daver@felix.UUCP (Dave Richards) (06/27/90)
In article <1415@yenta.alb.nm.us> yenta!dt@bbx.basis.com writes: >from a 440-A based well tempered scale.) But even when I was five years >[etc] ^^^^^^^^^^^^^ and later: >a 'just' scale), not well tempered ones, as the just intervals are more >[etc] ^^^^^^^^^^^^^ The same phrase appears a few more times. David, I think you mean "equal- tempered", don't you? (ET: every interval between adjacent semitones is the same ratio.) "Well tempered" is some other compromise. Dave
dt@yenta.alb.nm.us (David B. Thomas) (06/28/90)
daver@felix.UUCP (Dave Richards) writes: >David, I think you mean "equal- >tempered", don't you? (ET: every interval between adjacent semitones is the >same ratio.) "Well tempered" is some other compromise. Yikes! That's what I meant. Thanks! David
torkil@psivax.UUCP (Torkil Hammer) (07/04/90)
In article <1415@yenta.alb.nm.us> yenta!dt@bbx.basis.com writes:
#
# It is interesting that you mentioned alternate tuning schemes. Hermann
# Helmholz (sp?) in his classic "On the sensations of tone" notes that
# seasoned string players tend to automatically play just intervals (from
# a 'just' scale), not well tempered ones, as the just intervals are more
# harmonious. Often they have not been explicitly trained to do this.
There is a simple explanation. When 2 strings are bowed together,
they interact via the bow so that they try to pull into a phase lock,
which is a Just interval. If they are too far away to do this, the
resulting disharmony makes the instrument and the bow shake in an
offending way, and in addition the bowing is likely to miss.
This holds true for unisons as well as intervals, and if you play a
violin you can try the effect by playing an f# on the d string
together with an open a.
The same is true for tuning. All violinists I know of tune the a
from the conductor's pitch pipe or an electronic device, then tune
the d and e strings in just fifths to that a, then the g in a just
fifth to the d. (Those that crosstune use the same principle with
different intervals). Because otherwise 2 open strings bowed together
sound and feel like a catfight.
As an interesting aside, when I play melodic tunes using seventh
chords they come out in the Just 4:5:6:7 interval, which means that
a d7 chord will have d, f#, a, and midway between b and c on the top.
The 4:7 interval is "sufficiently Just" to phase lock between an open
d string and the b/c tone on the a string.
#
# One more thing while I'm squandering bandwidth anyway...I have long
# been fascinated with quarter tone intervals. By themselves they sound
# terrible (at least, to my western ear). But I have found, so far,
# a very few examples of western music where a note a quarter step away
# from the nearest 'piano' note sounds sweeter in the passage than either
# of its neighbors. Very unusual, and very interesting. I have what is
You can probably recognize the 4:7 (or n:7) interval, even when played
as separate tones. It is only a matter of training.
Torkil Hammerericm@FtCollins.NCR.com (Eric.Mintz) (07/05/90)
In article <3434@psivax.UUCP> torkil@psivax.UUCP (Torkil Hammer) writes: > There is a simple explanation. When 2 strings are bowed together, > they interact via the bow so that they try to pull into a phase lock, > which is a Just interval. If they are too far away to do this, the > resulting disharmony makes the instrument and the bow shake in an > offending way, and in addition the bowing is likely to miss. > This holds true for unisons as well as intervals, and if you play a > violin you can try the effect by playing an f# on the d string > together with an open a. Though I understand, in principal, the concept of tempered and "pure" tuning, I have never (no my knowledge) heard pure tuning. Is there any way I could tune my guitar to demonstrate the sound of pure tuning? -- Eric.Mintz@FtCollins.NCR.COM ____________ _____ ____ / / - / / / / / | / / O ---- _________ O _ _ / (_ ___ / / / / / / / | / ___ | / / / |/ | / _ ) / \ / / / / / ( / (| | / () ) / /___/ (_/ |_/ / | ( _/ () ) |/ / / \___/ /\___ \_/ /\__/ |___________/^_/\___/ |_____/\__/ O Eric Mintz, Software Development, NCR Microelectronics 2001 Danfield Court, |~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Ft. Colling, CO 80525 | "Get your crummy feet off my bed ya (303) 223-5100 ext 422 | little goof." Wally Cleaver
alves@alcor.usc.edu (William Alves) (07/06/90)
In article <ERICM.90Jul5110915@gershwin.FtCollins.NCR.com> ericm@FtCollins.NCR.com (Eric.Mintz) writes: > >Though I understand, in principal, the concept of tempered and >"pure" tuning, I have never (no my knowledge) heard pure tuning. Is >there any way I could tune my guitar to demonstrate the sound of pure >tuning? Unfortunately, your instrument is not a good one for demonstrating just intonation because the frets have been set into place (for each string) to facilitate equal temperament. However, you hear the difference between a just and non-just fourth every time you tune your instrument. When you tune the fourths between the strings so that there are no beats, you have tuned a just perfect fourth (4/3 ratio). This interval is about 2 cents flat of a fourth in equal temperament. Not a great difference, but enough to be noticeable. The difference between just and non-just thirds is much greater though, and can also be demonstrated on open strings. The way a guitar is normally tuned (E-A-D-G-B-E with perfect fourths up from the bottom E-A-D-G and down from the top E-B with the two E's in tune) will result in the ratio 81/64 between the G and the B, quite harsh in comparison with the just 5/4. In fact, the 81/64 third is a full 22 cents sharp of the just third (an interval called the syntonic comma), and the equal tempered major third is about 14 cents sharp. To hear the difference, try tuning the B string flat until the beats disappear. Of course you will no longer have a just fourth between the B and the E, but such is the dilemma of tuning. But unless you're playing all on open strings (or with natural harmonics, another way to hear just intervals), you won't be able to actually play in just intonation on an instrument with fixed frets. Variable tuning sys- tems are best suited to instruments with a separate sounding body for each pitch (such as a keyboard instrument or harp). Instruments with continuous pitch selection (fretless strings, voice, trombone) can also, of course, vary their tuning, but, in my experience, with less accuracy or consistency, especially with no external reference (such as playing along with a key- board instrument in that system). By the way, books, recordings, and software concerning alternate tuning systems are available from (with apologies to those who have seen this plug before): The Just Intonation Store 535 Stevenson St. San Francisco CA 94103 (415)864-8123 Run by the Just Intonation Network, this store has a catalog which they'll send to you. Membership in the Network will get you discounts and a sub- scription to their journal. Bill Alves