so how much sharper are sharps and flatter are flats. For example how much difference should a d flat be from a c#? What technique do y'all (from Texas) use play the difference? 
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Double Bass Enharmonic differences...
- Thread starter salbassrock
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Stick_Player
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- Nov 13, 2009
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... What technique do y'all (from Texas) use play the difference?
My ears.
Are you playing with a piano or other instrument tuned using equal temperament? If you are, then there is no difference.
However, I'll defer to the all-knowing TBers on this potentially rambling topic.
It is a bit more complicated as you might think.
First, it depends on what you are used to hear, tempered or pure tunings. And depending on that you either need to stay with what you heat or need to adjust in one or the other direction. Often enough the advice you will get is in the wrong direction...
Second, it depends on the function of the note in the chord (and the function of the chord in the tonality) how much and in which direction the adjustment is needed.
A pure major third (5/4) is 14 cent lower than the tempered major third.
A pure fifth (3/2) on the other hand is 1 cent sharp than the tempered fifth.
For a fourth you need to go a fifth down (and then up an octave), so the pure fourth is 1 cent lower than the tempered.
A major seventh is a fifth plus a major third, so a pure major seventh is -14 cent + 1 cent = -13 cent compared to the tempered major seventh.
You should read a bit about tunings and pure tuning relationships. You can always deconstruct the relationships into factorials (2 means an octave, 3 a fifth, 5 a major third, nominator means up, denominator menas down).
Exact pure tunings are seldom used in our times. It happens sometimes with strings and choir (without keyboard), but often it goes towards a pure tuning but only part of the way. So try to accomodate to what you are hearing. Maybe experiment on what you learned in theory, but your pitch reception of the ensemble and your instrument should lead you finally, not theory. (Otherwise you get in the situation "I'm doing it right, but anybody else is wrong".)
First, it depends on what you are used to hear, tempered or pure tunings. And depending on that you either need to stay with what you heat or need to adjust in one or the other direction. Often enough the advice you will get is in the wrong direction...
Second, it depends on the function of the note in the chord (and the function of the chord in the tonality) how much and in which direction the adjustment is needed.
A pure major third (5/4) is 14 cent lower than the tempered major third.
A pure fifth (3/2) on the other hand is 1 cent sharp than the tempered fifth.
For a fourth you need to go a fifth down (and then up an octave), so the pure fourth is 1 cent lower than the tempered.
A major seventh is a fifth plus a major third, so a pure major seventh is -14 cent + 1 cent = -13 cent compared to the tempered major seventh.
You should read a bit about tunings and pure tuning relationships. You can always deconstruct the relationships into factorials (2 means an octave, 3 a fifth, 5 a major third, nominator means up, denominator menas down).
Exact pure tunings are seldom used in our times. It happens sometimes with strings and choir (without keyboard), but often it goes towards a pure tuning but only part of the way. So try to accomodate to what you are hearing. Maybe experiment on what you learned in theory, but your pitch reception of the ensemble and your instrument should lead you finally, not theory. (Otherwise you get in the situation "I'm doing it right, but anybody else is wrong".)
That last sentence you wrote is absolutely true. I once read on a Texas Music Educators Association program about some bass guy who was going to talk about the factorial relationship between hand positions and notes on a bass. Ever heard of that?
also;
Sometimes composers and arrangers, especially when writing for potentially under-rehearsed circumstances, will decide to ignore accurate harmonic labeling for clarity and simplicity of reading. So your ear has to supercede your eyes.
Steven Schuster
Sometimes composers and arrangers, especially when writing for potentially under-rehearsed circumstances, will decide to ignore accurate harmonic labeling for clarity and simplicity of reading. So your ear has to supercede your eyes.
Steven Schuster
Yes, even in the music of Beethoven, Schubert etc... It is not uncommon to find a pitch written enharmonically for ease of reading if you do the analysis and figure out what it really "should be."
the Eb of an Ab major chord is actually higher in pitch than the D# of a B major chord. Put that in your pipe and smoke it!
The strange thing is that the pure minor (!) third is about 15 cent higher (!) than the tempered minor third and the pure major (!) third is about 14 cent lower (!) than the tempered major third.
No, I didn't mix them up. They are closer than we expect. But if we play tempered, we need to make the difference larger than with pure harmony.
No, I didn't mix them up. They are closer than we expect. But if we play tempered, we need to make the difference larger than with pure harmony.
You don't need to make a difference, that's equal temperament and totally valid for a lot of music.
You don't need to play with keyboards, also a fretted guitar plays equal temperament, wind instruments do (most would be able to correct their intonation to pure intonation by changing embochure, but in general they don't do that).
As I said, don't do it differently than the others you play with.
But for those who want to play pure harmonies (with choir or unfretted strings) they should at least know how much they should correct their intonation (which depends on the function of the tone) and even more important in which direction (the advise one gets regarding the direction is often wrong).
You don't need to play with keyboards, also a fretted guitar plays equal temperament, wind instruments do (most would be able to correct their intonation to pure intonation by changing embochure, but in general they don't do that).
As I said, don't do it differently than the others you play with.
But for those who want to play pure harmonies (with choir or unfretted strings) they should at least know how much they should correct their intonation (which depends on the function of the tone) and even more important in which direction (the advise one gets regarding the direction is often wrong).
Not of the guy, but the thing.
Pythagoras (Monochord) did this long, long ago, but only with pure fifths. Thirds are to high in this tuning, so it went to a pure fifths and pure thirds system.
Frequencies and string lengths have inverse relation: Twice the string length (same string and tension) gets half the frequency.
A pure fifth up is 3 in nominator and 2 in denominator, down 2 in nominator and 3 in denominator.
A pure major third up is 5 in nominator and 4 in denominator, down 4 in nominator and 5 in denominator.
An octave up is two in nominator and 1 in denominator, down 1 in nominator, 2 in denominator.
Multiply the numbers as factors if you use several intervals to get there. Simple example:
Two times a fifth up gets a ninth up: (3/2) * (3/2) = 9/4 (this is more than an octave: 9/4 > 8/4 = 2/1).
The ninth and an octave down gets a major second: (9/4) * (1/2) = 9/8
You only have to know which function the note has in the chord and which function the chord root has to tonality to calculate the correct relation to tonality (which indeed can change over time and then it gets complicated).
Also look at the tritone, it is often the major third of the double dominant, but could also be the minor third of a minor chord built on the minor third of the root, whatever this means functionwise. (Minor third is fifth up and major third down. Once for the root of the chord, once for the third in the chord. This will be different from the double dominant third.)
For comparison you try (a slightly incorrect approximation of) the ratio in decimal point view.
Now you can calculate the string length relation from pitch relation (just invert the ratio) for pure intonation.
For tempered tuning you will use the twelfth root of two for the frequency or length relation of a tempered halftone. Simpler to understand but less simple to calculate without technical help.
for example, in the key of G, a G major chord has a significantly lowered B for a 3rd, and a slightly raised D for a fifth. No problem. What about a B minor chord, or iii chord, in the key of G? Should we use the lowered B for the root of the iii chord? Which intonation system would be best for finding the roots of all 7 chords in a key? If you use the lowered B, then the D and F# are waaaaaaay off after "just" adjustments have been made.
"just play it where it sounds good"-Wendy Morton, assistant principal cellist of the Columbus Symphony Orchestra
disclaimer: I know iii chords are rare in pre-20th century music. they are most often "I" chords in first inversion, and the lowered 3rd would be correct. Just go with me on this one
"just play it where it sounds good"-Wendy Morton, assistant principal cellist of the Columbus Symphony Orchestra
disclaimer: I know iii chords are rare in pre-20th century music. they are most often "I" chords in first inversion, and the lowered 3rd would be correct. Just go with me on this one
I observed a master class of Donovan Stokes last month in San Francisco. In it he observed that playing with a drone was helpful. No news there. But he gave me a new way of looking at intonation, which is that all intervals are most in tune when the least dissonance is present. May seem obvious, but it applies to minor seconds and tritones as well as octaves and fifths. It was a new thought for me, and very valuable.
Steven Schuster
Steven Schuster
Yes.
No.
You forgot that the minor third is higher and the major third is lower than tempered pitch. So they compensate mostly.
The fifth is the same going from G to D or from G to B to D. You can simplify the ratio then the ratios look the same (they are the same even if the numbers don't look like without simplification).
The major seventh (F#) is the same from G to D to F# (fifth the major third) and from G to B to F# (major third then fifth). In the product you can exchange the factors, so it doesn't matter which steps you make first only that they are the same.
Try to calculate it. It's not hard. Then you will see what happens. If your results differ you might not have simplified the ratios. Think about how you tranfered intervals to ratios and check for errors.
There are a lot of tuning systems, tempered and pure (just) intonation are the conceptually most extreme ones.
And play so, that it sounds best.
If you look up equal temperament on Wikipedia, you'll see a chart explaining the difference between equal and just intonation. Look at the columns with the "cents" in each form.
As a rule of thumb, you will see that the minor intervals(3rds, 6ths, 7ths) in just int. are higher than in equal, and the major ones are lower. Having said that, file that in back of your mind, and listen to where your notes fit in the best when you play.
Ike
As a rule of thumb, you will see that the minor intervals(3rds, 6ths, 7ths) in just int. are higher than in equal, and the major ones are lower. Having said that, file that in back of your mind, and listen to where your notes fit in the best when you play.
Ike
Huh. Rare? IMO you hear the mediant as the mediant not an inversion of the tonic. From Bach to Brahms......Tchaikovsky too.disclaimer: I know iii chords are rare in pre-20th century music. they are most often "I" chords in first inversion, and the lowered 3rd would be correct. Just go with me on this one
This was a topic of discussion in a recent drone thread. I had made more or less the same observation based on a lot of drone practice, which led me to read a fair amount of material regarding tuning systems and theory. In the end, all of that was interesting, but I concluded that using your ears and trusting them is the best system of all, no matter what name you give that system of intonation.
so how much sharper are sharps and flatter are flats. For example how much difference should a d flat be from a c#? What technique do y'all (from Texas) use play the difference?
depends what tuning system you are talking about. if you are in what is called 5-limit just intonation (all intervals are formed from primes 2, 3, and 5), then the difference between enharmonic notes is the comma 81/80, or 21.5 cents. this is essentially the difference between a 3-limit and 5-limit version of the same note, as in 10/9 vs. 9/8 for a major 2nd.
if you are in a meantone system (where this notation stuff really comes into play), the difference between enharmonic notes depends on how the 81/80 comma is distributed. in 1/4-comma meantone, historically the most popular, the difference between enharmonics is about 41 cents.
it's good that you are asking these questions. i've met too many 'pro' musicians that have literally no idea why pitches are where they are or that there is anything outside of equal temperament
