 Oct 02 - 08:41 PM
Kaleea 21 Oct 02 - 05:37 AM
Pied Piper 21 Oct 02 - 08:17 AM
GUEST,Arne Langsetmo 21 Oct 02 - 10:36 AM
GUEST,Arne Langsetmo 21 Oct 02 - 10:39 AM
Pied Piper 21 Oct 02 - 12:23 PM
GUEST 21 Oct 02 - 03:39 PM
Thomas the Rhymer 21 Oct 02 - 04:11 PM
JohnInKansas 21 Oct 02 - 05:15 PM
pavane 22 Oct 02 - 02:40 AM
Pied Piper 22 Oct 02 - 06:47 AM
JohnInKansas 22 Oct 02 - 01:25 PM
treewind 22 Oct 02 - 01:51 PM
JohnInKansas 22 Oct 02 - 05:37 PM
GUEST,Arne Langsetmo 22 Oct 02 - 09:38 PM
Thomas the Rhymer 22 Oct 02 - 11:10 PM
pavane 23 Oct 02 - 07:29 AM
GUEST 23 Oct 02 - 08:57 AM
Jeri 23 Oct 02 - 10:06 AM
GUEST,Arne Langsetmo 23 Oct 02 - 10:42 AM
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Subject: Is the tempered scale overrated?
From: Thomas the Rhymer
Date: 19 Oct 02 - 12:51 PM

Having spent over a thousand hours tuning strings to 'natural' scales... only to have to change them into 'tempered' tonings, I so often wonder if the tempered scales were really so great an idea as all that... Is all this transmodal playing just tacky tribulation? Are we missing out on some of the finer and subtler musical magic? What do you think? ttr


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Subject: RE: Is the tempered scale overrated?
From: treewind
Date: 19 Oct 02 - 01:44 PM

The natural scales do sound sweeter: if you have an instrument that can be tuned to them and don't mind sticking to the keys in which they work there is a difference in sound. But there's a long tradition of fully chromatic instruments now, and they will always be in equal temperament because they'll be played in all keys.

My first anglo concertina was a two row in C and G and because of not having the third row it couldn't be played at all in other keys, and it was in natural tuning. When I upgraded to a three row which is full chromatic, that was tuned in equal temperament. It was a long time before I discovered that was one reason why they sounded different.

Mary's just got a new electric piano and found in the manual that it can be set for about half a dozen different tuning schemes. As it mostly gets played only in few related keys, we're going to experiment with this...

Anahata


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Subject: RE: Is the tempered scale overrated?
From: Clinton Hammond
Date: 19 Oct 02 - 01:44 PM

I think if I understood ANY of what you just said, I'd be a better musician...

;-)


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Subject: RE: Is the tempered scale overrated?
From: pavane
Date: 19 Oct 02 - 02:07 PM

Painos are not tuned to the tempered scale anyway. The bass is flatter than it should be, and the treble is sharper. This is called 'stretched' tuning, and without it, apparently the piano sounds lifeless.


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Subject: RE: Is the tempered scale overrated?
From: belfast
Date: 19 Oct 02 - 02:30 PM

As far as I know it was the spread of the piano accordion which practically guaranteed the disappearance of the "natural" scales. There are those who would claim that this is only on of the crimes that can be laid at the door of that instrument. There was a great programme on Channel 4 a year or two ago about this. I think it was called "Howard Goodall's Big Bangs".


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Subject: RE: Is the tempered scale overrated?
From: JohnInKansas
Date: 19 Oct 02 - 02:34 PM

What is really overrated is the notion that you can tune and play most instruments accurately enough to tell the difference.

Unless your "instrument" permits independent "tuning" of each individual note each and every time you play it, it is virtually impossible to "play" in "natural tuning" unless you limit yourself to music with less than a very few "chords." Carried to the extremes advocated (eventually) by most people who propose your argument, you would need a different B in a G chord than the one you would play in a an E (or B) chord.

In "a capela" singing (i.e. Barber Shop Quartets) good close harmony is always to natural tunings - and a goal is to get the voices to "blend" to the natural chord. Small ensemble fretless strings can often achieve the same result. Theoretically, a slide trombone quartet might get it fairly easily.

If you have frets on your instrument, or "keys" or "holes," you're not likely to get there - even in one key. With "modern" instruments, with accurate note-to-note intonation, a quartet of instruments all in the same family such as four clarinets, four saxophones, four cornets/trumpets, can harmonize to "natural chords" briefly - if all the players are skilled enough to "lip" the individual notes together - but it requires a lot of rehearsal to get there.

With plucked, fretted, instruments, the "ideal" of playing in natural tunings is also complicated by the change in pitch that accompanies any change in dynamics. A plucked string starts at a slightly higher pitch than the pitch at which it "settles" during sustain. The "louder" you play, the greater the difference. It is very difficult to "see" this variation with most accurate (electronic) tuners, since virtually all of them incorporate a "hold" feature that keeps the indication for the "first pitch sensed." Normal tuners "lag" the instantaneous changes in pitch enough to make the variations invisible.

If you have access to a "rapid response" tuner, you will find that a "hard" pluck on a typical guitar string will start as much as "8 or 10 cents" higher than the pitch at which is settles. This is MUCH more than the difference between "natural" and "equal temperament" tuning for most of the notes you'll use. (This is also the reason why the player who tunes "softly on the sidelines" and then plays at super-dynamo-air-raid-siren level is always out of tune during the "performance.")

There are times when "natural" tuning is appropriate. You should use them then. Most of the time, equal tempered tuning is better than what you'll actually play. If it makes you feel good to "tweak things" once you're close, then by all means do so, but don't sweat the theory.

John


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Subject: RE: Is the tempered scale overrated?
From: Thomas the Rhymer
Date: 19 Oct 02 - 03:39 PM

Interesting reply John, and I commend you on your zeal and your well earned experience... you have spoken well. I must respectfully disagree with you. I am interested in the mono modal sound, with it's peculiar anomalies, which sound foriegn to us like the major third sounded to folks in the middleages... Sure, I'm speaking of what may be unattainable... our ears have been so deluged by the fanciful shift of modes... (heck, if you don't shift modes with regular frequency, people just start yawning...) but the attraction that I have to the natural scale is alot like archiology... on harp and hammeredulcimer and whistle, the natural scale is possible... and sometimes so beautiful!


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Subject: RE: Is the tempered scale overrated?
From: BanjoRay
Date: 19 Oct 02 - 07:01 PM

When you play Appalachian Old Time tunes on fiddle and banjo, the banjo is usually tuned to a natural chord, while the fiddle is often cross tuned AEAE or GDGD, with the strings tuned against each other to minimize beats and sound their best in double string drones - ie natural tuning. Maybe that's why Old Time sounds so good (to me, anyway). I knew there was a reason why I can't stand accordions! (runs for cover...)
Cheers
Ray


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Subject: RE: Is the tempered scale overrated?
From: Thomas the Rhymer
Date: 19 Oct 02 - 08:04 PM

Right On Ray, yer on it man! Fiddlers 'do it in the natural!'... I find that the pipes that play with me do it too... I try to limit my use of the tempered third in the guitar chords... its just that my guitar has such a temper tantrum... ;^{

ttr


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Subject: RE: Is the tempered scale overrated?
From: Peter K (Fionn)
Date: 19 Oct 02 - 08:37 PM

It is unlikely that the human ear would detect the differance over a couple of octaves. Over several, and particularly where notes from either end are likely to be played simultaneously, tempering (as well as stretching, in the case of a piano) is in my view is the best solution.

In western "classical" music (European art music; symphonic music; whatever) the equal temperament system (as opposed to "mean-tone temperament") is the norm worldwide, as it has been for a couple of centuries at least.

This site explains the various tuning systems in detail for those who (unlike me) are not mathematically challenged.


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Subject: RE: Is the tempered scale overrated?
From: Helen
Date: 19 Oct 02 - 08:48 PM

As a player of a Celtic Harp I am interested in this topic, although I am self-taught and I don't know a lot about the theory behind all of this. I love Middle Eastern music, and I believe that the scales they use are not tempered. I have a video tape of Robert Plant and whasisname - had to look it up - Jimmy Page - of Led Zeppelin fame playing with an Egytian band - brilliant!! Called "No Quarter - UnLedded".

The Egyptian music may have been modified slightly to play our scales but it sounds to me more like Plant & Page have modified our scale to fit their music. They have been interested in that style over many years and it shows most obviously in the song Kashmir.

I realised that many of the pop songs I really love have that Middle Eastern sound to them, including The Rolling Stones song Painted Black.

I saw the Howard Goodall documentary. It was very interesting and enlightening. I also have on tape - taped from the show - a documentary called "What is Music" (described briefly here) which examined a large range of interesting aspects of music, including the way sound changes when it gets louder. They used a trumpet as an example and said that digital sounds of a trumpet, at that stage, did not replicate the sound very well because of the changes over the time that the note is blown and depending on loudness.

Also relating to the harp: the Harplist (e-mail list) often discusses pentatonic scales, and when I flip the levers in a certain pattern on my larger harp which has levers on all strings, I can change it to pentatonic scale. Alan Stivell apparently used this tuning for a number of his tunes. The advantage for the harp music in doing this is that all strings are then in harmony with each other and it increases the sound quality of the harp because the harmonics it sets up creates a much fuller sound.   

Lately I have been thinking about different styles of music in relation to different scales, and wondering how it would work on the lever harp - i.e. mainly whether there would be too many accidentals requiring too many lever flips within one piece of music. I heard a Jewish song accompanied by harp a couple of days ago on the radio and I noticed that the tuning sounded different. The main (the only??) advantage to having to constantly retune harp strings is that the choice of tuning can be made with relative ease.

Helen


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Subject: RE: Is the tempered scale overrated?
From: Thomas the Rhymer
Date: 19 Oct 02 - 09:35 PM

I may be mistaken, but to my ear, some of the sephardic songs I've been listening to lately may be in the 'natural' mode... I'm sorry to be so insistant... but ear tuning a harp (esp. a piano) can be very educational,... and maddening...


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Subject: RE: Is the tempered scale overrated?
From: JohnInKansas
Date: 20 Oct 02 - 02:13 AM

Thomas -

Your reference to "natural" versus "equal tempered" made it sound like you were refering to the old argument of how best to divide the octave into a "standard western" 12 semitone scale. In that usage, the answer I gave is still applicable (in my opinion).

If, however, you - and others who have commented - are refering to scales in other music traditions, then the choice is not one of harmonic intervals versus equi-tempered intervals. Many other music traditions do not use a 12 semitone division of the octave. In quite a few "eastern" traditions, there seems to be no standard number of notes in the octave - although some academicians resolve this problem by saying there are arbitrarily "many ways" of tuning.

Certainly, if you are looking at music that does not use the twelve-tone scale, then you need to ignore equal-tempered tuning. You also need to ignore what is commonly refered to as "natural" or "harmonic" scale tuning, and simply find and use the "scale(s)" appropriate to the tradition of interest.

One of the difficulties you should keep in mind is that for the most part "non-western/non-twelve-tone" instruments are seldom made to "machine" tolerances (precisely tuned to established standard pitches), so that being (to our western ears) slightly "out of tune" is often part of the tradition. If you are going to play within one of these traditions, you will need to do things largely "by ear," so the argument of tempered vs harmonic/natural is not really applicable.
That argument applies only within the confines of how to tune for "western academic" music.

Try some good native-American flute music. Every flute, and every flutist, sounds somewhat different - and plays a different "scale."

John


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Subject: RE: Is the tempered scale overrated?
From: BlueSage
Date: 20 Oct 02 - 02:57 AM

I'm slightly confused by this thread. Is the term 'natural scale' being used to describe what is sometimes called a 'just' tuning? When I hear the phrase "natural scale", I think of a scale ( "G natural as opposed to G minor" ) not a tuning.

If this thread is about 'just' tuning, then many of us will have only an academic interest in the subject as our instruments will only play tempered tunings of some type or another. If you play a fretted instrument, unless you have removable fretboards for each key and mode, you will be stuck with a tempered tuning of some sort no matter how you tune.

Therefore even if I prefer the sound of a 'just' scale, I'm stuck with a tempered tuning on my particular instruments (guitar, mandolin, banjo).

Maybe I need to buy a fretless banjo and then revisit this thread.....

Mike


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Subject: RE: Is the tempered scale overrated?
From: pavane
Date: 20 Oct 02 - 03:47 AM

'Natural' tuning is based on a mathematical principle, that the perfect 5th is a frequency multiple of exactly 3/2.
(Discovered by Pythagoras)
As you go round the 'cycle of 5th's, taking the 5th of the 5th, (C - G - D - A - E etc) and so on, you get all the other notes, but as no power of 2 is ever equal to a power of 3, you never get back to where you started. As you wander further from the original note, (into other keys) it gradually sounds more out of tune.

Equal tempered tuning is a compromise which spreads the discrepancies
equally and makes ALL keys slightly out of tune.


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Subject: RE: Is the tempered scale overrated?
From: JohnInKansas
Date: 20 Oct 02 - 05:59 AM

The term "natural scale" is a little loose. As Pavane notes, the term "just tuning" is more descriptive - and more accurate, although I think that's what was meant in the original post.

It might be worth noting that having a fretted instrument doesn't mean that you have to use equal-tempered tuning, although usually the choice has to made before the frets are mounted.

It is perfectly possible to "just-tune" a fretted instrument, if that's how you choose to locate the frets. The problem is that such an instrument is playable (accurately in tune) in only one key, unless you are able to move the frets when you change keys. Early instruments did use "adjustable" frets, often consisting of loops of "gut" that could be nudged up and down to tune the individual notes. (There is a little problem of whether the same position of the fret is in tune for all the strings, when more than one string is used - but we'll leave that as an exercise for the students.)

Since a little before Pythagoras' time, some academics have had the notion that "nature is better pleased" with relationships that can be expressed as ratios of whole numbers, and just tuning sort of "fits" with that idea. It's a pleasant little notion, but mother seems to produce numerous "physical constants" that don't seem to want to work that way; so it's debatable whether it's her idea or ours.

You can make music as long as you can "find a pleasant tone." You can make music with others only if you can both "find the same pleasant tone." You tune to suit the purpose at hand.

John


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Subject: RE: Is the tempered scale overrated?
From: BlueSage
Date: 20 Oct 02 - 03:14 PM

Thanks, John, for answering my inquiry concerning 'just' tempered scales. I thought that might be what everyone was discussing but I wasn't positive.

I have encountered guitars with fret boards that slide out from under the strings and can be replaced with fret boards that are fretted for 'just' tempered scales for specific keys.

A lot of work for minimal gain?

Just a thought.... Mike


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Subject: RE: Is the tempered scale overrated?
From: Thomas the Rhymer
Date: 20 Oct 02 - 04:41 PM

Well now, I am pleased, perplexed, and misunderstood... ;^)

In my reference to 'natural' tuning, I am speaking of 'just' tuning. I am not attempting to discuss modes at all really, in fact I am trying to relate with you in the realm of just one mode... It doesn't matter which one you chose... just pick one, and lets move forward from there.

Next for me is this 'radical' notion... For this discussion, we are not going to change keys/modes. Dull?... Antiquated?... Pre-evolutionary?... I guess you can call it what you like, but this IS a folk/trad thread base, so the theory is Kinda over the top here now isn't it...

Many folk traditions are based on one key/mode exclusively, and we tend IMHO to forget that our improvements and embellishments are not the 'real thing'...

Here's an experiment; ...try taking a harp to just tuning. This means tuning all the notes to the tonic drone. If you are very careful to do it accurately BY EAR, you will not be able to get 'beats' or the phasing in and out of the conflicting and not quite in tune tempered tradition... Now... for all the imperfections and and inabilities spoken of above, there is a significant difference between this 'just scale' and the tempered modern counterpart. Now. Play that scale on the harp, with a tempered scale in the same key on another instrument. The difference is obvious, and immediately apparent. I believe that there is something to this.

My point is illustrated by an assertion. I have to say, that as much as I like classical music, it seems odd that the pieces based on folk/trad session jottings (more than we know, I'd be heard saying) really don't get it... IMHO... This may be one of many reasons. ttr


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Subject: RE: Is the tempered scale overrated?
From: GUEST,Arne Langsetmo
Date: 20 Oct 02 - 08:27 PM

JohnInKansas:

Yes, you'd need different D strings for different
chords, and that's precisely what the autoharp I
built a while back has.

It is basically a C diatonic harp, but the ability to
play some extra chords (and related minors), with extra
strings for some of the "accidentals" in some of
these (so you won't get a diatonic scale just strumming
up the strings).

The chords were mostly standard: Cmaj, Fmaj, Gmaj,
Amin, Gmaj7.

I added a few extra chords on (mainly to be able to
play a few extra chords and get out of the three-chord
rut on some of my favourite songs): Dmajmin7, Emaj, and Dmin
These necessitated adding a F# (at 588 cents) and
a G# (at 772 cents, off by almost a quarter tone!).

The D string is doubled, with one D for the GMaj chord
at 204 cents above C (9/8 = [3/2]*2 / 2). But there's
a different D in the Dmaj7 and Dmin chord, at 182 cents
above C (making for a perfect minor third up to the F,
and a perfect major fifth to the A).

I'll write it up in a bigger description when I
get a chance. Feel free to e-mail me (zuch@ix.netcom.com)
if you're interested in details.

Cheers,

                               -- Arne Langsetmo


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Subject: RE: Is the tempered scale overrated?
From: GUEST,Arne Langsetmo
Date: 20 Oct 02 - 08:37 PM

Oh, btw, anyone interesting in semitones, and even microtones,
and tuning adjustments on the fly, should look at the Turkish
zither, the canun.

Each string has some six sharping levers, each adding just
a smidgen, and the skilledplayers are flippng the levers
as they play, constantly modulating the tuning as required.

Whether they do this to bring the music into a more
"natural tuning" depending on how the keys modulate,
or whether they do this to drive Westerners crazy,
I don't know. . . .

Cheers,

                         -- Arne Langsetmo


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Subject: RE: Is the tempered scale overrated?
From: GUEST,Arne Langsetmo
Date: 20 Oct 02 - 08:41 PM

Ooops. Try "kanun".

Cheers,

                -- Arne Langsetmo


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Subject: RE: Is the tempered scale overrated?
From: Kaleea
Date: 21 Oct 02 - 05:37 AM

The main reason that we tune is so that we will be able to play an instrument with another instrumentalist and not cause rioting or the throwing of tomatoes. Perhaps we might go back to the way things were before J.S. Bach wrote "The Well Tempered Clavier" when the (so-called) black keys were 2 separate notes! In the olden days, the ones on the piano which we call "white keys" were back then the black ones. And the ones we call "black" . . .
ah, but that's another argument entirely!
Actually, I believe that the piano I was raised with was definately NOT tuned to equal temperament! It was so "sweet-tuned" (or rather, not tuned) that going up an octave was more like going up a minor 7th!! Middle C was closer to Bb. O-W-OUCH!! Many, many moons ago, when merely a slip of a girl, & I was in the Far East, I discovered that I could hear those darn "semi-tones" which are not supposed to be there. Then when I ran into some Polynesian guys with guitars & ukes, & their singing included some of those same darn "semi-tones." I was humming along with them, cause I didn't know the Polynesian words then, and they asked me how I knew the tunes. I had no answer for them. But I hummed along, nevertheless! They told me that the songs were some of the oldest ones that the elders remembered, and they had never met someone who was not from the Islands or mid/far east who could hear those notes. They said they thought that I was someone who had lived there (Polynesia/Hawaii) in a previous life! I said, "Can I go back there, & then? 'Cause that's the most beautiful music I have ever heard!" Funny thing is, a man sitting at a table in a street in the Far East told me I had lived in the Far East before, too! hmmmmm. . .)


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Subject: RE: Is the tempered scale overrated?
From: Pied Piper
Date: 21 Oct 02 - 08:17 AM

Equal temperament was developed to allow modulation between Keys. Earlier tuning systems allowed for some limited modulation, but Keys had "nasty" sounding "Wolf" chords. By putting all intervals equally out of tune by a small amount, all the chords sound the same (non-just) intervals regardless of Key.
This is a musical compromise made for certain types of music. Bach's music just would not be possible in any other type of tuning system. I love Bach's stuff, and for music of this type Equal temperament is the only option.
Now when we come to some other musical forms, this compromise is at best unnecessary, and at worst destructive to the inherent beauty of such forms.
Obviously to play all the many "natural" intervals you need an instrument with infinite pitch resolution (the Human voice, Fiddle, ect). But it is a mistake to think that wind instruments with holes cannot be played in this way (listen to any good Arabic Nay or Indian Shanai player).
Even if your instrument has intervals that you cannot adjust whilst playing you can set them up at the start in interesting ways.
I play Highland Pipes using the following non-ET tuning.

The first note of the GHB scale is a Harmonic Seventh below the Tonic (drone note). Expressed in terns of ratios to the tonic, the intervals are: -

8/7    1/1    9/8    5/4    4/3    3/2    5/3    16/9    2/1
Harmonic Tonic   Major   Major Fourth   Fifth   Major   Major Octave
seventh          Tone    3rd                     6th    Tone
                                                         down
All the intervals being "Just"
   
   Experimenting with intonation is fascinating, and will make you a more informed musician, but more importantly puts You in charge of your intonation.

All the best PP


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Subject: RE: Is the tempered scale overrated?
From: GUEST,Arne Langsetmo
Date: 21 Oct 02 - 10:36 AM

How do you know when the highland pipes are sounding
dissonant?    ;-)

Wasn't that "harmonic seventh" 7/8, and not 8/7?
That's in any case a weird one. At 231 cents
down (or up, if it was 8/7), 31 cents off the
equal temperament, it seems way out of from the
others. But it's not all that bad if it's the
the 7/8 frequency, and the denominator is 8.

As I understand it, chords sound "sweeter" when
there is some high LCD of the frequencies
(i.e. all the frequencies are harmonics of
some fundamental somewhat above a thud).

Looks like your 7/8 may be related to the G# on
my autoharp (in the Emaj chord), down 231 cents
from the tonic, but off ~228 cents from the
major town down. Coincidence, maybe ... I'll
have to go check the math ... the 7 in there
shouldn't show up in my tuning, but then again,
I think I also came up with a LCM of 72 in the
denominator when all was said and done.

Cheers,

                      -- Arne Langsetmo


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Subject: RE: Is the tempered scale overrated?
From: GUEST,Arne Langsetmo
Date: 21 Oct 02 - 10:39 AM

Ooops. GCD (greatest common denominator), not LCD.
LCD is what your wristwatch has.

Cheers,

                               -- Arne Langsetmo


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Subject: RE: Is the tempered scale overrated?
From: Pied Piper
Date: 21 Oct 02 - 12:23 PM

Hi Arne.
I expressed the lowest note on the highland pipes as 8/7 rather than a 7/4 because it is below the tonic note.
This interval I agree is a lot flatter than an ET tone down. It is the interval that a barbershop singer would sing in a seventh chord.
Bellow is one of Harry Partch's "insipient tonality diamonds". All the intervals played together diagonally from the bottom corner up towards the right produce perfect Major seventh chords, and from the bottom towards the left produce perfect Minor seventh chords in downwards order. This uses all the simple ratios within the limit of 7, giving 4 Major Seventh and 4 Minor Seventh Chords (and of course 4 Major and 4 Minor chords   

                         7/7
                      12/7 7/6
                   10/7 3/3 7/5
                   8/7 5/3 6/5 7/4
                     4/3 5/5 3/2
                      8/5 5/4
                         1/1

I hope this makes things clearer (I've got to admit it totally confused me when I first came across it, but its worth persevering with).
The above is from Harry Partch's book "Genesis of a music", well worth a read if your interested in Just scales and Harmony.

All the best PP.


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Subject: RE: Is the tempered scale overrated?
From: GUEST
Date: 21 Oct 02 - 03:39 PM

Thanks, PP, for the info and the reference.

Looks like it should be 7/8 for the harmonic seventh.

The 8/7 comes into the minor seventh:

(Assuming key of Cmin)
Minor seventh (basically /freq of each tone for the major 7th):
note freq   cents +/-cnt abs    diff from prev note
B~: 8/7:   231   +31    +0
C:   8/6:   498   -2    +267   +267
E~: 8/5:   814   +14    +583   +316 (minor third)
G:   8/4: 1200   0      +969   +386 (major third)
B~': 16/7: 1431   +31    +1200 +231 (harmonic seventh)

Here the 7th is down 267 cents from the "tonic" (_waaayy_ down),
but also 231 cents up from the fifth in the minor chord.
So if you're doing perfect minor sevenths, looks like
a different tuning for that seventh down below.
note freq      harmonic          (note in series)
B~: 840/14 = 60 * fundamental (x/7)
C:   840/12 = 70 * fundamental (x/6)
E~: 840/10 = 84 * fundamental (x/5)
G:   840/8   = 105 * fundamental (x/4)
B~': 840/7   = 120 * fundamental ((x/7)*2))

Dunno how that sounds though, which is the real test, eh?

Cheers,

                           -- Arne Langsetmo


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Subject: RE: Is the tempered scale overrated?
From: Thomas the Rhymer
Date: 21 Oct 02 - 04:11 PM

I am getting quite a kick outta this...

Thank you Arne, John, Kaleea, PP et all! This math adds some insight to my intuition, and though my musical approach is largely intuitive/instinctual, it is really good to have relevant theory behind it. I wonder though... I don't know how to measure the absolute/relative cents of a given note. Since I play predominantly by ear, I would enjoy the verifying process of measuring existing notes (ones chosen previously by ear). How is it done? ttr


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Subject: RE: Is the tempered scale overrated?
From: JohnInKansas
Date: 21 Oct 02 - 05:15 PM

TtR -

One of the most thorough analyses of most of what has been discussed can be found in the Dover paperback On the Sensations of Tone, by Hermann Helmholtz. The original "2d edition" that Dover copied dates to 1885, but one advantage of its age is that it discusses measurement of sounds in terms of apparatus and techniques that are a little more accessible to the amateur than some of the more modern stuff. The Dover edition is still in book stores in my area, and you should be able to pick it up for $15 - $18 (US) or so.

It should be noted that Helmholtz made some minor errors, that later research has found, but they shouldn't detract from usefulness of the book. It should also be noted that it's nearly 600 pages of analysis, experiment, and discussion of fairly technical stuff - so you need a serious interest to get through it all. All the ratios and deviations between just and tempered note frequencies are there.

More recent, Fundamentals of Musical Acoustics by Arthur H. Benade, originally published 1976, is also available as a $18 US or so Dover reprint.

As to measuring notes that you've tuned by ear, most electronic "tuners" will give you some indication at least whether the note is sharp or flat relative to "standard" for the nearest note. Somewhat better ones allow you to change the "A" frequency so that you can shift all of the notes. You do need to get into a true "metering" tuner in order to be able to read how far you are away from the "standard" note, and unless you shop around you can easily pay $100 (US) or more for a good one.

As mentioned previously, most simple tuners have a "sample and hold" mode built in, so that they hold the reading for the first few cycles that they "hear." This makes it impossible to measure the difference between the initial pitch when you pluck a string and the pitch it settles to as the sound decays. You'll have to look pretty hard to find a cheap tuner with a "rapid mode" if you're interested in this phenomenon.

If you're mechanically inclined, you can do it like Pythagorus did and make yourself a one string dulcimer with a movable "fret." Tune the open string to a known value, and move the "fret" until it sounds a match to your chosen note. Calculate the frequency from the active string length. (He really did do it that way, I'm told.)

John


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Subject: RE: Is the tempered scale overrated?
From: pavane
Date: 22 Oct 02 - 02:40 AM

Another thing to consider is that each instrument produces a (different) variety of 'overtones' which are multiples of the fundamental pitch. (If they didn't, they would all be producing pure sine waves, and all sound EXACTLY the same!)

The first overtone is double, and is an octave above the fundamental, so no problem there. The second is three times the fundamental, and is equal to an octave and a fifth (Natural, not tempered!). This may therefore, if loud enough, clash with a tempered fifth being played.
The third overtone is four times, and is another octave. The fourth is five times the fundamental, and APPROXIMATES to a third, if I remember my calculations correctly. But this and higher overtones are usually faint enough not to clash.

This also provides part of the explanation for the old 'valve versus transistor amp' argument. Overloaded transistor amps used to introduce more third harmonic (=second overtone) distortion, which is quite noticeable.


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Subject: RE: Is the tempered scale overrated?
From: Pied Piper
Date: 22 Oct 02 - 06:47 AM

Pavan is absolutely right here.
   Any mechanical oscillating system be it a string, a column of air, or whatever, generates a whole load of notes other than the fundamental. This set of notes is called the harmonic series, and consists of hole number multiples of the fundamental. For the note A-440Hz (vibrations per second): -
   Frequency    Interval ratio       Name
                expressed as within
                1 octave (2/1)

A   440Hz          1/1             Tonic
x2   880Hz          2/1             Octave 1
x3   1320Hz       3/2             Perfect 5th
x4   1760Hz       1/1             Octave 2
x5   2200Hz       5/4             Perfect Major 3rd (2nd Octave)
x6   2640Hz       3/2             Perfect 5th (2nd Octave)
x7   3080Hz       7/4             Harmonic 7th (2nd Octave)
x8   3520Hz       1/1             Octave 3
x9   3960Hz       9/8             Major 2nd
x10 4400Hz       5/4             Perfect Major 3rd (3rd Octave)
x11 4840Hz       11/8          Augmented 4th/Diminished 5th ?

    And so on theoretically fore ever, but in real systems the amount of energy in these "partials" diminishes as the harmonic number increases, so you only hear the first few.
   This series also produces other intervals between the harmonics.

   You can see above, the intervals produced by the GHB Drone correspond to notes in the Pipe scale. Its interesting to note that traditionally tuned Pipes have a Sharp 4th possibly the 11/8 interval from the series.

      All the best PP


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Subject: RE: Is the tempered scale overrated?
From: JohnInKansas
Date: 22 Oct 02 - 01:25 PM

One of the difficulties usually ignored in "discussions" about just tuning and equal tempered tuning is that most physical devices only approximate the "pure" integer frequency relationships between the fundamental tone and their harmonics.

Arguments about any "superiority" of just tuning are almost required to include the assumption that the harmonics are in strict integer frequencies. x1, x2, x3, ... etc.

For a reasonably long string at reasonably high tension, it works out pretty well - which is a reason, perhaps, why strings are much favored in music. It holds pretty well for long "pipes," provided that they don't get too "fat." It doesn't work at all for "free-reed" instruments like harmonicas and accordians.

For a "free-reed," the first harmonic is NOT at twice the frequency of the fundamental tone - and the deviation increases as you consider higher harmonics. This may be one reason why - as offered above - squeezeboxers were among the first to truly accept equal tempered tuning (to the extent that you can "tune" one).

Even for a simple "pipe" like a whistle, the "effective length" of the tube depends on the wavelength. The wave node (or peak, depending on how the tube is stopped) actually extends a little past the end, making the "acoustic length" a little different than the physical length. Since a short wave (high harmonic) doesn't "stick out as much," the higher harmonics of the tube actually tend to go a little sharp relative to the fundamental tone. The situation is even a little worse with a "finger hole" since the pneumatic resistance of the "rest of the tube" makes the effective length pretty "squishy," and significantly different for each "harmonic" contained within the tone.

Reference has been made to the "Barbershop" effect of just tuning, but it is quite possible for your "lead" to sing to an equal tempered scale - if that's what he/she has learned, while the "harmony parts" tune (in just intonation) to each individual note that the lead sings. Most people will not be able to detect the "scale" in use - but will still be impressed with the "great resonance" of the well "intoned" harmony. (Actually, your lead would need a pretty tin ear not to automatically "drift into" a just scale, but I've encountered a few people who are "stuck in equal temper.")

The theory is there to help with quessing what mother nature does; but you've got to remember that "she don't do math," and she can get pretty sarcastic with people who rely on simple math try to do too much. More complex math can get you a little closer, but the instrument-to-instrument (and even note-to-note) variations make it difficult to make general statements with any great confidence.

John


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Subject: RE: Is the tempered scale overrated?
From: treewind
Date: 22 Oct 02 - 01:51 PM

As far as I know, free reed harmonics are in tune and I can't see any reason why they shouldn't be, since the sound comes from the periodic interruption of the airflow past the reed. Strings (especially piano strings) have out-of-tune harmonics because of "end effects" meaning the effective length of the string isn't the actual length (because there's some elasticity in the end points) and the end effect has different proportional influence on the vibration for harmonics, where the string is vibrating in sections.

The real reason why squeezeboxes are equal tempered is simply that many of them are fully chromatic and can be played in a wide variety of keys.

In fact, diatonic accodions two row anglo concertinas are no equal tempered, as both are restricted to a small range of keys and therefore can safely be in just (harmonic based) tuning.

Anahata


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Subject: RE: Is the tempered scale overrated?
From: JohnInKansas
Date: 22 Oct 02 - 05:37 PM

treewind -

There are a lot of fully chromatic instruments whose "drivers" resisted the equal tempered thing for quite a while, and continue to do so.

The comment about "whether squeezeboxes can be tuned" was meant as a friendly jest. The fact is that the fundamental note of a free reed can be quite readily and accurately tuned, but the harmonics produced by a free reed, as in a squeezebox, harmonica, or reed organ, are not harmonically related to the fundamental in the simple "ratio of integers" way one might expect from simple analyses of strings and air columns.

When any "simple" instrument plays, for example, a D, one expects the "hear" a first harmonic at d and a second harmonic at a. Another "just" tuned instrument playing an A or a either is precisely "in sync" with, or at least has its own harmonics exactly synchronised with, the harmonic content of the first player's note. This is what gives a chord in "just intonation" its "full and mellow resonance," which is so appealing.

Unfortunately, a resonant bar, such as a squeezebox free reed, does not produce linearly related harmonics, so it is NOT possible to play two different "real notes" that share the frequencies of the harmonics of a free reed. It is thus NOT possible to play or sing a "justly intoned" chord to accordian (or reed organ) accompaniment.

Apparently this is seldom a problem, as reed instruments survive and prosper. Congratulate yourself on your selection of a "much richer toned" instrument than those simple gittars and such, and enjoy.

John


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Subject: RE: Is the tempered scale overrated?
From: GUEST,Arne Langsetmo
Date: 22 Oct 02 - 09:38 PM

Tuners: You can get chromatic tuners (I've owned three different
makes of chromatic tuners, and used others) that give you
a more or less accurate cent deviation from even tempered
tone (and usually an adjustable A440 as well). You should
be able to get a reasonable one for < $50 if you need one.
Some have "slow/fast" settings on how long they sample,
so that you can check the initial attack if that's important
or the sustain if that's what you want (depends of the
instrument and music you're playing what's important).

The initial attack, it should be noted, has an intrinsic
broad spectrum (or frequency spread), so that the
frequency is probably not as critical for this part
of the note.

Harmonics: Thanks to all for their comments here; I
learned a few things. Yes, the harmonics are not
really integral. I would assume that the ear itself
is also not "perfect" in the way it responds to
mixed frequencies, so this should also be taken into
account. In the end, it's what _sounds_ best that
you (hopefully) are trying to achieve.

Harmonics 2: Fiddles and other strings are very strong
in the low harmonics because of the excitation of the
sustained note approximates a saw-tooth (which has
real strong components of _all_ the harmonics).
That and the sustained notes make the harmonics
more noticeable (which is why a nonfretted neck is
probably a good idea for these).

Harmonics 3: Yes, distortion of amps can be noticeable
(although proper design of both tube (valve) and
transistor amps currently makes the difference
between the two less significant nowadays). The
same "distortion" is in fact what you purposely
use on an electric guitar with a distortion box
(or simply a badly overdriven amp), and sometimes
this is the desired effect.

Frequency of strings, reeds, etc.: Pretty much all
instruments will show a frequency shift for a loud
note versus a soft note (as others have noted for
strings). This needs to be taken into account as
well.


And agreed, all the math in the world, while interesting,
doesn't explain everything that makes things sound
"bad" or "good". Which is readily apparent in banjoes and
accordions.    ;-)

Cheers,

                            -- Arne Langsetmo


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Subject: RE: Is the tempered scale overrated?
From: Thomas the Rhymer
Date: 22 Oct 02 - 11:10 PM

It's all the math in the world, you see
That's lost the simple tune, tra la
But when we dance and when we sing,
We laugh with the fanciful moon, tra la

Well now, I must be getting back to my original quandry...

There does seem to be adequate proof prevailing that the tempered scale, though a bit off, is a compromise worth it's future in modulation and group musical enjoyment. I myself, have been known as a wreckless modulator, of sorts, and I've enjoyed some of the most wild and frequent shifts of keys... I am strutting resplendently here... But I am still faced with this nagging harranguing meekly persistant little voice that says:

"The natural scales kick ass on the competition"...

And it 'drones'... on and on... :^)


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Subject: RE: Is the tempered scale overrated?
From: pavane
Date: 23 Oct 02 - 07:29 AM

Re Free Reeds: (I play harmonica, melodoen, anglo concertina)

Maybe that is why you don't seem to be able to get a decent accordian or harmonica sound from any MIDI players?


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Subject: RE: Is the tempered scale overrated?
From: GUEST
Date: 23 Oct 02 - 08:57 AM

John in Kansas - I understood you the first time, about the harmonics not being in tune. With all due respect I don't believe it, but I am willing to be educated. Can you supply references to evidence for this?

I can hear the 2nd and third harmonics of notes from my concertina quite clearly and they don't seem to be out of tune.

As for difficulty of synthesis, the strings of a piano, especially the low end, definitely have their overtones badly out of tune i.e. not simple ratios, so that should be difficult to synthesise too. Of course good synths use samples of real instruments anyway but I digress...

Anahata


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Subject: RE: Is the tempered scale overrated?
From: Jeri
Date: 23 Oct 02 - 10:06 AM

Just to butt in with some HTML, you can add pre-formatted text tags to get charts to line up correctly. You just need a <pre> at the beginning, a </pre> at the end, and use the space bar (not 'Tab') to even things out. Here's Pied Piper's chart as an example:

<pre>

Frequency       Interval ratio       Name
                expressed as within
                1 octave (2/1)

A   440Hz       1/1                  Tonic
x2 880Hz       2/1                  Octave 1
x3 1320Hz      3/2                  Perfect 5th
x4 1760Hz      1/1                  Octave 2
x5 2200Hz      5/4                  Perfect Major 3rd (2nd Octave)
x6 2640Hz      3/2                  Perfect 5th (2nd Octave)
x7 3080Hz      7/4                  Harmonic 7th (2nd Octave)
x8 3520Hz      1/1                  Octave 3
x9 3960Hz      9/8                  Major 2nd
x10 4400Hz      5/4                  Perfect Major 3rd (3rd Octave)
x11 4840Hz      11/8                Augmented 4th/Diminished 5th ?

</pre>

As to equal vs just tunings, I suspect I use just when I sing - especially harmonies. I've tried recording myself over myself. If I memorise the harmony and sing it separate from the melody, I'm out of tune. Probably because I'm using equal-tempered scales. If I can hear the melody while I sing, I can adjust my voice to sound right.

See Bruce Olson's website for a version of ABC "Trial version of ABC player and tune stressed note-keynote-mode and mode number coder. Play just intonation or 12 tone equal temperament scale for tunes in ABC notation in large files of ABCs. Requires MODETABL.TXT and .DLL files below. New 08/14/02- Plot up to 8 tunes simultaneously, with adjustable scale factors and origin, and see what the % of total time is used for each note."


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Subject: RE: Is the tempered scale overrated?
From: GUEST,Arne Langsetmo
Date: 23 Oct 02 - 10:42 AM

Hi Pavane:

"Get a decent accordion or harmonica sound". . . .
Ummmmmmmm, have you considered any _other_ explanations?   ;-)

(full disclosure: I have an accordion myself). . . .

Cheers,

                                 -- Arne Langsetmo


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Subject: RE: Is the tempered scale overrated?
From: JohnInKansas
Date: 23 Oct 02 - 06:20 PM

Guest - anonymous

The resonant frequencies and harmonics for bars, which approximate the behavior of a free read, were calculated early in the 18th century, and the calculation can be found in any number of textbooks. Im sure I have a half-dozen textbooks with the calculation, but I don't recall which ones (of my 1500 or so) gives the simple form.

The Helmholtz and Benade Dover editions that I suggested at 21 Oct 02 - 05:15 PM both make reference to the results, although neither gives the calculation (which is a lot simpler in tensor form).

Where a string (or uniform air column) theoretically has its first and higher harmonics at 2, 3, 4 etc times the "fundamental" frequency, a uniform bar has its first partial at 2.756 times the fundamental (approximately), and the next higher "overtone" at about 5.404 times the fundamental.

A "real world" reed is not, of course, a uniform bar; but in general that just makes things even more "messy." Typically, the lower reeds are thicker at the outer end than at the attached end, while the higher ones are just the opposite, and the width may also vary. It is also significant that a "straight" reed won't vibrate - you need enough "kink" in them to open the air passage enough to get a starting air flow. A twist - sometimes added for "easy starting" of the notes can add additional "torsional mode partials" that have no fixed relation to the fundamental frequency of the reed.

The Helmholtz book in particular gives some fairly detailed discussion of free reeds, although its mostly in the extensive "footnotes" citing other sources, and it's scattered (according to index entries) all the way from page 55 to page 572. There is some good stuff on tuning and adjusting them, if you need it.

If an accordian produced linearly related partials, it would sound like a flute. You probably wouldn't want that.

(Helmholtz also discusses why the partials for the low piano strings aren't where the "should be." The simple put there is that it's because you can't whack them at the right spot - because of their length.)

It's a fun subject, but not really one to get too uptight over.

John


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Subject: RE: Is the tempered scale overrated?
From: GUEST
Date: 23 Oct 02 - 07:46 PM

For the record, a Just Tempered scale is not a "Natural" scale--it is derived from a formula, based on the octave (2:1), the perfect fifth (3:2), and the major third (5:4)--a "natural" scale would be follow the Pythagorean series, which would follow the circle of fifths, the notorious "comma", which means that the last note in the series overshoots the first one by about 24 cents--the formula for the just scale was devised to work around the comma-

The just scale itself is not very practical for a couple reasons:

A) The C major scale features two different sized whole steps--the one from C-D is a bit larger than our whole step, and the one from D-E is a lot smaller--

B)The fifth interval between D and A is so far off that it is a noticeable dissonance--

C) Even the simplest key change, from C to G is impossible because the first three steps in the scale, C-D-E and G-A-B are not space the same way--(you'd need to have to change the pitch of A when you changed to the G)--

This is not to say that it is not possible to play and write music on a just tuned instrument--only that the type of melodies that we use most, which use horizontal chords and diatonic chord changes, will lose a lot of their lustre--

Modal music, such as is played on the pipes, or the multiferous droned stringed instruments, works just fine--

Actually, if you dispense with the need to change keys, and eighty-six all those chords (often in favor of a couple of octave/fifth drone notes) you can pretty much set the pitches for scale notes as your own taste dictates--

There are a a number of musical traditions where the pitch values are a matter of personal taste--who needs harmony? Melody and rhythm could keep you busy for a dozen lifetimes!


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Subject: RE: Is the tempered scale overrated?
From: GUEST,M.Ted
Date: 23 Oct 02 - 07:57 PM

That was me. Sorry, I just installed and subsequently de-installed a new browser--I think it took the cookies with it when it left--


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Subject: RE: Is the tempered scale overrated?
From: Thomas the Rhymer
Date: 23 Oct 02 - 08:53 PM

For the record...

I originaly mentioned the 'natural' interval scale, and then waffled towards a term I 'just' didn't really understand... sorry... I am very consistant when I am 'free' tuning to a drone note... and the scale that I come up with 'doesn't play well with others', but it sounds 'right' to my ear. The resolve of the dominant chords pertaining to the tonic drone are very satisfying, and soothing. Although the effect is considered minimal, to my ear, it is consistantly preferred. If I am playing fixed tone tempered instruments, this question never comes up... and this thread is helping me get to the marrow on this nagging issue for me... Thanks so much!

Come to think of it, this may be why the fiddle is so difficult for me... Cheerio! ttr


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Subject: RE: Is the tempered scale overrated?
From: Thomas the Rhymer
Date: 23 Oct 02 - 09:25 PM

OOPS! ...difficult for me TO PLAY!


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Subject: RE: Is the tempered scale overrated?
From: pavane
Date: 24 Oct 02 - 02:26 AM

Even sampling doesn't give synthesisers the correct sound over the whole of the range of a instrument, because they only sample a small selection of notes, and extrapolate. THey will not pick up the full range of variation.


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Subject: RE: Is the tempered scale overrated?
From: treewind
Date: 24 Oct 02 - 05:05 AM

J in K - I am the anonymous guest you replied to - didn't notice I had lost my cookie that time.

I agree with everything you say about the vibrations of free reeds, and that accounts for why if you press the reed pan of a concertina to your ear (or put a microphone or contact pickup on it) and
'ping' the reed, you get a rather jangly bell-like sound that bears no relation to the sound of the instrument when played.

However, the vibration of the reed is not what you hear when the instrument is played. The reed alternately opens and closes a slot in metal plate, and air under pressure is alternately passed and blocked. The interrupted air flow is what you hear, and is not far off a square wave, probably a bit asymmetrical (which gives it some even harmonics) and with less sharp corners than a pure square wave (which makes it less shrill). The harmonics of that square wave are certainly in tune and predominate.

Anahata


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Subject: RE: Is the tempered scale overrated?
From: Pied Piper
Date: 24 Oct 02 - 10:25 AM

Thanks Jeri. I'll use that tag in the future makes things a lot easer.
John you said, "If an accordian produced linearly related partials, it would sound like a flute". I don't think that's correct, the main factor in Timbre is the relative volumes of the partials. The GHB drone does not sound at all like a flute but its Harmonic Series is most definitely Linear.
Jews harps produce in tune integer multiple harmonics, even though the vibrating bar presumably does not. In this case the bar merely excites the resonant space of the vocal tract. I'm not shore of the relevance of this to Western free reed instruments, but in Oriental free reed instruments the reed is started vibrating by being coupled to a resonant length of tube, which would force it into a pretty accurate linear harmonics.
One group of instruments that does produce non-integer multiple harmonics, are simple Drums. Having said that you only have to listen to Tablas or Kettledrums to realise that more sophisticated designs can force linearity on at least the first few harmonics.

   All the best PP.


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Subject: RE: Is the tempered scale overrated?
From: Pied Piper
Date: 25 Oct 02 - 08:04 AM

Refresh


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Subject: RE: Is the tempered scale overrated?
From: Uncle_DaveO
Date: 09 Jan 07 - 02:06 PM

A little pedantry here: To refer to "tempered tuning" is not meaningful.

There are a number of ways a scale (or an instrument) may be tempered. The ones best known are "equal tempered" and "well tempered", which are not the same thing, a-tall, a-tall.

Dave Oesterreich


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Subject: RE: Is the tempered scale overrated?
From: Anglo
Date: 09 Jan 07 - 03:18 PM

There's an interesting blog here.

Music theorist Kyle Gann's Post-Classic column on the Arts Journal site, "The Tuning Tide Turns," Jan. 4 2007.

(Well, I thought it was interesting).


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Subject: RE: Is the tempered scale overrated?
From: Big Al Whittle
Date: 21 Apr 07 - 03:06 AM

what would be a tempered tuning for the guitar?


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Subject: RE: Is the tempered scale overrated?
From: pirandello
Date: 21 Apr 07 - 07:57 AM

I just use an A440 tuning fork and my ears. Lucky I play the guitar!

Steganpid; um, is there something you need to tell us?


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Subject: RE: Is the tempered scale overrated?
From: leeneia
Date: 21 Apr 07 - 10:38 AM

John in Kansas wrote: "Since a little before Pythagoras' time, some academics have had the notion that "nature is better pleased" with relationships that can be expressed as ratios of whole numbers, and just tuning sort of "fits" with that idea."

After studying this thread, I have decided that Just or Natural tuning is one of those ideas that the ancients had that actually never worked out. Other ideas like that were:

the planets must have circular orbits,

there must be a Terra Australis somewhere to balance Eurasia, because God wouldn't make a seriously asymmetrical world. (They didn't know how big Africa was, apparently.)

the stars are immutable.

plants resemble the organs whose diseases they cure. (liverwort, pulmonaria.)

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I am not trying to be snide when I say that after a certain point, tuning should be entrusted to the ears, not to theory. I am thinking of recorder groups I have been in, where the teacher tells us to play a certain chord and tune it ourselves. It is amazing what nexperienced players can do just by listening intently and aiming for a beautiful sound.

Hearing is a primitive function, and it can accomplish things that language cannot put into words.


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Subject: RE: Is the tempered scale overrated?
From: Stringsinger
Date: 21 Apr 07 - 12:03 PM

The tempered scale was created so that instruments could play together without sounding out of tune with each other. Bach's "Well Tempered Clavichord" was probably written with this in mind since musical aggregations were getting larger culminating in the Viennese symphonic styles.

Tempered scales are probably not important in music from Asian, African or less urban areas of the world. They are useful for soloists who don't have large musical aggregations with which to contend.

Frank Hamilton


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Subject: RE: Is the tempered scale overrated?
From: Jack Campin
Date: 21 Apr 07 - 01:35 PM

It is absolutely dead certain that Bach did *not* have equal temperament in mind for any piece he ever wrote. We don't know for sure what temperament he had in mind for The Well-Tempered Keyboard, but "anything reasonable" sounds like a good bet. He circulated it in his lifetime and didn't provide an accompanying secret decoder ring. He wouldn't have got many takers if it didn't work on the usual unequal temperaments of his own time.

It is very easy for instruments to play together in large heterogeneous groups whatever the tuning they use. There have been court orchestras in the Far East much larger than any present-day symphony orchestra.


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